Chapter 9
Frequency Response of Circuits and Filters

m9.4 Cascaded Active Filters

A telephone line provides sufficient bandwidth (3 kHz) for intelligible voice conversations, but human hearing has a much higher bandwidth, typically 20 Hz to 20,000 Hz.

1. Design an active bandpass filter to mimic the bandwidth of a telephone line subject to the following constraints:
   1. Cascade a first-order active lowpass filter and a first-order active highpass filter,
   2. Set the corner frequencies to 300 Hz and 3.0 kHz,
   3. Set the passband gain to 0 dB,
   4. Choose resistors in the range 1.0 kΩ to 100 kΩ, and
   5. Use a total of four fixed-value resistors and two fixed-value capacitors selected from the parts listed in Appendix A.

   Draw the schematic diagram of your finished design.

2. Predict the performance of your finished design by calculating the following values:
   1. Low-frequency passband corner in Hz,
   2. High-frequency passband corner in Hz, and
   3. Passband gain in dB.

NI Multisim Measurements

1. Enter your bandpass filter.
2. Plot the frequency response of the filter over the audio frequency range 20 Hz to 20 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.
3. Evaluate the performance of your design by measuring the following values:
   1. Low-frequency passband corner in hertz (move cursor to -3.0 dB and read its frequency),
   2. High-frequency passband corner in hertz, and
   3. Passband gain in decibels.

NI myDAQ Measurements

1. Build your bandpass filter. 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 audio frequency range 20 Hz to 20 kHz with the ELVISmx Bode Analyzer. Increase “Steps” as needed to plot a smooth curve.
3. Evaluate the performance of your design by measuring the following values with cursors:
   1. Low-frequency passband corner in hertz (move cursor to -3.0 dB and read its frequency),
   2. High-frequency passband corner in hertz, and
   3. Passband gain in decibels.

Additional helpful tips:

• You can obtain more accuracy on the low- and high-frequency corners by sweeping the frequency over a narrow range that brackets the frequency of interest and substantially increasing the number of sweep steps.

Further Exploration with NI myDAQ

Listen to the audible effects of your telephone line emulator:

1. Remove the AO0 connection,
2. Connect your audio player’s output to your filter’s input using the 3.5 mm stereo audio cable included with your NI myDAQ product; use test leads to connect the left channel similar to the connection pictured in Figure m4.2a.
3. Connect your headphones to the filter output; 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),
4. Play music through your filter, and
5. Compare the sound of the music “with filtering” and “without filtering” by temporarily shorting the high-pass filter capacitor and disconnecting the low-pass filter capacitor. 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.

For more sophistication, use the DG413 analog switch to conveniently engage or disengage the telephone line emulator under control of one of the myDAQ DIO digital outputs. Use one normally-open switch and one normally-closed switch for single-line control of the two switches necessary to engage/disengage the filter.