Angle Modulation (Phase & Frequency Modulation)
Angle Modulation (Phase & Frequency Modulation)EE 442 Lecture 7Spring SemesterAngle ModulationStamp issued 1983FM invented 19331
Summary of Lecture 6 – Page 1Modulation is the systematic alteration of a carrier wave so that it “carries” the informationof the message or data signal m(t).Modulation allows for the designated frequency bands (with the carrier frequency at thecenter of the band) to be utilized for communication and allows for signal multiplexing.Amplitude modulation (AM) is an analog and linear modulation process as opposed tofrequency modulation (FM) and phase modulation (PM).AM involves the variation of the carrier signal’s amplitude in direct proportion to themodulating signal m(t).AM is simple to implement and can be accomplished inexpensively with a small number ofcomponents; but AM has a low power efficiency (ratio of power in the message signalrelative to the total transmitted power) and is very susceptible to noise and interference.The landline telephone (PSTN or POTS) uses and voice signal bandwidth of 300 Hz to3,400 Hz and a transmission voice channel of 0 to 4,000 Hz.The Foxhole radio (from World War I) consists of an antenna, inductive coil (paired withparasitic capacitance to form a frequency selective resonator), earphones, and rectifiermade from a razor blade and sharply pointed needle from a safety pin).Review2
Summary of Lecture 6 – Page 2An amplitude modulation time-varying signal (double sideband with carrier – DSB-WC) is AM (t ) AC m(t ) cos( C t )AM can be interpreted using phasors where the carrier of the AM signal is a phasor ofconstant amplitude AC rotating CCW at frequency fC and the modulating signal m(t) madeup of a collection of slower rotating Fourier components of m(t) attached to the tip of thecarrier phasor. The vector sum of the phasors gives the AM phasor.The corresponding amplitude modulation spectrum is AM ( ) 11M( C ) M( C ) AC ( C ) ( C ) 22which is related to the frequency shift property of the Fourier transform.The AM modulation index is defined as mp/AC, where mp is the peak amplitude ofm(t). When 100% overmodulation results in an AM waveform (i.e., envelopedistortion).The power efficiency of AM is defined as message powerP 2 m,total powerAC Pmwhere Pm is the message power. The power efficiency is 11.1% when 0.5 and is33.3% when 1.0 (best case).Review3
Summary of Lecture 6 – Page 3There are two ways to improve on the power efficiency of amplitude modulated signals: (a)suppress the carrier power (known as DSB-SC) in the transmission, and (b) eliminate boththe carrier and one of the sidebands (SSB-SC).Modulators: (a) Nonlinear component modulator, (b) switching modulator and (c) electronicmultipliers (such as using a Gilbert cell).A nonlinearity generates Taylor series terms beyond the term linear in variable v, such asv2, v3 and so on. Terms of v2 (so-called square law behavior) and higher generate newfrequencies that produce amplitude modulation.Square-law modulators are very useful because they produce the DSB-SC AM signal thatcan be demonstrated from( AC m(t ) cos( C t ) )2 m(t ) cos( C t )which is the DSB-SC AM signal as desired.The switching modulator relies upon the generation of a square-wave pulse train p(t) togenerate new frequencies as required to perform modulation, namelyp (t ) 1 2 11 cos( C t ) cos(3 C t ) cos(5 C t ) 2 35Review 4
Summary of Lecture 6 – Page 4The switching modulator generates DSB-SC AM signals directly.A pn-junction is a nonlinear device in its forward biased state that makes a widely usedmodulator (and detector also).An AM signal can always be demodulated using a coherent demodulator (needs acoherent carrier that exactly matches the carrier of the transmitter to recover the messagesignal m(t).However, there are two non-coherent methods to perform AM demodulation. These are (a)envelope detection and (b) rectifier detection.Envelope demodulation depends upon performing half-wave rectification and letting thepeaks of the AM waveform charge a capacitor which decays at a rate allowing for thecapacitor voltage to approximately follow the envelope of the half-wave rectified waveform.The envelope recovery is proportional to message signal m(t).For rectifier demodulation the capacitor of the envelope detector is omitted and therectified AM signal is fed directly into a low-pass filter which recovers [AC m(t)]. The DCcomponent AC may be removed using a series blocking capacitor.With DSB-SC the power efficiency approaches 100% because the square of amplitudeAC is zero from the elimination of the carrier.Review5
