Broadcasting , Switching and Transmission

Basic Principles of Frequency ModulationA sine wave carrier can be modified for the purpose of transmitting information from one place to another by varying its frequency. This is known as frequency modulation (FM).In FM, the carrier amplitude remains constant and the carrier frequency is changed by the modulating signal.Basic Principles of Frequency ModulationAs the amplitude of the information signal varies, the carrier frequency shifts proportionately.As the modulating signal amplitude increases, the carrier frequency increases.With no modulation the carrier is at its normal center or resting frequency.

Basic Principles of Frequency ModulationFrequency deviation (fd) is the amount of change in carrier frequency produced by the modulating signal.The frequency deviation rate is how many times per second the carrier frequency deviates above or below its center frequency.The frequency of the modulating signal determines the frequency deviation rate.A type of modulation called frequency-shift keying (FSK) is used in transmission of binary data in digital cell phones and low-speed computer modems.Basic Principles of Frequency ModulationFigure FM and PM signals. The carrier is drawn as a triangular wave for simplicity, but in practice it is a sine wave. (a) Carrier. (b) Modulating signal. (c) FM signal. (d) PM signal.

Principles of Phase ModulationWhen the amount of phase shift of a constant-frequency carrier is varied in accordance with a modulating signal, the resulting output is a phase-modulation (PM) signal.Phase modulators produce a phase shift which is a time separation between two sine waves of the same frequency.The greater the amplitude of the modulating signal, the greater the phase shift.

Principles of Phase ModulationThe maximum frequency deviation produced by a phase modulator occurs during the time that the modulating signal is changing at its most rapid rate. Principles of Phase ModulationFigure A frequency shift occurs in PM only when the modulating signal amplitude varies. (a) Modulating signal. (b) FM signal. (c) PM signal.

Principles of Phase ModulationRelationship between the Modulating Signal and Carrier Deviation In FM and in PM, the frequency deviation is directly proportional to the amplitude of the modulating signal.In PM, the maximum amount of leading or lagging phase shift occurs at the peak amplitudes of the modulating signal.In PM the carrier deviation is proportional to both the modulating frequency and the amplitude.Principles of Phase ModulationFigure : Frequency deviation as a function of (a) modulating signal amplitude and(b) modulating signal frequency.

Principles of Phase ModulationConverting PM into FMIn order to make PM compatible with FM, the deviation produced by frequency variations in the modulating signal must be compensated for.This compensation can be accomplished by passing the intelligence signal through a low-pass RC network.This RC low-pass filter is called a frequency-correcting network, pre-distorter, or 1/f filter and causes the higher modulating frequencies to be attenuated.The FM produced by a phase modulator is called indirect FM.Principles of Phase ModulationPhase-Shift KeyingThe process of phase modulating a carrier with binary data is called phase-shift keying (PSK) or binary phase-shift keying (BPSK).

The PSK signal has a constant frequency, but the phase of the signal from some reference changes as the binary modulating signal occurs.Principles of Phase ModulationFigure Phase modulation of a carrier by binary data produces PSK.

Modulation Index and SidebandsAny modulation process produces sidebands.When a constant-frequency sine wave modulates a carrier, two side frequencies are produced.Side frequencies are the sum and difference of the carrier and modulating frequency.The bandwidth of an FM signal is usually much wider than that of an AM signal with the same modulating signal.Modulation Index and SidebandsModulation IndexThe ratio of the frequency deviation to the modulating frequency is known as the modulation index (mf).In most communication systems using FM, maximum limits are put on both the frequency deviation and the modulating frequency.In standard FM broadcasting, the maximum permitted frequency deviation is 75 kHz and the maximum permitted modulating frequency is 15 kHz.The modulation index for standard FM broadcasting is therefore 5.Modulation Index and SidebandsBessel Functions The equation that expresses the phase angle in terms of the sine wave modulating signal is solved with a complex mathematical process known as Bessel functions.

