Frequency and Step Responses of First-Order Passive Filters

Prelab:

1. Design a passive first-order RC low-pass filter with cutoff frequency f_H = 10 KHz. Derive the step response, voltage transfer function, and sketch Bode plots (magnitude and phase).

2. Design a passive first-order RC high-pass filter with cutoff frequency f_L = 1 KHz. Derive the step response, voltage transfer function, and sketch Bode plots (magnitude and phase).

Experiments:

1. Build and test the low-pass filter designed in part 1 of the Prelab.

a. Using a sine-wave input voltage of magnitude 1V, measure f_H of the filter.

b. Keeping the input voltage magnitude constant, measure the output magnitude and time shift of the output waveform at several different frequency (i.e. 100 Hz, 500Hz, 1KHz,..., 1MHz). use this data to generate Bode plots of A_v and phase.

c. Apply a square-wave input voltage of magnitude 1V with f = 1.0 f_H. Sketch the step response of the filter and measure the time constant t.

2. Repeat Experiments 1  for the high-pass filter designed in part 2 of the Prelab.

Postlab: Submit a written report.

1. Compare the measured and theoretical values of f_H, f_L, and t.

2. Use Excel or MATLAB to plot the data measured in Step 1(b). compare these plots with the theoretical Bode plots from the Prelab.

3. Compare the observed step response with the theoretical response.