Summary of Lecture 6 – Page 5A mixer can be used to generate DSB-SC AM where the RF port is driven by the messagesignal m(t) and the LO port is driven by the carrier signal cos( Ct). The basebandmessage signal is centered about the carrier frequency in the LSB and USB even thoughthe carrier power is zero.For DSB-SC AM demodulation, again a mixer can be used to receive DSB-SC AM wherethe RF port is driven by the message signal m(t) cos( Ct) and the LO port is driven by thecarrier signal cos( Ct). The IF port outputs m(t) m(t) cos(2 Ct), thus allowing for m(t) tobe filtered out and recovered.Synchronous demodulation requires detection of the carrier frequency using the DSB-SBAM signal. One way to do this is to square the incoming AM signal, filter it with abandpass filter and divide the signal by two, thereby recovering a signal in step with thetransmitted carrier frequency and use this signal to drive the LO port of the demodulatingmixer.Multipliers may be built using log and anti-log block (with op amps) to sum two inputs togive a modulated output. Another very widely used method uses the Gilbert cell which isintegrated to produce a linear modulator.Review6
Summary of Lecture 6 – Page 6A commonly used method to generate DSB-SC AM is shown in the block diagram:BPF DSB SC (t )The ring diode modulator for DSB-SC AM is a balanced modulator that operates as aswitching modulator – shown below.You shouldunderstand howthis mixer works.Review7
Summary of Lecture 6 – Page 7Mixers are used for frequency conversion and for heterodyning. Heterodyning uses anelectronic circuit to combine an input radio frequency (RF) with one that is generated (LO)in order to produce new frequencies: one that is the sum of the two and the other thedifference of the two. Heterodyning is typically used to band-shift incoming frequenciesinto intermediate frequencies (IF) for demodulation.Heterodyne receivers can provide (a) selectivity in signal reception, (b) handle a widerange of modulation formats, and (c) are capable of accommodating very high frequencies(even into the millimeter frequency bands).One problem in heterodyne receivers is image signal pickup. Mixers convert two RFsignals to the IF signal using a single LO signal. Thus, both RF signals ( RF1 and RF2)combine with the LO signal LO to give two IF outputs [( LO - RF1) and ( RF2 - LO)].The superheterodyne receiver is universally used in radio and a single conversion stagesuperheterodyne receiver is shown e receiverReview8
Summary of Lecture 6 – Page 8Bandwidth efficiency can be improved is with quadrature amplitude modulation (QAM).QAM involves two data streams: the I-channel and the Q-channel. Bandwidth efficiency isimproved because two signals to share the same bandwidth of a channel. But this canonly be done if the two modulated signals are orthogonal to each other.Modulating one message (call it the in-phase message mI) with cos( Ct) and anothermessage (call it the quadrature message mQ) with sin( Ct) makes the two signalsorthogonal to each other. Thus, both messages can be independently modulated anddemodulated.The QAM signal is of the form, QAM (t ) mI (t ) cos( C t ) mQ (t ) sin( C t )QAM transmits two DSB-SC signals in the bandwidth of one DSB-SC signal. Interferencebetween the two modulated signals of the same frequency is prevented by using twocarriers in phase quadrature. The In-phase (I-phase) channel modulates the cos( Ct)signal and the Quadrature-phase (Q-phase) channel modulates the sin ( Ct) signal. Thecarriers used in the transmitter and receiver are synchronous with each other. In fact, theymust be almost exactly in quadrature with each other; otherwise, they experiencecochannel interference. Low-pass filters are used to extract the baseband signals mI(t)and mQ(t) in the receiver.QAM is used extensively as a modulation scheme for digital telecommunication systems,such as in 802.11 Wi-Fi standards.Review9
