Fundamentals of Microelectronics, 2nd Edition Razavi Solution Manual

Type:

Solution Manual

Resource:

Fundamentals of Microelectronics

Edition:

2nd Edition

Author(s):

Behzad Razavi

2N4401 / MMBT4401

2N4401

MMBT4401 C

E C

B

TO-92

SOT-23

E

B

Mark: 2X

NPN General Pupose Amplifier This device is designed for use as a medium power amplifier and switch requiring collector currents up to 500 mA.

Absolute Maximum Ratings* Symbol

TA = 25°C unless otherwise noted

Parameter

Value

Units

VCEO

Collector-Emitter Voltage

40

V

VCBO

Collector-Base Voltage

60

V

VEBO

Emitter-Base Voltage

6.0

V

IC

Collector Current - Continuous

600

mA

TJ, Tstg

Operating and Storage Junction Temperature Range

-55 to +150

°C

*These ratings are limiting values above which the serviceability of any semiconductor device may be impaired.

NOTES: 1) These ratings are based on a maximum junction temperature of 150 degrees C. 2) These are steady state limits. The factory should be consulted on applications involving pulsed or low duty cycle operations.

Thermal Characteristics Symbol

TA = 25°C unless otherwise noted

Characteristic

Max

Units

2N4401 625 5.0 83.3

*MMBT4401 350 2.8

RθJC

Total Device Dissipation Derate above 25°C Thermal Resistance, Junction to Case

RθJA

Thermal Resistance, Junction to Ambient

200

357

PD

mW mW/°C °C/W °C/W

*Device mounted on FR-4 PCB 1.6" X 1.6" X 0.06."

 2001 Fairchild Semiconductor Corporation

2N4401/MMBT4401, Rev A

(continued)

Electrical Characteristics Symbol

TA = 25°C unless otherwise noted

Parameter

Test Conditions

Min

Max

Units

OFF CHARACTERISTICS V(BR)CEO

Collector-Emitter Breakdown Voltage*

IC = 1.0 mA, IB = 0

40

V(BR)CBO

Collector-Base Breakdown Voltage

IC = 0.1 mA, IE = 0

60

V V

V(BR)EBO

Emitter-Base Breakdown Voltage

IE = 0.1 mA, IC = 0

6.0

V

IBL

Base Cutoff Current

VCE = 35 V, VEB = 0.4 V

0.1

µA

ICEX

Collector Cutoff Current

VCE = 35 V, VEB = 0.4 V

0.1

µA

2N4401 / MMBT4401

NPN General Purpose Amplifier

ON CHARACTERISTICS* hFE

DC Current Gain

VCE(sat)

Collector-Emitter Saturation Voltage

VBE(sat)

Base-Emitter Saturation Voltage

IC = 0.1 mA, VCE = 1.0 V IC = 1.0 mA, VCE = 1.0 V IC = 10 mA, VCE = 1.0 V IC = 150 mA, VCE = 1.0 V IC = 500 mA, VCE = 2.0 V IC = 150 mA, IB = 15 mA IC = 500 mA, IB = 50 mA IC = 150 mA, IB = 15 mA IC = 500 mA, IB = 50 mA

20 40 80 100 40

0.75

300 0.4 0.75 0.95 1.2

V V V V

SMALL SIGNAL CHARACTERISTICS fT

Current Gain - Bandwidth Product

Ccb

Collector-Base Capacitance

Ceb

Emitter-Base Capacitance

hie

Input Impedance

hre

Voltage Feedback Ratio

hfe

Small-Signal Current Gain

hoe

Output Admittance

IC = 20 mA, VCE = 10 V, f = 100 MHz VCB = 5.0 V, IE = 0, f = 140 kHz VBE = 0.5 V, IC = 0, f = 140 kHz IC = 1.0 mA, VCE = 10 V, f = 1.0 kHz IC = 1.0 mA, VCE = 10 V, f = 1.0 kHz IC = 1.0 mA, VCE = 10 V, f = 1.0 kHz IC = 1.0 mA, VCE = 10 V, f = 1.0 kHz

250

MHz 6.5

pF

30

pF

1.0

15

kΩ

0.1

8.0

x 10

40

500

1.0

30

µmhos

15

ns ns

-4

SWITCHING CHARACTERISTICS td

Delay Time

VCC = 30 V, VEB = 2 V,

tr

Rise Time

IC = 150 mA, IB1 = 15 mA

20

ts

Storage Time

VCC = 30 V, IC = 150 mA

225

ns

tf

Fall Time

IB1 = IB2 = 15 mA

30

ns

*Pulse Test: Pulse Width ≤ 300 µs, Duty Cycle ≤ 2.0%

3

(continued)

V CE = 5V

400 125 °C

300 200

25 °C

100 - 40 °C

0 0.1

0.3

1 3 10 30 100 I C - COLLECTOR CURRENT (mA)

300

Base-Emitter Saturation Voltage vs Collector Current β = 10

1

- 40 °C

0.8

25 °C 125 °C

0.6

0.4 1

10 100 I C - COLLECTOR CURRENT (mA)

500

V CESAT - COLLECTOR-EMITTER VOLTAGE (V)

500

V BE(ON) - BASE-EMITTER ON VOLTAGE (V)

Typical Pulsed Current Gain vs Collector Current

V BESAT - BASE-EMITTER VOLTAGE (V)

h FE - TYPICAL PULSED CURRENT GAIN

Typical Characteristics

0.4 β = 10 0.3

125 °C

0.2 25 °C

0.1 - 40 °C

1

10 100 I C - COLLECTOR CURRENT (mA)

500

Base-Emitter ON Voltage vs Collector Current 1 VCE = 5V 0.8

- 40 °C 25 °C

0.6 125 °C

0.4

0.2 0.1

1 10 I C - COLLECTOR CURRENT (mA)

25

Emitter Transition and Output Capacitance vs Reverse Bias Voltage

Collector-Cutoff Current vs Ambient Temperature 500 100

V

CB

20

= 40V

CAPACITANCE (pF)

I CBO - COLLECTOR CURRENT (nA)

Collector-Emitter Saturation Voltage vs Collector Current

10 1 0.1

f = 1 MHz

16 12 C te

8 C ob

4 25

50 75 100 125 T A - AMBIENT TEMPERATURE (° C)

150

0.1

1 10 REVERSE BIAS VOLTAGE (V)

100

2N4401 / MMBT4401

NPN General Purpose Amplifier

(continued)

Typical Characteristics (continued)

Turn On and Turn Off Times vs Collector Current 400 I B1 = I B2 =

Switching Times vs Collector Current 400

Ic

320 TIME (nS)

V cc = 25 V

240 160

240 ts

160

tr

t off

80

tf

80

t on

td

100 I C - COLLECTOR CURRENT (mA)

0 10

1000

100 I C - COLLECTOR CURRENT (mA)

Power Dissipation vs Ambient Temperature 1 PD - POWER DISSIPATION (W)

TIME (nS)

10

320 V cc = 25 V

0 10

Ic

I B1 = I B2 =

10

SOT-223

0.75

TO-92

0.5 SOT-23

0.25

0

0

25

50 75 100 o TEMPERATURE ( C)

125

150

1000

2N4401 / MMBT4401

NPN General Purpose Amplifier

(continued)

V CE = 10 V T A = 25oC

6 hoe 4 h re 2 h fe h ie 0

0

10

20 30 40 50 I C - COLLECTOR CURRENT (mA)

60

CHAR. RELATIVE TO VALUES AT TA = 25oC

Common Emitter Characteristics 8

CHAR. RELATIVE TO VALUES AT VCE = 10V

CHAR. RELATIVE TO VALUES AT I C= 10mA

Typical Common Emitter Characteristics (f = 1.0kHz)

Common Emitter Characteristics 2.4

V CE = 10 V I C = 10 mA

2

h re

h fe

1.6

hoe

1.2 0.8 0.4 0

0

20 40 60 80 T A - AMBIENT TEMPERATURE ( o C)

Common Emitter Characteristics 1.3

I C = 10 mA T A = 25oC

1.25

h fe

1.2 1.15 h ie

1.1 1.05 1

h re

0.95 0.9 0.85

hoe

0.8 0.75

0

5

h ie

10 15 20 25 30 VCE - COLLECTOR VOLTAGE (V)

35

100

2N4401 / MMBT4401

NPN General Purpose Amplifier

(continued)

Test Circuits 30 V

200 Ω

16 V Ω 1.0 KΩ 0 ≤ 200ns

500 Ω

FIGURE 1: Saturated Turn-On Switching Timer

6.0 V

- 1.5 V

NOTE: BV EBO = 5.0 V

1k

30 V Ω 1.0 KΩ 0 ≤ 200ns

50 Ω

FIGURE 2: Saturated Turn-Off Switching Time

37 Ω

2N4401 / MMBT4401

NPN General Purpose Amplifier

TRADEMARKS The following are registered and unregistered trademarks Fairchild Semiconductor owns or is authorized to use and is not intended to be an exhaustive list of all such trademarks.

ACEx™ Bottomless™ CoolFET™ CROSSVOLT™ DOME™ E2CMOSTM EnSignaTM FACT™ FACT Quiet Series™ FAST 

FASTr™ GlobalOptoisolator™ GTO™ HiSeC™ ISOPLANAR™ MICROWIRE™ OPTOLOGIC™ OPTOPLANAR™ PACMAN™ POP™

PowerTrench  QFET™ QS™ QT Optoelectronics™ Quiet Series™ SILENT SWITCHER  SMART START™ SuperSOT™-3 SuperSOT™-6 SuperSOT™-8

SyncFET™ TinyLogic™ UHC™ VCX™

DISCLAIMER FAIRCHILD SEMICONDUCTOR RESERVES THE RIGHT TO MAKE CHANGES WITHOUT FURTHER NOTICE TO ANY PRODUCTS HEREIN TO IMPROVE RELIABILITY, FUNCTION OR DESIGN. FAIRCHILD DOES NOT ASSUME ANY LIABILITY ARISING OUT OF THE APPLICATION OR USE OF ANY PRODUCT OR CIRCUIT DESCRIBED HEREIN; NEITHER DOES IT CONVEY ANY LICENSE UNDER ITS PATENT RIGHTS, NOR THE RIGHTS OF OTHERS. LIFE SUPPORT POLICY FAIRCHILD’S PRODUCTS ARE NOT AUTHORIZED FOR USE AS CRITICAL COMPONENTS IN LIFE SUPPORT DEVICES OR SYSTEMS WITHOUT THE EXPRESS WRITTEN APPROVAL OF FAIRCHILD SEMICONDUCTOR CORPORATION. As used herein: 1. Life support devices or systems are devices or 2. A critical component is any component of a life support device or system whose failure to perform can systems which, (a) are intended for surgical implant into be reasonably expected to cause the failure of the life the body, or (b) support or sustain life, or (c) whose support device or system, or to affect its safety or failure to perform when properly used in accordance with instructions for use provided in the labeling, can be effectiveness. reasonably expected to result in significant injury to the user.

PRODUCT STATUS DEFINITIONS Definition of Terms Datasheet Identification

Product Status

Definition

Advance Information

Formative or In Design

This datasheet contains the design specifications for product development. Specifications may change in any manner without notice.

Preliminary

First Production

This datasheet contains preliminary data, and supplementary data will be published at a later date.

Fairchild Semiconductor reserves the right to make changes at any time without notice in order to improve design.

No Identification Needed

Full Production

This datasheet contains final specifications. Fairchild Semiconductor reserves the right to make changes at any time without notice in order to improve design.

Obsolete

Not In Production

This datasheet contains specifications on a product that has been discontinued by Fairchild semiconductor.

The datasheet is printed for reference information only.

Rev. G

Agilent4155C/HP4145B Parameter Analyzer Tutorial Contents 1 Introduction

1

2 The Hardware Interface

1

3 The Software Interface

2

4 Microsoft Excel

4

1

Introduction

The Agilent4155C/HP4145B is a parameter analyzer. It can apply test signals (voltages or currents) to one or more nodes of a circuit and then measure the voltages and currents at other nodes in the same circuit.

What makes the parameter analyzer particularly useful is that it can sweep a test voltage across hundreds of values in a matter of seconds. You can think of its capabilities like those of a DC analysis in SPICE.

2

The Hardware Interface

The hardware interface to the Agilent4155C/HP4145B is a metallic box (called a test fixture) located at every lab station. Inside the test fixture, you’ll notice a socket, many numbered slots, and eight labeled terminals: 4 SMU, 2 VS, and 2 VM (newer models have more terminals, but all models have at least these eight). The SMU is the most flexible terminal: it can be used to apply or measure a current or a voltage.

The VS can act only as a voltage source, and the VM can act only as a voltmeter. For any measurement you’re conducting having fewer than five nodes, you should use the SMU terminals for all of the nodes since they provide the most functionality. Figure 1 shows the old test fixture and Figure 2 shows the new test fixture. SMU terminals are labeled with red, VS with blue, VM with black, and ground with green. Note that the HP 16147 test fixture has two numbering schemes for the SMU terminals—use the the numbering scheme with black numbers on a white background (as labeled in Figure 2).

When using the Agilent4155C/HP4145B, you can either connect a pin to the ground terminal in the test fixture or you can connect it to an SMU or VS and set the SMU/VS to supply 0V. According to the test fixture documentation, the ground terminals are just connected to the chassis of the test fixture, so using the ground terminal can mean a noisy ground. For best results (in particular with small signals or sensitive circuitry), you should use an SMU or VS for ground.

Build your circuit on the breadboard, then use the special cables to connect nodes in your circuit to the SMU, VS, and VM terminals.

3

The Software Interface

Before using the software interface, you must turn on the Agilent4155C/HP4145B. There is a power button in the lower left hand corner (it may take 20-30 seconds for the machine to start).

1. Start ICS Metrics. Click Start → Programs → Metrics → ICS. You may get an error, but just click OK to ignore it.

2. Click Instruments → Select Instrument... (or the icon in Figure 3). You should see a list of “Available” instruments on the left side of the window. Select the instrument that is installed at your lab station (select HP4145 for the HP 4145 and HP4155-6 for the Agilent4155C). Click Connect and the device should be listed under “Selected”. Click OK to exit this window.

1

3

2

THE SOFTWARE INTERFACE

Figure 1: HP 16058 test fixture

Figure 2: HP 16147 test fixture

Figure 3: Icon for selecting an instrument

3

THE SOFTWARE INTERFACE

3

3. Click Measure → Edit Setup... (or the icon in Figure 4) to open the Setup Editor. Click New to create a new setup and give it a name (any name is fine).

Figure 4: Icon for setting up a measurement (a) You should now see a schematic of a MOSFET with blue squares at each terminal. Click Device to pick a different device. Note that the device shown is only to help you organize and connect the terminals to your circuit. It does not change anything other than the number of terminals available. After selecting the device, click OK. If you picked a different device layout, the schematic will change and the number of terminals will change. (b) Now you must assign an SMU, VM, or VS to each of the terminals in the diagram. This interface allows you to specify how the circuit is connected to the hardware interface. Click Source Units.

A new window will come up with all of the SMU, VM, and VS terminals of the hardware interface available for you to select. Click the source unit you want to assign, then click on one of the terminals to assign that source unit to that terminal. The schematic will change to show you which SMU, VS, or VM you’ve assigned to which terminal. (c) You can now assign stimuli and measurements to the terminals that you’ve labeled. For each terminal, click on the icon next to the label and a new window will come up showing all of the available measurement and stimulus options. For the VS and VM terminals, you’ll only be able to apply or measure a voltage, respectively. For SMU terminals, you can choose to have either a voltage or a current stimulus by selecting the respective button located in the upper-left corner.

You can choose to measure voltage or current in the upper middle of the window. Finally, you can select the actual values for the stimulus in the middle portion of the window. (Note: If you want to measure the voltage at a terminal without applying a signal, you can apply a current stimulus of amplitude zero, which won’t change your circuit.) (d) There are four primary ways you can set a stimulus (current or voltage) on the Agilent4155C/HP4145B. The first method is to set a constant value. You won’t be using this method much though, since constant measurements are easy to do with a DC power supply and multimeter and don’t require something as sophisticated as the Agilent4155C/HP4145B. You can also set a node to common, in other words, ground (this is exactly equivalent to setting a terminal to a constant value of 0V).

Finally, the interesting options are stepping and sweeping values.

• Stepping a value causes a measurement to occur at every voltage you select. You can set a starting voltage, a stopping voltage, and how many points you want to test.

• Sweeping a value causes a measurement sweep to occur at every stepped voltage. For example, you could step a voltage V1 from 0 V to 5 V in increments of 1 V and sweep another voltage V2 from 0 V to 5 V in increments of 0.1 V. This would cause the Agilent4155C/HP4145B to set V1 = 0 V and sweep V2 , then set V1 = 1 V and sweep V2 again, and so forth, until V1 = 5 V and V2 is swept for the last time. Using this feature, you can obtain a family of curves, such as the I-V curves of a transistor.

Note that when stepping and sweeping values, we often tell ICS Metrics to use one more data point than you’d expect. For example, when stepping from 0 V to 5 V, we would use 6 data points rather than 5 in order to achieve a step size of 1 V. Similarly, when sweeping a voltage from 0 V to 5 V, we would use 101 data points rather than 100 in order to get a step size of an even 0.05 V. When you’re done assigning SMU, VS, and VM terminals and associated measurements, click Done to close the Setup Editor.

4. All that’s left is to run the measurements you’ve done. In order to do this, click Measure → Measure....

This will bring up a panel on the right side of the screen. Click the button labeled Single, which has

4

4

MICROSOFT EXCEL

the appearance of a right arrowhead. Once the measurement is completed, a new window will come up showing all of the data in a spreadsheet (the spreadsheet may be minimized, so click the restore icon to make it show).

Figure 5: Icon for running a measurement 5. Now that you have measurement data, you can use ICS to create a plot. Click Window → New Plot... (or the icon in Figure 6). A new window will come up allowing you to choose which values in the spreadsheet should be used on the x and y axes. Make the appropriate choices (you may also select linear or log scales), then click Done to close the window. You should be able to see the plot you created.

Figure 6: Icon for plotting measurement results • If you want to print the plot directly from ICS, do not print without setting a white background first. You will waste an immense amount of ink if you do not set a white background.

In order to set a white background, click Setup → Colors... and select the radio button labeled Monochrome. Click Done and you’ll see the plot is now black with a white background.

• You can also use Microsoft Excel to make plots. This can be useful because of Excel’s ability to fit curves. See the section on Microsoft Excel for details on plotting and fitting data in Excel.

4

Microsoft Excel 1. Click Start → Programs → Microsoft Office → Microsoft Office Excel. A window titled “Windows Installer” may come up. If it does, click Cancel and Excel should start.

2. Select your data in ICS by dragging your mouse over all of the data you measured. Copy it by clicking on Edit → Copy and paste it into Excel using ctrl +v.

3. Click Insert → Chart. Under “Chart type”, select XY (Scatter). Under “Chart sub-type”, select the second option (the description is “Scatter with data points connected by smooth lines.”). Click Next.

4. Select the Series tab. Select the appropriate “X Values” and “Y Values” in this window (use Microsoft Excel’s help feature if you need help doing this), then click Next.

5. Label your chart and the x and y axes in this window. You can also include a legend if you have more than one curve on the graph.

6. Click Next. Choose whether you want the chart to be a new sheet or an object in the current sheet.

Click Finish.

7. Your chart should now be visible. To add a trendline, right-click the curve you want to add the trendline too, then click Add Trendline.... Select the type of trendline to use (most likely you’ll want a linear trendline). Select the Options tab and click the checkbox labeled “Display equation on chart”.

Click OK. 8. The trendline and associated equation will be displayed on the chart. You can use the equation to get the slope of the line and the x–intercept, which are often related to device parameters.

Agilent 33220A Function Generator Tutorial Contents 1 Introduction

1

2 Quick Notes (to get started fast)

1

3 Voltage Divider Discussion

2

4 Interface Details 4.1 Bottom-Right Buttons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.2 Middle Buttons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.3 Upper-Middle Blue Buttons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.4 Upper-Right Buttons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 2 2 3 4

5 Examples 5.1 Sinusoid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.2 Pulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 4 4

1

Introduction

The Agilent 33220A is a voltage waveform generator. It can be used to apply periodic voltage waveforms to a circuit (e.g., sinusoids, square waves, triangle waves, and pulses). You will use the function generators to supply time-varying input to circuits for transient or frequency analysis (e.g., to characterize a filter or an amplifier).

This tutorial starts with quick notes on the most vital information, so if you feel somewhat familiar with the function generator you can check over the quick notes and figure out the details yourself. The later sections include more detailed descriptions of the Agilent 33220A interface.

2

Quick Notes (to get started fast) • Make sure the “Output” button is lit (in the lower-right corner).

• Set parameters in Ampl/Offset mode, not in HiLevel/LoLevel mode. If HiLevel/LoLevel mode is selected, push the blue buttons below HiLevel/LoLevel until Ampl/Offset mode is selected instead.

• The Ampl parameter sets the peak-to-peak amplitude, not the peak amplitude. See Figure 1.

• Delivered voltage varies with output load impedance. With an infinite load impedance at the output, the voltage amplitude delivered to the load will be double the panel setting. See Section 3.

• Choose parameters to adjust via the blue buttons that are below the screen. Change the parameter values using the top-right knob as well as the arrow keys; an alternative is to use the numbered keys to input the desired value. If you do use the numbered keys, note that after punching in the numbers, you must select the proper units and order of magnitude using the blue buttons below the screen.

• Offset is the voltage offset for the waveform. You can use it to add a constant voltage (DC component) to the wave (e.g. if you want to have a cosine vary around 2 V).

• The function generator’s ground is earth-grounded, i.e. the black lead from the BNC cable is not a floating ground. Since the oscilloscope is earth-grounded as well, the function generator and oscilloscope grounds are connected.

1

3

2

VOLTAGE DIVIDER DISCUSSION

Figure 1: Definitions of various wave parameters

3

Voltage Divider Discussion

When displaying voltage value settings (e.g. the Ampl parameter displaying Vpp ), the function generator panel displays the voltage that will be delivered to the load at the output under the assumption that the total load impedance is 50 Ω. The function generator also has an internal impedance of 50 Ω, and so the load impedance forms a voltage divider with the internal impedance of the function generator. The equivalent voltage divider is shown in Figure 2. + vs

50Ω RL

− Figure 2: Function generator panel displays voltage values for RL = 50 Ω Under the assumption that the load impedance is 50 Ω, the voltage delivered to the load (the effective voltage output) is half the generated voltage of vs . Loading the output with an impedance much greater than 50 Ω (such as connecting the output directly to an oscilloscope) will drop the majority of the voltage across the load, and thus the measured output voltage can be up to double the panel setting. Loading the function generator with RL < 50 Ω will cause the voltage delivered to be less than the panel setting.

The function generator is often used to create an input signal to amplifiers. Voltage amplifiers often have a high input impedance (e.g. an effectively infinite input impedance for a MOS amplifier), and so the function generator will often be loaded with an infinite RL . Thus the voltage delivered to the amplifier input will often be double the panel setting.

4

Interface Details

To begin, you should know where the power button, output port, and sync port are located on the function generator. The power button is in the lower-left corner of the front panel. The output port is in the lower-right corner and requires a special cable. In contrast, the sync output port is located in the back of the function generator and is used to send a triggering signal to an oscilloscope. The trigger allows the oscilloscope to synchronize its measurement with the function generator’s output (e.g. so as to capture a short pulse). Notice that after turning on the function generator, the display shows the value of the currently selected parameter as well as the units and order of magnitude (e.g. mV V).

The notes below correspond to the button groups shown in Figure 3. They are generally in the order that you would use them to set up an output waveform.

