Lab 4: AC Generation, Measurements and Filters

by · February 3, 2023

Apparatus

  1. Signal Generator
  2. Oscilloscope
  3. Two Resistors: R=5\mathrm{k}\Omega
  4. Two Capacitors: C=10\mathrm{nF}

Procedure

Values Verification

Low-Pass Filter in Time-Domain

Figure 1: RC Low-pass Filter Circuit
  1. Set V_1 to be a square-wave input with frequency of 100Hz and voltage of 5\mathrm{V_{PP}} (no offset).
  2. Capture the graphs (CH1: v_x and CH2: v_y) during positive and negative step functions.
  3. Measure the time where the output voltage rises to half of the input voltage t_\mathrm{half} and calculate time time constant \tau_\mathrm{meas} by \tau_\mathrm{meas} = \frac{t_\mathrm{half}}{\mathrm{ln(2)}}.
  4. Verify that the system reaches steady-state around 2\pi\tau.

High-Pass Filter in Time-Domain

Figure 2: RC High-pass Filter Circuit
  1. Set V_1 to be a square-wave input with frequency of 100Hz and voltage of 5\mathrm{V_{PP}} (no offset).
  2. Capture the graphs (CH1: v_x and CH2: v_y) during positive and negative step functions.

Band-Pass Filter in Time-Domain

Figure 3: Cascaded LPF and HPF to construct a Band-pass Filter Circuit
  1. Set V_1 to be a square-wave input with frequency of 100Hz and voltage of 5\mathrm{V_{PP}} (no offset).
  2. Capture the graphs (CH1: v_x and CH2: v_y) during positive and negative step functions.

Low-Pass Filter in Frequency-Domain

Figure 1: RC Low-pass Filter Circuit
  1. Set V_1 to be a sinusoidal input with frequency of 2 krad/s and voltage of 5\mathrm{V_{PP}} (no offset).
  2. Capture the graphs (CH1: v_x and CH2: v_y) and record the output voltage and phase.
  3. Change the frequency to 20 krad/s and 200 krad/s then record the values.

High-Pass Filter in Frequency-Domain

Figure 2: RC High-pass Filter Circuit
  1. Set V_1 to be a sinusoidal input with frequency of 2 krad/s and voltage of 5\mathrm{V_{PP}} (no offset).
  2. Capture the graphs (CH1: v_x and CH2: v_y) and record the output voltage and phase.
  3. Change the frequency to 20 krad/s and 200 krad/s then record the values.

Band-Pass Filter in Frequency-Domain

Figure 3: Cascaded LPF and HPF to construct a Band-pass Filter Circuit
  1. Set V_1 to be a sinusoidal input with frequency of 2 krad/s and voltage of 5\mathrm{V_{PP}} (no offset).
  2. Capture the graphs (CH1: v_x and CH2: v_y) and record the output voltage and phase.
  3. Change the frequency to 20 krad/s and 200 krad/s then record the values.