n Integrator Phase Modulator Output Suppressed carrier Differentiator Frequency Modulator Output Figure 18.10 Alternative methods of generating angle modulation: (a) use of phase modulator to generate FM; Residual (b) use of frequency modulator to generate PM applying its output to a non-linear circuit to generate harmonics, one of which is selected by a bandpass filter. If the nth harmonic is selected, the frequency deviation is increased by a factor n. A phase modulated wave can be demodulated by using a coherent demodulator whose local carrier is in quadrature with the incoming carrier when unmodulated. When the incoming carrier is modu- lated, the output voltage is given by Equation 18.32. sinwit (18.32) Figure 18.9 Phasor diagrams for Armstrong's phase The component at frequency is removed by the low pass modulator of Figure 18.8: (a) product modulator output filter and the output signal is as in Equation 18.33. (V1); output from circuit (V) wave, as shown in Figure 18.9(a), and the carrier is added to this after shifting its phase by 90°. This produces a phase deviation of (18.33) the resultant signal, as shown in Figure 18.9(b). This method is only suitable for small values of modulation index. It produces an output containing only two side frequencies, whereas it is shown in One method of demodulating FM is to use the incoming carrier to the next section that significant additional side frequencies are generate a train of pulses and to count the number of these per unit present with high index modulation. These higher order side fre- of time (Gosling, 1986). However, more widely used circuits oper- quencies serve to keep the amplitude of the signal constant, whereas ate indirectly by converting frequency variations of the incoming the circuit of Figure 18.8 produces some residual amplitude modu- signal to variations of amplitude or phase and demodulating these. lation. The locus of the end of phasor V is a straight line, whereas Such circuits are called discriminators. it would be a circle for perfect pha