International Journal of Electrical and Electronics Engineering Research (IJEEER) ISSN 2250-155X Vol. 3, Issue 4, Oct 2013, 223-232 © TJPRC Pvt. Ltd.
DESIGN OF 1V, 0.18µ FOLDED CASCODE OPERATIONAL AMPLIFIER FOR SWITCH CAPACITOR SIGMA DELTA MODULATOR RATNAPRABHA W. JASUTKAR1, P. R. BAJAJ2 & A. Y. DESHMUKH3 1 2
Research Scholar, G. H. Raisoni College of Engineering, Nagpur, Maharashtra, India
Director and Professor, G. H. Raisoni College of Engineering, Nagpur, Maharashtra, India 3
Professor, G. H. Raisoni College of Engineering, Nagpur, Maharashtra, India
ABSTRACT In this paper, the concept of folded topology and design methodology in terms of equations, criteria and procedures is presented for folded cascode operational amplifier which is to be used in switch capacitor sigma delta modulator. The design of folded cascode operational amplifier results in high gain and high unity gain bandwidth. The circuit performance has been simulated with ±10% voltage supply variations. A prototype of an operational amplifier has been built in 0.18µm CMOS process with 1V supply voltage. Further the results of folded cascode operational amplifier are compared with simple two stage operational amplifier and two stage cascode operational amplifier.
KEYWORDS: CMOS, Folded Topology, Folded Cascode Amplifier (FCA), Folded Cascode Operational Amplifier (FCOA), Sigma Delta Modulator, Analog to Digital Converter (ADC)
INTRODUCTION Operational amplifiers (op amps) are an integral part of many analog and mixed-signal systems. Opamps with vastly different levels of complexity are used to realize functions ranging from dc bias generation to high-speed amplification or filtering, analog to digital conversion etc. Here we are likely to use this FCOA in sigma delta modulator as analog to digital converter (ADC). Sigma delta modulator is an oversampling converter and require high loop gain. Fully differential output operational amplifiers are widely used because they provide a large output voltage swing and they are less susceptible to common-mode noise than the single-ended versions. Fully differential amplifiers are used in a noisy environment when external noise can mask low input signals. Also, the differential operation in switchedcapacitor analogue circuits is a good way to minimize the influence of clock feedthrough and charge injection. A disadvantage of fully differential operational amplifiers is the fact that they require the use of a common mode feedback (CMFB) circuit to control the common-mode output voltage. This paper deals with the analysis and design of CMOS op amps. Following a review of performance parameters, the simple folded cascode amplifier and then folded cascode operational amplifier topologies are described. Next, we studied two-stage and gain-boosting configurations and the problem of common-mode feedback. Also the complete biasing and buffering for FCOA is also described in detail. Finally, we have introduced the concept of slew rate and analyze the effect of supply rejection and noise in op amps. In order to achieve fast settling time and high dc gain, the folded-cascode operational amplifier is used in many analog circuit designs. The cascode configurations can be used to design high voltage gain of CMOS transistor amplifier. The stage gain of the folded-cascode amplifier can be increased to increase the voltage gain output volts a range, current sourcing/sinking capability.
224
Ratnaprabha W. Jasutkar, P. R. Bajaj & A. Y. Deshmukh
CONCEPT OF CASCODE TOPOLOGY The cascade of a common source stage and common gate stage is called a “Cascode” topology, providing many properties. The idea behind the cascode structure is to convert the input voltage to a current and apply the result to a common gate stage. The different types cascode amplifiers include.
Simple Cascode Amplifier
Multi – level cascode Amplifier
Gain boosted Cascode Amplifier
Folded Cascode Amplifier
Folded Cascode Amplifier Folded-cascode amplifier circuit with proper biasing with the source terminal of M1 at VDD and at a suitable bias voltage at VB is shown in figure 1. Folded cascode amplifier offer more freedom to choose the DC input voltage at Vin (such as figure 1(a)), higher voltage swing, convenience in shorting the input and the output in feedback configurations. In Figure 1, I1 is the current flowing through M3 and is equal to the sum of ID1 and ID2, VTH1 = VTH. When Vin >VDD-IVT1I, M1 is off and M2 carries all of I1 yielding V out =VDD-I1RD.For Vin < VDD-IVT1I, M1 turns on in saturation. As Vin drops, ID2 decreases future, falling to zero if ID1=I1(Vin =Vin1). If Vin < Vin1, M1 enters triode region.
