Phase Modulators:- Most modern FM transmitters use some form of phase modulation to produce indirect FM. The reason for using PM instead of direct FM is that the carrier oscillator can be optimized for frequency accuracy and stability. Crystal oscillators or crystal-controlled frequency synthesizers can be used to set the carrier frequency accurately and maintain solid stability.

The output of the carrier oscillator is fed to a phase modulator where the phase shift is made to vary in accordance with the modulating signal. Since phase variations produce frequency variations, indirect FM is the result. Some phase modulators are based upon the phase shift produced by an RC or LC tuned circuit. It should be pointed out that simple phase shifters of this type do not produce linear response over a large range of phase shift.

The total allowable phase shift must be restricted to maximize linearity, and multipliers must be used to achieve the desired deviation. The simplest phase shifters are RC networks like those shown in Fig. 6-10(a) and (b). Depending on the values of R and C, the output of the phase shifter can be set to any phase angle between 0 and 90°. In (a), the output leads the input by some angle between 0 and 90°. For example, when Xc equals R, the phase shift is 45°. The phase shift is computed by using the formula

A low-pass RC filter can also be used, as shown in Fig. 6-10(b). Here the output is taken from across the capacitor, so it lags the input voltage by some angle between 0 and 90°. The phase angle is computed by using the formula

A simple phase-shift circuit can be used as a phase modulator if the resistance or capacitance can be made to vary with the modulating signal. One way to do this is to replace the capacitor shown in the circuit of Fig. 6-10(b) with a varactor. The resulting phase-shift circuit is shown in Fig. 6-11. In this circuit, the modulating signal causes the capacitance of the varactor to change. If the modulating signal amplitude at the output of amplifier A becomes more positive, it adds to the varactor reverse bias from R1 and R2, causing the capacitance to decrease.

This causes the reactance to increase; thus, the circuit produces less phase shift and less deviation. A more negative modulating signal from A subtracts from the reverse bias on the varactor diode, increasing the capacitance or decreasing the capacitive reactance. This increases the amount of phase shift and the deviation. With this arrangement, there is an inverse relationship between the modulating signal polarity and the direction of the frequency deviation.

This is the opposite of the desired variation. To correct this condition, an inverting amplifier A can be inserted between the modulating signal source and the input to the modulator. Then when the modulating signal goes positive, the inverter output and modulator input go negative and the deviation increases. In Fig. 6-11 C1 and C2 are dc blocking capacitors and have very low reactance at the carrier frequency. The phase shift produced is lagging, and as in any phase modulator, the output amplitude and phase vary with a change in the modulating signal amplitude.

**Example 6-2** A transmitter must operate at a frequency of 168.96 MHz with a deviation of 65 kHz. It uses three frequency multipliers––a doubler, a tripler, and a quadrupler. Phase modulation is used. Calculate (a) the frequency of the carrier crystal oscillator and (b) the phase shift ¢ϕ required to produce the necessary deviation at a 2.8-kHz modulation frequency

a. The frequency multiplier produces a total multiplication of 2 x 3 x 4 5= 24. The crystal oscillator frequency is multiplied by 24 to obtain the final output frequency of 168.96 MHz. Thus, the crystal oscillator frequency is

A simple formula for determining the amount of frequency deviation fd represented by a specific phase angle is

Assume that the lowest modulating frequency for the circuit with the shift of 0.75 rad is 300 Hz. The deviation is fd = 0.75(300) = 225 Hz or 6112.5 Hz. Since this is PM, the actual deviation is also proportional to the frequency of the modulating signal. With the same maximum deviation of 0.75 rad, if the modulating frequency is 3 kHz (3000 Hz), the deviation is fd = 0.75(3000) 2250 Hz or 61125 Hz. To eliminate this effect and to generate real FM, the audio input frequency must be applied to a low-pass filter to roll off the signal amplitude at the higher frequencies in a low-pass filter.

**Example 6-3** For the transmitter in Example 6-2, a phase shifter like that in Fig. 6-10 is used, where C is a varactor and R = 1 kV. Assume that the total phase-shift range is centered on 45°. Calculate the two capacitance values required to achieve the total deviation.

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