Chapter 9
Frequency Response of Circuits and Filters

m9.1 Scaling

Figure m9.1 shows a prototype bandreject filter with center frequency ω0 = 1 rad/s. The prototype component values are R = 1 Ω, L = 1.817 H, and C = 0.5505 F.

  1. Apply magnitude and frequency scaling to the bandreject filter so that R′ = 100Ω and L′ = 33 mH. Draw the finished circuit diagram.
  2. Determine the center frequency in Hz of the scaled bandreject filter.

PIC


Figure m9.1: Circuit for Problem m9.1

NI Multisim Measurements

  1. Enter the circuit of Figure m9.1 using the scaled component values calculated earlier. 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 100 Hz to 10 kHz with Simulate → Analyses → AC Analysis. Change “Vertical Scale” to “Linear” and increase “Number of points per decade” as needed to plot a smooth curve. Use a cursor to identify the filter’s center frequency.
NI Multisim video tutorials:

NI myDAQ Measurements

  1. Build the circuit of Figure m9.1 using the scaled component values calculated earlier. Drive the filter input with AO0 strengthened by an op amp voltage follower. Monitor the filter input with AI0 and the filter output with AI1.
  2. Plot the frequency response of the filter over the range 100 Hz to 10 kHz with the ELVISmx Bode Analyzer. Change “Mapping” to “Linear” and increase “Steps” as needed to plot a smooth curve. Use a cursor to identify the filter’s center frequency.
NI myDAQ video tutorials:

Further Exploration with NI myDAQ

NI Multisim provides a way to compare simulated results and physical measurement results from NI myDAQ on the same ELVISmx instrument. Study the video tutorial below to learn how to simultaneously display simulated and measured frequency response on the ELVISmx Bode Analyzer, and then do the following:

  1. Plot the frequency response of the simulated and physical circuit of Figure m9.1 using the scaled component values calculated earlier. Compare the two plots and discuss their similarities and differences.
  2. The simulated circuit is a model of the physical circuit and may not capture every phenomenon of the real circuit. Recall that an inductor is formed by hundreds of turns of very fine (small diameter) wire, consequently the small yet finite resistance per unit length adds up to form a significant resistance. Measure the resistance of your inductor with the myDAQ DMM and then place a resistor with this value in series with the ideal inductor in your Multisim circuit. Re-run the simulator. Compare the two plots and discuss the performance of the improved circuit model.
NI Multisim video tutorials: