Page 332 - Analog and Digital Filter Design

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Filters for Phase-Locked Loops

Analog versus Digital Phase-Locked Loop

An analog phase-locked loop uses an analog phase detector and, usually, a
voltage-controlled oscillator having a sinusoidal output. Analog phase-locked
loops are most common in radio systems where high-frequency outputs are
required.

Digital phase-locked loops use logic gates as a phase detector, often arranged
as an edge triggered flip-flop. The voltage-controlled oscillator output is usually
a square wave. Digital phase-locked loops are used in frequency synthesizers and
tone decoder circuits.

Practical Digital Phase-Locked Loop

Now I will describe how to make a practical digital phase-locked loop circuit.
This will use a passive lead-lag network, so the component values for R1, R2,
and C need to be found. It will also use a common CMOS (Complementary
Metal Oxide Silicon) logic phase-locked loop integrated circuit, the 74HCT4046.

The circuit I am going to consider is a frequency synthesizer, producing a
frequency N times that of the input signal. The bandwidth of the loop filter
must be much smaller than the frequency used for comparison in the phase
detector, to prevent modulation of the voltage-controlled oscillator. The
damping factor of the system will be set at l/fi to ensure stability and a rea-
sonable impulse response. Now select R1 and C to provide a suitable bandwidth,
approximately given by 1/(R1. C) in rad/s. The values of R1 and C, and the loop
constants (N, K@J, KO) can be used to find a value for R2 that gives the correct
damping. This derivation will now be given.

As described earlier, the equations for a lead-lag network are:

uLp = 1/(R1+ R2).C, in rad/s.
wv =J(K@.Ko.w,,),in rad/s

K@ . KO
uLp can be replaced to give: us.
=

2
C-"[R2.C+(&)] , where N is the loop divider ratio.

Now, simplify the equation for R2 by letting <= 0.7071 or 1/42, so that = 112.