Bessel coefficients are widely available and it is not necessary to memorize or calculate them.FM Spectrum Bessel Coefficients.The FM signal spectrum may be determined from

The values for the Bessel coefficients, Jn() may be found from graphs or, preferably, tables of Bessel functions of the first kind. 18FM Spectrum Bessel Coefficients.In the series for vs(t), n = 0 is the carrier component, i.e.

, hence the n = 0 curve shows how the component at the carrier frequency, fc, varies in amplitude, with modulation index . 19

Jn() = 2.4 = 5FM Spectrum Bessel Coefficients.Hence for a given value of modulation index , the values of Jn() may be read off the graph and hence the component amplitudes (VcJn()) may be determined.A further way to interpret these curves is to imagine them in 3 dimensions

20Modulation Index and SidebandsFigure 5-8: Carrier and sideband amplitudes for different modulation indexes of FM signals based on the Bessel functions.

Modulation Index and Sidebands

Figure 5-9: Plot of the Bessel function data from Fig. 5-8.Modulation Index and SidebandsBessel Functions Narrowband FM (NBFM) is any FM system in which the modulation index is less than /2 = 1.57, or mf < /2.NBFM is widely used in communication. It conserves spectrum space at the expense of the signal-to-noise ratio. Types of FMNarrow Band FM (NBFM): The FM with small B.W is known as NBFM.modulation index is small as compared to one radian. Spectrum is consist of carrier,USB & LSB Permissible freq.deviation up to 5KHZ.Used in Police wireless,ambulanceetcWideband FM (WBFM) For large value of mf, the FM wave contains carrier & infinite number of sidebands located symmetrically around the carrier. Such FM have infinite B.W & hence it is WBFM.

Modulation index of WBFM is greater than 1.max. permissible deviation is 75 KHZ.

used in Broadcasting application such as FM-radio,TVetcModulation Index and SidebandsFM Signal BandwidthThe higher the modulation index in FM, the greater the number of significant sidebands and the wider the bandwidth of the signal.

When spectrum conservation is necessary, the bandwidth of an FM signal can be restricted by putting an upper limit on the modulation index.Modulation Index and Sidebands

The no.of sideband having significant amplitude will increase with increase in the value of modulation index.Bandwidth : Ideally B.W of FM is infinite.because infinite sideband transmitted ideally. Practically we have to consider those sideband whose amplitude is greater than 5% of amplitude of unmodulated carrier.strength of spectral component depends on M.I.so B.W is also depends on M.I B.W = 2 fm x number of significant band ------------------------1Carsons Rule: B.W = 2[ +fm .max.] --------------------------------------------------2 it gives correct result if M.I is greater than 6Modulation Index and SidebandsFM Signal BandwidthExample:If the highest modulating frequency is 3 kHz and the maximum deviation is 6 kHz, what is the modulation index?mf = 6 kHz/3 kHz = 2What is the bandwidth?BW = 2fmNWhere N is the number of significant* sidebandsBW = 2(3 kHz)(4) = 24 kHz

*Significant sidebands are those that have an amplitude of greater than 1% (.01) in the Bessel table.EFFECT OF NOISE/NOISE TRIANGLE

Consider a single noise voltage having a freq.which falls in the passband of the reciever. This noise voltage will mix with the carrier to produce interference. Noise vector is superimposed on carrier vector & it is rotating at a relative angular velocity (n-c).due to this the amplitude & phase of the carrier will change. The amplitude & phase angle of resultant shown in fig.will keep changing due to the relative rotation of the noise vector.

Max.deviation in the amplitude = Vn Max.deviation in phase = =Sin-1(Vn/Vc) Amplitude & phase both change due to noiseNoise-Suppression Effects of FMNoise is interference generated by lightning, motors, automotive ignition systems, and power line switching that produces transient signals.Noise is typically narrow spikes of voltage with high frequencies.Noise (voltage spikes) add to a signal and interfere with it.Some noise completely obliterates signal information.Noise-Suppression Effects of FMFM signals have a constant modulated carrier amplitude.FM receivers contain limiter circuits that deliberately restrict the amplitude of the received signal.Any amplitude variations occurring on the FM signal are effectively clipped by limiter circuits.This amplitude clipping does not affect the information content of the FM signal, since it is contained solely within the frequency variations of the carrier.

