Chapter 13
Fourier Analysis Techniques

m13.4 Circuit Analysis with Fourier Transform

The circuit of Figure m13.4a is excited by the double-pulse waveform shown in Figure m13.4b.

  1. Derive the expression for vo(t) using Fourier analysis.
  2. Plot vs(t) and vo(t) on the same graph over the time span 0 ≤ t ≤ 5 ms with MathScript or MATLAB for the following values: A = 5 V, T = 1 ms, R = 5.6 kΩ, and C = 0.1 μF.
  3. Determine the value of vo(t) at times t = 2 ms and t = 3 ms.

PIC


Figure m13.4: Double-pulse waveform and circuit for Problem m13.4

NI Multisim Measurements

  1. Enter the circuit of Figure m13.4 using an ABM_VOLTAGE source and the component values specified in the problem statement. Build the ABM voltage source “Voltage Value” string with multiple step functions u(TIME). Add, subtract, and delay the step functions as needed to create the double-pulse waveform of Figure m13.4 with the parameters specified in the problem statement.
  2. Set up a Simulate → Analyses → Transient to plot vs(t) and vo(t) over the time span 0 ≤ t ≤ 5 ms. Choose “Set to zero” for the “Initial Conditions” parameter to properly model a discharged capacitor before the first pulse occurs. Increase the minimum time step as necessary to obtain a smooth plot at discontinuities.
  3. Use the Grapher View cursors to measure the value of vo(t) at times t = 2 ms and t = 3 ms.
NI Multisim video tutorials:

NI myDAQ Measurements

  1. Build the circuit of Figure m13.4 using the component values specified in the problem statement. Drive the circuit with the ELVISmx Arbitrary Waveform Generator on AO0. Create the double-pulse waveform of Figure m13.4 with the parameters specified in the problem statement. Monitor vs(t) on AI0 and vo(t) on AI1.
  2. Display vs(t) and vo(t) on the ELVISmx Oscilloscope. Adjust the settings for a time span of 5 ms and an appropriate scale (volts per division) to clearly see the output trace behavior. Adjust the triggering level and horizontal position to place the leading edge of the first pulse at the far left of the display. You will likely need to use the “Run Once” acquisition mode to obtain a stable display; click “Run” repeatedly until you obtain a satisfactory display.
  3. Use the oscilloscope cursors to measure the value of vo(t) at times t = 2 ms and t = 3 ms.
NI myDAQ video tutorials: