2026 MECH 370 Lab 6 Experiment (Frequency Response of Passive Electrical Filters) Concordia Universi

2026 MECH 370 Lab 6 Experiment (Frequency Response of Passive Electrical Filters) Concordia University Lab 6: Frequency Response of Passive Electrical Filters

Lab Section EI – X Winter 2025 Professor Christopher Yee Wong Concordia University Montreal, QC, Canada

CONTENTS CONTENTS ........................................................................................... 2 LIST OF TABLES AND FIGURES ..................................................................... 3 OBJECTIVE .......................................................................................... 4 INTRODUCTION ..................................................................................... 4 PROCEDURE ......................................................................................... 5 RESULTS ............................................................................................. 6 EXPERIMENTAL ................................................................................... 6 SIMSCAPE........................................................................................ 12 SAMPLE CALCULATIONS ....................................................................... 23 DISCUSSION........................................................................................ 24 CONCLUSION ...................................................................................... 26 REFERENCES....................................................................................... 26

LIST OF TABLES AND FIGURES Table 1: Experimental Results for LC Low-Pass Circuit Table 2: Experimental Results for LC High-Pass Circuit Table 3: Experimental Results for Single Section RC LPF Circuit Table 4: Experimental results for Twin Section RC LPF Table 5: Experimental Results for BPF Circuit Figure 1: Radian Frequency vs Magnitude Ratio for LC Low and High Pass Circuit Figure 2: Radian Frequency vs Magnitude Ratio for Single and Twin RC LPF Figure 3: Radian Frequency vs Magnitude Ratio for BPF circuit Figure 4: Radian Frequency vs Magnitude Ratio for Double Resonance Circuit Figure 5: Figure 6-2 Simscape [1] Figure 6: Simulation for 1000hz of figure 6-2 Figure 7: Simulation for 5000hz of figure 6-2 Figure 8: Simulation for 10000hz of figure 6-2 Figure 9: Simulation for 15000hz of figure 6-2 Figure 10: Simulation for 20000hz of figure 6-2 Figure 11: Figure 6-4 Simscape [1] Figure 12: Simulation for 1000hz of figure 6-4 Figure 13: Simulation for 5000hz of figure 6-4 Figure 14: Simulation for 10000hz of figure 6-4 Figure 15: Simulation for 15000hz of figure 6-4 Figure 16: Simulation for 20000hz of figure 6-4 Figure 17: Figure 6-6 Simscape [1] Figure 18: Simulation for 1000hz of figure 6-6 Figure 19: Simulation for 5000hz of figure 6-6 Figure 20: Simulation for 10000hz of figure 6-6 Figure 21: Simulation for 15000hz of figure 6-6 Figure 22: Simulation for 20000hz of figure 6-6 Figure 23: Figure 6-4 Circuit Analysis Figure 24: Bode Diagram for Single Section RC Figure 25: Bode Diagram for Twin Section RC

OBJECTIVE The objective of this lab was to analyze the steady-state frequency response of passive RC and LC filters, explore their resonance characteristics, and compare the experimental results with those from computer simulations.

INTRODUCTION An electrical filter can be described as a signal processing circuit which transmits sinusoidal waves within a certain range of frequencies. Waves that are found within said frequency are known as the passband while waves that are out of the range of frequency are referred to as the stopband and are rejected. A passive filter is an example of a filter that uses resistors (R), inductors (L), and capacitors (C), and operates without requiring active components such as amplifiers. This filter can be divided into several categories, including low-pass filters (LPFs), high-pass filters (HPFs), band-pass filters (BPFs), and band-reject filters (BRFs). Each type exhibits unique frequency-response behavior determined by its design and the way its resistive and reactive elements interact.

Resonance is a key concept in which it is responsible for the range of frequencies a circuit will either accept or reject. Resonance can be described as when output value for certain circuits reaches a peak value at some specific frequency. This occurs when the inductive reactance balances out the capacitive reactance, and thus results in an impedance that is purely resistive, leading to either a peak or a dip in the frequency response. The quality factor Q, expressed as Q=, represents how well-defined the resonance is and serves as a measure of the circuit's energy efficiency.