Summary of Lecture 6 – Page 9QAM transmitter and receiver block diagram:Transmittercos( C t )zI (t )Receiver QAM (t )2 cos( C t ) Channelsin( C t )2 sin( C t )zQ (t )Effect of error in carrier frequencies between the in-phase and the quadraturechannels.yI (t ) mI (t ) cos( t ) mQ (t ) sin( t )yQ (t ) mQ (t ) cos( t ) mI (t ) sin( t )Review10
Summary of Lecture 6 – Page 10Single-sideband AM (SSB AM) is the most efficient AM signal of any AM transmissionformat with respect to efficient use of bandwidth (100% efficient).The phase-sift method of generating of AM SSB.HilbertTransformer SSB (t ) m(t ) cos( C t ) mh (t )sin( C t )where minus sign applies to USBand plus sign applies to the LSB.mh (t ) is m(t ) phase delayed by - /2Review11
Summary of Lecture 6 – Page 11The phase shift function labelled Hilbert Transform performs the following phase shiftfunction: Given a signal, for positive frequencies, multiply it by –j (phase shift by -90 deg)and for negative frequencies, multiply by j (or 90 deg). j or 90 oH( f )f j or 90 oThe phase shift method uses two balanced (and identical) to eliminate the carrier. Thenthe phase shift is used to cancel one of the sidebands (it can be either the upper sidebandor the lower sideband).With digital signals the closest digital modulation format is pulse amplitude modulation(PAM).Review12
Angle -wave/13
Some Applications for Various Modulation TechniquesNot a complete list of applications.We have studied AM, next is FM and PM.14
Amplitude, Frequency and Phase ModulationWith few exceptions,Phase Modulation (PM)is used predominantly indigital communicationRemember that f d dt15
Illustrating AM, PM and FM SignalsCarrier signalCarrier Wavem(t)tReference:Lathi & DingModulating Signal m(t)100%modulationshownAMAM Modulated SignalAngleModulationPMdm(t ) dtFM m(t )PM Modulated SignalFM Modulated Signaltime16
Focus Upon an FM Signal Modulated by a Single-ToneSingle-tone modulating signalFMSIGNALBASEBANDSIGNALm(t )17
Comparing AM, PM and FM for a Ramp m(t)carriercos( (t )dtfrequencymodulationm(t )https://www.princeton.edu/ mvaezi/ece3770/ECE3770 Lecture7.pdf18
General Observations on FM and PM Waveforms1. Both FM and PM waveforms are identical except for a time shift,when m(t) is a sinusoidal signal.2. For FM, the maximum frequency deviation occurs when modulatingsignal is at its peak values (i.e., at mp and – mp).3. For PM, the maximum frequency deviation takes place at the zerocrossings of the modulating signal m(t).4. It is generally difficult to know from looking at a waveform whetherthe modulation is FM or PM.5. The message resides in the zero-crossings alone, provided thecarrier frequency is large compared to frequency content of m(t).6. The modulated waveform doesn’t resemble the message waveform.Reference: Carlson & Crilly, 5th ed., Section 5.1, pages 208 to 212.19
Advantages of Angle Modulation1. Angle modulation is resistant to propagation-induced selective fadingbecause the amplitude variations don’t contain information.2. Angle modulation is very efficient in rejecting interference (i.e., itminimizes the effect of amplitude noise on the signal transmission).3. Angle modulation allows for more efficient use of transmitter power.4. Angle modulation can handle a greater dynamic range in themodulating signal without distortion (as would occur in AM).5. Wideband FM gives significant improvement in the signal-to-noise ratioat the output and is proportional to the square of the modulationindex , where fBB fBandwidthFrequency deviation20
Phase-Frequency Relationship When Frequency is Constant (t ) AC cos( (t )) (t) is generalized angle (t ) AC cos( C t 0 ) (t )No modulation C t 0 0 is constant 0d (t )Slope: i (t ) dt t ti Ctime t21
Concept of Instantaneous FrequencyAngleModulationin red line (t ) AC cos( (t )) (t) is generalized angle (t ) AC cos( C t 0 ) (t ) (t )Slope: i (t ) 0ti C t 0 0 is constantd (t ) dt t ti Ctime t22
Angle Modulation Gives PM and FMd (t ) i ( t ) dt t tiand (t ) t ( ) d i requency modulation and phase modulation are closely related!23
Comparing Frequency Modulation to Phase ModulationNo.Frequency Modulation (FM)Phase Modulation (PM)1Frequency deviation is proportional tomodulating signal m(t)Phase deviation is proportionalto modulating signal m(t)2Noise immunity is superior to PM (and ofcourse AM)Noise immunity better thanAM, but not FM3Signal-to-noise ratio (SNR) is better thanPM (and of course AM)Signal-to-noise ratio (SNR) isnot quite as good as with FM4FM is widely used for commercialbroadcast radio (88 MHz to 108 MHz)PM is primarily used for mobileradio services5Modulation index is proportional tomodulating signal m(t) as well as themodulating frequency fmModulation index isproportional to modulatingsignal m(t)24
