RC Bode Phase and Group Delay

The RC lowpass filter has a voltage transfer function H(iw) = 1 / (1 + iwRC), where the output is taken across the capacitor. Using the normalized frequency parameter u = wRC = f / fc, where fc = 1 / (2πRC) is the corner frequency, we can study the frequency response of the filter.

Examine the Bode responses

Open the RC Bode Phase and Group Delay module and use its controls to see how the frequency affects the transfer function.

1. Set Resistance kiloohms to 10 and Capacitance nanofarads to 1.
2. Set Frequency over corner to 1. Verify that the amplitude gain is approximately 0.707 and the gain in decibels is -3.01.
3. Observe that the phase is -0.785 radians (-45 degrees), and the group delay is 0.000005 seconds. The indicator on the Bode plot will be exactly at the -3 dB point on the gain curve.
4. Change Frequency over corner to 10. The gain decibels will drop to approximately -20 dB, indicating a -20 dB/decade roll-off for the lowpass filter.
5. Set Frequency over corner to 0. This simulates a DC signal where the transfer real part is 1, imaginary is 0, gain is 0 dB, phase is 0, and group delay is at its maximum value of RC = 10 μs.