Chapter 13
Fourier Analysis Techniques

m13.2 Circuit Applications

The sawtooth voltage waveform v_s(t) shown in Figure m13.2 with A = 5 V and T = 2 ms serves as the input to the circuit of Figure m13.2b.

1. Determine the Fourier series representation of v_o(t).
2. Plot v_o(t) and v_s(t) with MathScript or MATLAB as follows:
   1. Time 0 ≤ t ≤ 5 ms,
   2. Sum of n_max = 100 terms, and
   3. Circuit components R = 5.6 kΩ and C = 0.1 μF.

   Use sufficient time resolution to display Gibbs phenomenon ringing.

3. Measure the maximum value of v_o(t) from the plot, and also measure the first time at which the maximum value occurs after t = 0.

NI Multisim Measurements

1. Enter the circuit of Figure m6.4 using the same component values listed in the problem statement. Drive the circuit input with a TRIANGULAR_VOLTAGE source configured with the amplitude and period specified in the problem statement.
2. Plot v_o(t) and v_s(t) using Simulate → Analyses → Transient analysis. Extend the plot time to 7 ms to allow the output to reach AC steady-state. Increase the minimum number of time points as needed to produce a smooth plot.
3. Measure the maximum value of v_o(t) with the Grapher View cursors, and also measure the first time at which the maximum value occurs after t = 0; ignore the transient start-up behavior during the first period.

NI myDAQ Measurements

1. Build the circuit of Figure m6.4 using the same component values listed in the problem statement. Drive the circuit input with AO0 and use the ELVISmx Arbitrary Waveform Generator to produce the sawtooth waveform of Figure m13.2 with the amplitude and period specified in the problem statement. Monitor the input voltage v_s(t) with AI0 and the output voltage v_o(t) with AI1.
2. Display v_s(t) and v_o(t) on the ELVISmx Oscilloscope.
3. Use the oscilloscope cursors to measure the maximum value of v_o(t) and the first time at which the maximum value occurs after t = 0.