FM has superior noise immunity compared to AMFM has better noise (or RFI)rejection than AM, as shown inthis dramatic New Yorkpublicity demonstration byGeneral Electric in 1940. Theradio contained both AM and FMreceivers. With a million-volt arcas a source of interferencebehind it, the AM receiverproduced only a roar of static,while the FM receiver clearlyreproduced a music programfrom Armstrong's experimentalFM transmitter W2XMN in NewJersey.https://en.wikipedia.org/wiki/Frequency modulationNote: RFI stands for radio frequency interference.25
Phase Modulation (PM) i (t ) C t 0 k p m(t ) ;Usually we set 0 0, PM (t ) AC cos( C t k p m(t ))Agbo & SadikuSection 4.2; p. 159The instantaneous angular frequency (in radians/second) is i (t ) d i (t )dm(t ) C k p C k p m '(t )dtdtIn phase modulation (PM) the instantaneous angular frequency ivaries linearly with the time derivative of the message signal m(t)[denoted here by m’(t)].kp is the phase-deviation (sensitivity) constant. Units: radians/volt[Actually it is radians/unit of the parameter m(t).]26
Frequency Modulation (FM)But in frequency modulation the instantaneous angular frequency i varies linearly with the modulating signal m(t), i (t ) C k f m(t ) i (t ) t C k f m( ) d C t k ft m( ) d kf is frequency-deviation (sensitivity) constant. Units: radians/volt-sec.Thent FM (t ) AC cos C t k f m( ) d FM and PM are related to each other.In PM the angle is directly proportional to m(t).In FM the angle is directly proportional to the integralAgbo & SadikuSection 4.2; p. 159 m(t )dt .27
SummaryMessage signal is m(t)Definition: Instantaneous frequency is i (t ) Phase ModulationAngle i (t ) C t k p m(t )d i (t )dtFrequency Modulation i (t ) C t k ft m( ) d Frequency i C kpdm(t )dt i C k f m(t )In phase modulation m(t) drives the time variation of phase i.In frequency modulation m(t) drives the time variation of frequency fC.28
A Pictorial View of FM and PM GenerationH(j ) 1/j m(t ) t m( ) d PhaseModulatorGenerationof FM Agbo & SadikuFigure 4.1p. 160Frequency ModulatorAC cos( C t )H(j ) j m(t )ddtPhase Modulatordm(t )dt FM (t )FrequencyModulator PM (t )Generationof PMAC cos( C t )We require that H(j ) be a reversible (or invertible) operationso that m(t) is recoverable.29
Both FM and PM Generation are Nonlinear ProcessesConsider a phase modulated signal:Lets (t ) AC cos ( C t k p [m1 (t ) m2 (t )])Ifs1 (t ) AC cos ( C t k p m1 (t ) ) , ands2 (t ) AC cos ( C t k p m2 (t ) )It then holds thats1 (t ) s2 (t ) s (t ) additivity failsSo PM can't be linear.The same argument holds for FM.Note: Linearity requires both additivity and homogeneity to hold.30
Modulation Index for Angle ModulationLet the peak values of the message signal m(t) and its first derivative m’(t) berepresented byPeak value of m(t) mp ½(mmax – mmin)Peak value of m’(t) [ dm(t)/dt] m’pFrequency Deviation is the maximum deviation of the instantaneousmodulated carrier frequency relative to the unmodulated carrier frequency.It is (symbolically) represented by either or f.k f mpFM: k f m p or f 2 k p m pPM: k p m p or f 2 The ratio of the frequency deviation f to the message signal’s bandwidth BIs called the Frequency Deviation Ratio or the Modulation Index, and isdenoted by (unitless). f B 2 B31
Equations for FM Wave with Single-Tone ModulationCarrier signalCarrier frequencyModulating wave m(t )Modulating frequencyDeviation sensitivityAC cos( C t ) (volts) C 2 fC (radians/sec)Am cos( mt ) Single-tone modulation m 2 f m (radians/sec)k f (radians/volt-second)Frequency deviation k f Am (radians/sec) f k f Am (unitless)f m m mAInstantaneous frequency f i fC k f m cos( mt ) fC f cos( mt )2 t Remember FM (t ) AC cos C t k f m( )d , generally k f Am Tone modulated wave FM (t ) AC cos C t sin( mt ) m Modulation Indexor FM (t ) AC cos ( C t sin( mt ) ) 32