Noise-Suppression Effects of FMFigure : An FM signal with noise.

Noise-Suppression Effects of FMPre-emphasis Noise can interfere with an FM signal and particularly with the high-frequency components of the modulating signal.Noise is primarily sharp spikes of energy and contains a lot of harmonics and other high-frequency components.To overcome high-frequency noise, a technique known as pre-emphasis is used.A simple high-pass filter can serve as a transmitters pre-emphasis circuit.Pre-emphasis provides more amplification of only high-frequency components.Noise-Suppression Effects of FMFigure Preemphasis and deemphasis. (a) Preemphasis circuit.

Noise-Suppression Effects of FMDe-emphasisA simple low-pass filter can operate as a deemphasis circuit in a receiver.A de-emphasis circuit returns the frequency response to its normal flat level.The combined effect of pre-emphasis and de-emphasis is to increase the signal-to-noise ratio for the high-frequency components during transmission so that they will be stronger and not masked by noise. Noise-Suppression Effects of FMFigure: Preemphasis and deemphasis. (c) Deemphasis circuit.

Frequency Modulation Versus Amplitude ModulationAdvantages of FMFM typically offers some significant benefits over AM.FM has superior immunity to noise, made possible by clipper limiter circuits in the receiver.In FM, interfering signals on the same frequency are rejected. This is known as the capture effect.FM signals have a constant amplitude and there is no need to use linear amplifiers to increase power levels. This increases transmitter efficiency. Frequency Modulation Versus Amplitude ModulationDisadvantages of FMFM uses considerably more frequency spectrum space.FM has used more complex circuitry for modulation and demodulation.In the past, the circuits used for frequency modulation and demodulation involved were complex. With the proliferation of ICs, complex circuitry used in FM has all but disappeared. ICs are inexpensive and easy to use. FM and PM have become the most widely used modulation method in electronic communication today.Frequency Modulation Versus Amplitude Modulation

Major applications of AM and FMFrequency ModulatorsThere are many circuits used to produce FM and PM signals. There are two types of frequency modulator circuits: direct circuits and phase modulation circuits.A frequency modulator is a circuit that varies carrier frequency in accordance with the modulating signal.The carrier is generated by LC or crystal oscillator circuits.Frequency ModulatorsIn LC oscillators, the carrier frequency can be changed by varying either the inductance or capacitance.The idea is to find a circuit or component that converts a modulating voltage to a corresponding change in capacitance or inductance.In crystal oscillators, the frequency is fixed by the crystal.A varactor is a variable capacitance diode used to change oscillator frequencies.

Frequency ModulatorsVaractor OperationA junction diode is created when P- and N-type semiconductors are formed during the manufacturing process.A depletion region, where there are no free carriers, holes, or electrons, is formed in the process.This region acts like a thin insulator that prevents current from flowing through the device.A forward bias will cause the diode to conduct.A reverse bias will prevent current flow.Frequency ModulatorsVaractor OperationA reverse-biased diode acts like a small capacitor.The P- and N-type materials act as the two plates of the capacitor.The depletion region acts as the dielectric material.The width of the depletion layer determines the width of the dielectric and, therefore the amount of capacitance.All diodes exhibit variable capacitance.Varactors are designed to optimize this characteristic.Frequency Modulators

