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Module 7: AM, FM, and the spectrum analyzer.

Module 7:AM, FM, and the spectrumanalyzer. IntroductionElectromagnetic signals may be used to transmit information very quickly, over greatdistances. Two common methods by which information is encoded on radio signals, amplitudeand frequency modulation, will be reviewed in this Module . Also, the process of retrievinginformation from encoded signals will be discussed. Finally, the basic components of the spectrum analyzer will be ModulationWith the proper equipment, radio signals can be transmitted and received over large may therefore be exchanged over large distances by encoding information on radiowaves. This is accomplished through modulation of radio signals. Modulation is the process of encoding information onto a carrier signal which hasfrequency fc.

spectrum analyzer will be examined. 7.1 Modulation With the proper equipment, radio signals can be transmitted and received over large distances. Information may therefore be exchanged over large distances by encoding information on radio waves. This is accomplished through modulation of radio signals.

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Transcription of Module 7: AM, FM, and the spectrum analyzer.

1 Module 7:AM, FM, and the spectrumanalyzer. IntroductionElectromagnetic signals may be used to transmit information very quickly, over greatdistances. Two common methods by which information is encoded on radio signals, amplitudeand frequency modulation, will be reviewed in this Module . Also, the process of retrievinginformation from encoded signals will be discussed. Finally, the basic components of the spectrum analyzer will be ModulationWith the proper equipment, radio signals can be transmitted and received over large may therefore be exchanged over large distances by encoding information on radiowaves. This is accomplished through modulation of radio signals. Modulation is the process of encoding information onto a carrier signal which hasfrequency fc.

2 This carrier signal is called the modulated signal, while the informationcarrying, or baseband signal is referred to as the modulating types of modulation will be reviewed in this Module . Amplitude modulation consists encoding information onto a carrier signal by varying theamplitude of the carrier. Frequency modulation consists of encoding information onto a carrier signal by varyingthe frequency of the a signal has been modulated, information is retrieved through a demodulation process. Suppressed carrier amplitude modulation (double sideband)A general sinusoidal signal can be expressed asf(t) A(t) cos (t) .where the amplitude A and phase angle may, in general, be functions of time. It is convenient towrite time varying angle (t) as , therefore the sinusoidal signal may be expressed as ct (t)f(t) A(t) cos ct (t).

3 The term A(t) is called the envelope of the signal f(t), and c is called the carrier process of amplitude modulation consists of the amplitude of the carrier wave beingvaried in sympathy with a modulating signal. A mathematical representation of an amplitudemodulated signal is obtained by setting =0 in the expression for the general sinusoidal (t) WaveFigure 1. Amplitude , and letting the envelope A(t) be proportional to a modulating signal f(t). What results isa new (modulated)signal, given byy(t) f(t) cos ( ct) .The spectrum of the modulated signal can be found by using the modulation property ofy(t)the Fourier transform. In Chapter 3, the Fourier transform pair was defined asf(t) 12 F( )ej td F( ) f(t)e j Fourier transform of a signal is thenf(t)ej 0t f(t)ej 0t f(t)ej 0te j tdt f(t)e j( 0)tdt.

4 7-3f t( )cos() cty tf ttc( )( ) cos()= Figure 2: Amplitude modulation (suppressed carrier)Thus the Fourier transform of may be expressedf(t)ej 0t f(t)ej 0t F amplitude modulated signal y(t) may be written in terms of complex exponentialsy(t) f(t) cos ct 12f(t)ej ct e!j y(t) is expressed in this form, and from the example above, it can be seen that the Fouriertransform of y(t) is given by. f(t) cos ( ct) 12F( c) F( " # c) cm cm+ cLower sidefrequencyUpper sidefrequency m m Figure 3. Single modulating frequency AM signal , the spectrum of is translated by . It is seen that the modulation process causes thef(t) $cfrequencies associated with the modulating signal to disappear. Instead, a new frequency spectrumappears, consisting of two sidebands, known as the upper sideband (USB), and the lower sideband(LSB).

