5.3. 1 Amplitude modulation and demodulation n t)=x(t)cos exfo t Modulator y(t)cosa fot y(t) Y xm(D)=X(f)“Y( 2f m x(t) 出M 0 (b) Fig. 5. 14 Principle of AM
5.3.1 Amplitude modulation and demodulation Fig. 5.14 Principle of AM
5.3. 1 Amplitude modulation and demodulation The product of signal x(t)and the carrier is equivalent in frequency domain to a process of shifting the spectrum of x(t to the position of carrier frequency fo (Fig. 5. 14(b)), that is, the AM process is a process of frequency-shifting Sinusoidal signal as the modulating signal Let the modulating signal x t=As sino t, and the carrier signal y(t=Ac sin ot The modulated Signal is then xm=x()·y()=AsmO,t· A sim o t(62
5.3.1 Amplitude modulation and demodulation The product of signal x(t) and the carrier is equivalent in frequency domain to a process of shifting the spectrum of x(t) to the position of carrier frequency f0 (Fig. 5.14(b)), that is, the AM process is a process of frequency-shifting. ◼Sinusoidal signal as the modulating signal Let the modulating signal x(t)=As sinωs t , and the carrier signal y(t)= Ac sin ωc t. The modulated signal is then x x(t) y(t) A t A t m s s c c = = sin sin (5.26)
5.3. 1 Amplitude modulation and demodulation ere Asamplitude of signal -frequency of signal Ac amplitude of carrier o-frequency of carrier The frequency oc is greater(usually considerably greater) than @s. Attention should be paid to that the modulated signal is in phase with the carrier for the positive half cycle of the modulating signal, whereas the modulated signal is in opposite phase with the carrier for negative half cycle of the modulating signal
5.3.1 Amplitude modulation and demodulation where As=amplitude of signal ωs=frequency of signal Ac=amplitude of carrier ωc=frequency of carrier The frequency ωc is greater (usually considerably greater) than ωs . Attention should be paid to that the modulated signal is in phase with the carrier for the positive half cycle of the modulating signal, whereas the modulated signal is in opposite phase with the carrier for negative half cycle of the modulating signal
5.3. 1 Amplitude modulation and demodulation carrier Ae sin w/ Magnitude spectrum spectrum Magnitude AsAc I Output Output,;siny小4 sin wst spectrum 十 +90 ig. 5. 15 AM of sine-wave signal
5.3.1 Amplitude modulation and demodulation Fig. 5.15 AM of sine-wave signal
5.3.1 Amplitude modulation and demodulation The frequency spectrum can be obtained using trigonometric identity sin ax sin B=cos(a-B)-cos(a+B) (5.27) xm =3[cos(oe -@s)t-cos(oc +@)] (528) A A sin(0-0.t+ sin(o+o t (528) C An amplitude-modulating device is actually a multiplier. In practice, a bridge is often used as the device, which employs a high-frequency oscillating source as the carrier signal, and the output of the bridge is the modulated wave e
5.3.1 Amplitude modulation and demodulation The frequency spectrum can be obtained using trigonometric identity: = ( − ) − cos( + ) 2 1 cos 2 1 sin sin (5.27) ( )t ( )t A A x c s c s s c m = cos − − cos + 2 (5.28) ( ) ( ) + + − = − + 2 sin 2 2 sin 2 t A A t A A x c s s c c s s c m (5.28) An amplitude-modulating device is actually a multiplier. In practice, a bridge is often used as the device, which employs a high-frequency oscillating source as the carrier signal, and the output of the bridge is the modulated wave ey