4.1

Bottom-Right Buttons

The Output button turns on the output voltage, which should be off when the function generator is initially turned on. So, press the button once to turn on the output voltage. The Trigger button is used to enable

4

3

INTERFACE DETAILS

Figure 3: Agilent 33220A Front Panel the sync port, which is a feature used in conjunction with another equipment (e.g. an oscilloscope). However, in general, you will not need to use triggering in these labs.

4.2

Middle Buttons

These six buttons set the shape of the output waveform: • Sinusoidal: A sine or cosine wave; eigenfunctions of LTI systems.

• Square: Periodically switches between two values.

• Ramp: Also known as a “Sawtooth” wave.

• Pulse: A voltage pulse is sent periodically. The pulse width can be tuned separately from the period (the time interval between repeated pulses). The peak value of the pulse can also be set.

• Noise: Simulation of voltage noise.

• Arb: Create your own waveform.

4.3

Upper-Middle Blue Buttons

These six buttons allow you to select parameters of the output waveform. After selecting a parameter, the parameter value can be adjusted with the numbered keys, arrow buttons, and the knob located in the upperright corner of the front panel. Depending on the middle button selected, not all of these six upper-middle buttons will be active (i.e. not every waveform will require the use of all six buttons).

Each upper-middle button has two labels above it, with only one of the two labels lit at any given time.

The highlighted label corresponds to the parameter that is currently selected, and its value will be shown on the display. You will only need to adjust the Freq, Ampl, Offset, Width, and/or Duty Cycle parameters. If HiLevel and LoLevel are lit, press the button below LoLevel or HiLevel until Ampl and Offset are selected instead.

Here is a list of the parameter labels and their respective meanings: • Freq: Frequency in repetitions per second. In the case of a pulse, this parameter corresponds to the frequency at which repeated pulses are sent.

• Ampl: Amplitude (peak-to-peak), defined as the distance between the highest and lowest voltage points of a waveform.

5

EXAMPLES

4

• Offset: DC voltage offset. The time-varying waveform is offseted (“raised”) by the constant offset component (e.g. if you want a sinusoid of amplitude 1 V centered at 3 V, the offset should be 3 V).

• Width: Pulse width (for the pulse waveform).

• Duty Cycle: duration of a pulse.

As a reminder, for some waveforms, not all of the parameters are needed. For example, a sinusoidal waveform only has Freq, Ampl, and Offset available for adjustment.

4.4

Upper-Right Buttons

In the upper-right corner of the front panel, there is a knob, two arrow buttons, and a set of numbered buttons. Each of these offers a different way of adjusting the displayed parameter value: • Knob: This can be turned clockwise and counterclockwise to adjust the displayed parameter value.

Note that the knob only changes the digit (or number) selected by the blinking cursor.

• Arrow Buttons: Press the left and right arrow buttons to manually move the blinking cursor.

• Numbered Buttons: An alternative to the knob and arrow buttons is the set of numbered keys.

Simply punch in the desired value using the numbered key pad, and when prompted, select the proper order of magnitude. Note that the polarity of the output can be changed with the +/− button.

5

Examples

The following are two examples demonstrating the mentioned features of the function generator.

5.1

Sinusoid

Here are all of the steps necessary to set up a 5 kHz, 1 Vpp sinusoid wave with a 1 V offset on a large load (i.e. much larger than 50 Ω).

1. Turn on the function generator with the lower-left power button, and enable the output by pressing the “Output” button in the lower-right (so that the “Output” light is lit).

2. Press the sinusoid button in the middle set of buttons.

3. Press the Freq button in the upper-middle set of buttons, and use the upper-right numbered keys, knob, and/or the arrow buttons to select 5 kHz on the display.

4. Now press the Ampl button in the upper-middle set of buttons, and use the upper-right numbered keys, knob, and/or the arrow buttons to select 500 mVpp on the display. However, if the load impedance is much larger than 50 Ω, this step will produce a 1 Vpp output waveform instead of 500 mVpp . For further discussion about this discrepancy, please refer to section 3.

5. Next, press the Offset button in the upper-middle set of buttons, and use the upper-right numbered keys, knob, and/or arrow buttons to select a 500 mV offset on the display. This will lead to a 1 V offset if the load impedance is greater than 50 Ω.

5.2

Pulse

Here are all of the steps necessary to set up a 1 V pulse with a 1 µs duration and a repetition every 10 µs on a load impedance much larger than 50 Ω.

1. Turn on the function generator with the lower-left power button, and enable the output by pressing the “Output” button in the lower-right (so that the “Output” light is lit).

2. Press the pulse button located in the middle set of buttons.

5

EXAMPLES

5

3. Press the Freq button in the upper-middle set of buttons. Since we want 10 µs between repetitions, 1 = 105 Hz. Use the upper-right numbered keys, knob, and/or the arrow buttons to select we want 10µ 100 kHz. 4. Now press the Width button in the upper-middle set of buttons. Use the upper-right numbered keys, knob, and/or the arrow buttons to select a 1 µs width.

5. Then, press the Ampl button in the upper-middle set of buttons, and use the upper-right numbered keys, knob, and/or the arrow buttons to select 500 mV on the display. This step will produce a 1 V height pulse if the load impedance is much larger than 50 Ω. If necessary, see section 3 for further discussion about this discrepancy.

Agilent DSO5014A Oscilloscope Tutorial Contents 1 Introduction

1

2 Quick Notes (to get started fast)

1

3 Trigger

2

4 Interface Details 4.1 Auto Scale Button . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.2 Analog Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.3 Horizontal Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.4 Display Button . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.5 Measure Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.6 Cursors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 2 3 3 4 4 4

5 Examples 5.1 Measuring the Peak-to-Peak Voltage (Vpp ) of a Waveform . . . . . . . . . . . . . . . . . . . .

5.2 Measuring Frequency of a Waveform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.3 Measuring Voltage with Cursors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.4 Using Averaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.5 Measuring a Transfer Characteristic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5 5 5 5 6 6

1

Introduction

The Agilent DSO5014A is an oscilloscope, and it is used to measure voltages that vary with time. There are four independent input channels available on the DSO5014A; thus, it can be used to simultaneously measure and compare four different waveforms (e.g. input and output waveforms of an amplifier).

The default mode of the oscilloscope plots time on the horizontal axis and voltage on the vertical. The scaling of the axes can then be adjusted for each input signal. Scaling can either be done manually or with the “Auto Scale” button. There are other modes of operation for the oscilloscope as well, such as the XY mode that plots one channel against the other in a Voltage-Voltage plot. However, in these labs, you will primarily use the default mode.

This tutorial starts with quick notes on the most vital information. So, if you feel somewhat comfortable using the oscilloscopes, you can check over the quick notes and figure out the details on your own. Otherwise, please also read the later sections, which include more detailed descriptions of the Agilent DSO5014A interface as well as examples of common measurement procedures.

2

Quick Notes (to get started fast) • After connecting the probes, try the “Auto Scale” button. It will generally provide a good axis scaling if the waveform is not too irregular, small, or at a high-frequency.

• Each channel has an independent control knob to allow the manual setting of the vertical scale. Each channel only has one scale reading, which is displayed to the left of the corresponding channel number at the top of the screen. To adjust the scale, simply turn the knob in the ANALOG section. These knobs are located above the numbered buttons; there is one vertical scaling knob for each input channel.

1

3

TRIGGER

2

• To conduct measurements (e.g. measuring Vpp ), press the “Quick Measure” button in the MEASURE section of the panel. Notice the softkeys that appear on the bottom of the screen. Select the desired source and measurement using the first two menu buttons below the screen (e.g. Source 1, Pk-Pk).

Then initiate the measurement by pressing the third menu button (i.e. Measure).

• Cursors can be activated by pressing the “Cursor” button. Use the menu buttons below the screen to adjust the settings, and use the entry knob next to the “Cursor” button to move the cursors.

• AC coupling will remove any DC bias (offset) from the measured signal. This feature can be selected using the menu button below the screen; note that this can only be done in the channel menu. Press the corresponding numbered button (e.g. 2) in the ANALOG section to have the channel menu appear on the bottom of the screen.

• The oscilloscope’s ground is earth-grounded, so the black alligator wires on the probes are connected together. Since the function generator is also earth-grounded, the oscilloscope probe grounds are connected to the function generator ground. To avoid shorts to ground, you should always connect the oscilloscope ground clips to the same node. Do not try to use the probes to measure floating signals (as you can with the DMM).

3

Trigger

The Agilent DSO5014A has a TRIGGER section on its interface panel. Triggers are used to synchronize the oscilloscope with an external signal so that measurements can be taken at the right moment. For example, to capture a single voltage pulse, one might use a trigger input to signal the oscilloscope to take measurements at the pulse arrival. Triggers can also be used with periodic inputs. However, you will generally not need to use oscilloscope triggering in these labs.

4

Interface Details

The power button is in the lower-left corner of the front panel. Press it to turn on the oscilloscope.

The oscilloscope screen should now display a coordinate system. At the top of the screen, vertical and horizontal scaling units are displayed. The default mode will display vertical scaling for each input in volts/div and horizontal scaling in seconds/div. Note that these units correspond to the respective lines that make up the square grid.

The buttons below the screen are referred to as “menu buttons” or “context buttons” in this tutorial.

Their functionality changes with the selection of other buttons (e.g. by pushing the “Quick Measure” button). Each button’s current function is labeled on the screen by the text immediately above the button.

These menu buttons are essential to taking measurements and performing more complex functions on the oscilloscope.

The following sections cover the front interface panel in the general order you would consider them when making waveform measurements. At the end of the tutorial, there are examples of common measurement procedures.

Please refer to a photo of the Agilent DSO5014A in Figure 1; this might help in locating the mentioned controls/buttons.

4.1

Auto Scale Button

The “Auto Scale” button has the oscilloscope “guess” a good axis scaling based on the input waveform. This button is always a good first pass for scaling, and often, it will be the only scaling that you will need. You can also tune the scaling manually with the ANALOG and HORIZONTAL controls, which are described below.

4

3

INTERFACE DETAILS

Figure 1: Agilent DSO5014A Front Panel

4.2

Analog Section

The controls of the ANALOG section adjust the vertical scaling and position of each independent channel signal. Note that the controls for each channel are aligned vertically with respect to the input port.

• The knobs above the numbered buttons set the vertical scaling (vertical zoom) on the display.

• The “1”, “2”, “3”, and “4” (numbered buttons) toggle showing their respective inputs.

• The position knob is located below the numbered buttons and have up and down arrow markings next to them. These knobs control the voltage offset against the display axes. The horizontal axis does not represent 0 volts, but instead, the 0 volt position for each input is designated by a numbered ground symbol on the left side of the screen. When you adjust the offset with the position knob, you will see the corresponding channel’s ground symbol move vertically.

• The “Math” button can combine inputs with one of the following arithmetic operators: subtraction and multiplication. The operation can be selected with the menu buttons below the screen after pushing the “Math” button.

When using the ANALOG section (e.g. after pushing “1” or “2”), the menu buttons below the screen correspond to various options related to the probe inputs. The list below assumes that the “1” button has been pressed.

Menu 1 • 1: ON/OFF - Toggles the display of input 1.

• Imped: 50 Ω/1 MΩ - Toggles the input impedance of the channel input. Should usually be set at 1 MΩ.

• Coupling: DC/AC/ground - Sets the coupling for the channel input: DC will show both DC and AC values. AC will only give time-varying voltage values and remove any offset. Ground will set the channel as a virtual ground.

• BW Lim: Off/On - Leave this at default.

• Vernier: Off/On - Leave this at default.

4

INTERFACE DETAILS

4

• Invert: Off/On - Leave this at default. This option can be used to invert the input signal (e.g. in combination with the math subtraction operator to result in input addition).

• Probe: Displays channel probe menu.

Probe Menu • AutoProbe - Leave this at default.

• Skew - Leave this at default.

• Units - Leave this at default.

• ↑ - Go to Menu 1

4.3

Horizontal Section

The horizontal axis is the same for all input channels.

• The knob with waveforms on both sides (in the HORIZONTAL section) sets the horizontal scaling (horizontal zoom) on the display for all input channels.

• Control the horizontal position using the knob marked with left/right arrows next to it.

4.4

Display Button

By pressing the “Display” button, the menu buttons below the screen become the following: • ∞ Persist: Off/On - Leave this setting Off. • Clear Display - Clears/refreshes the screen.

• Grid - Leave this setting at default.

• Vectors: Off/On - Leave this setting On.

4.5

Measure Section

The MEASURE section has buttons for “Quick Measure” and “Cursors”. Cursors are discussed in the next subsection.

To make a voltage measurement on an input signal, press the “Quick Measure” button. It will change the menu buttons below the screen so that you can select which voltage parameters to measure. Values will be displayed at the bottom of the screen, and automatic cursors will be placed around the selected measurement on the display. Additional measurements will line up at the bottom of the screen.

After pressing the “Quick Measure” button, the menu buttons below the screen become the following: • Source: 1 / 2 / 3 / 4 - Selects the source on which to perform the measurement.

• Select: P eak-P eak / Average / RM S / M aximum / M inimum / etc. - Press this button until the intended value to measure is selected or turn the entry knob (the one with a green above it) after pressing the button.

• Measure - Press this button to initiate the measurement selected.

• Clear Meas - Clear measurements on the bottom of the screen.

• Thresholds - Leave these settings on default.

5

EXAMPLES

5

Similarly, to make a time measurement on an input signal, press the “Quick Measure” button in the MEASURE section. It will change the menu buttons below the screen so that you can select which time parameters to measure via the Select button (e.g. F requency/P eriod/DutyCycle/RiseT ime/F allT ime/etc.).

As mentioned above, remember to press the Measure button to initiate the measurement. Values will be displayed at the bottom of the screen, and automatic cursors will be placed around the selected measurement on the display. Additional measurements will line up at the bottom of the screen.

An important note about the P hase/Delay measurement: • Settings - this option becomes availabe when P hase or Delay is selected. Use this option to select the input sources that are to be compared as well as whether the measurements should be made on the rising or falling edges of the input waveforms.

4.6

Cursors

Cursors are markers that you can place to manually to measure quantities on the display axes. For example, you can measure a specific voltage point on the vertical axis with a cursor or measure the voltage difference between two cursors placed on the vertical axis.

After pressing the “Cursor” button, use the menu buttons below the screen to activate a particular cursor.

You can use the entry knob (the one with a green above it) to adjust the position of the cursor manually.

Cursor measurements are displayed at the bottom of the screen.

The following is a list of the buttons in the Cursor menu: • Mode - leave on “Normal” to measure voltage and time.

• Source: 1 / 2 / 3 / 4 - Select the source on which to place the cursor(s).

• X Y: Select either the X (time) or Y (voltage) cursors. Note that in order to measure time, the X cursors are perpendicular to the x-axis, and similarly, the Y cursors are perpendicular to the y-axis.

The following options appear if X is selected: • X1: Select this to adjust the first X cursor. The value indicated by the cursor is displayed on the bottom of the screen below “X1”.

• X2: Select this to adjust the second X cursor. The value indicated by the cursor is display below “X2”.

• X1 X2: Select this to simultaneously move the X1 and X2 cursors.

1 , and etc. are displayed immediately above the cursor Note that the measurements △X = X2 − X1, △X menu options. Also, if Y is selected instead of X, the screen displays the Y counterparts of the options and cursors mentioned above.

5

Examples

These examples assume you already have the oscilloscope turned on and that the signal of interest is on Channel 1.

5.1

Measuring the Peak-to-Peak Voltage (Vpp ) of a Waveform

1. Press the “AutoScale” button and adjust the horizontal and vertical scaling so that the wave is visible.

2. Press the “Quick Measure” button in the MEASURE section.

3. Verify that the correct source is selected (1) on the leftmost menu button.

4. Press the second menu button that corresponds to Select and use the entry knob to choose Peak-Peak.

5. Press the third menu button that corresponds to Measure.

5

EXAMPLES

6

6. The Vpp value will be displayed at the bottom of the screen, and the measured peak-to-peak distance will be displayed via two horizontal cursors around the waveform.

5.2

Measuring Frequency of a Waveform

1. Press the “AutoScale” button and adjust the horizontal and vertical scaling so that the wave is visible.

2. Press the “Quick Measure”button in the MEASURE section.

3. Verify that the correct source (1) is selected on the leftmost menu button.

4. Press the second menu button that corresponds to Select and use the entry knob to choose Frequency.

5. Press the third menu button that corresponds to Measure.

6. The frequency value will be displayed at the bottom of the screen, and the measured period will be displayed with two vertical cursors on the waveform.

5.3

Measuring Voltage with Cursors

1. Press the “AutoScale” button and adjust the horizontal and vertical scaling so that the wave is visible.

2. Press the “Cursors” button in the MEASURE section.

3. Verify that the correct source (1) is selected using the second menu button.

4. Press the third menu button until Y is selected.

5. Press the fourth menu button that corresponds to Y1.

6. Turn the entry knob until the voltage cursor is moved to the desired vertical position.

7. The voltage value will be displayed at the bottom of the screen under “Y1”.

5.4

Using Averaging

1. Press the “Acquire” button in the WAVEFORM section.

2. Press the “Acq Mode” menu button until Averaging is selected.

3. Use the “# Args” menu button to select the number of samples to average over.

4. The signal noise should be reduced proportional to the number of samples that are averaged. A greater number of samples will take longer to be computed.

5.5

Measuring a Transfer Characteristic

1. Input the intended vin and vout each on its own channel. The following steps will assume that Channel 1 has vin and Channel 2 has vout .

2. Press the “Quick Measure” button in the MEASURE section, select Channel 1 as the source and P eak − P eak as the measurement. Then, press the third menu button that corresponds to Measure.

3. Repeat the previous step for Channel 2.

P k−P k(2) 4. At the bottom of the screen, each peak-to-peak voltage will be displayed. Calculate P k−P k(1) as the frequency response at the given frequency. The measurement is only a true scalar frequency response if the input signal is a sinusoid and the system is linear.

Agilent E3631A DC Power Supply Tutorial 1

Introduction

The DC power supply is simple, so this tutorial only contains a few bulleted notes and a simple example.

There is an image of the front panel interface in Figure 1.

2

Interface Notes • The power suppy can output independent values on the +6V and ±25 V outputs. However, the digital display can only show one value at a time.

• For displaying the ±25 V outputs, press the +25 V or −25 V buttons, respectively. For the 6 V output, press the +6 V button.

• The “Track” button is used to set the −25 V output as a proportion of the +25 V output setting. If the +25 V output is set to 9 V, then the −25 V output will be −9 V when the word “Track” appears on the bottom of the display. Track can be turned on by pressing and holding the “Track” button until “Track” appears on the display. This feature can be turned off by pressing the “Track” button again.

• The power supply can be switched into a current-source mode. However, for these labs, you will only use the voltage mode; so be sure the word “CV” appears on the right corner of the display when the output is on.

• The voltage and current limit can be set by using the following procedure: Press the “Display Limit” button. “LMT” should be shown on the bottom of the display. Now use the knob on the right to set the desired value. Toggle between setting voltage and current by pressing the “Voltage/Current” button. The digit that is blinking is the one being changed; to switch to a different digit, use the left and right arrow buttons below the knob. When the desired limit value is set, press the “Display Limit” button again. Note that the limit value is not always the output value (e.g. in the case of a short circuit).

• To temporarily turn off the DC output without turning off the equipment, press the “Output On/Off” button to display “Output Off” on the screen. Please remember to use this feature when making changes to your circuit connections. To turn on the DC output, press the “Output On/Off” button again.

3

Examples

Here are all of the steps necessary to set up +9 V and −9 V supply rails.

1. Turn on the power supply with the lower-left power button.

2. Press the +25 V button in the SELECT section and then press the “Display Limit” button to view the voltage setting for that output. Set the voltage limit to 9.00 V using the procedure mentioned above.

3. Press the −25 V button in the SELECT section and then, if necessary, press the “Display Limit” button again to view the voltage setting for that output. Press down on the “Track” button until the word “Track” is shown on the bottom of the display and then verify that the voltage reads −9.00 V. 4. Connect cables to the +25 V and −25 V output ports and then press the “Output On/Off” button to turn on the output if this was not done already.

1

3

2

EXAMPLES

Figure 1: Agilent E3631A front panel.

5. Check to be sure the word “CV” appears on the right corner of the display for each 25 V output.

If “CC” appears on the corner of the display instead of “CV” for any of them, then this means the respective DC output is acting as a current source. To correct for this, set the current limit to 1.00 A for the ±25 V outputs. (Note that the lab experiments in this manual do not require the DC supply to output more than 1.00 A.) 6. The power supply has a floating ground (the one labeled “COM”), so you can cascade outputs in series to reach higher voltages. The green output is earth-grounded.

Bode Plot Tutorial Contents 1 Introduction

1

2 Bode Plots Basics 2.1 Magnitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2 Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 2

3 Combining Poles and Zeroes

4

1

Introduction

Although you should have learned about Bode plots in previous courses, this tutorial will give you a brief review of the material in case your memory is fuzzy.

2

Bode Plots Basics

Making the Bode plots for a transfer function involves drawing both the magnitude and phase plots. The magnitude is plotted in decibels (dB) while the phase is plotted in degrees (◦ ). For both plots, the horizontal axis is either frequency (f ) or angular frequency (ω), measured in Hz and rad/s respectively. In addition, the horizontal axis should be logarithmic (i.e. increasing by factors of 10).

Most of the transfer functions we will encounter in this lab manual can be rearranged into the general form: jω/ωz1 (1 + jω/ωz2 ) (1 + jω/ωz3 ) . . . , (1) jω/ωp1 (1 + jω/ωp2 ) (1 + jω/ωp3 ) . . . √ where A is an arbitrary constant and j is −1. Besides the exception of jω/ωc , the basic component of this transfer function is 1 + jω/ωc, where ωc is some numerical constant. Let us analyze this basic component first before we analyze the transfer function as a whole.

H(jω) = A ·

2.1

Magnitude

Recall the definition of magnitude (measured in dB): |H(jω)|dB = 20 log |H(jω)| = 20 log

q (ℜ [H(jω)])2 + (ℑ [H(jω)])2

(2)

Let us apply this definition to our basic component (1 + jω/ωc ), which is also called a zero when it appears in the numerator of the transfer function: q 2 (3) |1 + jω/ωc |dB = 20 log |1 + jω/ωc | = 20 log 1 + (ω/ωc) For small values of ω, we have 20 log |1 + jω/ωc| ≈ 0 dB. For large values of ω, 20 log |1 + jω/ωc| → ∞.

When ω = ωc , the magnitude of the transfer function is approximately 3 dB. Since there is little change in the magnitude of the transfer function from ω = 0 to ω = ωc , we can approximate the magnitude expression as equal to 0 dB within this interval. As for the ω > ωc interval, the (ω/ωc ) term dominates in the expression; thus, we can approximate the magnitude as 20 log (ω/ωc ). Also, notice that, within the ω > ωc interval, the magnitude increases by 20 dB when ω increases by a factor of 10. Therefore, the overall Bode plot approximation for a zero is the following: 0 dB for ω < ωc and a 20 dB/decade line for ω > ωc . Please see Figure 1 for an illustration of this approximation.

1

2

2

BODE PLOTS BASICS

Figure 1 also shows the magnitude Bode plot for a DC zero, which has the form jω/ωc . Because the DC zero lacks the “1” term, its Bode plot approximation differs from the normal zero: instead of two different regions, the DC zero consists of only a 20 dB/decade line. Its intersection with the frequency axis is located at ωc because 20 log (ωc /ωc ) = 0dB. Note that ωc is 105 rad/s in this example.