Figure 1: Folded Cascode Amplifier
Figure 2: Large Signal Characteristics of Folded Cascode Amplifier
Design of 1V, 0.18Âľ Folded Cascode Operational Amplifier for Switch Capacitor Sigma Delta Modulator
225
FOLDED ASCODE OPERATIONAL AMPLIFIER The operational amplifier (op-amp) is a fundamental building block in analog integrated circuit design. Figure 3 Shows the architecture of an opamp called folded cascode opamp. This opamp uses cascoding in the output stage combined with an unusual implementation of differential amplifier to achieve good input common mode range. Thus the folded cascode opamp exhibits self compensation, good input common mode range and gain of two stage opamp.
Figure 3: Folded Cascode Operational Amplifier Figure 3 presents a basic fully differential folded cascode operational amplifier [8]. It is a two stage amplifier. The input stage is a differential output differential folded cascode amplifier with the transistors M1-M2. The high gain of this stage is a result of the cascode current mirrors M5-M8 and M9-M12. The nMOS devices M1 and M2 are chosen as the input differential pair because of larger transconductance compared to pMOS devices. The output stage is a common source amplifier with the transistors M13-M16. It is designed to drive resistive loads. Special attention is dedicated to the design of the output transistors in order to obtain a high voltage swing. The frequency compensation network consists of the compensation capacitors Ccp and Ccm and zero-nulling resistors Rcp and Rcm. The common mode feedback (CMFB) circuit is used in a fully differential operational amplifier to keep the operational amplifier outputs balanced around a known voltage VCM. The common mode feedback (CMFB) amplifier is shown in Figure 4. The common mode output voltage is detected by the resistive divider R1 and R2. One side of the large and equal resistors R1 and R2 is connected at the gate of MC1, where the common voltage is detected, while the other side of the resistors is connected to the basic FDFC amplifier output nodes vOUTP and vOUTM (Figure 3), respectively. The resistors R1 and R2 have to be large to prevent the gain loss of the output stage of the basic FDFC amplifier. On the other hand, the large resistances R1 an R2 and the parasitic gate-source capacitance of MC1 form the RC network that slows down the common mode detection. From the stability consideration, the common mode detection must be fast enough in order to ensure the stability of the whole amplifier. To ensure that the balance is maintained at high speed, two equal capacitors C1 and C2 are added in parallel with the resistors R1 and R2. At high frequencies the impedance of the capacitors becomes dominant, lowering down the total impedance. The value of the resistors is a trade-off between the fast common voltage detection and the gain
226
Ratnaprabha W. Jasutkar, P. R. Bajaj & A. Y. Deshmukh
of the output stage. The CMFB amplifier must have enough gain to ensure good tracking between the common voltage VCM and the detected common voltage at the outputs, which is equal to (vOUTP + vOUTM)/2.
Figure 4: Common Mode Feedback Circuit High gain is achieved by cascade connected active loads. The CMFB amplifier output is VCMFB. This common mode voltage regulation is applied to the gates of the transistors M7 and M8 of the FCOA amplifier in Figure 3. This is the best point for the regulation with respect to the stability of the circuit. The biasing circuit is shown in Figure 5. The voltages VBIASP2, VBIASP1, VBIASN1 and VBIASN2 determine all biasing currents for the FCOA operational amplifier in Figure 3 and the CMFB amplifier in Figure 4. The biasing current is controlled by the current source IBIAS. The transistors MB9-MB11 with transistors MB14 and MB15 form a low voltage wide-swing current source [7-8]. This type of source, that mirrors currents in input stage of basic amplifier, is necessary because of the stack of the transistors M3, M4 and M9-M12 in Figure 3. The series connection of the transistors MB9MB11 is used instead of a single nMOS transistor with longer channel. The usage of the series connection is also applied to the transistors MB16-MB18.
Figure 5: Biasing Circuit of Folded Cascode Opamp Design of Folded Cascode Operational Amplifier Design of the op-amp consists of determining the specifications, selecting device sizes and biasing conditions, compensating the op-amp for stability, simulating and characterizing the op-amp AOL (open-loop gain), CMR (commonmode range on the input), CMRR (common-mode rejection ratio) and PSRR (power supply rejection ratio).