Figure 6-2: Schematic symbols of a varactor diode.Frequency Modulators

Figure 6-4: A direct-frequency-modulated carrier oscillator using a varactor diode.Frequency ModulatorsVaractor ModulatorIn Figure 6-4, the capacitance of varactor diode D1 and L1 form the parallel tuned circuit of the oscillator.The value of C1 is made very large so its reactance is very low.C1 connects the tuned circuit to the oscillator and blocks the dc bias on the base of Q1 from being shorted to ground through L1.The values of L1 and D1 fix the center carrier frequency.The modulating signal varies the effective voltage applied to D1 and its capacitance varies.Frequency ModulatorsVaractor ModulatorMost LC oscillators are not stable enough to provide a carrier signal. The frequency of LC oscillators will vary with temperature changes, variations in circuit voltage, and other factors. As a result, crystal oscillators are normally used to set carrier frequency. Frequency ModulatorsFrequency-Modulating a Crystal OscillatorCrystal oscillators provide highly accurate carrier frequencies and their stability is superior to LC oscillators.The frequency of a crystal oscillator can be varied by changing the value of capacitance in series or parallel with the crystal.By making the series capacitance a varactor diode, frequency modulation can be achieved.The modulating signal is applied to the varactor diode which changes the oscillator frequency.Frequency Modulators

Figure 6-5: Frequency modulation of a crystal oscillator with a VVC.Frequency ModulatorsFrequency-Modulating a Crystal OscillatorVaractors are made with a wide range of capacitance values, most units having a nominal capacitance in the 1- to 200-pF range.A frequency multiplier circuit is one whose output frequency is some integer multiple of the input frequency.A frequency multiplier that multiplies a frequency by two is called a doubler.A frequency multiplier that multiplies a frequency by three is called a tripler.Frequency multipliers can also be cascaded.Frequency Modulators

Figure 6-6: How frequency multipliers increase carrier frequency and deviation.Frequency ModulatorsVoltage-Controlled OscillatorsOscillators whose frequencies are controlled by an external input voltage are generally referred to as voltage-controlled oscillators (VCOs).Voltage-controlled crystal oscillators are generally referred to as VXOs.VCOs are primarily used in FM.VCOs are also used in voltage-to-frequency conversion applications.Frequency ModulatorsReactance ModulatorA reactance modulator is a circuit that uses a transistor amplifier that acts like either a variable capacitor or an inductor.When the circuit is connected across the tuned circuit of an oscillator, the oscillator frequency can be varied by applying the modulating signal to the amplifier.Reactance modulators can produce frequency deviation over a wide range.Reactance modulators are highly linear, so distortion is minimal.Frequency Modulators

Figure 6-10: A reactance modulator.Phase ModulatorsMost modern FM transmitters use some form of phase modulation (PM) to produce indirect FM.In PM the carrier oscillator can be optimized for frequency accuracy and stability.Crystal oscillators or crystal-controlled frequency synthesizers can be used to set the carrier frequency accurately and maintain stability.The output of the carrier oscillator is fed to a phase modulator where the phase shift is made to vary in accordance with the modulating signal.Phase ModulatorsSimple phase shifters do not produce a linear response over a large range of phase shift. To compensate for this, restrict the total allowable phase shift to maximize linearity. Multipliers must also be used to achieve the desired deviation.Phase ModulatorsFigure 6-11: RC phase-shifter basics.

Phase ModulatorsVaractor Phase ModulatorsA simple phase-shift circuit can be used as a phase modulator if the resistance or capacitance can be made to vary with the modulating signal.A varactor can be used to vary capacitance and achieve phase shift modulation.Phase Modulators

Figure 6-12: A varactor phase modulator.Phase ModulatorsTransistor Phase ModulatorA transistor can be used as a variable resistor to create a phase modulator.A standard common emitter class A amplifier biased into the linear region is used in PM.The transistor from collector to ground acts like a resistor.The transistors resistance forms part of the phase shifting circuit.Phase Modulators

Figure 6-13: A transistor phase shifter.Phase ModulatorsTuned-Circuit Phase ModulatorsMost phase modulators are capable of producing a small amount of phase shift. The limited phase shift, therefore, produces a limited frequency shift.Phase and frequency shift can be increased by using a parallel tuned circuit.At resonance, a parallel resonant circuit acts like a large resistor.Off resonance, the circuit acts inductively or capacitively and produces a phase shift.Phase ModulatorsTuned-Circuit Phase ModulatorsPhase modulators are easy to implement, but they have two main disadvantages. The amount of phase shift they produce and the resulting frequency deviation are relatively low. All the phase-shift circuits produce amplitude variations as well as phase changes.Frequency DemodulatorsAny circuit that will convert a frequency variation in the carrier back into a proportional voltage variation can be used to demodulate or detect FM signals. Circuits used to recover the original modulating signal from an FM transmission are called:DemodulatorsDetectorsDiscriminatorsFrequency DemodulatorsSlope DetectorThe slope detector makes use of a tuned circuit and a diode detector to convert frequency variations into voltage variations.The main difficulty with slope detectors lies in tuning them.Frequency Demodulators

