Page 325 - Analog and Digital Filter Design

322 Analog and Digital Filter Design

Usually, more sophisticated digital phase detectors are used because the simple
exclusive-OR gate will give the same output if the reference signal is at a har-
monic (or subharmonic) of the oscillator frequency. Sophisticated phase detec-
tors are more accurately described as “phase and frequency detectors.” The gain
of a phase detector, in terms of volts per radian, is K@.

Analog phase detectors can be produced from multiplier circuits. This could be
an RF mixer or an analog multiplier. Both produce an output proportional to
the phase difference and the amplitude of the two input signals. These devices
take two inputs, the reference signal and the feedback signal, and multiply them
together. In-phase signals multiplied together produce, after averaging, a posi-
tive output. This is because two signals of the same polarity always produce a
positive output. Anti-phase signals produce a negative output after averaging
because one of the signals will always have the opposite polarity to the other.
Analog phase detectors are simple and cannot detect frequency differences
between signals. Therefore, harmonics of the reference signal will also produce
a locked condition.

In all phase-locked loops, the output of the phase detector controls the oscilla-
tor frequency. If the oscillator frequency drifts slightly, its phase will shift rela-
tive to the reference signal. The average output voltage from the phase detector
will change when this happens, and this will attempt to correct the frequency
drift. Thus, using feedback, the phase detector restores the phase difference
between the two signals. To prevent instability and to reduce noise, the output
voltage from the phase detector must be averaged, or integrated.

Averaging loop error signals is the purpose of the loop filter. The oscillator has
a gain, KO, which is in terms of radls per volt. Thus the phase is an integral of
KO times the input voltage. Hence, the phase-locked loop is an integrator fol-
lowed by a first-order filter that becomes a second-order system. This can there-
fore be unstable unless properly designed.

Now, it may seem pointless to produce an output signal that is identical to the
input reference signal, as shown in Figure 13.1, but there are two important
applications for modified versions of this circuit. Demodulation of a frequency-
modulated carrier is one application; frequency multiplication is the other.

As the carrier frequency at the reference input increases or decreases, that is it
is frequency modulated (FM), the oscillator frequency is forced to follow by the
control voltage feedback loop. The control voltage will vary in proportion to
the frequency deviation, hence providing a demodulated carrier output. The
output from the oscillator is only used to provide a second input to the phase
detector. If used as an FM detector, the loop filter must have a bandwidth at
least equal to that of the modulating signals; this is typically 15 kHz in a radio
broadcast signal. The circuit for an FM demodulator is illustrated in Figure 13.2.