I'm studying a Phase Locked Loop used for FM demodulation, obviously a phase detector is used in the system.
A basic implementation of a phase detector is a multiplier followed by a lowpass filter. I am a bit confused on how to select the cutoff frequency of this lowpass filter.
I know that the multiplication of the two signals will produce two signal components:
1) A component where the carrier frequency has been doubled.
2) A component where the carrier frequency has been eliminated. This produces a "phase error" component.
I know that the purpose of the lowpass filter is to isolate the "phase error" component but I am confused at what frequencies the "phase error" contains.
I'll setup an example with relatively simple numbers to illustrate my confusion:
Carrier Frequency : 1MHz
Peak Frequency Deviation : 75kHz (I believe this is common for U.S. radio stations?)
Max Frequency of Original Unmodulated Message : 25kHz
FM Modulation Transmission Bandwidth : Carsons Rule: 2*(peak frequency deviation) + 2*(Max message frequency) = 200kHz
This would mean that the incoming modulated signal would have a frequency range from 800kHz to 1200kHz. This means that after the multiplier in the phase detector, the double frequency component would change to a range of 1600kHz to 2400kHz. In this case, would I select the cutoff frequency of the lowpass filter to be below 1600kHz so as to eliminate these higher frequencies?
Or is it that without the carrier frequency, the remaining frequencies are centered around 200kHz so that the "phase error" component contains frequencies from 0Hz to 400kHz? This would be because the frequency needs to be able to deviate 200kHz +- from the center point as this is the transmission bandwidth? In this case the cutoff frequency would be ~400kHz.
Or at this point in the phase locked loop, would the message already be demodulated so that the maximum cutoff frequency would be near 25kHz?
I suppose my confusion is rooted in what frequencies remain in the "phase error" component that has the carrier frequency removed.
So I'm still a bit confused on the lowpass behavior of the loop as referred to in an answer below. I understand that the integrator has a laplace transformation of 1/s but when I actually find the loop transfer function it appears to have high pass behavior instead. Below is a photo of what I mean.
To me this looks like a high pass behavior?
Confusion lied in that I was viewing the system from an output/input relationship rather than an input/output relationship in which the lowpass behavior is indeed present.