Figure 6-16: Slope detector operation.Frequency DemodulatorsPulse-Averaging DiscriminatorsA pulse-averaging discriminator uses a zero crossing detector, a one shot multi-vibrator and a low-pass filter in order to recover the original modulating signal.The pulse-averaging discriminator is a very high-quality frequency demodulator.Originally this discriminator was limited to expensive telemetry and industrial control applications.With availability of low-cost ICs, this discriminator is used in many electronic products. 67FM receiverFM receiver is similar to the superhet layoutRFmixerLOlimiterDiscrimi-natordeemphasisAF powerampIFFrequency Demodulators

Figure 6-17: Pulse-averaging discriminator.Frequency DemodulatorsPhase-Locked LoopsA phase-locked loop (PLL) is a frequency- or phase-sensitive feedback control circuit used in frequency demodulation, frequency synthesizers, and various filtering and signal-detection applications. PLLs have three basic elements. They are:Phase detectorLow-pass filterVoltage-controlled oscillatorFrequency Demodulators

Figure 6-21: Block diagram of a PLL.Frequency DemodulatorsPhase-Locked LoopsThe primary job of the phase detector is to compare the two input signals and generate an output signal that, when filtered, will control the VCO. If there is a phase or frequency difference between the FM input and VCO signals, the phase detector output varies in proportion to the difference. The filtered output adjusts the VCO frequency in an attempt to correct for the original frequency or phase difference. Frequency DemodulatorsPhase-Locked LoopsThis dc control voltage, called the error signal, is also the feedback in this circuit.When no input signal is applied, the phase detector and low-pass filter outputs are zero. The VCO then operates at what is called the free-running frequency, its normal operating frequency as determined by internal frequency-determining components.5.74Frequency ModulationThe modulating signal changes the freq. fc of the carrier signalThe bandwidth for FM is highIt is approx. 10x the signal frequency

5.75The total bandwidth required for FM can be determined from the bandwidth of the audio signal: BFM = 2(1 + )B. Where is usually 4.

Note5.76Figure 5.18 Frequency modulation

5.77Figure 5.19 FM band allocation

5.78Phase Modulation (PM)The modulating signal only changes the phase of the carrier signal.The phase change manifests itself as a frequency change but the instantaneous frequency change is proportional to the derivative of the amplitude.The bandwidth is higher than for AM. 5.79Figure 5.20 Phase modulation

5.80The total bandwidth required for PM can be determined from the bandwidth and maximum amplitude of the modulating signal:BPM = 2(1 + )B.Where = 2 most often.

NoteChapter Four:Angle ModulationIntroductionThere are three parameters of a carrier that may carry information:AmplitudeFrequencyPhaseFrequency and Phase modulation are closely related and grouped together as phase modulationFrequency ModulationPower in an FM signal does not vary with modulationFM signals do not have an envelope that reproduces the modulationThe figure below shows a simplified FM generatorInsert fig. 4.2

Frequency DeviationFrequency deviation of the carrier is proportional to the amplitude of the modulating signal as illustrated

Frequency Modulation IndexAnother term common to FM is the modulation index, as determined by the formula:

Phase ModulationIn phase modulation, the phase shift is proportional to the instantaneous amplitude of the modulating signal, according to the formula:

Relationship Between FM and Phase ModulationFrequency is the derivative of phase, or, in other words, frequency is the rate of change of phaseThe modulation index is proportional to frequency deviation and inversely proportional to modulating frequencyModulating Signal FrequencyInsert fig. 4.4

