Amplitude Modulation, Modulators, and Demodulators
Amplitude Modulation, Modulators, and DemodulatorsESE 488Double Sideband Amplitude Modulation (AM)VS(1+m)VSVS(1-m)tvS(t)Figure 1 – Sinusoidal signal with a dc componentIn double sideband modulation (the usual AM) a dc component is added to the signal voltage before the signal is multiplied by a carrier. If the signal were a simple sinusoid, it would have the form:(1)vS(t) = VS (1 + m cos st) where VS is the dc component, s = 2fs is the signal frequency, and m is known as the modulation index. This waveform is shown in Figure 1. To avoid distortion in recovering the modulating signal with a simple demodulator, the modulation index, m, is constrained to lie in the range zero to one.In AM, the carrier signal has the form:vC(t) = VC cos ct(2)where c is the carrier frequency in radians/sec. The carrier frequency, c, is usually much greater than the signal frequency, s.The modulated signal is then:(3)vm(t) = A vS(t) vC(t),where A is a scale factor that depends on the equipment used for modulation. Using equations (1) and (2) we can write(4)(5)vm(t) = AVCVS (1 + m cos st) cos ctEquation (5) was obtained from equation (4) by using the trigonometric identity for the product of two cosines.tAVCVS(1+m)AVCVSAVCVS(1-m)VmaxVminVm(t)Figure 2 – Modulated signal vs. time(6)Figure 2 shows the modulated signal of equations (5) or (6) as a function of time. The waveform above zero is produced by the positive values of cos ct while the values below zero are the result of negative values of cos ct. Notice that the modulation index can be obtained by measuring Vmax and Vmin. That is Vm(f)AVCVSmAVCVS/2fc-fsfcfc+fsCarrierUpperSidebandLowerSidebandfFigure 3 – Frequency components of the modulated signalFigure 3 shows the frequency components of the modulated double sideband signal. It is evident from equation (5) that the modulated signal has a carrier component and upper and lower sidebands at the sum and difference frequencies, (fs + fc) and (fs – fc). Note that the largest values the sidebands can have relative to the carrier occurs when m = 1. This is referred to as 100% modulation and the sidebands are each half as large as the carrier. Double Sideband Suppressed Carrier ModulationVs(t)+mVs-mVs0tFigure 4 – Sinusoidal signal with no dc component A double sideband suppressed carrier signal has no dc component added to the signal so that(7)vs(t) = mVS cos stThe modulated signal is the product of the modulating signal of equation (7) and the carrier with the result(8)vm(t) = mAVCVS cos st cos ct(9)orComparing this equation to equation (5) for the case of AM with carrier, we see that equation (9) has no carrier frequency, c, term.+mAVCVS-mAVCVS0tvm(t)Figure 5 – Suppressed carrier modulated signal vs. timeFigure 5 shows the suppressed carrier signal of equation (9) as a function of time. The positive lobe from 0 to 90o is produced by the product of a positive carrier and a positive signal, while the positive lobe from 90o to 270o is produced by the product of a negative carrier and a negative signal, etc. Notice that there is no envelope of the original modulating signal in the modulated signal as there is in double sideband AM with carrier. Vm(f)mAVCVS/2LowerSidebandUpperSidebandfc-fsfc+fsfThe modulated signal as a function of frequency is shown in Figure 6. With no component at the carrier frequency, the transmission power requirements are lower than for AM with carrier.Figure 6 – Frequency components of suppressed carrier signalDemodulatorIf the carrier signal is available at the demodulator, AM signals, either suppressed carrier or with carrier, can be demodulated by multiplying the received AM signal by a local oscillator sine wave (phase-locked to the carrier at the carrier frequency) and low pass filtering. For the suppressed carrier case, for example, the product isVI(t) = AVCVS m cos st cos2ct (10)(11)orThe original signal is then recovered with appropriate low-pass filtering (i.e., removing the product of the cos2st and cos2ct terms).Figure 7 shows the spectrum of the output of the multiplier in the receiver showing baseband and double frequency components of (11).2fc+fsAVCVS/2LowerSidebandUpperSideband2fc-fsffs Vm(f)Figure 7 – Frequency components after multiplication by carrier in receiver See: for QAM. ................
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