Summary of Mathematical Equations for FM and PMType ofModulationModulating SignalAngle Modulated WavePhasemodulationm(t)AC cos ( C t k p m(t ) )Frequencymodulationm(t)AC cos C t k f m( )d PhasemodulationTone:m(t) Am cos( mt)AC cos ( C t k p Am cos( C t ) )FrequencymodulationTone:m(t) Am cos( mt)k f Am AC cos C t sin( C t ) m ( t )k f Am m33
Example- FM (t ) 10 cos ( 2 (10 6 )t 8 sin(2 (10 3 )t ) ) fC FM (t ) f34
Solution to ExampleStart with the basic FM equation: FM (t ) AC cos ( 2 fC t sin(2 f mt ) ) Compare this to FM (t ) 10 cos ( 2 (106 )t 8sin(2 (103 )t ) ) (a) We see that fC 1,000,000 Hz & fm 1000 Hz.(b) The modulation index is 8.(c) The peak deviation frequency f is f f m 8 1000 8, 000 HzNote: f /fC is 0.008 or 0.8 % deviation frequency to carrierfrequency.35
Average Power of a FM or PM WaveThe amplitude AC is constant in a phase modulated or a frequencymodulated signal. RF power does not depend upon the frequencyor the phase of the waveform. FM or PM (t ) AC cos C t g( kk , m(t )) AC2Average Power (always)2This is a result of FM and PM signals being constant amplitude.Note: kk becomes kf for FM and kp for PM.36
Average Power of a FM or PM WaveProblem:Consider an angle modulated signal given by (t ) 6 cos ( 2 106 t 2 sin(8000 t ) voltsWhat is the average power of this signal?Solution:AC2Average power PC where AC 6 volts262 36Therefore, PC 18 watts (assumes 1 ohm resistance)22Note that the result does not depend upon it being FM or PM.37
Comparison of FM (or PM) to AM#Frequency Modulation (FM)Amplitude Modulation (AM)1FM receivers have better noiseimmunityAM receivers are very susceptible tonoise2Noise immunity can be improvedby increasing the frequencydeviationThe only option in AM is to increasethe transmission power3Bandwidth requirement is greaterand depends upon modulationindexAM bandwidth is less than FM or PMand doesn’t depend upon amodulation index4FM (or PM) transmitters andreceivers are more complex thanfor AMA
Modulation allows for the designated frequency bands (with the carrier frequency at the center of the band) to be utilized for communication and allows for signal multiplexing. Amplitude modulation (AM) is an analog and linear modulation process as opposed to frequency modulation (FM) and phase modulation (PM).
4.1. ANGLE MODULATION 11 1 1 11 1 1 tt /3 phase step at t 0 3 Hz frequency step at 0 Phase Modulation Frequency Modulation f c f c f f 3 Hz Phase and frequency step modulation 4.1.1 Narrowband Angle Modulation Begin by writing an angle modulated signal in complex form x c.t/DRe A ce j!ctej .t/ Expand ej .t/in a power series x c.t/DRe A .
9/18/2016 9Nurul/DEE 3413/Modulation Types of Modulation Pulse Modulation Carrier is a train of pulses Example: Pulse Amplitude Modulation (PAM), Pulse width modulation (PWM) , Pulse Position Modulation (PPM) Digital Modulation Modulating signal is analog Example: Pulse Code Modulation (PCM), Delta Modulation (DM), Adaptive Delta Modulation (ADM), Differential Pulse
Types of Modulation 6 Flynn/Katz 7/8/10 Analog Modulation Amplitude Modulation, AM Frequency Modulation, FM Double and Single Sideband, DSB and SSB Digital Modulation Phase Shift Keying: BPSK, QPSK, MSK Frequency Shift Keying, FSK Quad
10.3 Analog Modulation Schemes 10.4 Amplitude Modulation 10.5 Frequency Modulation 10.6 Phase Shift Modulation 10.7 Amplitude Modulation And Shannon's Theorem 10.8 Modulation, Digital Input, And Shift Keying 10.9 Modem Hardware For Modulation And Demodulation 10.10 Optical And Radio Frequency Modems 10.11 .
3. Amplitude Modulation . a. General. The amplitude, phase, or frequency of a carrier can be varied in accordance with the intelligence to be transmitted. The process of varying one of these characteristics is called modulation. The three types of modulation, then are amplitude modulation, phase modulation
Ans: Modulation is defined as the process in which some characteristics of the signal called carrier is varied according to the modulating or baseband signal. For example – Amplitude Modulation, Phase Modulation, Frequency Modulation. In case of over modulation, the modulation index is
Before measuring an angle, it is helpful to estimate the measure by using benchmarks, such as a right angle and a straight angle. For example, to estimate the measure of the blue angle below, compare it to a right angle and to a straight angle. 90 angle 180 angle A right angle has a measure of 90
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