5 The spectrum of the modulated signal does not contain the spectrum of the originaly(t)carrier, but is still centered about the carrier frequency . Thus this type of modulation is$creferred to as double-sideband, suppressed-carrier amplitude modulation. A block diagram of thesuppressed carrier amplitude modulation operation is presented in Figure 2. If the modulating signal contains a single frequency $m, then $USB=$c+$m, and $LSB=$c - $m(Figure 3). If modulating signal f(t) has a bandwidth of $bw , then F($), the spectrum of f(t), willextend from -$bw to +$bw. The upper sideband of the spectrum of the modulated signal Y($) willextend from $c to $c+$bw. Likewise, the lower sideband will extend from $c-$bw to $c . Both thenegative and positive frequency components of the modulating signal f(t) appear as positivefrequencies in the spectrum of the modulated signal y(t).

6 It is also seen that the bandwidth of f(t) isdoubled in the spectrum of the modulated signal when this type of modulation is employed. 12[()()]FFcc ++ c c2 bw2 bw0120F( )120F( ) F() 0 bw bwFigure 4. Spectra of modulating wave and resulting AM AM demodulationAn AM signal is demodulated by first mixing the modulated signal with another sinusoidy(t)of the same carrier frequencyy(t) cos ($ct)%f(t) cos2($ct)%12f(t)1&cos ( 2$ct) .The Fourier transform of this signal is'{y(t) cos ($ct) }%'12f(t)1&cos ( 2$ct)or'y(t) cos ($ct)%12F($)&12F($(&2$c)&F($()2$c).By using a low-pass filter, the frequency components centered at can be removed to leave 2$conly the term. It is obvious that in order to properly recover the original signal it is1/2F($)necessary that $c>$bw.)

7 A block diagram of the demodulation process is shown in Figure () cty tf ttc( )( ) cos()= ()1212f ttc( )cos()+ LowPassFilter12f t( )Figure 5: AM Large carrier amplitude modulation (double sideband)In practice, the demodulation of suppressed carrier amplitude modulated signals requires fairlycomplicated circuitry in order to acquire and maintain phase synchronization. A much lesscomplicated (and thus less expensive) receiver can be used if a slightly different modulation schemeis employed. In large carrier amplitude modulation, the carrier wave information is incorporated as a partof the waveform being transmitted. It is convenient to let the amplitude of the carrier be largerthan any other part of the signal spectral density.

8 While this makes the demodulation process mucheasier, low-frequency response of the system is lost. For some signals however, frequencyresponse down to zero is not needed (such as in audio signals).Consider a carrier wave with amplitude A, and frequency $c, represented by7-6c(t)%Acos($ct) .The modulated waveform of a large carrier AM signal can be then be expressed mathematically asy(t)%f(t) cos ($ct)&Acos ($ct) .The spectrum associated with this modulated signal is given byY($)%12F($ & $c)&12F($ ) $c)&+*A,($ & $c)&+*A,($ ) $c) .It is seen that the spectrum of the large carrier AM signal is the same as that of the suppressedcarrier AM signal with the addition of impulses at $ large carrier AM signal may be rewritteny(t)%A&f(t)cos ($ct).

9 In this form, y(t) may be thought of as consisting of a carrier signal having amplitudecos ($ct). If the amplitude of the carrier A is sufficiently large, then the envelope of theA&f(t)modulated waveform will be proportional to f(t) (hence the name large carrier AM). Demodulation in this case is simply involves the detection of the envelope of a 6. Comparison of large carrier AM and suppressed carrier The envelope detectorAn envelope detector is any circuit whose output follows the envelope of an input signal. Thesimplest form of such a detector is a non-linear charging circuit which has a fast charge time and aslow discharge time. This is easily implemented by placing a diode in series with a parallelcombination of a capacitor and a resistor.

10 The envelope of an input signal is detected by thefollowing process:-The input waveform (in this case a large carrier AM signal) charges the capacitor to themaximum value of the waveform during positive half-cycles of the input signal. -As the input signal falls below maximum, the diode becomes reverse biased, and capacitor then begins a relatively slow discharge through the resistor until the nextpositive the input signal becomes greater than the capacitor voltage, the diode becomesforward biased, and the capacitor charges to a new peak optimum operation, the discharge time constant RC is adjusted so that the maximumnegative rate of the envelope never exceeds the exponential discharge the time constant is too large, the envelope detector may miss some positive half-cyclesof the carrier, and will not correctly reproduce the envelope of the input signal.


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