Converting PM to FMAn integrator can be used as a means of converting phase modulation to frequency modulation

The Angle Modulation SpectrumAngle modulation produces an infinite number of sidebandsThese sidebands are separated from the carrier by multiples of fmFor practical purposes an angle-modulated signal can be considered to be band-limitedBessel FunctionsFM and PM signals have similar equations regarding compositionBessel functions represent normalized voltages for the various components of an AM or PM signal BandwidthFor FM, the bandwidth varies with both deviation and modulating frequencyIncreasing modulating frequency reduces modulation index so it reduces the number of sidebands with significant amplitudeOn the other hand, increasing modulating frequency increases the frequency separation between sidebandsBandwidth increases with modulation frequency but is not directly proportional to itCarsons RuleCalculating the bandwidth of an FM signal is simple, but tedious using Bessel functionsCarsons Rule provides an adequate approximation for determining FM signal bandwidth:

Variation of FM SignalInsert fig. 4.9

Narrowband and Wideband FMThere are no theoretical limits to the modulation index or the frequency deviation of an FM signalThe limits are a practical compromise between signal-to-noise ratio and bandwidthGovernment regulations limit the bandwidth of FM transmissions in terms of maximum frequency deviation and the maximum modulation frequencyNarrow- and Wideband SignalsNarrowband FM (NBFM) is used for voice transmissionsWideband FM (WBFM) is used for most other transmissionsStrict definition of the term narrowband FM refers to a signal with mf of less than 0.5FM and NoiseOne of the original reasons for developing FM was to give improved performance in the presence of noise, which is still one of the major advantages over AMOne way to approach the problem of FM and noise is think of noise as a phasor of random amplitude and phase angleInsert fig. 4.10

FM StereoThe introduction of FM stereo in 1961 was accomplished in such a way so as to insure compatibility with existing FM monaural systemsThe mono FM receivers must be able to capture the L+R signal of a stereo transmitter

FM Broadcasting Spectra

FM MeasurementsThe maximum frequency deviation of an FM transmitter is restricted by law, not by any physical constraintTraditional oscilloscope displays are not useful in analyzing FM signalsA spectrum analyzer is much more useful in determining the qualities of an FM signalPhase-Locked LoopCan be a whole course. The most important part of receiver.Definition: a closed-loop feedback control system that generates and outputs a signal in relation to the frequency and phase of an input ("reference") signal A phase-locked loop circuit responds both to the frequency and phase of the input signals, automatically raising or lowering the frequency of a controlled oscillator until it is matched to the reference in both frequency and phase.

103Voltage Controlled Oscillator (VCO)W(t)=wc+ce0(t), where wc is the free-running frequencyExample

104Ideal ModelModel

Si=Acos(wct+1(t)), Sv=Avcos(wct+c(t))Sp=0.5AAv[sin(2wct+1+c)+sin(1-c)]So=0.5AAvsin(1-c)=AAv(1-c)Capture Range and Lock RangeLPFVCO105Carrier Acquisition in DSB-SCSignal Squaring method

Costas Loop

SSB-SC not working

106

Costas receiver107PLL ApplicationsClock recovery: no pilotDeskewing: circuit designClock generation: Direct Digital SynthesisSpread spectrum: Jitter Noise ReductionClock distribution

108FM BasicsVHF (30M-300M) high-fidelity broadcastWideband FM, (FM TV), narrow band FM (two-way radio)1933 FM and angle modulation proposed by Armstrong, but success by 1949.Digital: Frequency Shift Key (FSK), Phase Shift Key (BPSK, QPSK, 8PSK,)AM/FM: Transverse wave/Longitudinal wave

