Having established the basic properties of FM/PM signals we can now look at two examples of ways to generate them. The first example is electronic, the second uses optical techniques. The electronic example is based upon the phase shift oscillator we looked at in an earlier section.
Figure 12.1 shows an example of a Voltage Controlled Oscillator (VCO) based upon the phase shift oscillator we considered previously. In the VCO two of the original oscillator's capacitors have been replaced with Varactor diodes.
When we apply a Forward bias voltage to a diode it will conduct. When we apply a Reverse bias voltage, a Depletion Zone forms at the diode junction. Charge carriers can't cross this zone, so the diode won't conduct in the ‘reverse’ direction. The reverse biassed diode therefore has a capacitance of
where d is the width of the depletion zone and A is the area of each of diode junction. Increasing the applied reverse bias pulls the carriers in the two halves apart, widening the depletion zone.
This has the same effect as increasing the gap between the plates of a normal capacitor — the capacitance goes down. As a result the reverse biassed diode has a capacitance which depends upon the applied voltage which we can represent by something like
This effect occurs in all normal types of diodes, but varactor diode have been manufactured specifically to give a relatively high capacitance which varies over a wide range as the voltage is changed.
The oscillation frequency of the phase shift oscillator equals the value which is delayed by 180 degrees in passing through the RC network. By replacing a pair of normal capacitors with a pair of ‘back to back’ varactors we can therefore make an oscillator whose oscillation frequency can be varied as we wish by altering the input Control Voltage which sets the reverse bias on the diodes. We can now use the VCO to produce FM (or PM) signals by using the modulation, 
, as the control voltage.
Varactor-tuned phase shift oscillators and some other ‘electronic’ types of VCOs can be used at frequencies up to the microwave/mm-wave region (i.e. up to a few tens of GHz). Between 10 GHz and around 100 GHz varactors can be used to modify the frequency produced by Gunn oscillators and other types of negative resistance device. In the THz region and above we have to switch over to a different approach based upon optical devices. Here we will take the example of a phase modulator based upon a Longitudinal Electro-Optical Modulator (EOM). This system is illustrated in figure 12.2.
An electro-optic material has the property that its refractive index depends upon the fields applied to its crystal structure. The effective refractive index experienced by a wave passing though the material depend upon the magnitude and direction of any applied field. It also depends upon the polarisation state of the wave. EOM's can be used in various ways depending on the relative field, wave, and crystal orientations. For this example we'll assume that the device is laid horizontally and the wave passes through it in the horizontal plane in a beam parallel to the z-axis of our co-ordinate system. The polariser ensures that the input field is vertically polarised, and the EOM is aligned so that its effective refractive index for this polarisation is
i.e. the index depends upon the applied field along the direction of propagation. The value of the coefficient, 
, depends on the material. When we apply a longitudinal voltage of 
to a length of material, l, we will produce a field
where 
is the modulation pattern we wish the wave to carry. An input wave of frequency, 
, will therefore undergo a phase change when passing through the modulator of
The output's phase therefore differs from that of an unmodulated wave (
) by an amount
i.e. we produce an output whose phase is modulated by an amount proportional to the input modulating signal. The output signal will be of the form
(ignoring the ‘constant’ phase shift component through the material). For a sinusoidal modulation input
we can therefore say that
which we can see is a PM wave whose modulation index
Hence the EOM produces a PM/FM wave by imposing phase fluctuations on a steady input carrier. Note that this technique differs from the VCO approach where the wave is ‘created’ with the required modulation. Here we need a separate, fixed frequency coherent oscillator to provide the carrier input to the modulator.
The phase-shift VCO and the longitudinal EOM are just two examples of how we can produce FM/PM signals. Many other systems exist, although most have features have common with the two examples considered here.
Summary.
You should now know that Frequency Modulated (FM) and Phase Modulated (PM) waves are very similar and have many features in common. You should also know what we mean by the Instantaneous Frequency and Instantaneous Phase of FM/PM signals and waves. That the spectrum if an FM/PM signal is much more complicated than an AM wave, and that its sidebands can extend over a much wider transmission bandwidth. (In theory, infinite!) You should also know how we can specify the modulation in terms of a Modulation Index, and a Peak Deviation. That the minimum bandwidth required for transmission can be obtained using Carson's Rule. You should also understand how FM/PM signals can be created using a Voltage Controlled Oscillator or using an Electro-Optic Modulator to modulated an existing Carrier.
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