LC type circuits utilize resonance between L and C and have two types of circuits low pass and high pass. Low pass circuits resonate frequency between the natural resonant frequency which is as follows While high pass frequencies allow frequencies in above to pass, this is also based on the resonance concept mentioned above.

In comparison, RC filters lack inductive components and offer gradual signal attenuation without exhibiting any resonance. For RC low-pass filters, the cutoff frequency is given by ω =, with R and C setting the system's time constant. Twin-section RC filters, due to their higher order, provide steeper attenuation than single-section designs.

Bandpass and band reject circuits are LCR circuits that have parallel resonance or series resonance in their LC branches. In these filters the bandpass or stopband will be centered around the natural frequency of the series parallel resonance A double resonance circuit is a circuit which includes two resonance frequencies. These circuits have resonance that occur around the frequency

PROCEDURE 1. Use a multimeter to accurately measure and record the values of R and C, assuming L is 240 μH. 2. Set up the circuits on the RCL Box as shown in Figure 6.9, keeping wiring neat by using short patch cords. Ensure the Function Generator (FG) supplies the input signal, connected to Ch1 of the DPO, while the circuit output is connected to Ch2.

3. Set the FG to generate sinusoidal signals within the 1–20 kHz frequency range, with a peak-to-peak amplitude of around 3 V and no DC offset.

4. Set the DPO to AC input coupling, adjust the sensitivity and time base (or use AUTOSET), and utilize the MEASURE function to display peak-to-peak values on both channels. Record the frequency directly from the FG. 5. For each circuit, vary the FG frequency and record input/output amplitudes. Do this for LC low-pass and high-pass filters, single- and twin-section RC low-pass filters, band-pass or band-reject filter and double resonance circuit.

RESULTS EXPERIMENTAL

Table 1: Experimental Results for LC Low-Pass Circuit

Table 2: Experimental Results for LC High-Pass Circuit

Table 3:

Table 3: Experimental Results for Single Section RC LPF Circuit

Table 4: Experimental results for Twin Section RC LPF

Table 5: Experimental Results for BPF Circuit

Table 6: Experimental Results for Double Resonance Circuit

Figure 1: Radian Frequency vs Magnitude Ratio for LC Low and High Pass Circuit

Figure 2: Radian Frequency vs Magnitude Ratio for Single and Twin RC LPF

Figure 3: Radian Frequency vs Magnitude Ratio for BPF circuit

Figure 4: Radian Frequency vs Magnitude Ratio for Double Resonance Circuit

SIMSCAPE

Figure 5: Figure 6-2 Simscape [1]

Figure 6: Simulation for 1000hz of figure 6-2

Figure 7: Simulation for 5000hz of figure 6-2

Figure 8: Simulation for 10000hz of figure 6-2

Figure 9: Simulation for 15000hz of figure 6-2

Figure 10: Simulation for 20000hz of figure 6-2

Figure 11: Figure 6-4 Simscape [1]

Figure 12: Simulation for 1000hz of figure 6-4

Figure 13: Simulation for 5000hz of figure 6-4

Figure 14: Simulation for 10000hz of figure 6-4

Figure 15: Simulation for 15000hz of figure 6-4

Figure 16: Simulation for 20000hz of figure 6-4

Figure 17: Figure 6-6 Simscape [1]

Figure 18: Simulation for 1000hz of figure 6-6

Figure 19: Simulation for 5000hz of figure 6-6

Figure 20: Simulation for 10000hz of figure 6-6

Figure 21: Simulation for 15000hz of figure 6-6

Figure 22: Simulation for 20000hz of figure 6-6

Figure 23: Figure 6-4 Circuit Analysis

Figure 24: Bode Diagram for Single Section RC

Figure 25: Bode Diagram for Twin Section RC

SAMPLE CALCULATIONS 1

1

𝜔𝑛 = 2⋅𝜋√𝐿𝐶 =

2⋅𝜋√(240⋅10−6)(1.21⋅10−6)

