Modulation Techniques
`for Mobile Radio
`
`Mboie is the process ofencoding infor-
`
`mation from a messagesource in a mannersuitable for transmission. It gener-
`ally involves translating a baseband messagesignal (called the source) to a
`bandpass signal at frequencies that are very high when comparedto the base-
`band frequency. The handpass signal
`is called the modulated signal and the
`baseband message signal is called the modulating signal. Modulation may be
`doneby varying the amplitude, phase, or frequencyofa high frequencycarrierin
`accordance with the amplitudeof the message signal. Demodulationis the pro-
`cess of extracting the baseband message from the earrier so that it may be pro-
`cessed and interpreted hy the intendedreceiver(also called thesink).
`This chapter describes various modulation techniques that are used in
`mobile communication systems. Analog modulation schemes that are employed
`in first generation mobile radio systems, as well as digital modulation schemes
`proposed for usein present and future systems, are covered. Since digital madu-
`lation offers numerous benefits and is already being used to replace conventional
`analog systems, the primary emphasis of this chapter is on digital modulation
`schemes. However, since analog systems are in widespread use, and will con-
`tinue to exist, they are treatedfirst.
`Modulationis a topic that is covered in great detail in various communica-
`tions textbooks. Here, the coverage focuses on modulation and demodulation as
`it applies to mobile radio systems. A large variety of modulation techniques have
`been studied for use in mobile radio communications systems, and research is
`ongoing. Given thehostile fading and multipath conditions in the mobile radio
`channel, designing a modulation scbemethat is resistant to mobile channel
`impairmentsis a challenging task. Since the ultimate goal of a modulation tech-
`nique is to transport the message signal through a radio channel with the best
`Qualcomm Incorporated
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`197
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`various types of channel impairments.
`
`5.1 Frequency Modulation vs. Amplitude Modulation
`Frequency modulation (FM) is the most popular analog modulation tech-
`nique used in mobile radio systems. In FM, the amplitude of the modulated car-
`rier signal
`is kept constant while its frequency is varied by the modulating
`message signal. Thus, FMsignals have all their information in the phase orfre-
`quency of the carrier. As shown subsequently, this provides a nonlinear and very
`rapid improvement in reception quality once a certain minimumreceived signal
`level, called the FM threshold,
`is achieved.
`In amplitude modulation (AM)
`schemes, there is a linear relationship between the quality of the received signal
`and the powerof the received signal since AM signals superimposethe exact rel-
`ative amplitudes of the modulating signal onto the carrier. Thus, AM signals
`have all their information in the amplitude of the carrier. FM offers many advan-
`tages over amplitude modulation (AM), which makes it a better choice for many
`mobile radio applications.
`Frequency modulation bas better noise immunity when compared to ampli-
`tude modulation. Since signals are represented as frequency variations rather
`than amplitude variations, FM signals are less susceptible to atmospheric and
`impulse noise, which tend to cause rapid fluctuations in the amplitude of the
`received radio signal. Also, message amplitude variations do not carry informa-
`tion in FM,so burst noise does notaffect FM system performance as much as AM
`systems, provided that the FM received signal is above the FM threshold. Chap-
`ter 4 illustrated how small-scale fading can cause rapid fluctuations in the
`received signal, thus FM offers superior qualitative performance in fading when