Magnitude (dB)

40

20 20 log |1 + jω/ωc | 20 log |jω/ωc|

0

−20 −40 103

104

105 ω (rad/s)

106

107

Figure 1: Magnitude Bode plots of a normal zero and a DC zero (with both having ωc = 105 rad/s). Notice the plots overlap for ω > ωc .

The basic transfer function component, 1 + jω/ωc , can also appear in the denominator (in which case it is called a pole). Even though this may seem like an entirely different problem, the same principles apply. Recall that we took the logarithm of our transfer function when we expressed our results in decibels.

Also, recall that taking the logarithm of the inverse of a function simply gives the negated logarithm of the function. In other words, we simply have to negate the results of our zero analysis to get the appropriate expressions for poles. The same argument applies with DC poles, which has the form jω/ωc .

In general, a normal pole will have a constant 0 dB value for ω < ωc and will drop by 20 dB/decade for ω > ωc . A DC pole will drop by 20 dB/decade for any ω and will intersect the frequency axis (0 dB) at ω = ωc . The results are shown in Figure 2.

2.2

Phase

Now, let us take a look at the respective phases of a zero, DC zero, pole, and DC pole. Recall the definition of phase:

ℑ[H(jω)] (4) Arg (H(jω)) = arctan ℜ[H(jω)] Applying this definition to the normal zero: Arg(1 + jω/ωc ) = arctan

ω ωc

(5)

For ω = 0, Arg(1 + jω/ωc ) = 0. For ω → ∞, Arg(1 + jω/ωc) → 90◦ . For ω = ωc , Arg(1 + jω/ωc ) → 45◦ .

Thus, our approximation for the phase of a zero is the following: 0◦ for ω < 0.1ωc , 45◦ for ω = ωc , and 90◦ for ω > 10ωc . The phase Bode plot is then constructed using straight lines that join these regions together.

As for the DC zero, its phase stays constant at 90◦ . Please refer to Figure 3 for an illustration of these plots.

2

3

BODE PLOTS BASICS

Magnitude (dB)

40

20 1 20 log 1+jω/ω c

0

1 20 log jω/ω c

−20 −40 103

104

105 ω (rad/s)

106

107

Figure 2: Magnitude Bode plots of a normal pole and a DC pole (with both having ωc = 105 rad/s). Notice the plots overlap for ω > ωc .

100

Phase (degrees)

80 60

Arg (1 + jω/ωc ) Arg (jω/ωc )

40 20 0 3 10

104

105 ω (rad/s)

106

107

Figure 3: Phase Bode plots of a normal zero and a DC zero (with both having ωc = 105 rad/s). Notice the plots overlap for ω > 10ωc .

The phase analysis of poles and DC poles can be conducted in a similar fashion. Let us begin by applying the definition of phase to the pole and DC pole, respectively:

1 = Arg (1) − Arg (1 + jω/ωc ) = 0 − Arg (1 + jω/ωc ) = −Arg (1 + jω/ωc ) (6) Arg 1 + jω/ωc

3

4

COMBINING POLES AND ZEROES

Arg

1 jω/ωc

= Arg (1) − Arg (jω/ωc ) = 0 − Arg (jω/ωc ) = −Arg (jω/ωc )

(7)

As you might notice, our phase plots for poles and DC poles will simply be the negated versions of the zero plots. Please see Figure 4 for an illustration.

0

Phase (degrees)

−20 −40

Arg Arg

−60

1 1+jω/ωc 1 jω/ωc

−80 −100 103

104

105 ω (rad/s)

106

107

Figure 4: Phase Bode plots of a normal pole and a DC pole (with both having ωc = 105 rad/s). Notice the plots overlap for ω > 10ωc .

3

Combining Poles and Zeroes

Generally, a transfer function may involve many poles and zeroes (as well as their DC counterparts). In order to simplify the task of drawing Bode plots, your first step should be to factor the transfer function into the canonical form as shown in Equation 1. This makes it easy to identify all of the poles and zeroes.

Then, you’ll have to handle the constant coefficient, A (if it is present). The magnitude of A will affect your magnitude plot, and the sign of A will affect your phase plot. More specifically, your magnitude plot must be offset by 20 log |A|. For example, if A = 10, then your magnitude plot must be shifted up by 20 dB. Similarly, if A = 1/10, then your magnitude plot must be shifted down by 20 dB. If A < 0, then your phase plot must be shifted up (or down—it’s the same in this case) by 180◦. Next, you need to draw each pole and zero plot individually on the same graph (whether you’re making a magnitude or phase plot). Finally, add together all the curves that you have drawn to obtain the final Bode plot. Remember to shift your plots accordingly based on the constant A as mentioned previously. This superposition principle is possible because of the decomposition of the transfer function into zeroes and poles.

When adding the poles and zeroes in the final plot, remember that in areas where two curves are constant, the result will just be the sum of the constant values. When one is a constant and the other is linear, the result will be a line that starts at that constant value and progress with a slope equal to the linear curve.

Finally, when both are linear, the sum will be a line that has a slope equal to the sum of the slopes.

HP 34401A Digital Multimeter Tutorial 1

Introduction

The DMM is simple; so, this tutorial only contains a few bulleted notes and two examples. In Figure 1, there is an image of the front panel interface.

2

Interface Notes • To measure DC or AC current or voltage, use the two leftmost buttons in the FUNCTION section.

The options for measuring current are in blue, and require use of the Shift key.

• Use the blue “Shift” key to select options labeled in blue. For example, to measure DC current, first press Shift and then press the upper-left button labeled “DC I” in blue.

• To measure voltage or resistance, plug in the probes as in Figure 1. To measure current, you MUST switch the red probe to the lower-right input port (labeled “I”); otherwise, the current would not be measured. Also, please remember to switch back to the probe configuration shown in Figure 1 when measuring voltage again.

• When measuring current, never place the probes across a voltage source. The ammeter has a very small internal impedance, and so a voltage source would need to drive a very high current through the ammeter to maintain its voltage output. High currents may damage the DMM. • The DMM ground is floating, so you can always measure voltage differences with the two probes.

Note that some other devices are earth-grounded and thus, can only measure a voltage difference from earth-ground.

• As a side note, here are the explanations of some of the buttons found on the HP34401A: the “DC V” button measures DC voltage, the “AC V” button is used to measure Vrms , the “Ω 2W ” button measures resistance, and the “Freq” button measures frequency.

Figure 1: HP34401A front panel. The input cables on the right are set to measure voltage. To measure current, the red cable is moved to the bottom-right port while the connection for the black cable remains unchanged.

1

3

EXAMPLES

3

Examples

3.1

Measuring DC Voltage

2

Here are all of the steps necessary to measure a DC voltage between nodes.

1. Press the power button on the left.

2. Press the DC V button on the left side of the Function section.

3. Be sure that the probes are plugged into the DMM in the voltage configuration: the black probe should be in the right “LO” port while the red probe should be in the right “HI” port. (Please see Figure 1.)

4. Place the probe tips in parallel with the desired nodes to measure the DC voltage across them.

3.2

Measuring DC Current

Here are all of the steps necessary to measure a DC current through a branch.

1. Press the power button on the left.

2. Press the Shift button, and then the button labeled with the blue “DC I.” 3. Be sure that the probes are plugged into the DMM in the current configuration: the black probe should be in the right “LO” port while the red probe should be in the bottom-right “I” port.

4. Place the probe tips in series with the branch that you want to measure the DC current.

HSPICE Tutorial Contents 1 Introduction

1

2 Windows and Unix Version 2.1 Running HSPICE in Windows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2 Running HSPICE in UNIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 2

3 Simulating Circuits in HSPICE and Awaves 3.1 HSPICE Netlist Syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2.1 Transient analysis of a simple RC circuit . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2.2 Operating point analysis for a diode . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2.3 DC analysis of a diode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2.4 AC analysis of a high-pass filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2.5 Transfer function analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2.6 Pole-zero analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2.7 The .measure command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.3 Including another file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 3 3 3 4 5 6 8 9 9 10

4 Using Awaves 10 4.1 Interface description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 4.2 Deleting plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 4.3 Printing plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.4 Making a measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.5 Zooming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.6 Updating a panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 5 Syntax Reference

1

11

Introduction

This tutorial outlines how to run HSPICE, then delves into the details of creating netlists, simulating them, and using Awaves to plot the results. The appendix to this document serves as a reference that may be useful throughout the lab experiments.

Basically, HSPICE is just a program that takes in a netlist (a simple text file containing a circuit description and analysis options) and outputs the analysis it has performed on the circuit. An HSPICE netlist typically has an .sp extension, e.g. circuit.sp. Although HSPICE produces many output files, the only one that you will need to examine for the labs is the .lis extension file, e.g. circuit.lis. This file contains all of the important results from the HSPICE analysis—operating points, measurement results, error messages, etc. Typically after simulating a circuit, it is best to check this file first to ensure there were no errors in your netlist.

The other files that HSPICE generates are used by Avanwaves, or Awaves for short. Awaves is a program that allows you to graphically plot the results of the HSPICE analysis. However, you will need to explicitly command HSPICE to generate the extra files that Awaves needs; we will show you how to do this later in the tutorial. Generally, when running Awaves, you will need to open the .sp file of the circuit you analyzed.

Awaves will then automatically find the analysis files that it needs and allow you to plot the results.

You can create netlists in any text editor that you like. Notepad and Wordpad are common options under Windows. Emacs, Vim, and Pico are common options under UNIX. In this tutorial, we are going to assume you are familiar enough with one of these text editors. If you are working in the UNIX environment 1

2

WINDOWS AND UNIX VERSION

2

and are not familiar with any text editor, we recommend using Pico for now because it is the simplest to use.

2

Windows and Unix Version

There are two versions of HSPICE available; however, the same netlist will work in both versions. The following sections cover the procedures necessary for using HSPICE in the two different operating systems.

2.1

Running HSPICE in Windows

The example below demonstrates an HSPICE simulation and an analysis in Awaves.

1. Start Notepad. You can do this either by clicking Start → Run, typing “Notepad”, and hitting Enter.

Or, you can click Start → Programs → Accessories → Notepad.

2. Copy the text in Figure 1 into Notepad exactly as it is written (this is what we call a “netlist”).

SPICE Tutorial Example 1 - Simple RC Circuit vs vs gnd PWL(0s 0V 5ms 0V 5.001ms 5V 10ms 5V) r1 vs vo 1k c1 vo gnd 1uF .tran 0.01ms 10ms .option post=2 .end Figure 1: A simple RC circuit netlist 3. Save this file into a folder called “Tutorial”. Name it rccircuit.sp. Note: To ensure the filename has a .sp extension, be sure to select “All Files” in the “Save as type” listbox. You can put the filename in quotations if you want to be extra careful.

4. Open the “HSPICE UI” (HSPUI for short), a graphical user interface to HSPICE. Although you can run HSPICE and Awaves individually, HPSPUI puts HSPICE, Awaves, your netlist, and the HSPICE output (the .lis file mentioned earlier) in a convenient panel for easy access.

5. Click Open and select rccircuit.sp using the file browser. You will see that HSPUI automatically picks out the title and picks an output file called rccircuit.lis, which is also in the Tutorial directory.

6. Click Simulate to simulate the circuit. HSPUI will open HSPICE for you and run your netlist through HSPICE, producing rccircuit.lis and other output files used by Awaves.

7. Click Edit LL to view the output from HSPICE. This file contains information about the analysis done by HSPICE. Typically, you would look here for measurement results, operating points, and error messages. You should see no error messages at this time. If you do, check to make sure you copied the netlist exactly as shown in Figure 1. Once you have verified that there are no error messages, close the output file.

8. Click Avanwaves to start Awaves. You will see that HSPUI opens your circuit in Awaves, and you can immediately begin plotting data. We will cover Awaves through some examples later, but you can see the results of your analysis by selecting Transient: spice tutorial example 1 - simple rc circuit in the Results Browser and double-clicking vs and vo to plot them in the graph. As you may have guessed, vs is a step function input and vo is the output taken across a capacitor (a curve described

by vo (t) = vs 1 − e−t/RC ).

Now that you know how to run HSPICE and Awaves in Windows, you can skip ahead to the sections on SPICE itself. If you are interested in using the UNIX version of HSPICE, continue reading below.

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SIMULATING CIRCUITS IN HSPICE AND AWAVES

2.2

3

Running HSPICE in UNIX

1. Make a new directory called Tutorial. You can do this by typing mkdir Tutorial at the Bash shell.

Change to this directory by typing cd Tutorial.

2. Using your preferred text editor (e.g. Emacs, Vim, or Pico), copy the netlist in Figure 1 to a file called rccircuit.sp.

3. Run HSPICE by typing $ hspice rccircuit.sp > rccircuit.lis This command will send the output from HSPICE to a file called rccircuit.lis. If you exclude the second half of the command, the output will be shown in the shell itself. This can be inconvenient for referencing and debugging, so it is common to send the output to a file.

4. Open rccircuit.lis in your preferred text editor or pagination utility (e.g. more or less). This file contains information about the analysis done by HSPICE. Typically, you would look here for measurement results, operating points, and error messages. You should see no error messages at this time. If you do, check to make sure you copied the netlist exactly as shown in Figure 1. Once you’ve verified there are no error messages, close the output file.

5. Run Awaves by typing $ awaves rccircuit.sp & This will open your circuit in Awaves. We will cover Awaves in more detail later, but you can see the results of your analysis by selecting Transient: spice tutorial example 1 - simple rc circuit in the Results Browser and double-clicking vs and vo to plot them in the graph. As you might have already guessed from the netlist, vs is a step function input and vo is the output taken across a capacitor (a

curve described by vo (t) = vs 1 − e−t/RC ).

3

Simulating Circuits in HSPICE and Awaves

3.1

HSPICE Netlist Syntax

At this point you should be comfortable running HSPICE and Awaves under your current environment (Windows or UNIX). Now, we can begin describing the mechanics of writing a netlist. The first line of a netlist must always be a comment—it will be ignored by HSPICE no matter what you put on it. Typically, we put a brief description on the first line.

Next, we define the models that we are going to use. At this point you have not learned about MOSFET, BJT, or diode models, but you should that these devices have many parameters, unlike resistors, capacitors, inductors, and sources which are specified by a single value.

After defining device models, we write the description of the circuit topology itself. Each type of circuit element has its own command (e.g. resistors and capacitors are defined by unique commands). The way we describe the circuit topology is by giving each node (a node being the point connecting any two or more elements) a unique name and then connecting circuit elements between these nodes. Note that you do not have to specify these elements in any particular order (though it is often useful to specify them in an order that is logical to you).

The last line of any HSPICE netlist must be the command .end. This tells HSPICE where to stop reading the netlist.

Note that the organization of a netlist in the order described here is somewhat arbitrary (aside from the first and last lines). You can define a model before you use it in a document, and you can specify your analysis before you describe the circuit topology. What we’ve described is just one convenient way to organize your netlist so that it is easy to read and understand. Note that SPICE is not a programming language like what you may been familiar with; an example of this is that HSPICE is completely case insensitive. That means vs, VS, Vs, and vS are all the same to HSPICE.

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3.2

Examples

The specifics of writing a netlist are going to be taught through examples. We’ll start with simple examples and gradually progress to more complicated circuits to allow you to gradually build your proficiency with SPICE. 3.2.1

Transient analysis of a simple RC circuit

Let’s start with the simple RC circuit you analyzed earlier in the tutorial. The same netlist with line numbers is shown in Figure 2.

1 2 3 4 5 6 7

SPICE Tutorial Example 1 - Simple RC Circuit vs vs gnd PWL(0s 0V 5ms 0V 5.001ms 5V 10ms 5V) r1 vs vo 1k c1 vo gnd 1uF .tran 0.01ms 10ms .option post=2 nomod .end Figure 2: A simple RC circuit netlist with line numbers

First, note lines 1 and 7. Line 1 is a comment, as always. You can specify a comment at any time using the asterisk (*). Any text following the asterisk will be a comment. Line 7 is the .end command, another requirement for any netlist.

Lines 2–4 contain the description of the circuit topology. In this case, we have three nodes: vs, vo, and gnd. Note that elements and nodes can have the same name, so Line 2 is perfectly legal even though it is connecting the voltage source called vs to the circuit node called vs. In some circuits, you may need to refer to a voltage source or circuit node later in an analysis statement, but context will always make it clear which you are referring to so a source and node having the same name will never cause ambiguities.

In these lines you can also see the usage of suffixes to denote powers of 10. From 10−15 to 1012 , these are: f (femto), p (pico) , n (nano), u (micro), m (milli), k (kilo), meg (mega), g (giga), t (tera). HSPICE often reports values following by an x—this is short-hand for 106 , and you can use it interchangeably with meg.

The node gnd is a standard name used to reference ground. You can also use the number 0 to refer to the ground node (some people like to number their nodes instead of naming them, in which case 0 may be a more natural fit). Ground is a special node in the circuit, so only use gnd or 0 to refer to the ground node.

The other nodes have arbitrary names, but in this case I’ve named them intuitively: vs is the voltage of the source, and vo is the voltage across the capacitor, which I consider the output in this case. Figure 3 shows the circuit diagram corresponding to this netlist (with nodes labeled as they are in the netlist). vs + vs

1 kΩ r1 c1

vo 1 µF

− gnd Figure 3: Circuit diagram corresponding to the netlist in Figure 2 If you take another look at Line 3, you’ll see that when defining the source vs I put the node vs first and the node gnd second. This is an important distinction when dealing with elements that have positive and negative terminals. For a resistor, such as the one in Line 3, I can list the nodes in any order without changing the circuit’s behavior. Also note that the value of the source is a complicated PWL expression. Refer to the syntax reference at the end of this guide and you’ll see that this is actually a non-ideal step function (with a linear rise over 1 µs).

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SIMULATING CIRCUITS IN HSPICE AND AWAVES

Line 5 is our first analysis statement. It tells HSPICE to do a transient (i.e. measure values as a function of time) from time t = 0 ms to time t = 10 ms in increments of 0.01 ms. When you simulated this circuit earlier, you should’ve seen that the plot of vo is that of a capacitor charging due to a step function input.

This analysis statement is what allowed you to plot that time-based analysis of node vo.

Line 6 is a list of options that you can pass to HSPICE. In this case, I’ve used two options: post=2 and nomod. The first, post=2, tells HSPICE to generate extra files for Awaves to use in plotting data. If you do not specify post=2 (actually, you can also specify post=1 or post=3—the differences aren’t important for our purposes), you will not be able to plot your data in Awaves. The second option, nomod, just tells HSPICE not to print model information in the output file. Although this is unimportant for this example (since we haven’t included any models), it can be useful when you are dealing with real device models that can be half a page long.

Try simulating this circuit and plotting vo in Awaves like you did earlier in the tutorial. Now try to measure how long it takes for vo to go from 0V to 0.63(5) = 3.15 V once vs steps from 0 V to 5 V. If you remember your RC circuits, you’ll realize this should be the time constant of the circuit t = RC = 1 ms.

Measuring this on the graph in Awaves, I get almost exactly 1 ms.

3.2.2

Operating point analysis for a diode

Another very useful type of analysis is operating point analysis. You probably recall having to calculate operating points by finding the intersection between a diode’s IV curve and the load line created by a resistor.

Figure 4 shows a simple circuit diagram for which we’d like to calculate the operating point. Figure 5 shows the corresponding netlist (once again with line numbers). I’ve labeled the nodes and elements in the diagram consistently with how they’re named in the netlist. vs

5 kΩ

vd

rs

vs + − 5V

d1

gnd Figure 4: A diode circuit for operating point analysis 1 2 3 4 5 6 7

SPICE Tutorial Example 2 - Simple Diode Circuit .model tut_diode d (is=1e-14 vj=0.6 rs=10) vs vs gnd 5V rs vs vd 5k d1 vd gnd tut_diode .op .end Figure 5: The netlist corresponding to the diode circuit in Figure 4

Let’s take a look at the new features of this netlist. First, we’ve defined a model on Line 2 called tut_diode. Models are necessary whenever you are using diodes or transistors in your netlists. The model defines certain parameters related to the device you specify. In this class we’ll typically give you the parameters you need to define for your SPICE models, and our models will typically be very simple. Real device models can have dozens of parameters specified in excruciating detail. Note that a model name cannot start with a number in HSPICE (for example, 2N4401 would be an invalid name, but QN4401 would be a valid model name).

Line 5 shows how you can define a diode. Recall that a diode is asymmetric, so we have to specify the positive terminal first and the negative terminal second. You also have to specify which model to use, and in this case I’m using the model we just defined in Line 2.

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SIMULATING CIRCUITS IN HSPICE AND AWAVES

6

The last new command shown here is on Line 6, the .op command. This command stands for “operating point” and tells HSPICE to calculate the voltage at every node and the current through every branch in the circuit. Note that we’ve excluded the .option post=2 command in this netlist because we will not need to use Awaves for this analysis.

Simulate this circuit and open the SPICE output file. Scroll through this file until you see a line that says “operating point information”. Below that, you should see a list of all of the nodes in the circuit (in this case, we just have two nodes) and the voltages at those nodes, plus a list of all the elements in the circuit and the voltages and currents associated with those elements. We can read off the operating point we’re interested in: the voltage at vd is 655.8104 mV. Let’s compare this to the hand-calculated operating point for the same circuit using IS = 10−14 A for the diode. We have: IS eVD /VT =

1 VS − VD RS RS

Solving this equation gives VD = 654.889 mV, a percent error of 0.14 % compared to the value given by HSPICE. 3.2.3

DC analysis of a diode

Another type of analysis we can do is DC analysis. DC analysis allows us to measure values in our circuit as we sweep a voltage. For example, let’s look again at our diode circuit. Instead of looking at vd for vs at just 5 V, maybe we want to sweep vs from 0 V to 5 V and see how vd changes as a result. Let’s look at Figure 6 to see how we might do this (I’ve used the same node names as shown in Figure 4).

1 2 3 4 5 6 7 8

SPICE Tutorial Example 3 - Simple Diode Circuit .model tut_diode d (is=1e-14 vj=0.6 rs=10) vs vs gnd 5V rs vs vd 5k d1 vd gnd tut_diode .dc vs 0V 5V 0.01V .option post=2 .end Figure 6: Netlist for DC analysis of the diode circuit in Figure 4

Let’s see how this netlist has changed to allow us to do a DC analysis. First, note the Line 6, instead of being an operating point analysis .op, is now a DC analysis .dc. In this case, we are sweeping vs from 0 V to 5 V in steps of 0.01 V. Looking at Line 3, you may think this conflicts with the value I’ve already put there; however, when you do a DC analysis of a source, it ignores whatever value you gave the source earlier.

The second change I made was in adding Line 7, since we are going to be using Awaves to look at a plot of vd versus vs. Simulate the circuit and open it in Awaves. Before we continue, I’m going to briefly describe the Awaves interface that we’ve been using so far.

When you first open Awaves with your circuit, it will automatically open the Results Browser, a window that allows you to browse the results of the analysis that HSPICE has done. This will be the first place to look when you want to plot something you’ve measured. There are many extraneous quantities you’ll probably never want to plot (for example, you can plot the voltage at the ground node), but usually the quantity you’ll want to plot will be located somewhere in the Results Browser.

At the top of the Results Browser is a list of analyses that HSPICE has done on the circuit. In this case, we just did one analysis, a DC analysis, so you’ll only see one choice in the list. Go ahead and click DC: spice tutorial example 3 - simple diode circuit. The bottom half of the screen should populate with various options once you select the DC analysis. Under the “Types” column, you’ll see a number of different types of data you can plot: voltages and currents in this case (other types of analyses will give you other choices).