Design of 1V, 0.18µ Folded Cascode Operational Amplifier for Switch Capacitor Sigma Delta Modulator
227
Table 1: Design Specifications Parameters Voltage Gain Unity Gain Bandwidth CMRR Slew Rate Voltage Supply
Values 50dB 140MHz 60dB 15 V/usec ± 1V
Figure 6: AC Equivalent Circuit of FCOA Design Equations for the Folded Cascode Opamp The folded cascode opamp does not required perfect balance of current in the differential amplifier because excess dc current can flow into the current mirror. The biasing current I 11, I5, I6 of folded cascode opamp should be designed so that the dc current in cascode mirror never goes to zero. If the current go to zero its requires a delay in turning the mirror back on because of the parasitic capacitance that must be charged.
Selection of bias current I11 SR =
I11 CL
(1)
I11 = SR.CL
Selection of bias currents in the output cascodes I5 = I6 are selected such that there should not zero current in the output cascades I5 = I6 = 1 .2 I11 to 1.5 I11
(2)
Maximum output voltage Vout(max)
S6
8I 6 K V 2 SD 5
(3)
S4
8I 4 K V 2 SD 4
(4)
' p
' p
Let S5 = S6 and S3 = S4
VSD6 (Sat) = VSD4 (Sat) =
VDD - Vout (m in) 2
Minimum output voltage Vout (min)
(5)
228
Ratnaprabha W. Jasutkar, P. R. Bajaj & A. Y. Deshmukh
S10
8 I 10 K p' V 2 SD10
(6)
S8
8I 8 K V 2 SD8
(7)
' p
Let S9 = S10 and S7 = S8 VDS8 (Sat) = VDS11 (Sat) =
Vout (min) V SS
(8)
2
Determination of Gain bandwidth (GB)
GB
g m1 CL
S1 S 2
g m2 1 GB 2C L2 K N' I11 K N' I11
(10)
Minmum input at common mode\
S11
2 I11
K Vin (min) VSS ' N
(9)
I11 K N' S1
VT 1
2
(11)
Maximum input at common mode
S5 S6
2I 5 K VDD Vin (m ax) VT 1 ' p
(12)
S5 and S6 must meet or exceed the requirement of step 3.
Differential voltage gain
AV
Vout g m1 g m2 RII Vin 2 2(1 K )
2 K AV g m1 RII 2 2K where K
(13)
R8 ( g ds 2 g ds 5 ) g m 4 rds 4
RII gm8rds8rds11 gm4rds 4 rds 2 rds 6
Power dissipation
Pdiss VDD VSS I 12 I 11 I 9 I 10
(14)
Design of 1V, 0.18Âľ Folded Cascode Operational Amplifier for Switch Capacitor Sigma Delta Modulator
229
SIMULATION RESULTS Differential Voltage Gain(Avd) The differential voltage gain of an opamp is defined as Avd ď&#x20AC;˝
Vod Vid
This is also the small signal ac. Voltage gain decreases with increasing frequency after the system encounters its first pole. Thereafter, this gain decreases at 20 dB/decade until it reaches another pole after which the drop rate becomes 40 dB/ decade and so on. Differential Gain Bandwidth Product GBW The differential gain bandwidth product (GBW) is equal to the unity gain frequency (W) since out system is a dominant pole system. The gain bandwidth product should ideally be equal at any frequency. In other words, it indicates that with the increase in the gain of system bandwidth suffers and vice versa. Phase Margin
Figure 7: Transient Response of FCOA For a system to be stable it is very important to maintain a certain phase margin A system having phase margin less than 45 degrees is considered unstable. Similarly a large phase margin like 100 degrees, though acceptable makes the system response slow
Figure 8: AC Response of FCOA
230
Ratnaprabha W. Jasutkar, P. R. Bajaj & A. Y. Deshmukh
Common Mode Rejection Ratio (CMRR) Common Mode Rejection Ratio is a measure of the op amp which tells how good the op amp is at rejecting common mode signal at it two inputs. The CMRR of an ideal op amp is infinity. For all practical op amps, this value should be as high as possible. The CMRR is given by CMRR ď&#x20AC;˝
Adm Where Adm is Differential Mode Gain, Acm is Common Mode Gain. Acm
Slew Rate (SR) Slew Rate is the measure of an op-amps speed to respond to pulse edges at its inputs. For sharp rising edges at its inputs, the output of the op amp rises/ falls with a finite delay. We want this delay to be as low as possible. In other words, the output should have a slope as high as possible. The slew rate is approximately given by