`compared to AM. Also,
`in an FM system, it is possible to tradeoff bandwidth
`occupancy for improved noise performance. Unlike AM, in an FM system, the
`modulation index, and hence bandwidth occupancy, can be varied to obtain
`greater signal-to-noise performance. It can be shown that, under certain condi-
`tions, the FM signal-to-noise ratio improves 6 dB for each doubling of bandwidth
`occupancy. This ability of an FM system to trade bandwidth for SNR is perhaps
`the most important reason for its superiority over AM. However, AM signals are
`able to occupy less bandwidth as compared to FM signals, since the transmission
`system is linear. In modern AM systems, susceptibility to fading has been dra-
`matically improved through the use of in-band pilot tones which are transmitted
`along with the standard AM signal. The modern AM receiver is able to monitor
`the pilot tone and rapidly adjust the receiver gain to compensate for the ampli-
`tudefluctuations.
`
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`Class C power amplifiers to be used for RF power amplification of FM. In AM,
`however,it is critical to maintain linearity between the applied message and the
`amplitudeof the transmitted signal, thus linear Class A or AB amplifiers, which
`are not as power efficient, must be used.
`The issue of amplifier efficiency is extremely important when designing
`portable subscriber terminals since the battery life of the portable is tied to the
`power amplifier efficiency. Typical efficiencies for Class C amplifiers are 70%,
`meaning that 70%of the applied DC power to the final amplifier circuit is con-
`verted into radiated RF power. Class A or AB amplifiers haveefficiencies on the
`order of 30-40%. This implies that for the same battery, constant envelope FM
`modulation may provide twice as muchtalk time as AM.
`Frequency modulation exhibits a so-called capture effect characteristic. The
`capture effect is a direct result of the rapid nonlinear improvement in received
`quality for an increase in received power. If two signals in the samefrequency
`band are available at an FM receiver, the one appearing at the higher received
`signal level is accepted and demodulated, while the weaker oneis rejected. This
`inherent ability to pick up the strongest signal andreject the rest makes FMsys-
`tems very resistant to co-channel interference and provides excellent subjective
`received quality. In AM systems, on the other hand, all of the interferers are
`received at once and musthe discriminated after the demodulation process.
`While FM systems have many advantages over AM systems, they also have
`certain disadvantages. FM systems require a wider frequency bandinthe trans-
`mitting media (generally several times as large as that needed for AM) in order
`to obtain the advantages of reduced noise and capture effect. FM transmitter
`and receiver equipmentis also more complex than that used by amplitude modu-
`lation systems. Although frequency modulation systems are tolerant to certain
`types of signal and circuit nonlinearities, special attention must be given to
`phase characteristics. Both AM and FM may be demodulated using inexpensive
`noncoherent detectors. AM is easily demodulated using an envelope detector
`whereas FM is demodulated using a discriminatoror slope detector. AM may be
`detected coherently with a product detector, and in such cases AM can outper-
`form FMin weak signal conditions since FM mustbe received above threshold.
`
`5.2 Amplitude Modulation
`In amplitude modulation, the amplitude of a high frequency carrier signal
`is varied in accordance to the instantaneous amplitude of the modulating mes-
`sage signal. If A,cos (2nf.t)
`is the carrier signal and m(t) is the modulating
`message signal, the AM signal can be represented as
`
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`