If you click on Voltages, you’ll see a number of choices appear under “Curves”. These choices are all of the

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SIMULATING CIRCUITS IN HSPICE AND AWAVES

voltages you can plot. You may wonder what the x-axis of the plot will be, and that is given by the type of analysis you did. In this case, it will be the voltage you varied, vd. In the case of a transient analysis, it would be time. For AC analysis, it would be frequency. You can change your x-axis (this is sometimes necessary) by selecting the curve you want as your x-axis and clicking Apply in the “Current X-Axis” portion of the Results Browser.

Go ahead and double-click the vd curve under Voltages, then click Close to close the Results Browser.

The main window of Awaves, should show a plot of vs versus vd. This is the first example for which handcalculating a solution would’ve been extremely difficult or tedious. Remember that the equation describing the circuit’s behavior is IS eVD /VT =

1 VS − VD RS RS

Notice that it is impossible to algebraically solve this equation for VD as a function of VS . Without SPICE, you’d have to plug in each value of VS individually (remember, there are 5/0.01 = 500 of them) and solve the equation by iteration (or by using a graphing calculator) for each value.

3.2.4

AC analysis of a high-pass filter

Let’s take a look at a basic RC high-pass filter. Figure 7 shows the circuit diagram we’ll be simulating, and Figure 8 shows the associated netlist.

1 nF vs + vs

vo c1 r1

1 kΩ

− gnd Figure 7: A simple RC high-pass filter 1 SPICE Tutorial Example 4 - Simple RC High-Pass Filter 2 vs vs gnd ac 1V 3 c1 vs vo 1nF 4 r1 vo gnd 1k 5 .ac dec 500 100 1G 6 .option post=2 7 .end Figure 8: The netlist corresponding to the high-pass filter in Figure 7 First let’s look at how the netlist has changed once again. Look at Line 2. Although this looks extremely similar to all of our other voltage definitions, it has one extra parameter specified before the value: ac. This tells HSPICE that the AC analysis should be done by varying the frequency of this source. If you try to do an AC analysis of a circuit without any AC sources specified, HSPICE will give you an error.

Now look at the new analysis statement on Line 5. The .ac command tells HSPICE to do an AC analysis by sweeping the frequency of the AC source as you specify. The first parameter passed to this command, in our case dec, tells HSPICE whether to do a linear (lin) sweep, a sweep by octaves (oct), or a sweep by decades (dec). In this class, we’ll be using dec for all of our AC analyses. The second parameter tells HSPICE how many sample points to take per decade. The third parameter is the starting frequency of the sweep, and the fourth parameter is the ending frequency of the sweep. In this case, we’re taking 500 points per decade from f = 100 Hz to f = 1 GHz.

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SIMULATING CIRCUITS IN HSPICE AND AWAVES

8

Simulate this circuit and open it in Awaves. You’ll notice that in the Results Browser you can plot real and imaginary components, magnitudes, and phases of voltages and currents. You’ll also notice that your x-axis has been conveniently set to frequency in Hertz. Let’s make a Bode plot (magnitude and phase) of this high-pass filter to confirm that it behaves as we expect.

Let’s start with the phase Bode plot. This is easier to do than the magnitude Bode plot because HSPICE effectively calculates the phase for you already. Simply select Volts Phase from “Types” in the Results Browser, then double-click vo. Notice that the plot doesn’t look like a Bode plot yet because the x-axis is measured on a linear scale. To change it to a logarithmic scale, right-click the x-axis and select Set Logarithmic Scale. Now the phase Bode plot should be quite apparent.

Now let’s plot the magnitude Bode plot. Recall that for the magnitude Bode plot, the vertical axis is measured in decibels, or dB. HSPICE has calculated voltage magnitudes, but it hasn’t calculated them in dB. However, we can use Awaves to calculate the magnitude in dB. Click Tools → Expressions to open the Expression Builder. You can calculate any function you want from the curves that HSPICE has provided using the Expression Builder. In the left column under “Functions”, you should see decibel( ).

Double-click decibel( ) and Awaves will place it in the “Expression” box at the top of the window. Now, without closing the Expression Builder, open the Results Browser and select Volts Mag from “Types”. We want the magnitude of the output, so middle-click vo and, while holding the middle mouse button, drag your mouse between the parentheses of the decibel( ) function in the Expression Builder, then release the middle mouse button.

If you did this properly, you should see decibel(node(D0,"A0","vm(vo)","S-1")) in the “Expression” box in the Expression Builder. You can close the Results Browser at this point. Before you can plot this function, you need to give it a name. In the “Result” box, type a name (for example, “MagBode”), then click Apply. Your function will now appear under “Expressions” in the Expression Builder. Double-click your new expression and Awaves will plot it for you.

If you plotted the phase Bode plot first, you’ll see that the magnitude Bode plot is drawn on the same graph as the phase plot. However, the units for the magnitude plot are on the right side of the graph, so you can see both plots at the same time without getting confused. The magnitude Bode plot should be exactly what you’d expect from a high-pass filter. You can do the hand-calculations yourself this time and confirm that these plots are correct.

As a side note, normally when you make a Bode plot you’d need to take the magnitude of the output over the input in dB. In general this is true, but in our case we set the magnitude of our AC source to 1 V, so dividing by a magnitude of 1 V would not have changed the results. If you were to use a different magnitude, you’d have to use the same method described above to divide the magnitude of the output by the magnitude of the input before computing the expression’s value in dB. 3.2.5

Transfer function analysis

Let’s try to find the voltage gain (output over input) for the circuit in Figure 9. Since this a simple resistive network, you can hand-calculate the answer and compare it to the result you get in HSPICE. I’ve used more convential notation in the diagram this time and haven’t labeled the nodes. At this point, you should be able to recognize what is going on without those labels. Figure 10 shows the netlist for this circuit diagram.

The only new feature here is the analysis statement on Line 11, which is a .tf statement, short for transfer function. This calculates the DC gain, input resistance, and output resistance between the voltage node specified first (the output) and the voltage source specified second (the input). We don’t need the .option post=2 statement since we will not be using Awaves for this analysis.

Simulate the circuit in HSPICE and open the output file. Look for a line that says “small-signal transfer characteristics”. Underneath that, you should see values for v(vo)/vs, or the gain from vs to vo, the input resistance at vs, and the output resistance at vo. In this case, the gain is 109.8628 m ≈ 0.110. If you were to calculate the voltage at node vo by hand, you would get the same result.

3.2.6

Pole-zero analysis

HSPICE can also find poles and zeroes for you. Let’s take another look at the circuit in Figure 7. This time, we’ll use the netlist in Figure 11.

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SIMULATING CIRCUITS IN HSPICE AND AWAVES 1 kΩ

1.5 kΩ

R1

R5 R2

+ vs

500 Ω R6

700 Ω

800 Ω

1V

vo

R3

− R4

200 Ω R7

100 Ω

900 Ω R8 Figure 9: A complicated resistor network 1 SPICE Tutorial Example 5 - Complicated Resistor Network 2 vs vs gnd 1V 3 r1 vs 1 1k 4 r2 1 2 500 5 r3 2 vo 800 6 r4 2 gnd 200 7 r5 1 4 1.5k 8 r6 4 vo 700 9 r7 vo 5 100 10 r8 5 gnd 900 11 .tf v(vo) vs 12 .end Figure 10: SPICE netlist for a resistor network 1 SPICE Tutorial Example 6 - Pole-zero analysis of a high-pass filter 2 vs vs gnd ac 1V 3 c1 vs vo 1nF 4 r1 vo gnd 1k 5 .pz v(vo) vs 6 .end Figure 11: A netlist for finding the poles and zeroes in the circuit in Figure 7 As you can see, the .pz statement is used much like the .tf statement in that you first specify an output node, then an input source. After you simulate the circuit in HSPICE, open the output file and look for a line that says “pole/zero analysis”. You’ll notice that just below that line is a list of all of the poles and zeroes from the input source to the output node. In this case, we have just one zero, since this is a high-pass filter. You can confirm the result by hand-calculating the transfer function.

3.2.7

The .measure command

The .measure command is used to measure almost any parameter in your circuit under some specified conditions. For example, it can be used to measure rise time, fall time, delay, maxima and minima, etc.

Here we will cover just one use of the .measure command.

TRIG/TARG One use of the .measure command involves specifying a trigger and a target (TRIG and TARG, respectively). A trigger tells the command when to start measuring, and the target tells the

3

SIMULATING CIRCUITS IN HSPICE AND AWAVES

10

command when to stop measuring. The command will then report the value you want to measure at the trigger condition, target condition, and the difference between its values under those conditions. This is best illustrated through an example. Consider the RC circuit in Figure 3. Let’s say we want to measure the rise time of this RC circuit. First, we need to define the rise time metric—let’s say it’s the time it takes for vo to go from 10 % to 90 % of its final value (i.e. from 0.5 V to 4.5 V).

Now, let’s take a look at the netlist that will perform this measurement, shown in Figure 12. Pay close attention to line 6, which contains the .measure command. The structure of the command is as follows (note that the plus signs allow you to continue a command on the next line and are not necessary): .measure <ac|dc|tran> <name> + trig <node> val=<value> <rise|fall|cross>=<value> + targ <node> val=<value> <rise|fall|cross>=<value> The first argument specifies what analysis statement to associate the measurement with. For example, if measuring time the first argument should be tran. If measuring frequency, it should be ac, and if voltage, dc. The second argument is simply a name for your measurement. In the example for computing rise time, I use the name trise for my measurement. Now you must specify the trigger and target, which have identical structure. For each, you must specify what node you want to trigger/target on, the value it needs to equal at the time of the trigger/target, and how many rises/falls/crosses have occurred prior to the node reaching that value. You should understand the concept of rising and falling, i.e. a signal going from low to high or high to low. A cross is simply the sum of rises and falls.

Let’s look at our example again. I am triggering when v(vo), the voltage at the output node, is equal to 0.5 V, or 10 % of its final value. I want it to measure this value on the first rise, so I specify rise=1. I am targeting when v(vo) is equal to 4.5 V, or 90 % of its final value. Again, I want the value on the first rise, so I again specify that rise=1. That’s all there is to it. If your simulate this netlist in HSPICE and look at the output, under a line labeled “transient analysis” you should see values for trise, trig, and targ, where trise is just targ - trig.

One issue to watch out for is that you cannot set your trigger to at zero. If you want to trigger at zero, you can approximate the measurement by using a very small, but non-zero, trigger value. For example, I could trigger on the value 1n.

1 SPICE Tutorial Example 7 - Computing rise time 2 vs vs gnd PWL(0s 0V 5ms 0V 5.001ms 5V 10ms 5V) 3 r1 vs vo 1k 4 c1 vo gnd 1uF 5 .tran 0.01ms 10ms 6 .measure tran trise trig v(vo) val=0.5 rise=1 targ v(vo) val=4.5 rise=1 7 .end Figure 12: A netlist to compute the rise time of an RC circuit For more information on the .measure command, refer to Specifying User-Defined Analysis (.MEASURE).

3.3

Including another file

During the course of the semester, you’ll often have to use models that we provide on the course website.

Instead of copying and pasting the models, you can just include the model file in your circuit. To do this, place the model file in the same directory as your netlist (for example, circuit.sp and 2N4401.mod). Then, in your netlist, include the following line: .inc ‘<filename>’ In this case, we would use 2N4401.mod for the filename.

4

USING AWAVES

4

11

Using Awaves

Here we describe how to perform some common actions in Awaves. These are not related to simulation results at all, just the Awaves interface. For details on simulation and examples of how to use certain features, see the examples in the previous section.

4.1

Interface description

The Awaves interface has three windows that you’ll work with. These are the Results Browser, the Expression Builder, and the main window consisting of a wave list and graphical panel. The Results Browser can be opened by clicking Tools → Results Browser... (or by clicking the first icon at the top of the screen with a picture of a tree hierarchy). The Expression Builder can be opened by clicking Tools → Expression Builder... (or by clicking the second icon at the top of the screen that is labeled f (x, y)).

The Results Browser allows you to view data that has been directly measured from your circuit. For example, the voltage at a node, the current through a branch, etc. are available from the Results Browser.

The Expression Builder lets you build mathematical expressions from the data in the Results Browser.

For example, you can compute the absolute value, magnitude, derivative, etc. of any of the data available from the Results Browser.

The main window shows the data that you’re plotting. It consists of a wave list and graphical panel showing the plots of the functions in the wave list. You can add and hide these panels by clicking Panels → Add and Panels → Hide, respectively. Using multiple panels allows you to plot data on separate graphs at the same time. When adding a plot (through the Results Browser or the Expression Builder), it will be added to whatever panel is selected when you add the plot.

4.2

Deleting plots

To delete a plot in Awaves, simply select it from the “Wave List” on the left side of the screen and hit the Delete key on your keyboard.

4.3

Printing plots

To print a plot in Awaves, click Tools → Print.... If you’re printing in lab, you should select the “Printer” radio button. If you’re working from home, you should print to a file, transfer it to your home computer, and print it from your home computer. If you print to a file, save the plot in the PS format. You can then transfer it to your home computer using the methods described in section 2.1.2 or 2.2.2. To print the file, you will need software that can open a PS file (short for Postscript). A common tool for viewing PS files is GSView, which requires Ghostscript.

4.4

Making a measurement

There is a button at the top of the screen that shows a box with a single crosshair. This is used for measuring values on your plots. If you click this button then click any point on your plot, it will show the coordinates of that point and the derivative of the curve at that point. You can delete a measurement by selecting the measurement and clicking Measure → Delete Measure. If you want to delete all of the measurements you’ve made, simply click Measure → Delete All Measures.

If you want to increase the precision of the measurements you’ve made, click Measure → Measure Preferences and choose a higher precision value.

4.5

Zooming

There is a series of buttons at the top that allow you to zoom in and out of the plot you’re viewing. The one with a +, y, and x allows you to zoom in the x and y direction at the same time. Simply drag the cursor to form a box, and that box will fill the screen.

5

SYNTAX REFERENCE

12

The button that shows + and x allows you to zoom only in the x direction. Drag the cursor horizontally, and the length that you drag will fill the screen. The + and y button works similarly, except you drag the cursor vertically and it will zoom in the y direction.

Zooming out works similarly. However, instead of the distance you drag filling the screen, the opposite occurs—that is, the screen is reduced to the distance that you dragged.

Finally, if you clicked a zoom button but didn’t actually want to zoom, you can click the last zoom button, showing a magnifying glass with a cross through it, to cancel the operation.

4.6

Updating a panel

Awaves contains and extremely useful feature for quick simulation results: updating a panel. When you update a panel, it will re-read the simulation results and re-plot all of waves you had selected with the new data. This means you can keep Awaves open as long as you’re performing the simulations and update the panel you’re working on after each simulation to view your latest results. Students that haven’t discovered this feature often close and re-open netlists repeatedly to achieve the same effect. To update a panel, select the panel you want to update and click Panels → Update (or hit ctrl +u on your keyboard).

5

Syntax Reference

Any bracketed labels must be replaced entirely (i.e. if you want a value of 5 V, you should replace <value> with 5V).

• Independent voltage source v<name> <+ terminal> <- terminal> <value> • Independent current source i<name> <+ terminal> <- terminal> <value> • Voltage-controlled voltage source E<name> <+ terminal> <- terminal> <+ control> <- control> <gain> • Current-controlled voltage source (vcontrol refers to the voltage source which the controlling current flows through) H<name> <+ terminal> <- terminal> <vcontrol> <gain> • Voltage-controlled current source G<name> <+ terminal> <- terminal> <+ control> <- control> <gain> • Current-controlled current source (vcontrol refers to the voltage source which the controlling current flows through) F<name> <+ terminal> <- terminal> <vcontrol> <gain> • Sinusoidal source (used as a <value>) sin(<offset> <amplitude> <frequency> <delay> <damping> <phase>) • Square wave source (used as a <value>) pulse(<vmin> <vmax> <delay> <rise time> <fall time> <pulse width> <period>) • Piece-wise linear source (used as a <value>) pwl(<t0> <v0> <t1> <v1> <t2> <v2> ...)

• Resistor r<name> <terminal 1> <terminal 2> <value> • Capacitor c<name> <terminal 1> <terminal 2> <value>

5

SYNTAX REFERENCE

13

• Inductor l<name> <terminal 1> <terminal 2> <value> • Model (type can be nmos, pmos, NPN, PNP, or D for diode) .model <name> <type> (<parameter list>) • MOSFET (you can specify additional parameters, such as W=<value> L=<value>, in the parameter list) m<name> <drain> <gate> <source> <body> <model> <parameter list> • BJT q<name> <collector> <base> <emitter> <model> <parameter list> • Diode d<name> <+ terminal> <- terminal> <model> <parameter list> • AC analysis (pick either lin, dec, or oct) .ac <lin|dec|oct|> <number of samples> <freq start> <freq stop> • DC analysis .dc <source> <start> <stop> <step> • Nested DC analysis (source1 is swept, source2 is stepped) .dc <source1> <start1> <stop1> <step1> <source2> <start2> <stop2> <step2> • Operating Point .op • Transient analysis .tran <t step> <t stop> • TF analysis .tf v(<node>) <source> • PZ analysis .pz v(<node>) <source>

Experiment 1: Introduction to SPICE 1

Objective

SPICE stands for Simulation Program with Integrated Circuit Emphasis. It is the predominant tool used to simulate circuits and was developed at The University of California, Berkeley in the 1970s. This lab will teach you how to use a popular commercial package called HSPICE, which is one of many implementations based on the original Berkeley SPICE. In addition to learning how to specify and analyze circuits with HSPICE, you will also learn how to plot the results of your analysis with a tool called Avanwaves, or Awaves for short.

SPICE will be a very handy tool in verifying hand calculations. For future labs, it is highly recommended that you simulate your circuits in SPICE and verify your understanding of the circuit before actually building them on the breadboard.

2

Materials

For this lab, all you need is a computer with HSPICE installed. You can use either the Windows or UNIX version, but you will have to read the appropriate documentation for whichever version you choose. Please refer to the HSPICE Tutorial, if you have not already. Note: Be sure to answer the questions on the report as you proceed through this lab. The report questions are labeled according to the sections in the experiment (e.g. question 3.1.4 corresponds to section 3.1 step 4).

3

Procedure

3.1

Transient Analysis

1. Write a netlist for the RC low-pass filter shown in Figure 1. Let vs be a 1 kHz square wave oscillating between 0 and 5 V. You can model this square wave using the PULSE source type. + vs

1 kΩ

+

0.1 µF

vo

−

−

Figure 1: Low-pass filter 2. Now run a transient analysis on this circuit from t = 0 ms to t = 10 ms. For reference on how to proceed, please read section “3.2.1: Transient Analysis of Simple RC Circuit” from the HSPICE Tutorial.

3. Use Awaves to generate plots of vs and vo as functions of time and then, print copies of these plots.

Additional reference about generating these plots can be found in section “4.3: Printing Plot” from the HSPICE Tutorial.

4. In Awaves, use the cursor to estimate how long it takes for the capacitor to charge from 0 to 3.16 V. Is this value close to what you would expect? Note: The cursor can be activated by pressing Measure

→ Point. Hint: Notice that 3.16 is approximately 5 1 − e−1 ≈ 5 · 0.63.

5. Now use the .measure statement in HSPICE to measure how long it takes for the capacitor to charge from 0 to 3.16 V. How does this result compare to that obtained in Awaves? Note: When using TRIG/TARG, you must use a non-zero value for TRIG. If you want to measure from approximately zero seconds, simply use a very small, but non-zero, TRIG value. Additional explanation on the .measure statement can be found at “3.2.7: The .measure Command” from the HSPICE Tutorial.

1

3

2

PROCEDURE

6. As a side note, adjust the step time used in your transient analysis (try making it larger and smaller).

Does this variation change the result of your .measure statement?

3.2

DC Analysis

1. Figure 2(a) shows a transistor called an n-MOSFET, short for n-channel metal-oxide-semiconductor f ield effect transistor. The “n” in n-channel means the electrical carriers mainly consist of negative electrons (in contrast to p-channel, which mainly consists of positive holes). In addition, we often call n-MOSFET as NMOS or NFETs for short. Although you have not learned how these devices work, you can still simulate them in SPICE. The terminals of the device are labeled for you: Drain, Gate, Source, and Body. In Figure 2(a), the body terminal is shown connected to the source; this is a configuration often used. Figure 2(b) also shows an NMOS in the same configuration, but its body is implicitly tied to the source.

ID

ID

D G VGS

+ −

D B

S

G + V − DS VGS

+ −

(a)

S

+ V − DS

(b)

Figure 2: (a) NMOS transistor with body terminal explicity shown (b) NMOS transistor with body implicity tied to the source 2. Write a netlist for the circuit shown in Figure 2 using the following setup: • Step VGS from 0 V to 5 V in increments of 1 V • Sweep VDS from 0 V to 5 V in increments of 0.1 V; Hint: Use the “nested DC analysis” command as described in the appendix • The model for the NMOS should have the following parameters: kp=60e-6 vt0=1 lambda=0.05 • The dimensions of the transistor are W/L = 4.5 µm/1.5 µm 3. Use Awaves to plot ID versus VDS for all the values of VGS you stepped in your DC analysis. Note: You may have to use the “Expression Builder” to invert ID in Awaves—ID should be positive and increasing with VDS in your plot. Please put all the curves onto one graph. Notice that these plots are the I-V curves for a typical NMOS transistor.

3.3

Transfer Function (TF) Analysis

1. Figure 3 shows the small-signal model for an NPN BJT (bipolar junction transistor). We often model these transistors as a collection of simpler, linear components when analyzing them. Notice that we have labeled the terminals of this model transistor: collector, base, and emitter.

2. Write a netlist for the circuit shown in Figure 3 using the following setup: • RB = 1 kΩ, rπ = 2.6 kΩ, RC = 10 kΩ, RE = 5 kΩ, ro = 24 kΩ, and gm = 38 mS; hint: notice that gm is a voltage-controlled current source • Use a .tf statement to find the voltage gain, Av = vo /vs

4

3

APPENDIX B +

RB rπ + vs

C gm vπ

vπ −

E

ro

+ RC

− RE

vo −

Figure 3: The small-signal model of an NPN BJT with resistors attached to the terminals

4

Appendix

4.1

Syntax Reference

The following is a copy of the syntax reference list found in the HSPICE tutorial. Any bracketed labels must be replaced entirely (i.e. if you want a value of 5 V, you should replace <value> with 5V).

• Independent voltage source v<name> <+ terminal> <- terminal> <value> • Independent current source i<name> <+ terminal> <- terminal> <value> • Voltage-controlled voltage source E<name> <+ terminal> <- terminal> <+ control> <- control> <gain> • Current-controlled voltage source (vcontrol refers to the voltage source which the controlling current flows through) H<name> <+ terminal> <- terminal> <vcontrol> <gain> • Voltage-controlled current source G<name> <+ terminal> <- terminal> <+ control> <- control> <gain> • Current-controlled current source (vcontrol refers to the voltage source which the controlling current flows through) F<name> <+ terminal> <- terminal> <vcontrol> <gain> • Sinusoidal source (used as a <value>) sin(<offset> <amplitude> <frequency> <delay> <damping> <phase>) • Square wave source (used as a <value>) pulse(<vmin> <vmax> <delay> <rise time> <fall time> <pulse width> <period>) • Piece-wise linear source (used as a <value>) pwl(<t0> <v0> <t1> <v1> <t2> <v2> ...)

