RC circuit question: In vs. Out phase angle

[Habeebe]

In an RC circuit, the phase angle between the input and output voltages (not current and voltage) seems to be proportional to the amplitude of the output voltage. That is, as the phase angle between input and output goes to plus or minus 90 degrees, the output voltage goes to 0. Why is that?

 

[NascentOxygen]

In an RC circuit, the phase angle between the input and output voltages (not current and voltage) seems to be proportional to the amplitude of the output voltage. That is, as the phase angle between input and output goes to plus or minus 90 degrees, the output voltage goes to 0. Why is that?

Hi Habeebe. Phase does not vary with amplitude of the input. But output amplitude and phase are both frequency-dependent, so over a limited range there may be a roughly linear correspondence. What are the equations you have where you are interpreting there is such a correspondence?

 

[Habeebe]

Experimentally. I'm not getting it from equations. If you have a high pass filter, and you run the input voltage to a low frequency, the phase angle will go to about 90 degrees between input and output while the output voltage goes to some small amount. I don't know or really care about the exact relation between the two numerically, but it appeared as though that phase angle difference was somehow related to the change in output voltage. I'm really more interested in what physically is going on that both things happen together.

 

[berkeman]

Experimentally. I'm not getting it from equations. If you have a high pass filter, and you run the input voltage to a low frequency, the phase angle will go to about 90 degrees between input and output while the output voltage goes to some small amount. I don't know or really care about the exact relation between the two numerically, but it appeared as though that phase angle difference was somehow related to the change in output voltage. I'm really more interested in what physically is going on that both things happen together.

Both the change in amplitude and the phase shift are the result of the ratio of the real impedance of the resistor and the "imaginary" impedance of the capacitor (which varies with frequency). It's easiest to show it by using the math, but another way to think about it is that you are temporarily storing energy in the capacitor voltage with each swing of the AC waveform, whereas you are always just dissipating the energy with the voltage across the resistor.

Think of a resonant system that you excite off of resonance. Like a ball on a spring -- if you wiggle the end of the spring at a frequency that is not the natural resonant frequency of the ball+spring system, then the ball will often move with a phase shift compared to how you are wiggling the spring.

Anyway, here is a typical RC lowpass plot like the behavior you are describing:

https://www.library.cmu.edu/ctms/ctms/matlab42/freq/bode1a.gif
https://www.library.cmu.edu/ctms/ctms/matlab42/freq/bode1a.gif