Chapter 9
Frequency Response of Circuits and Filters

m9.2 Bode Plots

For the circuit in Fig. m9.2:

1. Determine the voltage transfer function H(ω) of the filter circuit. Write your finished result in standard form for creating a Bode plot.
2. Substitute ω = 2πf to express the voltage transfer function in terms of oscillation frequency f in Hz.
3. Generate Bode magnitude and phase plots for H(f) using oscillation frequency f as the independent variable. Use the following component values: R₁ = 3.3 kΩ, R₂ = 10 kΩ, C₁ = 0.01 μF, and C₂ = 0.1 μF.
4. Determine the following filter circuit properties by inspecting the Bode plot:
   1. Low-frequency asymptotes for magnitude and phase
   2. High-frequency asymptotes for magnitude and phase
   3. Corner frequencies (this filter circuit has two such frequencies)

NI Multisim Measurements

1. Enter the filter circuit of Figure m9.2. Drive the filter input with an AC_VOLTAGE source with “AC Analysis Magnitude” set to 1 V. Use the three-terminal virtual op amp model OPAMP_3T_VIRTUAL.
2. Plot the frequency response of the filter over the range 10 Hz to 100 kHz with Simulate → Analyses → AC Analysis. Set “Vertical Scale” to “Decibel” and “Sweep Type” to “Decade” to create a standard Bode plot presentation of frequency response. Increase “Number of points per decade” as needed to plot a smooth curve.
3. Determine the following filter circuit properties by inspecting the frequency response plot with cursors:
   1. Low-frequency asymptotes for magnitude and phase
   2. High-frequency asymptotes for magnitude and phase
   3. Corner frequencies; look for a change of 3 dB in magnitude from an asymptote

NI myDAQ Measurements

1. Build the filter circuit of Figure m9.2. Drive the filter input with AO0. Monitor the filter input with AI0 and the filter output with AI1.
2. Plot the frequency response of the filter over the range 10 Hz to 10 kHz with the ELVISmx Bode Analyzer; note that this frequency range omits the last decade compared to your analytical and simulation work. Increase “Steps” as needed to plot a smooth curve. IMPORTANT: Set “Peak Amplitude” to 1 volt.
3. Determine the following filter circuit properties by inspecting the frequency response plot with cursors:
   1. Low-frequency asymptotes for magnitude and phase
   2. High-frequency asymptotes for magnitude and phase
   3. Corner frequencies; look for a change of 3 dB in magnitude from an asymptote

Additional helpful tips:

• The low- and high-frequency phase asymptotes of any filter are always integer multiples of 90^∘. If the phase plot does not seem to flatten out enough, simply estimate the trend to the closest integer multiple of 90^∘.

Further Exploration with NI myDAQ

Use the technique described in the video tutorial below to simultaneously display the simulated and measured frequency response with the ELVISmx Bode Analyzer. You may need to set “Op-Amp Signal Polarity” to “Inverted” to make the measured phase response overlay the simulated response.

Discuss the level of agreement between the two plots and explain any discrepancies you observe.