109Angle Modulation vs. AMSummarize: properties of amplitude modulationAmplitude modulation is linearjust move to new frequency band, spectrum shape does not change. No new frequencies generated.Spectrum: S(f) is a translated version of M(f)Bandwidth 2WProperties of angle modulationThey are nonlinearspectrum shape does change, new frequencies generated.S(f) is not just a translated version of M(f)Bandwidth is usually much larger than 2W110Angle Modulation Pro/Con ApplicationWhy need angle modulation?Better noise reductionImproved system fidelityDisadvantagesLow bandwidth efficiencyComplex implementationsApplicationsFM radio broadcastTV sound signalTwo-way mobile radioCellular radioMicrowave and satellite communications111Instantaneous Frequency

Angle modulation has two forms - Frequency modulation (FM): message is represented as the variation of the instantaneous frequency of a carrier - Phase modulation (PM): message is represented as the variation of the instantaneous phase of a carrier

112Phase ModulationPM (phase modulation) signal

113Frequency ModulationFM (frequency modulation) signal

(Assume zero initial phase)

114FM CharacteristicsCharacteristics of FM signalsZero-crossings are not regularEnvelope is constantFM and PM signals are similar

115Relations between FM and PM

116FM/PM Example (Time)

117FM/PM Example (Frequency)

118fc=1000; Ac=1; % carrier frequency (Hz) and magnitudefm=250; Am=0.1; % message frequency (Hz) and magnitudek=4; % modulation parameter

% generage single tone message signalt=0:1/10000:0.02; % time with sampling at 10KHzmt=Am*cos(2*pi*fm*t); % message signal

% Phase modulationsp=Ac*cos(2*pi*fc*t+2*pi*k*mt);

% Frequency modulationdmt=Am*sin(2*pi*fm*t); % integrationsf=Ac*cos(2*pi*fc*t+2*pi*k*dmt); % PM

% Plot the signalsubplot(311), plot(t,mt,'b'), grid, title('message m(t)')subplot(312), plot(t,sf,'r'), grid, ylabel('FM s(t)')subplot(313), plot(t,sp,'m'), grid, ylabel('PM s(t)')Matlab119% spectrumw=((0:length(t)-1)/length(t)-0.5)*10000;Pm=abs(fftshift(fft(mt))); % spectrum of messagePp=abs(fftshift(fft(sp))); % spectrum of PM signalPf=abs(fftshift(fft(sf))); % spectrum of FM signal

% plot the spectrumsfigure(2)subplot(311), plot(w,Pm,'b'),axis([-3000 3000 min(Pm) max(Pm)]), grid, title('message spectrum M(f)'),subplot(312), plot(w,Pf,'r'), axis([-3000 3000 min(Pf) max(Pf)]), grid, ylabel('FM S(f)')subplot(313), plot(w,Pp,'m'), axis([-3000 3000 min(Pp) max(Pp)]), grid, ylabel('PM S(f)')Matlab120Frequency ModulationFM (frequency modulation) signal

(Assume zero initial phase)

121Examplem(t)0 T 2T

Consider m(t)- a square wave- as shown. The FM wave for this m(t) is shown below.

122Frequency DeviationFrequency deviation fdifference between the maximum instantaneous and carrier frequencyDefinition: Relationship with instantaneous frequency

Question: Is bandwidth of s(t) just 2f?

No, instantaneous frequency is not equivalent to spectrum frequency (with non-zero power)!

S(t) has spectrum frequency (with non-zero power).123Modulation IndexIndicate by how much the modulated variable (instantaneous frequency) varies around its unmodulated level (message frequency)

Bandwidth

A

124Narrow Band Angle Modulation

DefinitionEquationComparison with AMOnly phase difference of Pi/2Frequency: similarTime: AM: frequency constantFM: amplitude constant

Conclusion: NBFM signal is similar to AM signalNBFM has also bandwidth 2W. (twice message signal bandwidth)

125Example

126Block diagram of a method for generating a narrowband FM signal.

127A phasor comparison of narrowband FM and AM waves for sinusoidal modulation. (a) Narrowband FM wave. (b) AM wave.

128Wide Band FMWideband FM signal

Fourier series representation

129Example

130Bessel Function of First Kind

131Spectrum of WBFM (Chapter 5.2)Spectrum when m(t) is single-tone

Example 2.2

132Spectrum Properties