`k= An
`A,
`The modulation index is often expressed as a percentage, and is called percent-
`age modulation. Figure 5.1 shows a sinusoidal modulating signal and the corre-
`sponding AMsignal. For the case shown in Figure 5.1, A,, = 0.5A,, and the
`signal is said to be 50% modulated. A percentage of modulation greater than
`100%will distort the message signal if detected by an envelope detector. Equa-
`tion (5.1) may be equivalently expressed as
`=
`——
`tT
`—-r
`
`(5.2)
`
`mit)
`
`sam(t)
`
`time —»
`
`(a)
`
`
`t
`——
`T
`Tt Ts =
`j}+——_—— /fmeasage——
`
`Lf,
`f=
`
`
`L
`all
`mownil
`aneall a
`
`time —»
`
`(b)
`
`Figure 5.1
`(a) A sinusoidal modulating signal.
`(b) Corresponding AM signa! with modulation index 0.5
`
`Sam(#) = Re (g(t) exp G2nf.t) }
`where g(f) is the complex envelope of the AM signal given by
`
`g(t) = A,[]1+m(t)]
`
`(5.3)
`
`(5.4)
`
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`

`trum. Figure 5.2 shows an AM spectrum for a message signal whose magnitude
`spectrum is a triangular function. As seen from Figure 5.2, the AM spectrum
`consists of an impulse at the carrier frequency, and two sidebands which repli-
`cate the message spectrum. The sidebands above and below the carrier fre-
`quencyare called the upper and lower sidebands, respectively. The bandwidth of
`an AM signalis equal to
`
`(5.6)
`fo ear.
`is the maximum frequency contained in the modulating messagesig-
`where f,,
`nal. The total power in an AM signal can be shown to be
`ce
`Pay = Ag [1 +2(m(t)) + (m’(t)))
`represents
`the average value.
`If
`the modulating signal
`is
`(*)
`where
`m(t) = kcos (2nf,,t), equation (5.7) may be simplified as
`
`ke
`.
`Bey:
`(5.8)
`=
`sA,[1+P,] = P, 1+>
`Pig
`AM
`3
`where P. = A?/2 is the powerin the carrier signal, P,, = (m’(t)) is the power
`in the modulating signal m({t), and & is the modulation index.
`
`
`
`Example 5.1
`A zero meansinusoidal message is applied to a transmitter that radiates an
`AM signal with 10 kW power. Compute the carrier power if the modulation
`index is 0.6. What percentage of the total poweris in the carrier? Calculate the
`power in each sideband.
`
`Solution to Example 5.1
`Using equation (5.8) we have
`P
`p= —AM_ ._ 10_. ga7kw
`1+k?7/2
`14+0.6°/2
`Percentage power in the carrier is
`P
`
`=.
`x 100 = 8.47 100 = 84.7%
`Pam
`10
`Powerin each sidehand is given by
`]
`x
`5 (Pam Pe) = 0.5 (10-847) = 0.765 kW
`
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`
`
`(a)
`
`
`
`Sam(|
`
`
`upper
`lower
`upper
`sideband
`sideband
`sideband
`
`
`
`
`Set;m
`Se
`
`
`Je +f,”
`Sedm
`tc
`te +f,m
`f
`
`(b)
`
`Figure 5.2
`(a) Spectrum of a message signal.
`(b) Spectrum of the corresponding AM signal.
`
`5.2.1 Single Sideband AM
`Since both the sidebands of an AM signal carry the same information, it is
`possible to remove one of them without losing any information. Single sideband
`(SSB) AM systems transmit only one of the sidebands (either upper or lower)
`about the carrier, and hence occupy only half the bandwidth of conventional AM
`systems. An SSBsignal can be mathematically expressed as
`(5.9)
`Sgoy (t) = A, [m(t) cos (2nf,t) Fm (£) sin (2nf,t) ]
`where the negative sign in equation (5.9) is used for upper sideband SSB and the
`positive sign is used for lower sideband SSB. The term m(t} denotes the Hilbert
`transform of m (ft) which is given by
`
`(5.10)
`mit) = m(t) @hyp(t) = m(t) eo
`and H,,,(f), the Fourier transform of h,,,(t), corresponds to a —90° phase shift
`network
`
`Hif) =
`
`{ :
`“din.
`J
`
`had
`f<0
`
`5,1
`wee
`
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`

`is shown in Figure 5.3a. Excellent sideband suppression can be obtained using
`crystal filters at an intermediate frequency (IF).
`
` BandpassFilter
`
`(filters out one
`
`of the sidebands)
`
`
`Sgsplti
`
`A,cos(2nf.t)
`
`(a)
`
`
`
`Sgsplt)
`
`mit)
`
`m{t)
`
`
`Carrier
`Oscillator
`
`
`fe
`
`
`
`
`90°
`se Shift
`
`Pha
`
`Figure 5.3
`Generation of SSB using (a) a sideband filter, and (b) balanced modulator.
`
`(b)
`
`Figure 5.3b shows a block diagram of a balanced modulator whichis a
`direct implementation of equation (5.9). The modulating signal is split into two
`identical signals, one which modulates the in-phase carrier and the other which
`is passed through a —90° phase shifter before modulating a quadraturecarrier.
`The sign used for the quadrature component determines whether USSB or LSSB
`is transmitted.
`
`5.2.2 Pilot Tone SSB
`
`While SSB systems have the advantage of being very bandwidth efficient,
`their performance in fading channels is very poor. For proper detection of SSB
`
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`

