Chapter 9
Frequency Response of Circuits and Filters

m9.3 Filter Order

The filter circuit shown in Figure m9.3 uses the component values R = 1.0 kΩ and C = 1.0 μF.

  1. Obtain an expression for H(ω) = Vo/Vi in standard form.
  2. Substitute ω = 2πf to express H(ω) in terms of oscillation frequency f in Hz.
  3. Generate spectral plots for the magnitude and phase of H(f).
  4. Determine the cutoff frequency fc.

PIC


Figure m9.3: Circuit for Problem m9.3

NI Multisim Measurements

  1. Enter the circuit of Figure m9.3. Drive the filter input with an AC_VOLTAGE source with “AC Analysis Magnitude” set to 1 V.
  2. Plot the frequency response of the filter over the range 1 Hz to 10 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. Use cursors to measure the cutoff frequency fc (look for a change of 3 dB in magnitude).
NI Multisim video tutorials:

NI myDAQ Measurements

  1. Build the circuit of Figure m9.3. 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 1 Hz to 10 kHz with the ELVISmx Bode Analyzer. Increase “Steps” as needed to plot a smooth curve.
  3. Use cursors to measure the cutoff frequency fc (look for a change of 3 dB in magnitude).
NI myDAQ video tutorials:

Further Exploration with NI myDAQ

Listen to the output of the Bode Analyzer to develop a more intuitive feel for its operation. Connect AO0 AGND to your headphones similar to the connection pictured in Figure m4.2a; connect the filter output to both the right and left channels for best listening (the middle ring of the audio plug carries the right channel signal). Comment on your listening experience.

IMPORTANT – PROTECT YOUR HEARING!
Do NOT disturb your circuit connections while you are wearing earphones. Accidently shorting together circuit connections can produce a very loud and unexpected noise. Alternatively, use a speaker to listen to the amplifier output or hold the earphones some distance from your ears.