Frequency Response of a Circuit to an Arbitrary Periodic Signal Objectives:
- Determine the transfer function of a circuit with an operational amplifier
- Generate a Bode plot for the circuit
- Represent an arbitrary periodic signal as a function using Heaviside and other functions
- Use Fourier series to break the signal into a series of sinusoidal functions
- Perform circuit analysis on the individual sinusoids to predict the output of the circuit
Procedure:
- Determine the transfer function of the circuit included in this handout. Use of MATLAB is not only permitted, it is encouraged.
- Generate a Bode plot over a reasonable range of frequencies. (Label all axes, units, and remember to include both plots)
- Examine the signal included in this handout to be used as the input (VI) to the circuit. Represent the signal as a function of time. Plot your function and compare it to the desired signal.
- Use Fourier series to determine the coefficients (ak and bk) for the signal. Find coefficients for k=0 to 200. Plot the two coefficients on the same plot against the frequency of each.
- Estimate the original signal from a summation of sinusoids and plot it with your function found above. Use the same time domain as the one shown in this handout.
- Use the transfer function you found earlier and/or additional circuit analysis to predict the output of the circuit to the signal provided. Plot the input signal along with your predicted output using the same time domain as the one shown in this handout