`the pitch of the received audio signal. In conventional SSB receivers,it is diffi-
`cult to electronically tune the local oscillator frequency to the identical frequency
`of the incoming carrier. Doppler spreading and Rayleigh fading canshift the sig-
`nal spectrum causing pitch and amplitude variations in the received signal.
`These problems may be overcome by transmitting a low level pilot tone along
`with the SSBsignal. A phase locked loop at the receiver can detect this pilot tone
`and useit to lock the frequency and amplitude of the local oscillator. If the pilot
`tone andthe information bearing signal undergo correlated fading, it is possible
`at the receiver to counteract the effects of fading through signal processing based
`on tracking the pilot tone. This processis called feedforward signal regeneration
`(FFSR). By tracking the pilot tone, the phase and amplitude of the transmitted
`signal can be reestablished. Keeping the phase and amplitude of the received
`pilot tone as a reference, the phase and amplitude distortions in the received
`sidebands caused by Rayleigh fading can be corrected.
`Three different
`types of pilot
`tone SSB systems have been developed
`[Gos78],{Lus78],[Wel78]. All three systems transmit a low level pilet tone, usu-
`ally -7.5 dB to -15 dB below the peak envelope powerofthe single sideband sig-
`nal. They essentially differ in the spectral positioning ofthe low level pilot tone.
`One system transmits a low level carrier along with the sideband signal (tone-in-
`band), while the other twoplace a pilot tone above or within the SSB band.
`The tone-in-band SSB system offers many advantages which makeit par-
`ticularly suited to the mobile radio environment. In this technique, a small por-
`tion of the audio spectrum is removed from the central region of the audio band
`using a notch filter, and a low level pilot tone is insertedin its place. This has the
`advantage of maintaining the low bandwidth property of the SSBsignal, while
`at the sametime providing good adjacent channel protection. Due to very high
`correlation between the fades experienced by the pilot tone and the audio sig-
`nals, a tone-in-band system makes it possible to employ some form of feedfor-
`ward automatic gain and frequency control to mitigate the effects of multipath
`induced fading.
`For proper operation of tone-in-band SSB, the tone must be transparent to
`data and be spaced across the band to avoid spectral overlap with audio frequen-
`cies. McGeehan and Bateman |McG&4] proposed a Transparent Tone-In-Band
`(TTIB) system which satisfies these requirements. Figure 5.4 illustrates the pro-
`posed technique. The baseband signal spectrum is split into two approximately
`equal width segments. The upper frequency hand is filtered out separately and
`upconverted by an amount equal to the required notch width. The low level pilot
`
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`

`depends on the maximum Doppler spread induced by the channel, as well as
`practical filter rolloff factors.
`
`
`
`Transmitter
`
`Receiver
`
`tishaneSnr
`
`a
`
`Bandwidth =/5-f,
`——+ frequency
`
`:
`
`J3w
`
`——» frequency
`
`Figure 5.4
`[lustration of transparent tone-in-band system [From [McG84] © IEEE]. Only positive frequencies
`are shown, and the two different cross-hatcbings denote different spectral bands,
`
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`

`noncoherent detection requires no phase information. In practical AM receivers,
`the received signal is filtered and amplified at the carrier frequency and then
`converted to an intermediate frequency (IF) using a superhetrodyne receiver.
`The IF signal retains the exact spectral shape as the RF signal.
`Figure 5.5 shows a block diagram of a product detector which forms a coher-
`ent demodulator for AM signals. A product detector (also called a phase detector)
`is a down converter circuit which converts the input bandpass signal to a hase-
`band signal. If the input to the product detector is an AM signal of the form
`R(t) cos (2xf,t+9_), the output of the multiplier can be expressed as
`(5.12)
`v(t) = R(t) cos (2nf,t+6,)A,cos (2nf,t + 8,)
`where f, is the oscillator carrier frequency, and 8, and @, are the received signal
`phase and oscillator phases,
`respectively. Using trigonometric identities in
`Appendix D, equation (5.12) may he rewritten as
`(5.13)
`v(t) = ZAR (t) cos (8, ~ 9p) + SAgR(t) cos [x2f,t +8, + Bo]
`Since the low pass filter following the product detector removes the double
`carrier frequency term, the output is
`(5.14)
`vous (t) = SAR (t) cos [@,-@,] = KR(t)
`where K is a gain constant. Equation (5.14) shows that the outputof the low
`passfilter is the demodulated AM signal.
`AM signals are often demodulated using noncoherent envelope detectors
`which are easy and cheap to build. An ideal envelope detector is a circuit that
`has an output proportional to the real envelopeofthe inputsignal. If the input to
`the envelope detector is represented as R(t) cos (2nf.t+6,), then the output is
`given by
`
`(5.15)
`Vou: (f) = KIR(t)|
`where K is a gain constant. As a rule, envelope detectors are useful when the
`input signal poweris at least 10 dB greater than the noise power, whereas prod-
`uct detectors are able to process AM signals with input signal-to-noise ratios well
`below 0 dB.
`
`5.3 Angle Modulation
`FM is part of a more general class of modulation known as angle moduila-
`tion. Angle modulation varies a sinusoidal carrier signal in such a way that the
`
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`