• Resistor r<name> <terminal 1> <terminal 2> <value> • Capacitor c<name> <terminal 1> <terminal 2> <value> • Inductor l<name> <terminal 1> <terminal 2> <value>

4

APPENDIX

4

• Model (type can be nmos, pmos, NPN, PNP, or D for diode) .model <name> <type> (<parameter list>) • MOSFET (you can specify additional parameters, such as W=<value> L=<value>, in the parameter list) m<name> <drain> <gate> <source> <body> <model> <parameter list> • BJT q<name> <collector> <base> <emitter> <model> <parameter list> • Diode d<name> <+ terminal> <- terminal> <model> <parameter list> • AC analysis (pick either lin, dec, or oct) .ac <lin|dec|oct|> <number of samples> <freq start> <freq stop> • DC analysis .dc <source> <start> <stop> <step> • Nested DC analysis (source1 is swept, source2 is stepped) .dc <source1> <start1> <stop1> <step1> <source2> <start2> <stop2> <step2> • Operating Point .op • Transient analysis .tran <t step> <t stop> • Transfer Function (TF) analysis .tf v(<node>) <source> • Poles and Zeros (PZ) analysis .pz v(<node>) <source>

4.2

Using a GUI

In the HSPICE tutorial and in this lab, we mainly addressed the syntax of netlists. Now that you are familiar with netlists, the transition to a graphical editor should be quite straightforward. Although we aren’t going to provide tutorials for these programs, we will point you to other documentation that should help you get started.

One of the available SPICE GUIs is called Multisim. A tutorial, written by B. Muthuswamy, is available here to help you with the software. Another popular SPICE GUI is XCircuit. It allows you to draw a circuit and then export the drawing to a netlist. However, XCircuit will not handle analysis statements; thus, you will still have to edit the netlist by hand after exporting it.

Prelab 1: Introduction to SPICE Name: Lab Section: 1. Before you begin, you will need some instructions on how to run and use HSPICE. We have a tutorial that contains instructions for both the Windows and UNIX versions of HSPICE. The tutorial also includes a number of examples to help you get started.

• HSPICE Tutorial 2. Figure 1 shows a network of resistors and a capacitor. Derive the transfer functions, vx /vs and vy /vs (as functions of jω). There is additional space on the next page for you to show your work. Hint: The voltage divider equation will help in this analysis. +

1Ω

0.999 kΩ

vs

1 kΩ −

+ 1 µF

+

vx −

vy −

1 kΩ

Figure 1: Circuit to simulate for the prelab

1

2

vx = vs vy = vs 3. Using the transfer functions you just derived, create Bode plots (magnitude and phase) for vx /vs and vy /vs . Please put the magnitude and phase plots on the same graph for each respective transfer function and also, label your plots by indicating which curve is the magnitude and which is the phase.

Note: If you need a review of Bode plots, please read the Bode Plot Tutorial.

45

0

0

|vy /vs | (dB)

−20 10−1

100

101

102 103 ω (rad/s)

104

105

−45 106

60

135

40

90

20

45

0

0

−20

−45

−40

−90

−60 10−1

100

101

102 103 ω (rad/s)

104

105

Arg (vx /vs ) (degrees)

20

−135 106

Arg (vy /vs ) (degrees)

|vx /vs | (dB)

3

4

4. If you were designing the circuit in Figure 1 and wanted to move the pole frequency to 10 kHz, what capacitor value would you use to replace the existing one? On a separate note, if the capacitor value was now 100 nF, what is the new pole frequency? Note: If you need a review of poles and zeros, please read the Bode Plot Tutorial.

5. Now, you are going to verify your hand drawn graphs. Begin by writing an HSPICE netlist for the circuit in Figure 1. Hint: Section 3.2.4: AC Analysis of a High-Pass Filter from the HSPICE Tutorial covers the basics of writing a netlist for this AC analysis.

6. Conduct the AC analysis from .1 Hz to 1 MHz in HSPICE. Attach your netlist to this worksheet.

7. Now use Awaves to generate Bode plots (magnitude and phase) for vx /vs and vy /vs . Note: The default x-axis in Awaves has units Hz, not rad/s. Also, drag and drop expressions into the Awaves expression builder by using the middle button of a 3-button mouse or simply right-click and left-click simulataneously. Hint: As reference, Sections 4.1 to 4.6 of the HSPICE Tutorial covers the basic features of Awaves while the latter half of section 3.2.4 offers a useful example.

8. Do the HSPICE results agree with your hand calculations?

9. Turn in your hand calculations, netlist, and Bode plots (hand-made and simulated) at the beginning of your lab for checkoff. Please print your plots with a white background. You can set a white background in Awaves by clicking Window → Flip Color.

Report 1: Introduction to SPICE Name: Lab Section: Attach your netlists and plots in the order you created them for the lab. For section 3.1 in the experiment, only include the netlist for one transient analysis step time. Also remember to print your plots with a white background.

3.1.4 According to the graph, how long does it take for the capacitor to charge from 0 to 3.16 V? How does this value compare to the expected RC time constant?

3.1.5 What is the time measured with the .measure statement? How does this result compare to that obtained in Awaves (the one from the graph)?

3.1.6 What effect does changing the step time have on the result of the .measure statement?

3.3.2 What is the voltage gain of the circuit shown in Figure 3 of the lab experiment?

1

Experiment 2: Electronic Test Equipment 1

Objective

This lab experiment will help you become familiar with the equipments you will be using. Learning to use the equipments now will spare you some headaches later.

2

Materials

You will also need the components listed in Table 1. Note: Be sure to answer the questions on the report as you proceed through this lab. The report questions are labeled according to the sections in the experiment.

Component 20 kΩ resistor 10 kΩ resistor 100 Ω resistor 0.01 µF capacitor 1N4148 diode

Quantity 1 1 1 1 1

Table 1: Components used in this lab

3

Procedure

You can generally trust measurement equipments (like the digital multimeter and oscilloscope) to be more accurate than the output readings on generators (like the DC power supply and function generator). Several of these lab exercises involve measuring the output error on the generators using the digital multimeter (DMM) or oscilloscope. You will also try some basic circuit measurements.

When performing measurements or using multiple sources, be sure ground terminals are connected appropriately. Usually, you will create one ground node in your circuit and connect all device grounds to that node.

3.1

DC Measurements (DMM and DC Power Supply)

1. For the +6 V output terminal, set the DC power supply to read +5 V on the display. Then, measure the output with the digital multimeter (DMM). What is the percent error between the +5 V setting and the actual output value? Now, record the errors for the following settings: +1 V, +5 V, and +9 V. For the first two settings, +1 V and +5 V, use the +6 V output terminal. Use the +25 V output terminal for the +9 V setting.

2. On your breadboard, build the circuit shown in Figure 1. Use the ideal values given in the diagram to calculate the expected value of VO and compare this value with the voltage measured at VO . What is the percent error? Other than measurement error and error in the voltage source, what might contribute to the deviation from the ideal calculation? Hint: Measure the resistor values using the DMM. 3. You are not supposed to connect the DMM to the terminals of a voltage source while DMM is in current mode. Why not?

4. Measure the current through the 20 kΩ resistor and compare this value to your hand calculated one.

1

3

2

PROCEDURE

10 kΩ 2V + −

20 kΩ

+ VO −

Figure 1: Resistor circuit to build

3.2

AC Measurements (Oscilloscope and Function Generator)

The function generator panel often displays a different voltage amplitude than what is measured at its output because the panel setting assumes a certain load impedance (please see the function generator tutorial for details).

Note that in the labs, we will always use the word “amplitude” to refer to the maximum displacement from the offset (i.e. the traditional definition of amplitude) and “peak-to-peak” to refer to the peak-to-peak amplitude of a signal (i.e. double the amplitude).

1. Set the function generator to output a 1 kHz, 1 Vpp square wave according to the panel display.

Measure the wave on the oscilloscope by directly connecting the function generator to an oscilloscope probe. Record the measured values for the wave’s frequency and Vpp . Then, calculate the error in the function generator panel for both frequency and voltage. Remember to take into account the source and load resistances (assume that the input resistance of the oscilloscope is much greater than the output resistance of the function generator). When calculating the error, please refer to section 3: Voltage Divider Discussion from the function generator tutorial for a review of the voltage divider.

2. What is the highest frequency sinusoid that the generator can produce with a 1 Vpp setting? What is the error between the measured frequency and the displayed frequency setting?

3. What is the smallest Vpp sinusoid that the generator can produce at 1 kHz? What is the error between the measured Vpp and the panel setting? Like in one of the previous questions, remember to take into account the source and load resistances. Now, have the oscilloscope average over 64 measurements to compensate for system noise and to allow for better measurement accuracy. For assistance on using the averaging feature of the oscilloscope, please refer to section 5.4: Using Averaging from the oscilloscope tutorial . Without averaging, does the oscilloscope over-measure or under-measure the Vpp value?

4. Set the generator to deliver a pulse with height 500 mV and a repetition frequency of 1 kHz. Compare the period and frequency settings to the values measured on the oscilloscope. What is the shortest pulse width that the function generator can produce at 500 mV height and 1 kHz frequency?

5. Construct the RC circuit shown in Figure 2. + vs −

10 kΩ

+

0.01 µF

vo −

Figure 2: RC circuit to build 6. Set up vs as a sine wave with a frequency of 1 kHz and a delivered Vpp of 1 V. Measure the input signal with the oscilloscope to verify the amplitude setting. Hint: To achieve a delivered 1 Vpp amplitude, the panel setting should be 500 mV because the input impedance of the oscilloscope is much greater than the output impedance of the function generator. For further discussion on this discrepancy, please read section 3 from the function generator tutorial.

3

3

PROCEDURE

7. Measure the amplitudes of the input and output waves. Calculate the value of | vvos | based on your oscilloscope measurements. This value is the magnitude of the transfer function evaluated at 1 kHz.

3.3

Parameter Analyzer Basics

1. Using the Agilent4155C/HP4145B, plot the I-V characteristic of a 100 Ω resistor. What is the measured resistance according to your plot? Save and print the plot because you will need to turn it in with your lab report. For assistance with the parameter analyzer, please refer to the parameter analyzer tutorial.

2. Now plot the I-V characteristic of a diode (over an interval where it turns on). Again, save and print the plot because you will need to turn it in with your lab report.

3. Using your empirical plots and load-line analysis, determine the value of VO for the circuit shown in Figure 3. Verify your calculated operating point by building the circuit and measuring the appropriate voltage with the DMM. Note: If you have difficulty discerning the orientation of the real diode component, please refer to Figure 4, which illustrates the mapping between a real diode and its circuit symbol counterpart.

• You can generate the load-line plot in Excel. To perform a mathematical operation, first enter the desired expression at the top of a new column preceeded by an equals sign. Then click on the lower-right corner of the new cell and drag downwards to fill in the new column. For example, if your data is in the column starting with cell B1, you can add a constant (e.g. 2) to all your data entries by first entering = B1 + 2 in cell C1. Then click the lower-right corner of C1 and drag downwards until column C is filled appropriately.

100 Ω 1V + −

+ VO −

Figure 3: Diode circuit to build

Figure 4: Illustration of a diode component and its circuit symbol counterpart. Notice the marking at one end of the diode component indicates the negative terminal.

Prelab 2: Electronic Test Equipment You should become familiar with the lab equipments in advance. To begin, read the tutorials listed below; each describes an instrument that is used in these labs. For further reading, please refer to the device manuals. Note: You do not have to turn in anything for this prelab.

• Agilent E3631A DC Power Supply Tutorial • HP 34401A Digital Multimeter (DMM) Tutorial • Agilent 33220A Function Generator Tutorial • Agilent DSO5014A Oscilloscope Tutorial • Agilent4155C/HP4145B Parameter Analyzer Tutorial

1

Report 2: Electronic Test Equipment Name: Lab Section: 3.1.1 Record the error in the power supply at +1 V, +5 V, and +9 V. Voltage Setting 1V 5V 9V

DMM Measurement

% Error

3.1.2 What is the percent error? Besides measurement error and error in the voltage source, what can also contribute to the total error?

3.1.3 Why are you not supposed to connect the DMM to the terminals of a voltage source while the DMM is in current mode?

3.1.4 Measure the current and compare this value to your hand calculation.

3.2.1 What is the measured frequency and Vpp ? After taking into account the voltage divider factor, what is the error of the function generator output for a 1 kHz, 1 Vpp output signal?

3.2.2 What is the highest frequency sinusoid that the generator can produce with a 1 Vpp setting? What is the error between the measured frequency and the displayed frequency setting?

1

2

3.2.3 What is the smallest Vpp sinusoid that the function generator can produce at 1 kHz? What is the error between the measured and displayed value (take the voltage divider factor into account)? With the averaging feature turned off, does the oscilloscope over-measure or under-measure the Vpp value? (please circle one)

3.2.4 What is the shortest pulse that the function generator can produce at 500 mV height and 1 kHz frequency?

3.2.7 Calculate the value of | vvos | at 1 kHz using your oscilloscope measurements..

3.3.1 Attach the plot of the 100 Ω resistor I-V characteristic.

3.3.2 Attach the plot of the diode I-V characteristic.

3.3.3 What is the VO value calculated from your load-line? Does it match the value measured with the DMM?

Experiment 3: Bipolar Junction Transistor Characterization 1

Objective

The BJT was invented in 1948 by William Shockley at Bell Labs, and became the first mass-produced transistor. Having a good grasp of the physics of the BJT is key to understanding its operation and applications.

In this lab, we will explore the BJT’s four regions of operation and also determine its characteristic values, such as DC current gain β and Early voltage VA . The transistor used in this lab is the 2N4401, an NPN device. It is strongly recommended that you read and understand the section on BJT physics before beginning this experiment.

2

Materials

You will need the components listed in Table 1. Note: Be sure to answer the questions on the report as you proceed through this lab. The report questions are labeled according to the sections in the experiment. CAUTION: FOR THIS EXPERIMENT, THE TRANSISTORS CAN BECOME EXTREMELY HOT!!!

Component 1 MΩ resistor 5 kΩ resistor 100 Ω resistor 2N4401 NPN BJT

Quantity 1 1 4 2

Table 1: Components used in this lab

3

Procedure

3.1

Determining the Region of Operation

1. Set up the circuit shown in Figure 1, with RB = 1 MΩ, RC = 5 kΩ, RE = 100 Ω, and VCC = 5 V. If you need help identifying the terminals of the discrete BJT, please refer to Figure 2

RC

IC

IB RB VBB + −

VCC + − RE

IE

Figure 1: BJT measurement setup for this lab.

1

3

PROCEDURE

2

Figure 2: For your reference, this is an illustration of the mapping between the terminals of a discrete NPN BJT and those of its circuit symbol counterpart.

2. Now gradually ramp up the value of VBB until IC = 0.5 mA. Measure VBE and VBC . The transistor is in which region of operation?

Warning: Never set VBE higher than 5 V for any of the transistors used in the labs. Doing so will permanently damage the transistor and may cause personal injury.

3. Now measure IB . What is the value of β?

4. From the value found above, calculate α and use it to calculate IE . Afterwards, measure IE and check if the calculated and measured values agree.

5. Now take a look at the 2N4401 datasheet. Does your calculated β value agree with the value given in the datasheet? Hint: β is called hF E in the datasheet, and there is a plot of hF E versus IC under “Typical Characteristics”. If the values do not agree, explain why there is a discrepancy.

6. On another note, let us examine the temperature dependence of the collector and base currents: Put two fingers around Q1 to heat it up, and then, measure IB and IC (have your partner heat the BJT while you measure the currents if you are having trouble doing both at the same time). How do the values of IC and IB compare to the values you measured before you heated the transistor (i.e. do IC and IB increase or decrease)?

7. Explain, using the equation for the collector current, how you would expect IC to vary with temperature. Does this agree with your experimental results? If not, explain why this might be the case.

(Hint: IS depends on the intrinsic carrier concentration ni and the diffusion coefficients Dn and Dp .

Intuitively, how would ni , Dn , and Dp change with temperature? How would IS change with temperature as a result? Note: You do not need to explicitly answer the questions in the hint but do think about them.)

8. Let us now explore the different operation regions of a BJT. Set VBB to 4 V and VCC to 2 V. Measure IB , IC , VBE , and VBC . What is the region of operation for the BJT? 9. Set VBB to −3 V and VCC to 5 V. Measure IB , IC , VBE , and VBC . What is the region of operation for the BJT? 10. Now swap the emitter and the collector connections of the BJT in the circuit (you can do this by physically rearranging the BJT to face the opposite direction). Set VBB to 4 V and keep VCC at 5 V. Measure IB , IC , VBE , and VBC . What is the region of operation?

3.2

Determining the Early Voltage Using the Parameter Analyzer

Increasing the collector-base bias widens the depletion region at the collector-base interface. As a result, recombination decreases because the base is more depleted of available mobile holes, which are the main recombination source for electrons injected from the emitter. The widened depletion region also provides a greater electric field to sweep the injected electrons to the collector. Both of these effects result in an additional dependence of IC on VCE . The Early voltage is used to model this dependence.

3

3

PROCEDURE

1. Connect a BJT to the parameter analyzer’s test fixture (without any resistors). Use ICS, the software accompanying the parameter analyzer, to bias the emitter at 0 V and the base at 0.6 V. Sweep the collector from 0 V to 5 V using 101 datapoints. Measure the current through the collector terminal.

2. Next, plot IC versus VC , the collector voltage. What two regions of operation are shown, and where is the boundary?

3. Use this plot to determine the Early voltage, VA . Hint: The parameter analyzer tutorial has instructions on the trend line tool found in Excel and thus, can help you calculate the Early voltage.

4. Repeat your calculation of VA for base voltages of 0.625 V, 0.65 V, 0.675 V, and 0.7 V (you can step the base voltage in ICS to get this data). Does VA depend on the base voltage VB ? Why?

3.3

The BJT as a Diode

1. Connect a diode-connected BJT (i.e. the base and collector are shorted together) to the parameter analyzer’s test fixture. Use ICS to ground the emitter and sweep the base/collector from 0 V to 0.7 V. Measure the current through the base/collector. (Teh base/collector acts as the P side of a diode).

2. Run the measurement and plot the base/collector current, IC versus VBE . Which other semiconductor device has this kind of I-V curve?

3.4

The Darlington Pair (Super High β) VCC = 3 V 100 Ω

100 Ω VBB + − 1.2 V

100 Ω

Q1 100 Ω

Q2

Figure 3: Darlington configuration for measurement 1. Construct the Darlington pair as shown in Figure 3.

2. Measure IB1 , IC1 , IB2 , and IC2 . Calculate β1 = IC1 /IB1 and β2 = IC2 /IB2 .

3. What is the overall current gain, βtot = IC2 /IB1 , based on your measured values of IC2 and IB1 ?

Now, use the formula you derived in the prelab to calculate the overall current gain from β1 and β2 .

Compare this calculated βtot value to your measured βtot value.

Prelab 3: Bipolar Junction Transistor Characterization Name: Lab Section: 1. For the NPN device shown in Figure 1, label IC , IB , and IE next to their respective current arrows.

Figure 1: A simple NPN device 2. What is β in terms of IC and IB ? What is α in terms of IC and IE ? Express α in terms of β. β (IC , IB ) = α (IC , IE ) = α (β) =

3. Given that you are a circuit designer working with an NPN device and you want the device to have a gm of 1 mS, what VBE value would you need to properly bias the NPN? Assume IS is 5 × 10−16 A.

4. SPICE • Write a SPICE netlist for the BJT test circuit shown in Figure 2. Refer to the HSPICE Tutorial if you have trouble with SPICE. • Use the 2N4401 SPICE model provided on the course website.

• Using the .dc command, sweep VCC from 0 V to 5 V in 0.01 V increments and step VBB from 0.6 V to 0.7 V in 0.025 V increments.

• Run the simulation and check the output file for any errors.

• If there are no errors, plot ICC versus VCC and print out a copy of the plot. Note: If your ICC is negative, use Awaves to plot the absolute value of ICC . ICC appears to be negative because SPICE defines ICC to be going out of the BJT. 1

2 ICC

VBB + −

VCC + −

Figure 2: Circuit to simulate in SPICE IB1 Q1

IC2 Q2

Figure 3: Darlington configuration 5. The configuration shown below in Figure 3 is known as the Darlington pair. Assume Q1 has a DC current gain of β1 and Q2 has a DC current gain of β2 . Derive the overall current gain, βtot = IC2 /IB1 , as a function of β1 and β2 . Do not neglect any currents.

βtot =

Report 3: Bipolar Junction Transistor Characterization Name: Lab Section: For this lab, please record the values of current and voltage in the designated boxes.

3.1 Use this table to record and summarize relevant results as you proceed through the lab experiment: for each region of operation, fill in the appropriate entries in Table 1 and compute the resulting β and α values.

Parameters VBE VBC IB IC β α

Forward Active

Saturation

Cutoff

N/A N/A

N/A N/A

Reverse Active

Table 1: Regions of operations and measurements

3.1.2 Measure VBE and VBC . What is the region of operation?

VBE = VBC =

3.1.3 Measure IB and compute β.

IB = β=

3.1.4 Calculate α and use the result to calculate IE . What is the measured value of IE . Do the two values for IE agree?

1

2

α= (Calculated) IE = (Measured) IE =

3.1.5 Does your calculated β value agree with the value listed in the datasheet? If not, explain why there is a discrepancy.

3.1.6 Heat up the BJT with you fingers and record the respective values of IC and IB . How do the values of IC and IB change as you heat up the BJT?

IB = IC =

3.1.7 Explain, using the equation for the collector current, how you would expect IC to vary with temperature. Does this agree with your experimental results? If not, explain why this might be the case.

(Hint: IS depends on the intrinsic carrier concentration ni and the diffusion coefficients Dn and Dp .

Intuitively, how would ni , Dn , and Dp change with temperature? Also, how would IS change with temperature as a result? Note: You do not need to explicitly answer the questions in the hint but do think about them.)

3.1.8 Set VBB to 4 V and VCC to 2 V. Measure IB , IC , VBE , and VBC . What is the region of operation?

3

IB = IC = VBE = VBC =

3.1.9 Set VBB to −3 V and VCC to 5 V. Measure IB , IC , VBE , and VBC . What is the region of operation?

IB = IC = VBE = VBC =

3.1.10 Swap the emitter and collector connections of the BJT. Set VBB to 4 V and keep VCC at 5 V. Measure IB , IC , VBE , and VBC . What is the region of operation?

IB = IC = VBE = VBC =

Remember to fill out Table 1 using all the data you have collected thus far.

3.2.2 Attach the plot of the I-V curve to this worksheet. Label the two regions of operation and draw the boundary between them.

3.2.3 Use the I-V curve to determine VA .

VA = 3.2.4 Repeat your calculation of VA for base voltages of 0.625 V, 0.65 V, 0.675 V, and 0.7 V (you can step the base voltage in ICS to get this data). Does VA depend on VB ? Why?

4 VB 0.600 V 0.625 V 0.650 V 0.675 V 0.700 V

VA

Table 2: Early voltage calculations

3.3.2 Attach the plot of the I-V curve to this worksheet. Which other semiconductor device has this kind of I-V curve?

3.4.2 Measure IB1 , IC1 , IB2 , and IC2 . Calculate β1 and β2 .

IB1 = IC1 = IB2 = IC2 = β1 = β2 =

3.4.3 What is the overall current gain, βtot = IC2 /IB1 , based on your measured values of IC2 and IB1 ?

Now, use the formula you derived in the prelab to calculate the overall current gain from β1 and β2 .

Compare this calculated βtot value to your measured βtot value.

(Measured) βtot = (Calculated) βtot =

Experiment 4: Single Stage BJT Amplifiers: Common Emitter 1

Objective

Design and analysis of analog amplifiers is not usually done at the single transistor level, but instead, it is done by grouping together known configurations of single transistor amplifiers to create a new amplifier with just the right properties for the particular application. Such properties include input impedance, gain, and output impedance. However, before presenting to you the analysis and implementation of these robust multi-transistor amplifiers, we will present to you the fundamentals of a single transistor amplifier.

