t in applied. In this particular case, we have shown you a phase the message signal) or change of 180°, but smaller phase changes are also possible. Phase modulation is popularly used for digital signals. bw = 2[Afc fm (max)] (2.1.6) Phase modulation is synonymous with frequency mod- ulation in many ways because an instantaneous change in In FM radio broadcasting, the allocated channel band- phase 8 is also an instantaneous change in frequency and width is about 200 kHz. vice versa. Hence, much of what is said about FM also applies to PM. 2.1.3.3 Phase modulation 2.1.3.4 Combined modulation methods Phase modulation (PM) is particularly useful for digital waveforms. Figure 2.1-6 shows what happens when we Digital signals are often modulated on to a radio carrier apply phase modulation to a sinusoidal cartier wave. using both phase and amplitude modulation. For Figure 2.1-6(a) shows a digital modulating wave on its example, an eight level coded digital signal can be own. We have used a pulse waveform as opposed to a sine modulated on to a carrier by using distinct 90° phase wave in this instance because it demonstrates phase changes and two amplitude levels. This is shown di- modulation more clearly. Figure 2.1-6(b) shows the car- agrammatically in Figure 2.1-7 where eight different rier wave on its own. Figure 2.1-6(c) shows the resultant signals, points A to H, are encoded on to a radio carrier. Volts Volts 000000000000 Volts Fig. 2.1-6 Phase modulation waveforms: (a) modulating wave; (b) carrier wave; (c) modulated wave. Phase () = angular velocity (w) multiplied by time (t). Hence = wt. Note this equation is similar to that of distance = velocity X time. This because = amount of angle travelled = velocity (w) X time (t). CHAPTER 2.1 Basic features of radio communication systems Transmission line Amplitude 1 Radio Energy generator propagation Fig. 2.1-8 Energy propagation in a transmission line. The equivalence between the circuit and field descriptions of waves on transmission lines is demon- strated by the fac