`Vou (8) = AR Ct) cos (@, — 8,)
`
`A,cos (2nf.t +8)
`
`Figure 5.5
`Block diagram of a product detector.
`
`angle of the carrier is varied according to the amplitude of the modulating base-
`band signal. In this method, the amplitude of the carrier wave is kept constant
`(this is why FM is called constant envelope). There are a number of ways in
`which the phase 6(¢) of a carrier signal may be varied in accordance with the
`baseband signal; the two most important classes of angle modulation being fre-
`quency modulation and phase modulation.
`Frequency modulation (FM) is a form of angle modulation in which the
`instantaneous frequency of the carrier signal is varied linearly with the base-
`band message signal m/(t), as shown in equation (5.16).
`
`S,,(t) = A,cos[2nf,t+0(t)] = A,cosaa +ank,|mayan
`
`t
`
`(5.16)
`
`is the carrier frequency, and k, is the
`where A,is the amplitudeof the carrier, f,
`frequency deviation constant (measured in units of Hz/volt). If the modulating
`signal is a sinusoid of amplitude A,, , and frequency f,,, then the FM signal may
`be expressed as
`
`Siu (4) = A,cos|2nf,t + 7
`
` krAy,
`m
`
`.
`
`sin (2nfqt)
`
`(5.17)
`
`Phase modulation (PM) is a form of angle modulation in which the angle
`0(¢) of the carrier signal is varied linearly with the baseband messagesignal
`m(t), as shown tn equation (5.18).
`
`(5.18)
`Spy (4) = A,cos (2nf,t + kyr (t) ]
`In equation (5.18) k, is the phase deviation constant (measured in unitsof radi-
`ans/volt).
`From the above equations, it is clear that an FM signal can be regarded as
`a PM signal in which the modulating waveis integrated before modulation. This
`means that an FM signal can be generated byfirst integrating m(t) and then
`using the result as an input to a phase modulator. Conversely, a PM wave can be
`generatedbyfirst differentiating m(t) and then usingthe result as the input to
`a frequency modulator.
`
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`

`is the peak value of the modulating signal, Af is the peak frequency
`where A,
`deviation of the transmitter and W is the maximum bandwidth of the modulat-
`ing signal. If the modulating signal is a low pass signal, as is usually the case,
`then W is equal to the highest frequency component f,,,, present in the modu-
`lating signal.
`The phase modulation index f, is given by
`B, = kA, = AO
`where AO is the peak phase deviationof the transmitter.
`
`(5.20)
`
`
`
`Example 5.2
`A sinusoidal modulating signal, mit) = 4cos224 x 10°t, is applied to an FM
`modulator that has a frequency deviation constant gain of 10 kHz/V. Compute
`(a) the peak frequency deviation, and {b) the modulation index.
`
`Solution to Example 5.2
`Given:
`Frequency deviation constant ky = 10kHz/V
`Modulating frequency, f,, = 4 kHz
`a) The maximum frequency deviation will occur when the instantaneous value
`of the input signal is at its maximum. For the given mit), the maximum
`value is 4 V, and hence the peak deviation is equal to
`Af = 4V x 10kH2/V = 40 kHz
`b} The modulation index is given by
`
`5.3.1 Spectra and Bandwidth of FM Signals
`When a sinusoidal test
`tone is used such that m(t) = A,,cos2nf,t, the
`spectrum of S,,.(¢) contains a carrier component and an infinite number of
`sidebandslocated on either side of the carrier frequency, spaced at integer multi-
`ples of the modulating frequency /,,. Since S,,,(t) is a nonlinear function of
`m(t), the spectrum of an FMsignal mustbe evaluated on a case-by-case basis for
`a particular modulating wave shape of interest. It can be shown that for a sinu-
`soidal message, amplitudes of the spectral components are given by Bessel func-
`tions of the modulation index B,.
`
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`

