# Whats the principle of a PLL used as demodulator of a FM signal?

I didnt quite understand te following:

A basic PLL consists of the following parts:

• phase detector
• low pass filter
• VCO

If you input a 1MHz sine the PLL will try to lock on it by controlling the VCO. According to what i've found it's possible to demodulate a FM modulated signal.

Assume:

Input signal for example: (Carrier: 1Mhz sine and signal of 50Khz). you get 2 side-band frequenties with the carrier frequention (0.95Mhz, 1.0Mhz and 1.05Mhz).

I want to demodulate the 50Khz signal from the input signal.

From what i've found a DC signal from the Phase Detector is fed to the VCO to keep the PLL locked to the input frequency. My assumption was (i might be wrong) that when you input a signal with multiple frequency components the PLL keeps "re-locking" and the DC voltage fed to the VCO is the same as the difference of the frequention components of my input signal (so 1.0Mhz - 0.95Mhz = 50Khz).

edit:

Ye, there are some misconceptions in my story. With AM modulation you get the frequency components i was talking about (Dual Side-Band Full Carrier).

With FM modulation you have the following formula:

$v_c$ = carrier, $v_m$ = modulator

$v_c = V_c \sin(2 \pi f_c t)$
$v_m = V_m \sin(2 \pi f_m t)$

$f_c$ depends on the modulator voltage so $f_c = f_c + k*v_m$, where k is a amplifier factor.

the complete formula becomes:

$v = V_c \sin(2 \pi (f_c + k v_m) t) \rightarrow v = V_c \sin(2 \pi (f_c + k V_m \sin(2 \pi f_m t)) t)$

• The spectrum of a FM signal can be radically different depending on the modulation index. The Bessel function is used for computing it's components. See the link. – user6972 Jun 11 '13 at 18:07

With FM you get much more than two sideband frequencies. The sidebands you describe sound more like AM (amplitude modulation) sidebands. You may want to supply a link where you get this information from or re-check your information.

Next, in your final paragraph you might be getting confused. At any one moment in time the FM signal you describe will have a frequency that is somewhere between two limits. The limits are called the deviation meaning that's how much the carrier deviates +/- from its nominal centre frequency.

That deviation is nothing to do with the modulating signal's frequency but has everything to do with the modulating signal's amplitude. The bigger the peak amplitude the bigger the deviation from the nominal centre frequency.

If the PLL is designed correctly, and its low-pass filter permits the VCO to track the carrier within the deviation limits, the low-pass filtered signal (that feeds the VCO) will represent the signal that caused the original modulation i.e. the PLL is an FM demodulator.

You also mention "keeps re-locking" - this is not something that should happen in this type of circuit - the PLL will remain locked to the modulated carrier. There will be a slight error in the instantaneous lock because you need an error to drive the mechanism that tries to maintain lock but, this error will be small and this error is not regarded as the PLL losing-lock.

You might also be getting confused with what happens when the spectral content of FM is analyzed. Yes it has several components of frequency but these do not occur together at any one instant - the spectral content is a time averaged evaluation of what the carrier is doing - moving about following the amplitude of the input modulating signal.

## protected by clabacchio♦Jun 11 '13 at 17:58

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