Classical modulation procedures - Signals, Processes, and Systems - page 256

FM signal

input 1
Multiplier output

Sum frequency
and
difference
frequency
of the 2 inputs

changes frequency
in rhythm with the
source signal

Source signal

LP filter
for the difference frequency

The output signal
changes in rhythm of
the FM signal, i.e.
also in rhythm with
the source signal

input 2

Multiplier and LP filter form a Phase detector , which always measures the
phase difference between FM- and VCO-signal

VCO signal
has nearly the same
instantaneous frequency
as the FM signal

VCO
Voltage controlled oscillator
changes in the rhythm of
source signal

Illustration 178: Simplified block diagram of an analog PLL

Let us assume that the VCO signal had instantaneously (nearly) the same frequency as the received FM
signal. The sum and difference frequency f FM + f VCO and f FM - f VCO appears at the output as the result of
the multiplication. The lowpass filter filters out the sum frequency.

What frequency does the difference signal have as both frequencies f FM and f VCO are almost equally great?
At the output of the lowpass filter a “fluctuating direct current” appears which ought to have exactly the
level necessary to readjust the VCO to exactly the instantaneous frequency of the FM signal: the control
signal is therefore the LF signal.

If you haven't quite understood - a diagram speaks louder than words (see Illustration 179 -
Illustration 181 ).

In Illustration 178 the multiplier and the lowpass filter are intended to form a “phase
detector”. A phase detector compares two signals (of equal frequency) to see whether they
are in phase i.e. completely in synchrony. This can for example be achieved by a compa-
rison of the zero crossings of both signals. If the zero crossings are continuously displaced
towards each other the two signals only have roughly the same frequency. (see Illustration
179 in this connection).

Let us begin in a straightforward way and leave out the feedback. In Illustration 179 the
VCO is to be set at a frequency which corresponds approximately to the mid-frequency
of the FM signal. The FM signal varies its frequency in the rhythm of the upper (sinusoi-
dal) LF. In the diagram the zero crossings are compared. The sum and difference frequen-
cy appears at the output of the multiplier. The lowpass filter filters the sum frequency out
and the “residual voltage” which is intended to control the VCO corresponds more or less
to the LF signal (see Illustration 179). This voltage is greatest where the phase difference
of zero crossings is greatest if the delay caused by the lowpass filter is included.

We have cheated a little. This is shown by Illustration 180, where the control voltage or
the retrieved LF signal look very different from the original. The frequency domain shows
what actually happens. The multiplication of both signals in the time domain results in a
convolution in the frequency domain (sum and difference band). After the lowpass
filtering not the original LF signal is left over, but an FM signal which lies on the “mid-
frequency” f M = 0.