`(5.22)
`(Lower bound)
`By, = 2Af
`The above approximation of FM bandwidthis called Carson’s rule. Carson's rule
`states that for small values of modulation index (By< 1), the spectrum of an FM
`waveis effectively limited to the carrier frequency f,, and one pair of side band
`frequencies at f,+f,,, and that for large values of modulation index, the band-
`widtb approaches, andis only slightly greater than, 2A/.
`As a practical example of quantifying the spectrum of an FMsignal, the
`U.S. AMPScellular system uses a modulation index By = 3,and f,, = 4 kHz.
`Using Carson's rule, the AMPS channel bandwidth has an upper bound of 32
`kHz and a lower bound of 24 kHz. However, in practice, the AMPS standard only
`specifies that the medulation products outside 20 kHz from the carrier shall not
`exceed 26 dB below the unmodulatedcarrier. It is further specified that the mod-
`ulation products outside +45 kHz fromthe carrier shall not exceed 45 dB below
`the unmodulated carrier [EIA90].
`
`
`
`Example 5.3
`An 880 MHz carrier signal is frequency modulated using a 100 kHz sinusoidal
`modulating waveform. The peak deviation of the FM signal is 500 kHz. If this
`FMsignal is received by a superbeterodyne receiver having an IFfrequency of
`§ MHz, determine the IF handwidth necessary to pass thesignal.
`
`Solution to Example 5.3
`Given:
`Modulating frequency, f,, = 100 kHz
`Frequency deviation, Af = 500 kHz
`
`Therefore modulation index, By = Af/f,, = 500/100 = 5
`Using Carson’s rule, the bandwidth occupied by the FMsignalis given hy
`Br
`= 2(Bp+1)f,, = 2(5 +1) 100 kHz = 1200 kHz
`The IF filter at the receiver needs to pass all the components in this band-
`width, hence the IF filter should be designed for a bandwidth of 1200 kHz.
`
`5.3.2 FM Modulation Methods
`
`There are basically two methods of generating an FM signal: the direct
`method and the indirect method. In the direct method, the carrier frequency is
`directly varied in accordance with the input modulating signal. in the indirect
`method, a narrowband FM signal is generated using a balanced modulator, and
`
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`

`frequency ofthe carrier signal in accordance with the basebandsignal amplitude
`variations. These oscillators use devices with reactance that can he varied by the
`application of a voltage, where the reactance causes the instantaneous frequency
`of the VCO to change proportionally. The most commonly used variable reac-
`tance device is the voltage-variable capacitor called a varactor. The voltage-vari-
`able capacitor may be obtained, for example, by using a reverse biased p-n
`junction diode. The larger the reverse voltage applied to such a diode,
`the
`smaller the transition capacitance will be of the diode. By incorporating such a
`device into a standard Hartley or Colpitts oscillator, FM signals can be gener-
`ated. Figure 5.6 shows a simple reactance modulator. While VCOsoffer a simple
`way to generate narrowband FMsignals, the stability of the center frequency
`(carrier) of the VCO becomes a major issue whenit is used for wideband FM gen-
`eration. The stability of the VCO can be improved by incorporating a phase
`locked loop (PLL) which locks the center frequency to a stable crystal reference
`frequency.
`
`+ v
`
`aractor
`diode
`
`dulgtin
`magnal
`
`=
`
`Figure 5.6
`A simple reactance modulator in which the capacitance of a varactor diode is changedto vary the fre-
`quency of a simple oscillator. This circuit serves as a VCO,
`
`Indirect Method
`The indirect method of generating FM was first proposed by its inventor,
`Major Edwin Armstrong, in 1936. It is based on approximating a narrowband
`FM signal as the sum of a carrier signal and a single sideband (SSB) signal
`where the sideband is 90° out of phase with the carrier. Using a Taylorseries for
`small values of 0(t), equation (5.16) can be expressed as
`
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`