The objective of this lab is to teach you about the single stage BJT common emitter (CE) amplifier and all its wonderful properties. The next lab will cover the properties of the common collector (a.k.a. emitter follower) and common base amplifiers. By the end of this lab and the next, you will begin to see why these different configurations are useful and how they can be connected together to fulfill certain design specifications.

2

Materials

The items listed in table 1 will be needed. Note: Be sure to answer the questions on the report as you proceed through this lab. The report questions are labeled according to the sections in the experiment. Also, note that there is an accompanying post-lab appended to the end of the lab report. CAUTION: FOR THIS EXPERIMENT, THE TRANSISTORS CAN BECOME EXTREMELY HOT!!!

Component 2N4401 NPN BJT 8 Ω speaker 1 kΩ resistor 10 kΩ resistor 10 µF capacitor 10 kΩ potentiometer

Quantity 1 1 1 1 1 1

Table 1: Components used in this lab

3

Procedure

Note: All voltages mentioned in the following instructions are the effective voltages delivered, not the one shown on the function generator’s display. This discrepany is further explained in section 3: Voltage Divider Discussion from the function generator tutorial.

3.1

Biasing for Maximum Gain

We beginning by finding the proper biasing point for the common emitter (CE) amplifier shown in Figure 1.

Given the properties of the CE amplifier are greatly affected by the DC bias point, we are using a voltage source and a pull up resistor to bias the collector while using the DC offset from the function generator to bias the base. Note that this setup is quite different from multi-transistor amplifiers, which generally feature transistors being biased by other transistors to achieve the largest small signal gain.

1. To start off, build the circuit shown in Figure 1, a simple common emitter amplifier with no load attached. Let RC = 1 kΩ and VCC = 5 V. Also, please set up the parameter analyzer at this point 1

3

2

PROCEDURE

because you will be using it to analyze the circuit. Note: If you need a review of how to use the parameter analyzer, please refer to the parameter analyzer tutorial.

VCC RC

IIN + vin

+ vout −

− VIN + −

Figure 1: CE amplifier using an NPN BJT: the input is applied to the base and the output is taken from the collector 2. Using ICS, perform a sweep of VIN from 0 to 1 V with 101 datapoints spanning the interval. Then, graph VOUT vs. VIN . Now, using this plot, find the DC bias that achieves the maximum small signal gain. What is this gain? What are the corresponding values of VIN and VOUT ?

3. Using load line analysis for the pull up resistor (i.e. finding the intersection point of the load line and the BJT I-V curve), explain why the BJT will yield very low gain if it is not biased into forward active mode.

3.2

Amplifier Properties (a.k.a. Two-Port Parameters)

The operational characteristics of an amplifier can be quantified by three properties: input impedance, gain, and output impedance. These three properties are called the two-port parameters of an amplifier. The goal is now to measure and learn about these properties for the CE amplifier so that we may use this general knowledge later on in our design of multistage amplifiers.

1. Measuring Input Resistance: Sweep VIN from 0 to 1 V using 101 datapoints, and plot IIN vs. VIN using ICS. What is the input resistance of the amplifier when VIN is set to achieve maximum gain?

Hint: The inverse slope of the IIN vs. VIN curve (at a particular VIN value) corresponds to the input resistance of the amplifier (when the amplifier is biased to that value of VIN ).

2. Measuring Gain: Connect the function generator to the input and apply a 20 mVpp amplitude sine wave with a DC offset corresponding to the DC bias point that yields the maximum gain. Now measure the peak-to-peak amplitude of the output signal using the oscilloscope. What is the gain according to this measurement? Is this gain roughly the same as the gain you had previously measured (using ICS)?

3. Measuring Output Voltage Swing: Increase the amplitude of the input signal until the output waveform is clipped (flattened) on the top and bottom. Why does clipping happen at the top? Why does it happen at the bottom? Approximately how large can the output waveform be without clipping? This maximum peak-to-peak amplitude is called the output voltage swing. Note: Given you have set the proper VIN value, you can also read off the output voltage swing from your VOUT vs. VIN curve; it is just the range of VOUT values for which the curve is linear.

4. Now, attach a 10 µF AC coupling capacitor and a 10 kΩ potentiometer at the output as shown in Figure 2. (If you have never used a potentiometer before, please refer to Figure 3.) In this example,

3

3

PROCEDURE VCC RC

C + vin

+

RL

vout −

− VIN + −

Figure 2: CE amplifier with load attached the potentiometer is used to simulate a load for the amplifier to drive. Why is the capacitor necessary?

Hint: Consider the DC bias.

5. Measuring Output Resistance: Decrease the amplitude of the input signal until it is back to 20 mVpp .

Adjust the resistance of the potentiometer so that the amplitude of the signal across the potentiometer is exactly half of the output amplitude when no load is attached. The resistance of the potentiometer at this point will be equal to the output resistance of the amplifier. What is the value of the output resistance? Why does this method work in measuring the output resistance? (Hint: Model the output resistance as being in series with the potentiometer and then apply the voltage divider formula.)

Figure 3: A typical 10 kΩ potentiometer: the variable resistance can only be measured between two adjacent pins; the resistance measured between the leftmost and rightmost pins is constant.

3.3

The World’s Worst Speaker Amplifier

This part will demonstrate the capabilities of your CE amplifier on a physically observable load.

1. Using the function generator, apply a 1 kHz, 20 mVpp sine wave (with no DC offset) directly to the two terminals of the speaker. Qualitatively observe the sound from the speaker.

2. Now build the circuit shown in Figure 2 (if you do not already have it available from the end of section 3.2). Let RC = 1 kΩ and C = 10 µF. 3. Using the function generator again, bias VIN for maximum amplifier gain (you should have the bias voltage value from a previous section) and also apply a 1 kHz, 20 mVpp sine wave for vin . Attach the speaker to the output and qualitatively observe the sound. Do you hear anything? If so, is it louder, softer, or just as loud as when the speaker was directly connected to the function generator? Explain this result. Hint: Consider the output impedance of the amplifier.

3

4

PROCEDURE

3.4

Emitter Degeneration

Emitter degeneration refers to the placement of a resistor on the emitter terminal of a common emitter amplifier. We will now analyze the effects of this resistor: 1. Build the circuit in Figure 4; let VCC = 5 V, RC = 10 kΩ, and RE = 1 kΩ.

VCC

RC

+ +

vout

vin − VIN + −

− RE

Figure 4: CE amplifier with emitter degeneration 2. With the help of ICS, find the bias point that will allow the circuit to achieve maximum gain. A suitable range to sweep VIN is 0 to 3 V. What is the DC operating point that you found? What is the gain, Av , at this operating point? How does the gain without emitter degeneration compare to the gain with emitter degeneration (i.e. is it smaller or larger)? Give a qualitative explanation for your observation.

3. Measure the input and output impedances of the circuit using the technique described in section 3.2.

How are these impedance values affected by emitter degeneration? Explain.

4. Using the appropriate equations, calculate the theoretical values of the input and output impedances as well as the gain. Use β = 270, which is about what you should have measured in Experiment 3.

5. How might emitter degeneration be useful?

Prelab 4: Single Stage BJT Amplifiers: Common Emitter Name: Lab Section: VCC RC

+ +

vout

vin

−

− VIN + −

Figure 1: Common emitter amplifier

1. Let us analyze the common emitter amplifier illustrated in Figure 1. Let VCC = 5 V, VT = 26 mV, IS = 26.03 fA, VA = 90.7 V, RC = 1 kΩ, and β = 270. (a) For the transistor in Figure 1, draw a graph of IC vs. VCE for each of the following values of VBE : 600 mV, 620 mV, 640 mV, 660 mV, 680 mV, and 700 mV. (A grid is provided for your response.)

Please take care in drawing these plots as they will be used to answer some of the questions below.

Assume the boundary between deep saturation and forward active occurs at VCE = 400 mV. You may use a piecewise linear model for this graph. (b) Also on this graph, draw the load line for the resistor, RC . Hint: As a reminder, load line analysis is the application of Ohm’s Law to relate current (I) and voltage (V) via the resistance of a given resistor (R) (i.e. △V R = I, where △V is the voltage across the resistor). (c) Using the intersection points of the graphs from (a) and (b), plot a graph of VOUT vs. VIN on the designated grid. How might the VOUT vs. VIN graph be useful? (For a hint, please see Figure 2.)

(d) What is the gain at VIN = 650 mV? What is the region of operation of the transistor? Hint: The small signal gain, for a given VIN , corresponds to the slope of the VOUT vs. VIN curve at that particular VIN value.

2. Now that we have analyzed some of the large-signal properties of the amplifier, let us also analyze some of its small-signal properties. Assume VIN = 650 mV for the rest of the prelab. (a) Draw the small signal model of the amplifier (space for your response is provided on the next page).

1

2

15 12 IC (mA)

9 6 3 0

0

1

2

3

4

5

VCE (V) 5

VOU T (V)

4

3

2

1

0 600

610

620

630

640

650 660 VIN (mV)

670

680

690

700

3

Figure 2: Illustration of how a small input signal coupled to VIN can yield an amplified output signal coupled at VOUT (b) Calculate the following parameter values (be sure to take the Early effect into account): • VOUT • IC • Transconductance gm • Output impedance Rout • Input impedance Rin • Gain Av . Does this gain match your answer to question 1(d)?

(c) If we change the bias point, which of the above properties will also change?

4

3. Let’s explore what happens when we change the bias point by adding a load resistor. (a) Add a load of 5 kΩ to the output of the circuit. Intuitively, how do you think this will affect the gain? Explain why.

(b) Draw the new load line on the graph you made for question 1(a) (be sure to label which load line goes with which question). (c) If we keep the same bias point (i.e. the same VBE value), is the transistor still in forward active mode?

(d) What happens to the gain when the load resistor is added to the circuit? How about the output voltage swing? Note: The output voltage swing is the maximum and minimum values of vOUT for which all transistors stay in forward active mode.

(e) For what load resistance value does the amplifier’s BJT begin to transition between forward active mode and deep saturation (i.e. where VCE = 400 mV)?

Report 4: Single Stage BJT Amplifiers: Common Emitter Name: Lab Section:

1

Lab Questions

3.1.2 DC values and gain when the circuit is biased for maximum small signal gain: VIN = VOUT = Av = 3.1.3 Using load line analysis for the pull up resistor (i.e. finding the intersection point of the load line and BJT I-V curve), explain why the BJT will yield very low gain if it is not biased into forward active mode.

3.2.1 What is the input resistance?

Rin = 3.2.2 What is the measured gain? Is this measured value roughly the same as the gain you measured using ICS? Av = 3.2.3 Why does clipping happen at the top of the output waveform? Why does it happen at the bottom?

What is the output voltage swing?

1

1

LAB QUESTIONS

2

Output Voltage Swing = 3.2.4 Why is the capacitor needed when we attach the load?

3.2.5 What is the output resistance of the amplifier?

Rout = Why does the method work in measuring output resistance? (Hint: Model the output resistance as being in series with the potentiometer and then apply the voltage divider formula.)

3.3.3 Compare the respective volumes of the 1 kHz tones produced by the speaker for the following two cases: 20 mVpp , 1 kHz sine wave applied directly to speaker; and the output of the CE amplifier applied to the speaker. Do you hear anything from the latter case? If so, is it louder, softer, or just as loud as the former case? Explain this result. Hint: Consider the output impedance of the amplifier.

3.4.2 DC values and gain when the circuit is biased for maximum small signal gain: VIN = VOUT = Av = How does the gain without emitter degeneration compare to the gain with emitter degeneration (i.e. is it smaller or larger)? Give a qualitative explanation for your observation.

1

LAB QUESTIONS

3

3.4.3 Measured impedances for the amplifier: Rin = Rout = How are these values affected by emitter degeneration (i.e. do they increase, decrease, or stay the same)? Why?

3.4.4 Theoretical amplifier parameters: Rin = Rout = Av =

3.4.5 How might emitter degeneration be useful?

2

4

POST-LAB QUESTIONS

2

Post-Lab Questions

2.1

Amplifier Two-Port Model

Rout +

+

vin

Rin

va

+ + Av va −

vout

−

−

−

Figure 1: Generalized voltage amplifier 1. A CE amplifier can be modeled as the generalized voltage amplifier shown in Figure 1, where Rin , Rout , and Av are the values you found for input resistance, output resistance, and voltage gain, respectively.

This generalization was accomplished by applying the concept of Thévenin equivalent circuit to the CE small signal model. Now suppose that vin is an ideal source that supplies a 1 kHz, 20 mVpp sine wave. What is vout ? Use the values obtained from the lab for Rin , Rout , and Av (i.e. use data from the no emitter degeneration, 1 kΩ biasing resistor case).

1 kΩ

Rout +

vin

Rin

va −

+ Av va −

+ 1 kΩ

vout −

Figure 2: Voltage amplifier with non-ideal source and load attached 2. Now suppose a non-ideal voltage source with an internal source resistance of 1 kΩ is attached at vin , and a load resistance of 1 kΩ is attached at the output (Figure 2). If a 20 mV peak-to-peak amplitude sine wave is applied at the input, what should be the signal across the load?

2

POST-LAB QUESTIONS

5

3. For a given input, a good voltage amplifier is one that can create the greatest possible voltage swing across the load. Assuming the gain stays constant, what input and output impedances should the ideal voltage amplifier have? Why?

4. A CE amplifier can also be modeled as a transconductance amplifier: the input is voltage; and the output is current that has a magnitude equal to the input voltage times the constant, Gm . Applying the concept of Norton equivalent circuit to the CE small signal model, draw the CE amplifier as a generalized transconductance amplifier. (Hint: It will look similar, but not completely identical to Figure 1.) Find Gm using the data you have collected from the lab (i.e. use data from the no emitter degeneration, 1 kΩ biasing resistor case).

5. A good transconductance amplifier is one that can drive the greatest possible current through the load for a given input voltage. Assuming a fixed gain, what input and output impedances should the ideal transconductance amplifier have? Why?

6. Extending the idea further, we can also talk about current amplifiers. If a good current amplifier is one that can drive the greatest current through the load for a given input current, what input and output impedances should the ideal current amplifier have? Why?

Experiment 5: Single Stage BJT Amplifiers: Common Collector and Common Base 1

Objective

In lab 4, we explored the properties of a common emitter amplifier. However, even though the amplifier has an extremely high gain, its high output impedance prevents it from properly driving the speaker. In this lab, we will investigate the properties of two other single-stage amplifier configurations: the common collector (CC) and the common base (CB). You will be applying the techniques learned from lab 4 to evaluate the input impedance, output impedance, and gain for both of these amplifier configurations. If you need a review of these techniques, please refer to lab 4 now. By the end of this lab, you should be able to model any single stage amplifier using its two-port model as well as identify the strengths and weaknesses of each single-stage amplifier configuration.

2

Materials

The items listed in table 1 will be needed. Note: Be sure to answer the questions on the report as you proceed through this lab. The report questions are labeled according to the sections in the experiment. Also, note that there is an accompanying post-lab appended to the end of the lab report. CAUTION: FOR THIS EXPERIMENT, THE TRANSISTORS CAN BECOME EXTREMELY HOT!!!

Component 2N4401 NPN BJT 8 Ω speaker 100 Ω resistor 510 Ω resistor 1 kΩ resistor 2 kΩ resistor 10 kΩ resistor 51 kΩ resistor 10 µF capacitor 10 kΩ potentiometer screw driver

Quantity 1 1 1 2 1 1 2 1 2 1 1

Table 1: Components used in this lab

3

Procedure

3.1

The Common Base Amplifier

For a common base amplifier using an NPN BJT, the input is applied to the emitter and the output is taken from the collector.

1. Similar to the CE amplifier, the CB amplifier can also be used as a voltage amplifier. Set up the configuration as shown in Figure 1. Let VCC = 12 V, RC = 1 kΩ, and VB = 640 mV. 2. Measuring Gain Using ICS: Perform a sweep of VIN from −0.1 V to 0.1 V and plot VOUT vs. VIN .

Find the voltage gain using the slope at VIN = 0 V (when the input has no DC offset). Note: This technique was used in section 3.1.2 of lab 4. In contrast, section 3.2.2 of lab 4 uses the oscillscope for measuring gain.

1

3

2

PROCEDURE VCC RC

+ vOUT

VB + −

− + vIN −

Figure 1: CB amplifier 3. Measuring Input Resistance: Find the input resistance by sweeping VIN from −0.1 V to 0.1 V and plotting IIN . Hint: Section 3.2.1 from lab 4 demonstrates the same technique.

4. Measuring Output Resistance: Find the output resistance using the technique demonstrated in section 3.2.4-5 from lab 4.

5. Suppose the source resistance of VIN is 50 Ω. Will the CB amplifier perform well in amplifying the signal from vin ? Why?

3.2

The Common Collector Amplifier

For a common collector amplifier using an NPN BJT, the input is applied to the base while the output is taken from the emitter. Before we begin, there is a chance that your transistor will heat up during this experiment; if that is the case, please substitute a 51 kΩ resistor for RS . (See Figure 2.)

1. Build the circuit shown in Figure 2, a common collector amplifier with no load attached. Let R1 = 1 kΩ, R2 = 891 Ω, RS = 10 kΩ, RE = 100 Ω, C = 10 µF, and VCC = 12 V. Hint: To form the 891 Ω resistance, note that 510 Ω//2 kΩ = 406 Ω, 510 Ω//10 kΩ = 485 Ω, and resistances in series sum up to form one equivalent resistance. Before you build the circuit, consider this tip that may save you a lot of time: Build the biasing network at one end of the breadboard and build the CC amplifier at the other end. Then, use a wire to connect or disconnect the two parts. Such a setup will help facilitate your measurements, especially for the one on input resistance.

2. A common collector amplifier is typically biased so that it yields the greatest output voltage swing. For the design in Figure 2, measure the DC bias input voltage, VIN , and the corresponding VOUT value.

3. Now find the voltage gain, input impedance, output impedance, and output voltage swing. Note: For these measurements, you must disconnect the biasing network from the amplifier and use the techniques demonstrated in lab 4. With the exception of the output resistance, all other measurements must be conducted using ICS to minimize error and to save time. Also, remove RS only when finding the input impedance; keep it otherwise. (See Figure 2.)

4. Another name for the CC amplifier is the emitter follower. Based on the gain that you have found, why do you think it is given this name?

3

3

PROCEDURE VCC R1 C

RS

+

ROUT

vin −

VIN

R2

+

RIN

vOUT

RE

−

Figure 2: Common collector amplifier with biasing network

3.3

The World’s Second Worst Speaker Amplifier

This part will demonstrate the capabilities of your CC amplifier. Note: Due to impedance mismatch, the voltage delivered by the function generator does not necessarily match the displayed value.

When in doubt, check with an oscilloscope.

1. Apply a 1 kHz, 2 Vpp sine wave directly to the two terminals of the speaker using the function generator.

Measure the voltage drop across the speaker using the oscilloscope and qualitatively observe the volume of the 1 kHz tone.

2. Reconnect the circuit as shown in Figure 2.

3. Apply a 1 kHz, 2 Vpp sine wave at the input. Attach the speaker (which is modeled as RL in Figure 3) as well as the 10 µF capacitor, C. Measure the output waveform, and observe the volume of the tone.

Is it louder, softer, or about the same as when the signal was directly applied to the speaker? Explain your observations. Hint: Consider the gain and I/O impedances.

VCC R1 C

RS

+ vin

C R2 +

− RE

RL

vout −

Figure 3: CC amplifier with biasing network and load speaker attached

Prelab 5: Single Stage BJT Amplifiers: Common Collector and Common Base Name: Lab Section: VCC R1 C

RS

+

ROUT

vin −

VIN

R2

+

RIN RE

vOUT −

Figure 1: Common collector amplifier with biasing network

1. What ratio of R1 to R2 is required if the input bias, VIN , is 5.65 V and VCC is set to 12 V? Note: R1 and R2 approximately forms a “voltage divider” that provides the input DC bias point (just in case you did not notice). Also, regard the current flowing through RS as negligible for this calculation only.

In addition, recall that a capacitor is a DC open circuit.

2. Draw the small signal model for the common collector amplifier shown in Figure 1.

3. State (do not derive) the formulas for the input impedance (RIN ), output impedance (ROUT ), and voltage gain (Av ) of a common collector amplifier. Note that the most general formulas should suffice because the biasing network can be modeled using the Thévenin equivalent circuit (i.e. a voltage source with one resistor in series).

1

2

4. Now use these formulas to calculate the numerical values of the mentioned properties. Please also use the following parameters in your calculations: IS = 26.03 fA, RS = 10 kΩ, RE = 100 Ω, and β = 270.

Assuming the ratio of R1 to R2 is correct, the DC input bias (VIN ) should be 5.65 V. Ignore the Early effect and make approximations when appropriate. Also, if necessary, apply concepts from the Thévenin equivalent circuit to simplify the biasing network.

5. If VIN is now 6 V due to faulty biasing circuitry, which of the mentioned properties will change? Note: A qualitative answer will suffice; you do not need to recalculate any values.

6. In general, how do these properties compare to those of the common emitter amplifier?

3 VCC RC

iout

VB + −

iin

Figure 2: Common base amplifier with a current input 7. Draw the small signal model for the common base amplifier shown in Figure 2. Note: The source iin is a small signal AC current source, not a DC current source; thus, you must include iin in the small signal model.

8. State (do not derive) the formulas for input impedance (RIN ), output impedance (ROUT ), and current gain (Ai = iout /iin ) of a common base amplifier.

4

9. Calculate the numerical values of the properties mentioned above using the following parameters: IS = 26.03 fA, RC = 1 kΩ, and VBE = 640 mV. Ignore the Early effect and make approximations when appropriate.

10. How do these properties compare to those of the common emitter amplifier?

Report 5: Single Stage BJT Amplifiers: Common Collector and Common Base Name: Lab Section:

1

Lab Questions

3.1.2–4 CB amplifier parameters: Av = Rin = Rout =

3.1.5 Suppose the source resistance of VIN is 50 Ω. Will the CB amplifier perform well in amplifying the signal from vin ? Why?

3.2.2 DC voltage values when biased at maximum output voltage swing: VIN = VOUT =

3.2.3 CC amplifier parameters: Av = Rin = Rout = Output Voltage Swing =

1

2

POST-LAB QUESTIONS

2

3.2.4 Another name for the CC amplifier is the emitter follower. Based on the gain that you have found, why do you think it is given this name?

3.3.3 Is the tone louder, softer, or about the same as when the signal was directly applied to the speaker?

Explain your observations. Hint: Consider the gain and I/O impedances.

2

Post-lab Questions

2.1

Common Collector Amplifier as a Voltage Buffer

1. Even though the common collector amplifier has roughly unity gain, why is it still a useful amplifier configuration?

2. What are the advantages and/or disadvantages of using a larger RE in our common collector amplifier?

2

POST-LAB QUESTIONS

2.2

3

Common Base Amplifier as a Current Buffer

1. The CB amplifier is rarely used as a voltage or transconductance amplifier while the CE amplifier is typically used. Based on the values of the CB and CE two-port parameters (that you found in lab), explain why this is the case.

2. The CB amplifier is commonly used as a current amplifier. Approximate the current gain of a CB amplifier. (Hint: What is the relationship between the emitter and collector currents of a CB amplifier? ) Draw the two-port model of the CB current amplifier and find Ai .

2

POST-LAB QUESTIONS

4

3. For this question and the next, we will demonstrate the benefits of the CB amplifier. Suppose that a small signal source current of 10 µA peak-to-peak is applied directly to a load resistor of 5 kΩ.

Assuming the source resistance is 100 Ω, what is the peak-to-peak current flowing through the load resistor? Hint: As a start, use the Norton equivalent circuit (i.e. current source in parallel with a source resistance).