𝑄

=𝜔

𝐿

𝑛𝑅

𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙𝑠𝑒𝑟𝑖𝑒𝑠

= 9339.46 ⋅

= 9339.46 Hz

240⋅10 −6

= 0.112

20

𝑄𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 = 𝜔𝑛 ⋅ 𝐶 ⋅ 𝑅 = 9339.46(1.21 ⋅ 10−6)(20) = 0.226 𝑄{𝑒𝑥𝑝 =

𝜔𝑛 ∆𝜔

=

𝜔𝑛 𝜔𝑐1−𝜔𝑐2

9339.46

= (100380)= 0.093

DISCUSSION 1. The LPF circuit is designed to allow low frequencies to pass and reject higher frequencies, shows a decreasing magnitude ratio after peaking, which then flattens as the frequency increases. This ensures that only lower frequency components are transmitted through the LPF. In contrast, the HPF is showing an increasing magnitude ratio as frequencies rise, indicating its effectiveness in rejecting lower frequencies and allowing higher frequencies to pass through, eventually leveling off to a steady magnitude ratio at higher frequency ranges. These filters are performing optimally, with the LPF filtering out higher frequencies and the HPF eliminating lower frequencies, showing the effectiveness in frequency-selective filtering.[1] 2. Comparing the twin-section and single-section RC Low-Pass Filters (LPF) graphs, both designs showed different performance characteristics. The twin-section LPF is likely to output a more dynamic response with fluctuations in its magnitude ratio, reflecting the ability to define which frequencies are being passed and which are attenuated. This behavior could be due to the additional RC sections, which increase the filter's precision in controlling frequency response. In contrast, the single-section LPF is displaying a smoother, more consistent decrease in magnitude ratio, a characteristic of first-order filters making it ideal for applications that require smooth frequency transitions.[1]

3. The calculated Quality Factor (Q) values for the theoretical and experimental scenarios presented provide insight into the characteristics of the filter under consideration. The theoretical Q values were calculated to be 0.112 and 0.226 for series and parallel RLCcircuits respectively, indicating how effectively the filter can differentiate between desired signal bandwidths. The experimental Q value which was found to be 0.093 is slightly lower, suggesting that in practical settings, the filter may not be as sharp in distinguishing between frequencies close to the cutoff as predicted theoretically. This discrepancy could be attributed to non-ideal components, environmental factors, or calculation errors.

4. Figures 1-4 5. The bode diagrams from figures 24 and 25 have large differences with figure 2. The magnitude for the single section RC circuit only went as far as a bit past –6db while the bode diagram nearly reached –30db. Likewise, the twin section barely passed –5db while the bode diagram nearly reaches –100db. The experimental results also fluctuate while the bode diagram gives a smooth curve.

6. Figures 5-22

SOURCES OF ERROR The main source of error for our results is likely a lack of information about resistor 2 and capacitor 2. These values were not recorded as it was not called for in the lab manual procedure, but they were needed when doing the circuit analysis to get an accurate transfer function for the twin section RC circuit. Other possible error sources could be from the equipment as it is fairly old and used often so calibration may be off. Tolerances on the electrical components also mean that we cannot know for certain the values of the resistors, capacitors or inductors.

CONCLUSION To conclude, this experiment demonstrated the expected frequency-selective behavior of passive RC and LC filters. In the end both the Low Pass and High Pass RC filters were able to only accept signals in their respective frequency ranges as intended. While the Band-Pass filter showed clear signs of both series and parallel resonance. Although our results difference from the theoretical values calculates this can be blamed of the sources of error mentioned above.

Furthermore, we were able to create a Simscape to model this experiment. Differences were found there too proving that the Simscape can sometimes struggle to reproduce exact replicas of real-world circuits. Overall, the experiment successfully demonstrated the fundamental frequency response characteristics of RC and LC filters and provided insight into the relationship between theoretical predictions and experimental outcomes.

REFERENCES [1] W. Storr, “Low pass filter - passive RC filter tutorial,” Basic Electronics Tutorials, https://www.electronics-tutorials.ws/filter/filter_2.html (accessed Apr. 9, 2025).