Fundamentals of Measurement Technology (12) Prof Wang Boxiong
Fundamentals of Measurement Technology (12) Prof. Wang Boxiong
5. 3 Modulation and demodulation Modulation is a process of controlling or changing a parameter(amplitude, frequency, or phase)of a high-frequency oscillation by use of a measurand, usually a low-frequency signal >Controlled parameter is the amplitude of the high frequency oscillations: amplitude modulation or AM Frequency varied with the measurand frequency modulation, or FM >Controlled parameter is the phase of the oscillations: phase modulation, or PM
5.3 Modulation and demodulation Modulation is a process of controlling or changing a parameter (amplitude, frequency, or phase) of a high-frequency oscillation by use of a measurand, usually a low-frequency signal. ➢Controlled parameter is the amplitude of the high frequency oscillations: amplitude modulation, or AM. ➢Frequency varied with the measurand: frequency modulation, or FM. ➢Controlled parameter is the phase of the oscillations: phase modulation, or PM
5.3 Modulation and demodulation The measurand, usually a low-frequency signal controlling the high frequency oscillation, is called modulating signal, the high-frequenc oscillation used for carrying the low-frequency signal is known as carrier, and the resulting signal from the modulation process, still a high-frequency oscillation, is known as modulated signal In time domain, modulation is a process in which a certain parameter of the carrier is varied with the modulating signal, while in frequency domain, it is a process of phase-shifting
5.3 Modulation and demodulation The measurand, usually a low-frequency signal controlling the high frequency oscillation, is called modulating signal, the high-frequency oscillation used for carrying the low-frequency signal is known as carrier, and the resulting signal from the modulation process, still a high-frequency oscillation, is known as modulated signal. In time domain, modulation is a process in which a certain parameter of the carrier is varied with the modulating signal, while in frequency domain, it is a process of phase-shifting
5.3 Modulation and demodulation Demodulation is the reverse process of modulation, in which the original low frequency signal the measurand. is recovered from the modulated signal MODEM has wide applications in engineering
5.3 Modulation and demodulation Demodulation is the reverse process of modulation, in which the original lowfrequency signal, the measurand, is recovered from the modulated signal. MODEM has wide applications in engineering
5.3. 1 Amplitude modulation and demodulation 1. Amplitude modulation(AM) Amplitude modulation To multiply a high frequency signal(carrier) with the measurand (modulating signal)so that the carrier amplitude is varied with the measurand xm(t)=x(t)cos 2yfot the Fourier transform pair x(O)y(t)eX()*Y() accordingly, we have x()osx1x()*6(+)+1x(0)*(/-f)(625
5.3.1 Amplitude modulation and demodulation 1. Amplitude modulation(AM) Amplitude modulation: To multiply a highfrequency signal (carrier) with the measurand (modulating signal) so that the carrier amplitude is varied with the measurand. x t x t f t m 2 0 ( ) = ( )cos the Fourier transform pair: x(t) y(t) X ( f ) *Y( f ) ,accordingly, we have: ( ) ( ) ( ) ( ) 0 0 * 0 2 1 ( ) * 2 1 x t cos 2f t X f f + f + X f f − f (5.25)
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