4. Now, assume the small signal current of 10 µA peak-to-peak with source resistance of 100 Ω is applied to the input of the CB amplifier. Assume a 5 kΩ load resistor is also attached to the output of the CB amplifier. Using the two port characteristics found during lab and the approximated current gain, what is the current flowing through the load resistor? Based on this result, why is the CB amplifier used as a current buffer?

Experiment 6: Biasing Circuitry 1

Objective

Setting up a biasing network for amplifiers often involves using transistors to build voltage and current sources to deliver the right amount of biasing to the main amplifier components. In this lab, we explore how to build these sources and fine tune their output values to achieve the optimal biasing environment.

2

Materials

The items listed in table 1 will be needed. Note: Be sure to answer the questions on the report as you proceed through this lab. The report questions are labeled according to the sections in the experiment. CAUTION: FOR THIS EXPERIMENT, THE TRANSISTORS CAN BECOME EXTREMELY HOT!!!

Component 2N4401 NPN BJT 2N4403 PNP BJT 10 kΩ resistor 100 Ω resistor 100 kΩ resistor 10 kΩ potentiometer

Quantity 1 2 1 1 1 1

Table 1: Components used in this lab

3

Procedure

3.1

Voltage Sources

In this part of the lab, we use a BJT as a voltage source to supply 650 mV, which is a typical bias voltage for the base of a common emitter.

Figure 1: A typical potentiometer

1. Before building the circuit for this part of the lab, be sure to setup your potentiometer so that the leftmost two terminals have the MAXIMUM possible resistance across them (which should be about 10 kΩ). For assistance, please refer to Figure 1, which illustrates a typical potentiometer. Please be absolutely sure that you use these terminals as the initial resistance for your circuit; otherwise your transistor may BURN UP! 1

3

2

PROCEDURE VCC RSUP

100 Ω

RC

IC

+ VOUT −

Figure 2: Voltage source using a transistor 2. Now build the circuit shown in Figure 2, setting VCC = 5 V. 3. Adjust the potentiometer until the output voltage reaches 650 mV. What is the value of RC at this point?

4. Perform load-line analysis by plotting the IC vs. VOUT curves for both the transistor and RC . On the plot, indicate the fixed point solution for VOUT . How should we adjust the potentiometer to increase VOUT (i.e. do we increase or decrease the value of RC )?

5. Will the voltage source become better or worse as the resistance of RC decreases (with better defined as being closer to an ideal source)? Explain. Hint: Consider the characteristics of an ideal voltage source.

6. Now use ICS to plot IOUT vs. VOUT and use the graph to find the output impedance of the voltage source. Be sure to set the potentiometer resistance to the value found in part 3.1.3. Also, do not exceed 700 mV on your sweep of VOUT !

7. Suppose you want your voltage source to output 1.3 V. Clearly, having 1.3 V as the VBE of a diodeconnected BJT is not a good idea (please, don’t even try setting VBE to 1.3 V). Draw a circuit topology that can achieve this output voltage without requiring an extremely high VBE .

3.2

Current Sources

Besides voltage sources, current sources are also needed to bias transistors.

1. Build the circuit shown in Figure 3, setting VCC = 5 V and VBIAS = 4.35 V. As you adjust VBIAS , be sure to check that VBE stays less than or equal to 0.65 V at all times; otherwise, your transistor may BURN UP! (Warning: It is very easy to make a mistake and burn out a transistor. Therefore, it is highly recommended that you check your values for VBIAS and VCC with the multimeter or oscilloscope before connecting them to the transistor.)

2. Now measure the short circuit output current.

3. In terms of the small-signal characteristic(s) (e.g. gm , ro , β), what is the output resistance of this current source?

3

3

PROCEDURE VCC

VBIAS + − IOUT + VOUT −

Figure 3: Transistor current source VCC

VBIAS + − IOUT + VOUT −

Figure 4: Current source using transistors in parallel 4. Using ICS, sweep VOUT from 0 V to 5 V and plot IOUT vs. VOUT . What is the output impedance at VOUT = 2.5 V? What happens to the output impedance as VOUT approaches 5 V? Explain your observation.

5. Now set up the circuit shown as in Figure 4 by adding a transistor in parallel to the first one. Continue to use the same bias voltage as before (i.e. VBIAS = 4.35 V).

6. What is the new short circuit output current?

7. Using ICS, measure the output impedance for this modified circuit. Explain how the additional transistor affects the output impedance.

3.3

Biasing a Common Emitter Amplifier Using a Current Mirror

A current mirror is simply a series of current sources biased by a voltage source (see Figure 5). This circuit is useful for replicating a biasing current that is used in many places throughout your overall circuit design.

As shown in Figure 6, we can use a current mirror to bias a common emitter amplifier.

1. Build the circuit shown in Figure 6, setting VCC = 12 V, RC = 10 kΩ, and RE = 100 Ω.

3

4

PROCEDURE VCC

VCC

VCC

VCC

. . .

RC

Figure 5: General PNP current mirror VCC

VCC

Q2

Q3

IC2

IC3 +

RC +

Q1

vin − VIN + −

Vout −

RE

Figure 6: Biasing a CE amplifier with a current mirror 2. Plot the VOUT vs. VIN curve to determine the operating point for maximum gain. What is the value of VIN at this point?

3. What is the gain at this point?

4. Now use ICS to measure the input impedance of the amplifier for the value of VIN you found. Afterwards, use the DC offset from the function generator to bias your amplifier to that value of VIN .

5. Then, measure the currents, IC2 and IC3 . Do they match?

6. Use the function generator to also apply a 20 mVpp , 1 kHz sine wave at the input and plot the output on the oscilloscope. Because of the huge gain, the output waveform may be clipped. Attach a 100 kΩ load resistor at the output (which should make the output no longer clipped) and measure the peakto-peak voltage across the resistor. Using the value of this voltage and the gain previously measured, calculate the output impedance.

7. How do the output impedance and gain compare with a common emitter biased with a resistor?

8. Now examine the temperature effects: (a) Apply a small signal sine wave, vin , with an amplitude of 20 mVpp and frequency of 1 kHz. View the output waveform on the oscilloscope.

3

PROCEDURE

5

(b) (CAUTION: Before proceeding with this part of the experiment, please verify that the transistors are not hot to the touch. If they are, then turn off the power supply and check the circuit connections.) Use your finger to warm up only one of the transistors in the current mirror. Observe the effect on the output waveform. (c) Now warm up both transistors that form the current mirror and observe the effect on the output waveform. (d) Explain your observations using information about the temperature dependence of BJTs. Based on your observations, do current mirrors still replicate current when the entire circuit warms up?

Prelab 6: Biasing Circuitry Name: Lab Section: VCC R1 + R2

VOUT −

Figure 1: Resistive divider “voltage source” 1. Consider the resistor network shown in Figure 1. Let VCC = 10 V, R1 = 9.35 kΩ, and R2 = 650 Ω. We can apply Thévenin’s equivalent circuit to this resistive divider to model it as an independent voltage source with an output resistance. Find the open circuit voltage and the output resistance for this resistive divider.

VCC RC

IC

+ VOUT −

Figure 2: BJT voltage source 2. Now, consider a BJT voltage source such as the one shown in Figure 2. Pick the appropriate value for RC so as to achieve an output voltage of 650 mV. Let VCC = 10 V, IS = 26.03 fA, and VT = 26 mV. 1

2

Ignore the Early effect for this calculation.

3. Find the power dissipated by this BJT voltage source as well as the output impedance. Hint: Recall the definition of power, P = IV .

4. If we resized the resistors in the resistive divider (shown in Figure 1) to achieve the same output impedance as the BJT voltage source, what should the values of the two resistors be so that the output voltage stays the same? How much power will the circuit now consume?

VCC R

IOUT

+ VOUT

RL

−

Figure 3: Resistor “current source” 5. Consider the circuit shown in Figure 3. Let VCC = 10 V and R = 10 kΩ. Roughly sketch IOUT vs.

VOUT (space is provided on next page). Note: The specific value for RL is not required for this analysis.

6. Find the short-circuit output current and the output impedance of the current source. Note: RL represents a hypothetical load to the circuit; it can be replaced with an open-circuit for this analysis.

3

1 0.8 0.6

IOU T (mA)

0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 −1

0

10

20

VOU T (V)

7. For the current source, is it possible to increase the output impedance without decreasing the output current and without changing VCC ? Explain.

Report 6: Biasing Circuitry Name: Lab Section:

1

Lab Questions

3.1.3 Adjust the potentiometer until the output voltage reaches 650 mV. What is the value of RC at this point?

RC =

3.1.4 Perform load-line analysis by plotting the IC vs. VOUT curves for both the transistor and RC . On the plot, indicate the fixed point solution for VOUT . How should we adjust the potentiometer to increase VOUT (i.e. do we increase or decrease the value of RC )?

3.1.5 Will the voltage source become better or worse as the resistance of RC decreases (with better defined as being closer to an ideal source)? Explain. Hint: Consider the characteristics of an ideal voltage source.

3.1.6 Find the output impedance of the voltage source.

Rout =

3.1.7 Suppose you want your voltage source to output 1.3 V. Clearly, having 1.3 V as the VBE of a diodeconnected BJT is not a good idea (please, don’t even try setting VBE to 1.3 V). Draw a circuit topology that can achieve this output voltage without requiring an extremely high VBE .

1

1

LAB QUESTIONS

2

3.2.2 Now measure the short circuit output current. : IOUT =

3.2.3 In terms of the small-signal characteristic(s) (e.g. gm , ro , β), what is the output resistance of this current source?

Theoretical Rout =

3.2.4 What is the output impedance at VOUT = 2.5 V? What happens to the output impedance as VOUT approaches 5 V? Explain your observation.

At VOUT = 2.5 V, measured Rout =

3.2.6 What is the new short circuit output current?

IOUT =

3.2.7 Measure the output impedance for this modified circuit. Explain how the additional transistor affects the output impedance.

ROUT =

1

LAB QUESTIONS

3

3.3.2–6 Properties of the CE amp with current mirror: VIN = Av = Rin = IC2 = IC3 = Rout = Do the currents match?

3.3.7 How do the output impedance and gain compare with a common emitter biased with a resistor?

3.3.8 Explain your observations using information about the temperature dependence of BJTs. Based on your observations, do current mirrors still replicate current when the entire circuit warms up?

Experiment 7: Frequency Response 1

Objective

You have already seen the performance of several BJT amplifiers. Even though they were each designed to operate well at certain small-signal frequencies, there is a frequency limit imposed on each of them by the innate parasitic capacitances of the BJTs. In this lab, you will observe how an amplifier responds to different frequencies as well as the effects of external capacitative loads and innate parasitic capacitances.

2

Materials

The items listed in table 1 will be needed. Note: Be sure to answer the questions on the report as you proceed through this lab. The report questions are labeled according to the sections in the experiment. CAUTION: FOR THIS EXPERIMENT, THE TRANSISTORS CAN BECOME EXTREMELY HOT!!!

Component 2N4401 NPN BJT 10 kΩ resistor 1 kΩ resistor 51 Ω resistor 1 nF Capacitor

Quantity 1 1 1 1 1

Table 1: Components used in this lab

3

Procedure

The two following subsections are instructions on how to use the oscilloscope to make Bode magnitude and phase measurements. Please use them as references.

3.1

Technique for Measuring Magnitude using the Oscilloscope

The following instructions assume you have an amplifier already built and that it has one input, vin , and one output, vout . In addition, the input, vin , must be controlled by the function generator.

1. Use the function generator to create a sine wave with the frequency of your choice; this shall be the vin for your circuit.

2. Also connect vin and vout to their respective channels on the oscilloscope. The following steps will assume that vin is on Channel 2 and vout is on Channel 1.

3. Press the “Quick Measure” button in the MEASURE section. Next, select Channel 1 as the source and P eak − P eak as the measurement. Now, press the third menu button that corresponds to Measure.

4. Repeat the previous step for Channel 2. k−P k(1) 5. At the bottom of the screen, each peak-to-peak voltage will be displayed. Calculate P P k−P k(2) ; this value should be the magnitude of the frequency response at the chosen frequency. k−P k(1) 6. To obtain the magnitude in decibels, simply scale the logarithm of the magnitude by 20 (i.e. 20 log P P k−P k(2) ).

7. Record this value on paper or in Windows Excel.

1

3

PROCEDURE

2

8. Repeat the same procedures again for a different frequency by simply changing the frequency setting on the function generator.

9. When the desired frequency range has been swept, simply plot the values to acquire the magnitude Bode plot.

3.2

Technique for Measuring Phase using the Oscilloscope

The following instructions assume you have an amplifier already built and that it has one input, vin , and one output, vout . In addition, the input, vin , must be controlled by the function generator.

1. Use the function generator to create a sine wave with the frequency of your choice; this shall be the vin for your circuit.

2. Also connect vin and vout to their own respective channels on the oscilloscope. The following steps will assume that vin is on Channel 2 and vout is on Channel 1.

3. Press the “Quick Measure” button in the MEASURE section. Next, select Channel 1 as the source and P hase as the measurement.

4. Adjust the “Settings” - this option opens up a new menu and is only availabe when P hase or Delay is selected. Use this option to select the order of comparison (i.e. the phase of Source 1 relative to Source 2 or vice versa). For this example, set Channel 1 for the first source and Channel 2 for the second.

5. When finished making adjusts, go back to the previous menu and press the third menu button that corresponds to Measure.

6. At the bottom of the screen, the phase difference should be displayed. This value is the phase of the frequency response at the chosen frequency.

7. Record this value on paper or in Windows Excel.

8. Repeat the same procedures again for a different frequency by simply changing the frequency setting on the function generator.

9. When the desired frequency range has been swept, simply plot the values to acquire the phase Bode plot.

3.3

IMPORTANT FACTS

1. Since the oscillscope can simultaneously display multiple measurements, you can easily conduct the Bode magnitude and phase measurements in one experiment run. All you have to do is setup the equipment as mentioned above to measure both magnitude and phase. Then, simply record the magnitude and phase values while sweeping through the frequency range using the function generator.

2. Also, autoscale does not work very well at high frequencies. For such cases, you must manually scale the vertical and horizontal axes as well as use the averaging feature. For a review of how to do so, please see the oscilloscope tutorial.

3. As a reminder, the output impedance of the function generator is mismatched from the input impedances of the amplifiers in this lab. Thus, the actual delivered voltage is doubled the amount displayed on function generator. FOR THIS LAB, ALL LISTED VOLTAGES ARE THE ACTUAL DELIVERED VOLTAGES (NOT THE ONE DISPLAYED ON THE FUNCTION GENERATOR).

3

3

PROCEDURE VCC RC

IBIAS vOUT

− VBIAS

+ −

vin

+

RS

Figure 1: Common emitter amplifier test setup

3.4

Frequency Response of a Common Emitter Amplifier

1. Construct the common emitter amplifier as shown in Figure 1. Use a RC = 10 kΩ, RS = 51 Ω, and VCC = 5 V. 2. For the input signal, use a 25 mV peak-to-peak sine wave with a DC offset of 580 mV. This signal is both VBIAS and vin combined, and will be referred to as vIN . Note: You may notice some nonlinear effects on the output waveform. This is due to the high input signal amplitude that we are using. We chose this amplitude to avoid noise from the oscilloscope interfering with the Bode plot measurements.

3. What are the respective values of IBIAS and VOUT (the DC voltage at the output)?

4. Using the oscilloscope, plot vIN on Channel 2 and vOUT on Channel 1. Make sure to transfer the waveforms over to the lab report.

5. At 1 kHz, what are the magnitude and phase of vout /vin as measured from the oscilloscope?

6. Using the techniques mentioned above, create the Bode magnitude and phase plots. To save time, sweep the frequency in decades first (i.e. increment by factors of 10) and do not exceed 2 MHz for this circuit. Then, take more measurements in frequency ranges where the poles are located.

7. Find the frequency where the gain decreases from its DC value by 3 dB; this frequency is called the dominant pole of the amplifier. What is the phase at this frequency? Is the phase consistent with the magnitude? (Recall that at the −3 dB point, the phase should drop from its DC value by 45 degrees.)

3.5

Miller Effect

1. Let us evaluate the impact of the Miller effect by adding a 1 nF capacitor, CM , as shown in Figure 2.

2. Create the Bode magnitude and phase plots. Do not exceed 500 kHz. Attach the plots to the lab report.

3. How does the dominant pole of this amplifier compare to the dominant pole of the previous amplifier?

Is this expected?

4. In this amplifier, we are using a 1 nF capacitor to simulate a large base-collector capacitor (Cµ ). If we are to design an amplifier with high bandwidth, is a transistor with a large Cµ desirable?

3

4

PROCEDURE VCC RC

IBIAS vOUT

CM − VBIAS

+ −

vin

+

RS

Figure 2: Miller capacitor test setup VCC RC

IBIAS vOUT

− VBIAS + −

vin

+

RS CM

Figure 3: Output capacitance test setup

3.6

Output Capacitance

1. Let us examine the impact of output capacitance on a common emitter amplifier: reposition capacitor CM , from the previous section, by placing it at the output (see Figure 3).

2. Create the Bode magnitude and phase plots. Do not exceed 500 kHz. Attach the Bode plot to the lab report.

3. How does the dominant pole of this amplifier compare to the respective poles of the previous two amplifiers? Is this result agreeable?

3.7

Common Collector Amplifier

1. The common collector amplifier is a wide bandwidth amplifier. Let us examine the frequency response of this amplifier by first building the common collector amplifier shown in Figure 4. Let RS = 51 Ω, RE = 1 kΩ, and VCC = 5 V. 2. Use a 2 Vpp input signal that has a DC offset of 3 V. 3. Create the Bode magnitude and phase plots. Attach the Bode plots to the lab report. Keep in mind that the breadboard has a parasitic capacitance that will start to deform the output signal when the frequency goes beyond 1 MHz. To observe this effect, plot the output voltage using the oscilloscope and set the input frequency beyond 1 MHz. Because of this parasitic capacitance, the results of these

3

5

PROCEDURE VCC

− VBIAS

+ −

vin

+

RS vOUT RE

Figure 4: Common collector amplifier test setup experiments are only an approximation. Note: Due to the limitations of the lab equipment, the pole frequency might not be attainable. If this is the case, just mention that you cannot find the pole.

4. How does the bandwidth of this amplifier compare to the respective bandwidths of the previous amplifiers? Note: If you could not measure the dominant pole, a qualitative answer is sufficient (i.e. smaller, larger, much larger).

Prelab 7: Frequency Response Name: Lab Section: i(t) C

v1 (t)

v2 (t) A

Figure 1: Amplifier with a “Miller” capacitor The Miller effect plays an important role in determining the poles of an amplifier. If there is gain, A, across the capacitor, C, as shown in Figure 1, then the current across C can be written as: d d (v1 (t) − v2 (t)) = C dt (v1 (t) − Av1 (t)) i(t) = C dt

By distributing the derivative, this simplifies to: d i(t) = C(1 − A) dt v1 (t)

Therefore, the equivalent capacitance looking into v1 (t) is the capacitance C multiplied by (1 − A). If the gain, A, is large enough, this Miller effect can make the capacitor dominate over other capacitances and thus, contribute to the dominant pole of the amplifier. Similarly, the equivalent capacitance looking into 1 v2 (t) can be derived as C 1 − A .

VCC = 5 V RC

0.25 mA vOUT

− VBIAS + −

vin

+

RS

Figure 2: Common emitter amplifier. Note that this amplifier has negative gain.

1

2

1. For the common emitter amplifier shown in Figure 2, derive/state expressions for the two poles of vout /vin in terms of Cµ , Cπ , gm , RS , rπ , and/or ro . (Remember to use the Miller approximation.)

Fill in your answers in the designated boxes. Keep in mind that these expressions will later help you predict and understand the results of the lab experiment.

ωp1 =

ωp2 =

2. If RS = 51 Ω, RC = 10 kΩ, Cµ = 11 pF, Cπ = 25 pF, gm = 3 mS, rπ = 10 kΩ, and ro = 100 kΩ, what are the poles of this amplifier? Please provide numerical answers.

ωp1 = ωp2 =

3. What will happen to the poles if a capacitor CM is added across the base collector junction?

3

4. Suppose there is a biasing error in a CE amplifier circuit, causing VBE to become smaller than it should be. How will this affect the biasing current, gm , rπ , and ro ? Now, based on these responses, how will the pole frequencies be affected? Note: Qualitative answers will suffice. Make approximations when appropriate.

5. SPICE • Construct the common emitter amplifier circuit shown in Figure 2 in SPICE. Use VBIAS = 0.58 V, RS = 51 Ω, and RC = 10 kΩ.

• Use the 2N4401 SPICE model provided on the course website.

• Perform an AC analysis of the circuit from 100 Hz to 10 GHz in HSPICE. • Also perform a poles/zeros analysis using the .pz command. The results of this command should appear in the output text file. No need to print out the whole output file, just write down the values below. Note: If necessary, refer to the appendix of the HSPICE Tutorial for instructions on how to use poles/zeros analysis.

• Use Awaves to generate Bode plots (both magnitude and phase) for vout /vin . Attach the Bode plots to this prelab worksheet. Do the results agree with your hand calculations (check the pole frequencies)?

Report 7: Frequency Response Name: Lab Section: 3.4.3 What are the respective values of IBIAS and VOUT (the DC voltage at the output)?

IBIAS = VOUT = 3.4.4 Sketch the waveforms of vIN and vOUT .

3.4.5 At 1 kHz, what are the magnitude and phase of vout /vin as measured from the oscilloscope?

|vout /vin |dB = ∠vout /vin =

1

2

3.4.6 Attach the Bode plots to the lab report.

3.4.7 What is the frequency at which the gain drops by 3 dB? What is the phase at this frequency? Is the phase consistent with the magnitude?

f−3 dB = ∠vout /vin |f−3 dB = 3.5.2 Attach the Bode plots to the lab report.

3.5.3 How does the dominant pole of this amplifier compare to the respective poles of the previous two amplifiers? Is this result agreeable?

3.5.4 If we are to design an amplifier with high bandwidth, is a transistor with large Cµ desirable?

3.6.2 Attach the Bode plots to the lab report.

3.6.3 How does the dominant pole of this amplifier compare to the respective poles of the previous two amplifiers? Is this result agreeable?

3.7.3 Attach the Bode plots to the lab report.

3.7.4 How does the bandwidth of this amplifier compare to the respective bandwidths of the previous amplifiers? Note: If you could not measure the dominant pole, a qualitative answer is sufficient (i.e. smaller, larger, much larger).

Experiment 8: Multi-stage Amplifiers 1

Objective

A single transistor amplifier stage usually does not provide enough gain and/or the proper I/O impedances for the desired application. To remedy this, we can cascade several amplifier stages to form a multi-stage amplifier that has the appropriate properties. In this lab, we begin with an evaluation of the cascode amplifier before moving on to the multi-stage amplifier. Note that multi-stage amplifiers can be made from several different combinations of amplifiers; however, we only utilized the common emitter and common collector amplifier for this particular experiment.

2

Materials

The items listed in table 1 will be needed. Note: Be sure to answer the questions on the report as you proceed through this lab. The report questions are labeled according to the sections in the experiment. CAUTION: FOR THIS EXPERIMENT, THE TRANSISTORS CAN BECOME EXTREMELY HOT!!!

Component 2N4401 NPN BJT 2N4403 PNP BJT 51 kΩ resistor 20 kΩ resistor 100 Ω resistor 51 Ω resistor 10 kΩ potentiometer 10 µF capacitor

Quantity 4 2 2 1 2 1 1 2

Table 1: Components used in this lab

3

Procedure

3.1

Cascode Amplifier

1. Construct the cascode amplifier (Q1 and Q2 ) and the current mirror (Q3 and Q4 ) as shown in Figure 1(a). Use two 51 kΩ resistors in parallel to make the 25.5 kΩ resistance for RREF and use a 51 Ω resistor for RS . Also, set VBIAS2 to 1.5 V. 2. Use the function generator to create vIN , a 1 kHz, 20 mVpp sine wave with a DC offset between 580 mV to 650 mV; you may have to adjust the offset to get a clean output signal.