`5.7, A narrow band FMsignal is generated using a balanced modulator which
`modulates a crystal controlled oscillator. Figure 5.7 is a direct implementation of
`equation (5.23). The maximum frequency deviation is kept constant and small in
`order to maintain the validity of equation (5.23), and hence the output is a nar-
`rowband FMsignal. A wideband FM signal is then produced by multiplying in
`frequency the narrowband FM signal using frequency multipliers. A disadvan-
`tage of using the indirect method for wideband FM generation is that the phase
`noise in the system increases with the frequency multiplying factor N.
`
`modulating
`signal m(t)
`
`
`
`
` Multiplier| wideband
`
`
`FM
`
`+|narrowband
`FM
`
`
`
`Carrier
`
`Oscillator
`
`Figure §.7
`Indirect method for generating a wideband FMsignal. A narrowband FMsignal is generated using a
`balanced modulator and then frequency multiplied to generate a wideband FM signal.
`
`5.3.3 FM Detection Techniques
`There are many ways to recover the original information from an FM sig-
`nal. The objective of all FM demodulators is to produce a transfer characteristic
`that is the inverse of that of the frequency modulator. That is, a frequency
`demodulator should produce an output voltage with an instantaneous amplitude
`that is directly proportional to the instantaneous frequency of the input FM sig-
`nal. Thus, a frequency-to-amplitude converter circuit is a frequency demodula-
`tor. Various techniques such as slope detection, zero-crossing detection, phase
`locked discrimination and quadrature detection are used to demodulate FM.
`Devices which perform FM demodulation are often called frequency discrimina-
`tors. In practical receivers, the RF signal is received, amplified, and filtered at
`the carrier and then converted to an intermediate frequency (IF) which contains
`the same spectrum as theoriginal received signal.
`
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`

`is first passed through an amplitude limiter which
`ure 5.8. The FM signal
`removes any amplitude perturbations which the signal might have undergone
`due to fading in the channel, and produces a constant envelope signal. Using
`equation (5.16) the signal at the outputof the limiter can be represented as
`t
`
`u,(t) = V,cos [2nf,t+0(t)] = V,cos| 2nf.t + 2nk,[ m (nian
`
`xn
`
`(5.24)
`
`U,
`
`in (€)
`
`
` Envelope
`Limiter
`Differentiator
`Sjatecbor
`zed
`{
`;
`
`
`
`
`
`Vous (8)
`
`Figure 5.8
`Block diagram of a slope detector type FM demodulator.
`
`(5,25)
`
`Equation (5.24) can be differentiated in practice by passing the signal
`through a filter with a transfer function that has gain that increases linearly
`with frequency. Sucha filter is called a slopefilter (which is where the term slope
`detector derives its name), The output of the differentiator then becomes
`u,{f) = ~V,|2nf.t +2) sin (2nf,t + 0(t))
`and the output of the envelope detector becomes
`vayft) = ¥, [2nf, +F9it)|
`= V2nf_+ V2nkmn (£)
`The above equation showsthat the output of the envelope detector contains
`a de term proportional to the carrier frequency and a time-varying term propor-
`tional to the original message signal m(t). The de term canbefiltered out using a
`capacitor to obtain the desired demodulated signal.
`Zero-crossing Detector
`Whenlinearity is required over a broad range of frequencies, such as for
`data communications, a zero-crossing detector is used to perform frequency-to-
`amplitude conversion by directly counting the numberof zero crossings in the
`input FM signal. Therationale behind this technique is to use the output of the
`zero-crossing detector to generate a pulse train with an average value thatis
`
`(5.26)
`
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`