SR ď&#x20AC;˝
dVout Volts /usec. dt
Figure 9: Response of FCOA to Square Signal Table 2: Comparison between Different Types of Opamps Parameters Max. gain UGB Phase margin
Two-Stage Opamp 16.62db 7.19KHz 88.370
Cascode Opamp 6.10db 77.43MHz 91.660
Folded Cascode Opamp 31.59db 125.60MHz -96.590
Figure 10: Frequency Response of Different Operational Amplifiers
Design of 1V, 0.18µ Folded Cascode Operational Amplifier for Switch Capacitor Sigma Delta Modulator
231
CONCLUSIONS Folded Cascode Operational amplifier is designed and implemented for given specification and then results are compared with simple two stage opamp and two stage cascode opamp . Folded cascode Opamp Amplifier (FCOA) provide amplification to the input voltage in the range of 100mV to 1.0V with maximum differential gain of 34.15db .It offer large unity gain bandwidth of 125.60MHz which is nearly double the bandwidth of simple cascode Opamp. It provide good common mode rejection capability with CMRR of 62.68db .Also the output response time of FCOA is less with the slew rate of 13.33V/usec. Folded cascode Opamp gives highest unity gain bandwidth which is nearly double the simple cascode Opamp and 10,000 times the two stage of Opamp. FCOA provide the highest differential gain with good circuit stability. AS FCOA provides high differential gain ,high unity gain bandwidth and CMRR, it can be used in electronic circuits of wide frequency range from very low like biomedical signals to radio frequencies.
REFERENCES 1.
K. Bult and G. Geelen, "A fast-settling CMOS op amp for SC circuits with 90-dB DC gain," IEEE J. Solid-state Circuits, VOL. 25, NO. 6, Dec. 1990,pp. 1379-1384.
2.
J. Lloyed and H.-S. Lee, " A CMOS op amp with fullydifferential gain-enhancement,'' IEEE Trans. On Circuits and Systems 11: Analog and Digital signal processing, Vol. 41, No.
3.
P. C. Yu, H.-S. Lee, "A 2.5-V, 12-b, 5-MSample/s pipelined CMOS ADC," IEEE Journal of Solid-state circuits, Vol. 31, No. 12, December 1996, pp. 1854-1861.
4.
S. H. Lewis, H. S. Fetterman, G. F. Gross, Jr., R. Ramachandran, and T. R. Viswanathan, "A 10-b 20-Msample/s analog-to digital converter," IEEE J. Solid-State Circuits, vol. 27, pp.
5.
K. Y. Kim, N. Kusayanagi, and A. A. Abidi, "A lO-b, 100-MS/s CMOS AID converter," IEEE J. Solid-state Circuits, vol. 32
6.
E. Opris, L. D. Lewicki and B. C. Wong, "A single-ended 12-bit 20Msample/s self-calibrating pipeline A/D converter" , IEEE Journal of Solid-state circuits, vol. 33, No. 12, December 1998
7.
D. Fu, K. Dyer, S . Lewis, and P. Hurst, "Digital background calibration of a 10-b 40 MSls parallel pipelined ADC," in Proc. Int. Solid-state Circuits Conf., Feb. 1998, pp. 140-141.
8.
K. Dyer, D. Fu, S. Lewis, and P. Hurst, "Analog background calibration of a 10-b 40 MSls parallel pipelined ADC," in Proc. Int. Solid-state Circuits Conf., Feb. 1998, pp. 142-143
9.
Benjamin J. Blalock, Phillip E. Allen “Designing 1V Opamp using standard Digital CMOS Technology” , IEEE and Gabriel A. Rincon-Mora.
10. Xin Jiang, Sanghyun Seo and Yumin Lu “A CMOS single stage fully differential Opamp with 120db DC gain” , EECs Dept. University of Muchigan at Ann Arbor, MI. 11. Kimmolasanen, Elvi Raisansen-Ruotsalaisen, Juha Kostamovaara “A 1V-5uw CMOS opamp with bulk driven input transistors”, University of Oulu, Finland. 12. P. E. Allen and D. R. Holberg, “CMOS Analog Circuit Design”, 2nd edition, Oxford University Press, 2002.
232
Ratnaprabha W. Jasutkar, P. R. Bajaj & A. Y. Deshmukh
13. Randall L. Geciger, Phillip E. Allen and Noel R. Strades, “VISI Design Techniques for analog and digital circuit“ 14. R. Jacob Backer, harry W. Li, David E. Boyce, “CMOS circuit Design, Layout and Simulation”.