3. Measure IBIAS and the DC output voltage, VOUT .

4. Using the oscilloscope, plot both vIN and vOUT . Sketch the waveforms you observe.

5. Why is vOUT not sinusoidal?

6. Now add a 10 µF capacitor and a 20 kΩ resistor to the vOUT node (see Figure 1(b)); this resistor will act as the load for the amplifier.

7. Measure the peak-to-peak voltage of the output waveform (i.e. the voltage signal across RL ). What is the gain of the amplifier when the resistive load is attached?

1

3

2

PROCEDURE VCC = 12 V

VCC = 12 V

Q3

Q4

Q3

Q4

vOUT

vOUT

Q2

VBIAS2 + −

Q2

VBIAS2 + −

C

+ +

Q1

RS

RREF

IBIAS

RS

+

vIN

Q1 RL

vL

RREF

IBIAS

−

vIN −

−

(a)

(b)

Figure 1: (a) Cascode amplifier test setup (b) Cascode amplifier test setup with load resistance

3.2

Common Emitter-Common Collector Multi-stage Amplifer

From the previous lab experiments, you were asked to use a speaker as the load for the common emitter amplifier. However, the common emitter (CE) amplifier delivered very small voltages to the speaker because it had a large output impedance. In this section of the lab, you will use the common collector amplifier (which has low output impedance and low gain) as a voltage buffer between the speaker and the CE stage.

1. To begin, use the function generator create a sine wave with peak-to-peak voltage of 40 mV and a frequency of 1 kHz. Next, apply this signal directly to the speaker. Can you hear anything from the speaker?

2. Construct the multi-stage amplifier as shown in Figure 2. Set the potentiometer’s resistance to around 8 kΩ for RC . For the rest of the circuit, let RS = 51 Ω, RREF = 200 Ω (use two 100 Ω resistors in series), and C = 100 µF. VCC = 5 V RC

IBIAS1

RREF Q2

vOUT 1 + vIN

RS

Q1

IBIAS2

vOUT 2 C Q3

Q4

−

Figure 2: Multi-stage amplifier test setup 3. For vIN , use a 40 mV peak-to-peak, 1 kHz frequency sine wave with a DC offset of around 540 mV

3

PROCEDURE

3

to 600 mV. Now, try to maximize the gain of the amplifier by increasing the resistance of the potentiometer, RC . Can you hear anything from the speaker now? Feel free to try out other frequencies to observe how the speaker responds.

4. Measure IBIAS1 , IBIAS2 , and the DC voltages at vOUT 1 and vOUT 2 , respectively.

5. Measure the VBE of Q2 . Is the DC voltage at vOUT 1 large enough to bias Q2 into forward active mode?

6. Using the oscilloscope, plot both vIN and vOUT 2 . Sketch the observed waveforms onto your lab report.

7. Measure the voltage gain vout2 /vin .

8. Now increase the DC offset of the input waveform to 620 mV. What happens to the waveform at vOUT 2 ?

3.3

Reading: Biasing a Two-Stage Amplifier

This section covers the necessary game plan for determining the proper biasing condition for a two-stage amplifier. However, the techniques can be applied to multiple stages as well.

To warn against a deadly bad habit: guess work (i.e. build the circuit and then blindly tweak the bias voltages and resistors values until something reasonable shows up on the output) is one of the worst possible ways of building your circuit. It is a strenuous, time consuming trial and error approach.

Instead, consider this alternative: given the circuit topography is correct, the only parameters left to adjust are the biasing voltages and currents. The values of these quantities directly affect the gain and I/O impedances. So the objective is to exploit the design specifications and work backwards to retrieve information about the biasing point, resistances, etc.

We demonstrate the technqiue using Figure 2 as an example. Note that the analysis is rather qualitative to keep it from being too heavy: 1 1 //ro3 ≈ gm2 . Since gm2 = IVC2 , Constraining Output Impedance: The output resistance of Figure 2 is gm2 T you automatically know the required biasing current if the output impedance is constrained to be less than that of the speaker (i.e. less than 8 Ω). Given that Q3 and Q4 are the same size transistors, IC2 should be to solve for VBE4 and the value of RREF . Because the mirror of IBIAS2 . Now use IBIAS2 = IS exp VVBE4 T IC3 = IC2 , you also know how to solve for VBE3 and VBE2 . Using these values, you can estimate a range for VOUT , which then implies a range for IBIAS1 .

Constraining Gain: Now you need another design specification to determine the rest of the parameters; we chose gain for this example. Since voltage gain is directly dependent on gm and ro (and hence indirectly depends on IBIAS1 ), a constraint on gain would imply a value for IBIAS1 and RC . Now, use IBIAS1 = IS exp VVBE1 to calculate VBE1 . Afterwards, find VIN from IBIAS1 = βIB1 and Ohm’s Law. That’s T it; you have just solved the circuit.

Even though this analysis was rather hand wavy, it should be enough to help get you started. Also, note that this approach is by no means the only way of working backwards; I could have started with constraining input impedance and gain instead. In general, the insight is to know how the different parameters are interrelated.

Prelab 8: Multi-stage Amplifiers Name: Lab Section: VCC = 5 V ISUP P LY vOUT Q2

VBIAS2 + −

− VBIAS1 + −

vin

+

Q1

RS

Figure 1: Cascode amplifier with ideal current source 1. The cascode in Figure 1 is biased by an ideal current source. Let RS = 51 Ω, IS = 1 × 10−15 A, VA = 100 V, β = 200, ISUP P LY = 1 mA, T = 300 K, vOUT,DC = 3.5 V, and VBIAS2 = 2 V. Calculate the value of VBIAS1 that corresponds to these biasing conditions.

VBIAS1 =

2. What is the gain of this amplifier?

Av =

1

2

VCC = 5 V RC

IBIAS1

RREF Q2

vOUT 1 +

RS

Q1

IBIAS2

vOUT 2

vIN

Q3

Q4

−

Figure 2: Multi-stage amplifier 3. Now construct a SPICE netlist for the multi-stage amplifier shown in Figure 2. Let RC = 10 kΩ, RS = 51 Ω, and RREF = 200 Ω. Bias transistor Q1 with VIN = 560 mV. What is the small signal gain (Av1 ) between vIN and vOUT 1 ? What is the small signal gain (Av2 ) between vOUT 1 and vOUT 2 ?

Using Av1 and Av2 , find the overall gain (Av,tot ) between vIN and vOUT 2 . Attach the SPICE netlist to the end of this prelab. Hint: When making your netlist, recall the notation: vIN = vin + VIN .

Av1 = Av2 = Av,tot =

4. Using the same setup from the previous question, simply change VIN to 610 mV and rerun the test.

What are the new values for Av1 , Av2 , and Av,tot ? From your results, does DC biasing have a profound effect on the small signal gain? Explain.

Av1 = Av2 = Av,tot =

Report 8: Multi-stage Amplifiers Name: Lab Section: 3.1.3 Measure IBIAS and the DC output voltage, VOUT .

IBIAS = vOUT =

3.1.4 Using the oscilloscope, plot both vIN and vOUT . Sketch the waveforms you observe.

3.1.5 Why is vOUT not sinusoidal?

1

2

3.1.7 Measure the peak-to-peak voltage of the output waveform (i.e. the voltage signal across RL ). What is the gain of the amplifier when the resistive load is attached?

vL,p−p = vL = vin

3.2.1 Can you hear anything from the speaker when it is directly connected to the function generator?

Yes or No

3.2.3 Can you hear anything from the speaker when it is connected to the output of the amplifier?

Yes or No

3.2.4 Measure IBIAS1 , IBIAS2 , and the DC voltages at vOUT 1 and vOUT 2 .

IBIAS1 = IBIAS2 = vOUT 1,DC = vOUT 2,DC =

3.2.5 Measure the VBE of Q2 . Is the DC voltage at vOUT 1 large enough to bias Q2 into forward active mode?

VBE = Yes or No

3

3.2.6 Using the oscilloscope, plot both vIN and vOUT 2 . Sketch the observed waveforms.

3.2.7 Measure the gain vout2 /vin .

vout2 = vin

3.2.8 Now increase the DC offset of the input waveform to 620 mV. What happens to the waveform at vOUT 2 ?

Experiment 9: MOS Characterization and Amplifiers 1

Objective

The MOS transistor is another circuit element typically used in integrated circuits. Although they have similar functions to BJTs and can be put into several analogous topography (e.g. the cascode, common drain, common gate, common source), MOS transistors are completely different in terms of their characteristics and physical mechanisms underlying their operation. This lab will explore the differences between BJTs and MOSFETs as well as analyze their advantages and disadvantages.

2

Materials

The items listed in table 1 will be needed. Note: Be sure to answer the questions on the report as you proceed through this lab. The report questions are labeled according to the sections in the experiment. CAUTION: FOR THIS EXPERIMENT, THE TRANSISTORS CAN BECOME EXTREMELY HOT!!!

Component BS170 NMOSFET 8 Ω speaker 100 Ω resistor 5.1 kΩ resistor 51 kΩ resistor 10 µF capacitor Microphone

Quantity 2 1 1 1 1 1 1

Table 1: Components used in this lab

3

Procedure

3.1

The Three Regions of Operation

Similar to a BJT, a MOSFET also has several regions of operation.

VD ID VG

Figure 1: Configuration for obtaining the I-V characteristics of an NMOS

1. Set up an NMOS transistor on the breadboard as shown in Figure 1.

1

3

2

PROCEDURE

2. Using ICS, step VG from 2.1 V to 2.3 V in 0.05 V increments and sweep VD from 0 V to 3 V to obtain the MOSFET I-V characterization curve. Print out the plot.

3. On your printout, please label the cutoff, triode, and saturation regions. Attach this sheet to your lab report as well. What is the expression that describes the boundary between the saturation and triode region? Hint: Manipulate the current equations for triode and saturation. Then, apply the boundary condition for these equations.

4. Given a bias of VGS = 2.1 V and VDS = 1.5 V, extract the transconductance gm and the small signal resistance ro from your plot. What region of operation is this?

5. Given a bias of VGS = 2.1 V and VDS = 0.06 V, extract the transconductance gm and the small signal resistance ro from your plot. What region of operation is this?

3.2

MOSFET Model Parameters

The model for the MOSFET consists of several parameters. This section will attempt to extract the threshold voltage VT H , the channel length modulation factor λ, and the constant Kn = W L µn Cox .

1. Using the I-V characteristic plot from before, extract λ from the slope of the plot. Note that this will vary somewhat depending on which VGS you use.

VD ID VG

Figure 2: Diode connected MOSFET 2. Now, diode connect the NMOS as shown in Figure 2. Sweep VG from 0 V to 2.5 V and measure the current ID .

1

3. Using Excel, plot (ID ) 2 vs. VG . Print and attach this plot to your report.

4. (1/2Kn)1/2 is the slope of the linear portion of the curve. Find Kn . Hint: If you are an Excel guru, you can probably find the slope and intercept easily in Excel. For the rest of you, it is probably easier to do it by hand.

1

5. The threshold voltage VT H can be found by measuring where the linear portion of the (ID ) 2 vs. VG curve would intersect the VG axis if it was extended. Find VT H .

3.3

Simple Two-Stage Microphone to Speaker MOS Amplifier

If you haven’t noticed by now, finding input and output impedances is boring. So instead, we will build a two-stage MOS microphone-to-speaker amplifier and analyze its performance.

1. Set up the circuit shown in Figure 3. Let VDD = 6 V, RD = 51 kΩ, and RS = 51 Ω.

2. Identify the transistor configuration for each of the two stages (e.g. common base, common source, source follower).

3

3

PROCEDURE VDD

VDD RD

+ +

vin RS

− VIN + −

Vout −

Figure 3: Microphone to speaker amplifier 3. Using ICS, find the value of VIN that yields the maximum voltage gain. Find the gain and the output voltage swing at this DC bias point. What problems might we encounter if we biased the circuit exactly at the point for maximum gain?

VS R1 + VOUT Microphone

−

Figure 4: Microphone input 4. The microphone needs a bit of DC current flowing through it in order to function. Set up a resistive divider for the microphone as shown in Figure 4. Let R1 = 5.1 kΩ. What problems might we run into if the resistor has too much or too little resistance?

5. Adjust the supply voltage VS (using the knob on the DC power supply) until VOUT of the voltage divider is at VIN = 1.95 V. 6. Attach the output of this resistive divider to the input of the amplifier and attach the speaker to the output of the amplifier. Remember to capacitively couple the output!

7. If you built it all correctly, you should be able to hear some sounds from the speaker when someone speaks into the microphone.

Prelab 9: MOS Characterization and Amplifiers Name: Lab Section: VCC

+ vin − VIN + −

+ RS

vout −

Figure 1: Common drain amplifier 1. Draw the small signal model for the common drain amplifier shown in Figure 1.

2. Derive the output impedance.

3. Derive the voltage gain.

1

2 VCC RD

+ vout VB + −

− + vin −

Figure 2: Common gate amplifier 4. Draw the small signal model for the common gate amplifier shown in Figure 2.

5. Derive the output impedance.

6. Derive the voltage gain.

Report 9: MOS Characterization and Amplifiers Name: Lab Section: 3.1.2 Print out the I-V plot.

3.1.3 Label the operating regions on your printout and attach it to this report. Approximately what criterion determines the boundary between saturation and triode?

3.1.4 Properties (for VDS = 1.5 V) gm = ro = Region of Operation: 3.1.5 Properties (for VDS = 0.06 V) gm = ro = Region of Operation: 3.2.1 Channel Length Modulation Factor λ= 1

3.2.3 Print and attach the plot of (ID ) 2 vs. VG .

3.2.4 Find Kn .

Kn =

3.2.5 Find VT H .

VT =

1

2

3.3.2 Identify the two amplifier configurations.

3.3.3 Find the value of VIN that yields the maximum voltage gain. Find the gain and output voltage swing at this bias point. What problems might we encounter if we biased the circuit exactly at the point for maximum gain?

VIN = Av = Output Voltage Swing:

3.3.4 What problems might we run into if the resistor has too much or too little resistance?

Experiment 10: Differential Amplifiers 1

Objective

Differential amplifiers are designed to amplify the difference between two signals; thus, such amplifiers are capable of reducing noise that is common to both inputs. We can quantify the differential-mode versus common-mode gain in a quantity called the common-mode rejection ratio (CMRR). Differential amplifiers also lend themselves to use in feedback, though we will not explore that usage in this lab. A typical differential amplifier with a single-ended output is the op-amp.

2

Materials

The items listed in table 1 will be needed. For this lab, assume all NPN transistors are identical 2N3904 BJTs and all PNP transistors are identical 2N3906 BJTs. Note: Be sure to answer the questions on the report as you proceed through this lab. The report questions are labeled according to the sections in the experiment. CAUTION: FOR THIS EXPERIMENT, THE TRANSISTORS CAN BECOME EXTREMELY HOT!!!

Component LM741 op-amp 2N3904 NPN BJT 2N3906 PNP BJT 1 kΩ resistor 5.1 kΩ resistor 10 kΩ resistor 0.1 µF capacitor

Quantity 1 4 2 2 2 2 1

Table 1: Components used in this lab

Component 2N3904 NPN BJT 2N3906 PNP BJT

IS (A) 6.734 × 10−15 1.41 × 10−15

VA (V) 74.03 18.7

Table 2: Transistor properties

3

Procedure

3.1

Generating a differential signal

Before building a differential amplifier, let us first generate a differential signal, which would require inverting an analog signal. One way we can do this is by using an op-amp in negative feeback, as shown in Figure 1.

1. Construct the circuit in Figure 1 using the LM741 op-amp. The pin layout for the LM741 op-amp is in Figure 2. Note: If your LM741 doesn’t have a notch as shown in the figure, check for a small dot; this dot labels pin 1.

2. Apply a 60 mVpp , 1 kHz sine wave to the input. Display the input and output on the oscilloscope and verify that the output is the inverse of the input.

1

3

2

PROCEDURE 1kΩ

vin

VCC

1kΩ −

vout

+

−VCC Figure 1: Inverting amplifier

Figure 2: LM741 pin layout

3.2

Differential pair with resistive load

1. Construct the circuit in Figure 3 using 2N3904 transistors for the NPN BJTs. Use R1 = 10 kΩ, R2 = R3 = 5.1 kΩ, and VCC = 9 V. Note that this is the same circuit you analyzed in the prelab.

VCC R2

R3 + vout −

R1

vin+

Q1

Q3

Q4

vin−

Q2

−VCC Figure 3: Differential pair with resistive load 2. Ground the inputs and measure IC1 , IC2 , IC3 , and VOUT,DC . How do these values compare to your hand calculations?

3. Apply a 60 mVpp , 1 kHz sine wave to vin+ and ground vin− . Use the oscilloscope to display the input waveform (vin+ ) and the output waveform (vout+ ); sketch the results on your lab report. If the input signal is noisy, use the averaging feature of the oscilloscope to get a more accurate result.

4. Use the oscilloscope to measure the peak-to-peak voltages of vin+ and vout+ .

5. Now display vout+ and vout− on the oscilloscope. Do they appear as you would expect?

3

3

PROCEDURE

6. Now use the oscilloscope to display vout+ − vout− . Measure the peak-to-peak voltage of the signal and calculate the differential gain of the circuit. Does this match the gain you calculated in the prelab?

7. Apply a 30 mV amplitude, 1 kHz sine wave to both vin+ and vin− . Use the oscilloscope to display the output waveforms from vout+ and vout− . What do you see at the output? Why? 8. Use the inverting amplifier (from section 3.1) to apply a 40 mVpp , 1 kHz differential sine wave to the inputs (i.e. a 20 mVpp sine wave applied to vin+ and the inverted sine wave to vin− ). Use the oscilloscope to measure the peak-to-peak voltage of the differential input and output. Now use these measurements to determine the gain. Does this gain match your prelab calculations? Does it match the gain you observed in step 3.2.6?

3.3

Differential pair with active load VCC Q5

Q6 vout

R1

vin+

Q1

Q3

Q4

vin−

Q2

−VCC Figure 4: Differential pair with active load

1. Construct the circuit in Figure 4 using 2N3904 transistors for the NPN BJTs and 2N3906 transistors for the PNP BJTs. Use R1 = 10 kΩ and VCC = 9 V. 2. Apply a 60 mVpp , 1 kHz sine wave to vin+ and ground vin− . Use the oscilloscope to display the output waveform from vout and sketch the result. Why is the output not sinusoidal?

3. We would like to reduce Rout by loading the amplifier with a small resistor. Attach a load to the amplifier as shown in Figure 5. Use CL = 0.1 µF and RL = 5 kΩ.

4. Calculate the differential gain for the amplifier with the new load resistance.

5. Apply a 40 mVpp , 1 kHz sine wave to vin+ and ground vin− . Use the oscilloscope to display vin+ and vout . Sketch vout . What is the measured differential gain of the circuit? How does this compare with your hand calculations? Does the gain match the differential gain you measured in step 3.2.6? Should they match?

3.4

SPICE Analysis

1. Write a netlist for the circuit in Figure 3. Apply a differential input of 20 mV amplitude, 1 kHz as you did in step 3.2.8. Hint: Generate a 20 mV amplitude, 1 kHz sine wave and use dependent sources to generate the non-inverted and inverted 10 mV amplitude sine waves.

3

4

PROCEDURE VCC Q5

Q6

+

CL R1

vin+

Q3

Q4

vin−

RL

vout −

Q1

Q2

−VCC Figure 5: Differential pair with reduced output resistance 2. Use SPICE to find IC1 , IC2 , IC3 , and VOUT,DC . Compare these values with your prelab calculations and lab measurements.

3. Plot the differential input and differential output signals in Awaves. Print the plot and attach it to your lab report. Use the plot to calculate the gain. Does it match your hand calculations? Does it match your lab measurements?

Prelab 10: Differential Amplifiers Name: Lab Section: For this lab, assume all NPN transistors are identical 2N3904 BJTs and all PNP transistors are identical 2N3906 BJTs. Component 2N3904 NPN BJT 2N3906 PNP BJT

IS (A) 6.734 × 10−15 1.41 × 10−15

VA (V) 74.03 18.7

Table 1: Transistor properties

A differential pair with a resistive load is shown in Figure 1; use this circuit to answer the following questions. Note: You can ignore base currents for this analysis, but you must use the device parameters given in Table 1. Assume VCC = 9 V and that the inputs are biased at 0 V DC. VCC R2

R3 + vout −

R1

vin+

Q3

Q1

Q4

vin−

Q2

−VCC Figure 1: Differential pair with resistive load

1. What value of R1 corresponds to IC1 = 2 mA?

R1 = 2. In lab, we have 500 Ω, 1 kΩ, 5.1 kΩ, and 10 kΩ resistors. Suppose you only wanted to use one resistor for R1 , which value would give the IC1 closest to 2 mA? What current would you get with the resistor you chose? Use this value for R1 in the remainder of this prelab.

1

2

R1 = IC1 = 3. We would like to bias the output half-way between 0 V and 9 V to achieve maximum voltage swing; calculate the values for R2 and R3 that will let us achieve an output bias of 4.5 V. (For this example, assume R1 is the resistor you chose for the previous question). Among the available resistors mentioned, which ones should we use for R2 and R3 , respectively? What output bias does this combination achieve? Use these values (of the available resistors) for R2 and R3 in the remainder of this prelab.

(Exact) R2 = R3 = (Available) R2 = R3 = Vout,DC = 4. What is the output resistance of the circuit (be sure to take into account the Early Effect)? Assume R2 and R3 have the values you chose for them (from among the available resistors).

Rout = 5. What is the differential-mode gain of the circuit?

ADM = 6. What is the common-mode gain of the circuit?

3

ACM = 7. What is the common-mode rejection ratio of the circuit? Use CM RR =

CM RR =

ADM ACM

.

Report 10: Differential Amplifiers Name: Lab Section: 3.2.2 Measure IC1 , IC2 , IC3 , and VOUT,DC . How do they compare with your hand calculations?

IC1 = IC2 = IC3 = VOUT,DC =

3.2.3 Sketch the waveforms at vin+ and vout+ .

3.2.4 Measure the peak-to-peak voltages of vin+ and vout+ . vin+,p−p = vout+,p−p = 3.2.5 Qualitatively describe vout+ and vout− (i.e their similarities and differences). Is this result agreeable?

3.2.6 Measure the peak-to-peak voltage of vout+ − vout− and calculate the differential gain of the circuit.

Does this match the gain you calculated in the prelab?

1

2

vout,p−p = ADM =

3.2.7 What do you see at the output? Why?

3.2.8 Measure the gain. Does it match your prelab calculations? Does it match your result from 3.2.6?

ADM =

3.3.2 Sketch the output waveform. Why is it not sinusoidal?

3.3.4 Calculate the differential gain of the amplifier with the added load resistor.

ADM = 3.3.5 Sketch vout . What is the measured differential gain of the circuit? How does it compare with your hand calculations? Does it match the gain you observed in step 3.2.6? Should they match?

ADM =

3

3.4.1 Attach your netlist to this report.

3.4.2 Use SPICE to find IC1 , IC2 , IC3 , and Vout,DC . Compare these values with your prelab calculations and lab measurements.

IC1 = IC2 = IC3 = VOUT,DC =

3.4.3 Attach your plot to this report. What is the gain according to the plot? Does it match your hand calculations? Does it match your labs measurements?

ADM =