`lated pulse train. This pulse train v, (t) is then passed through a differentiator
`whose output is used to trigger a monostable multivibrator (also called a “one-
`shot”). The output of the one-shot consists of a train of pulses with average dura-
`tion proportional to the desired messagesignal. A lowpassfilter is used to per-
`form the averaging operation by extracting the slowly varying de component of
`the signal at the output of the one-shot. The output of the lowpassfilter is the
`desired demodulated signal.
`PLL for FM Detection
`The phase locked loop (PLL) method is another popular technique to
`demodulate an FM signal. The PLLis a closed loop contrel system which can
`track the variations in the received signal phase and frequency. A block diagram
`of a PLL circuit is shown in Figure 5.10. It consists of a voltage controlled oscilla-
`tor H({s) with an output frequency which is varied in accordance with the
`demodulated output voltage level. The output of the voltage controlled oscillator
`is compared with the input signal using a phase comparator, which produces an
`output voltage proportional to the phase difference. The phase difference signal
`is then fed hack to the VCOtocontrol the output frequency. The feedhack loop
`functions in a manner that facilitates locking of the VCO frequency to the input
`frequency. Once the VCOfrequencyis locked to the input frequency, the VCO
`continues to track the variations in the input frequency. Once this tracking is
`achieved, the control voltage to the VCOis simply the demodulated FM signal.
`Quadrature Detection
`Quadrature detection is one of the more popular detection techniques used
`in the demodulation of frequency modulated signals. This technique can be eas-
`ily implemented on anintegrated circuit at a very low cost. The detector consists
`of a network which shifts the phase of the incoming FMsignal by an amount pro-
`portional
`to its instantaneous frequency, and uses a product detector (phase
`detector) to detect the phase difference hetween the original FM signal and the
`signal at the output of the phase-shift network. Since the phase shift introduced
`by the phase-shift network is proportional to the instantaneous frequency of the
`FM signal, the output voltage of the phase detector will also be proportional to
`the instantaneous frequencyof the input FM signal. In this manner, a frequency-
`to-amplitude conversion is achieved, and the FM signal is demodulated.
`To achieve optimum performance from a quadrature detector, a very small
`(no more than +/- 5 degree) phase shift should be introduced across the modu-
`lated signal bandwidth. The phase-shift network should have a constant ampli-
`tude response and a linear phase response over the spectrum occupied by the FM
`
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`

`Zero-crossing detector
`
`Vint)
`
`vip)
`
`F
`vot} [
`
`30)
`
`Vourlt)
`
`t—
`
`t —
`
`|
`
`{—>
`
`‘—
`
`
`
`Figure 5.9
`Block diagram of a zero-croasing detector and associated waveform.s
`
`signal, as shown in Figure 5.11. Further, the network should have a nominal 90°
`phaseshift at the carrier frequency.
`Figure 5.12 shows a block diagram of a quadrature detector. The following
`analysis shows that this circuit functions as an FM demodulator. The phase
`response function of the phase-shift network can be expressed as
`
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`

`
`Voltage
`Controlled
`Oscillator (VCO)
`
`
`Figure 5.10
`Block diagram of a PLL used as a frequency demodulator.
`
` Zip)
`
`&o
`
`a9]
`
`Ba
`ve]a
`
`Se
`frequency —»
`
`frequency —»
`
`Figure 5.11
`Characteristics of the phase-shift network with constant gain and linear phase.
`
`(5.27)
`o(f) = -5+20K (f-f,)
`where K is a proportionality constant. When an FMsignal (see equation (5.16))
`is passed through the phase-shift network, the output can be expressed as
`(5.28)
`v4 (t) = pA,cos[2nf,t + 2nk/|m(n)dn +o (F,(t)) ]
`where p is a constant, and f(t) is the instantaneous frequency of the input FM
`signal, which is defined as
`
`f(t) = f, thy m (t)
`
`(5.29)
`
`The output of the product detector is proportional to the cosine of the phase
`difference between v,(¢) and S,,,(¢) (see Figure 5.12), and is given by
`
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`
`
`
`
`Phase-shift network
`Zp
`with -90 °shift at f
`
`Figure 5.12
`Btock diagramof a quadrature detector
`
`Uy (t)
`
`p'A-cos (6 (fF, (t)))
`c
`pA. cos (—n/2 + 2nK [f,(t) —f,])
`= p'Acsin [21Kk, m (t)]
`If the phase shift varies only over