rier is defined as [fc (max) - fc (min)] or When the amplitude of the carrier is made to vary about Vc by the message signal Vm, the modulated signal Afc =fc(max) = - -fc (min) (2.1.5) amplitude becomes [Vc Vm cos (wmt)] (2.1.3) The resulting envelope AM signal is then described by substituting Equation 2.1.3 into Equation 2.1.1 which Volts yields + Vm cos (wmt)] cos (wct + Oc) (2.1.4) It can be shown that when this equation is expanded, there are three frequencies, namely (fo - fm), fc and (fo + fm). Frequencies (fc - fm) and (fc + fm) are called sideband frequencies. These are shown pictorially in Volts Figure 2.1-4. The modulating information is contained in one of the sideband frequencies which must be present to extract the original message. The bandwidth (bw) is defined as the highest frequency minus the lowest frequency. In this case, it is + fm) - (fc - fm) = 2fm where fm is the highest modulation frequency. Hence, a radio receiver must be able to accommodate the bandwidth of a signal. 7 Volts 2.1.3.2 Frequency modulation Frequency modulation (FM) is the modulation method used in VHF radio broadcasting. Figure 2.1-5 shows what happens when we apply frequency modulation to a sinu- soidal carrier wave. Figure 2.1-5(a) shows the modulating wave on its own. Figure 2.1-5(b) shows the carrier wave Fig. 2.1-5 Frequency modulation waveforms: (a) modulating on its own. Figure 2.1-5(c) shows the resultant wave. The wave; (b) carrier wave; (c) FM wave. This is not unusual because speech or music also have low notes and high notes and to hear them our own ears (receivers) must be able to accommodate their bandwidth. Older people tend to lose this bandwidth and often are unable to hear the high notes. Basic features of radio communication systems CHAPTER 2. 1 According to Carson's rule, the frequency bandwidth wave. Note particularly how the phase of the carrier required for wideband FM is approximately 2 X (maxi- waveform changes when a positive modulating voltage is mum frequency deviation + highest frequency presen