Lesson 7Angular ModulationA modulation technique wherein the amplitude of the carrier is kept constant, while the angle or the argument of the carrier is varied in accordance with the intelligence signal.Kinds of Angular Modulation-A form of angle modulation where the frequency of the carrier is varied in accordance with the instantaneous value of the intelligence signal.Parts-Carrier Signal-Modulating Signal-FM SignalPeak(+)-Maximum DeviationMiddle(zero)-Rest Frequncy )(no modulation)Peak(-)-Maximum DeviationMathematically,eFM = EcSin(theta)(theta) = Wc(t) + mf sin (wm(t))eFM = Ec Sin (Wc(t)+mf*sin(wm(t)))eFM = instantaneous value of the FM Signal, (V)wc = angular velocity of the carrier, (rad/s)mf = modulation indexEc = peak amplitude of the carrier, (V)Frequency Deviation-The Amount of change in the carrier frequency produced by the modulating signalf=f(+ -)(frequency deviation)frequency deviation is directly proportional to the peak intelligence amplitudefrequency deviation = K*(Em)Where:Frequency Deviation (Hz)K= deviation sensitivity (Hz/V)Em= peak intelligence signal amplitude (V)-In FM the intelligence amplitude Em, determines the amount of carrier frequency change and the intelligence frequency fm, determines the rate of change of the carrier frequency.Modulation IndexRatio of the frequency deviation over modulation frequencyMf=(sigma/fm)Where:Sigma= maximum frequency shift caused by the intelligence signal, (Hz)fm = intelligence frequency (fm)mf= modulation indexFM Percent Modulation%mf=(sigma(actual)/sigma(max))x100%Where:Sigma(max)=maximum carrier deviation(Hz)Sigma(actual)=actual carrier deviation(Hz)%mf=FM percent modulationDeviation Ratio-Whenever the maximum allowable frequency deviation and the maximum modulation frequency are used in computing the modulation index- Expression of the worst case modulation indexDR=(sigma(max)/fm(max))Where:Sigma(max)=maximum carrier deviation (Hz)Fm(max)=maximum allowable intelligence frequency (Hz)DR= deviation ratio

FCC RulesFMSigma(max)=75KhzFm(max)=15KhzTV soundSigma(max)=25KhzFm(max)=15KhzPublic Safety ServicesSigma(max)=5KhzFm(max)=3KhzAmateur Band RatioSigma(max)=3KhzFm(max)=3KhzeFM can be rewritten using the Bessel functioneFM=Ec*(summation(from n=negative infinity to n positive infinity))*mf*sin(wc(t)+n*wm(t))eFM=Ec*(J0*mf*sin(wc(t)) + J1*mf*(sin(wc+wm)-sin(wc-wm)*t))+ J2*mf*(sin(wc+2wm)-sin(wc-2wm)*t))+ J3*mf*(sin(wc+3wm)-sin(wc-3wm)*t))+..+ J2*mf*(sin(wc+N*wm)-sin(wc-N*wm)*t))Where:J0(mf)=carrier componentJ1(mf)=1rst set frequencies displaced from the carrier by fm.J2(mf)=2nd set frequencies displaced from the carrier by 2fm.JN(mf)=Nth set frequencies displaced from the carrier by Nfm.The Amplitude of the side frequencies, Jn, is given by the equation.Jn(mf)=( (mf/2)^n ) ( (1/n) [(mf/2)^2 / 1!(n+1)! ] + [(mf/2)^4 / =2!(n+2)! ] + [(mf/2)^6 / =3!(n+3)! ] )-It is seen that the FM signal consists of a carrier and theoretically infinite number of pairs of sidebands, each preceded by J coefficients, but only those sidebands with significant amplitudes are transmitted.FM SpectrumBessel Function TableBand Width of FM-Practical Bandwidth using Bessel FunctionBW = f(usb)- f(lsb) = (fc+N*fm) - (fc-N*fm)Bw=2*fm*(number of sidebands)Carsons FormulaBW=2*(fm+frequency deviation)=2(1+mf)*fm-The number of sidebands selected should be the minimum number that will result in the transmission of no less than 98% of the total power.Significant sidebands considered are greater than 2% of the carrier.NarrowbandBW=2*fmFor an FM signal where mf((pi/2)Observations on FM-unlike Am where there are only three frequencies (carrier, and the first two sidebands), FM has a carrier and an infinite number of sidebands. The sidebands are separated from the carrier by fm, 2fm,3fm,.. and thus have a recurrence frequency of fm.-The J coefficients eventually decrease in value as n increases.-The modulation index determines how many sidebands components have a recurrence frequency of fm.-The sidebands at equal distances from fc have equal amplitudes, so that the sidebands distribution is symmetrical about the carrier frequency. The J coefficients occasionally have negative values, signifying a 180 degrees phase change for that particular pair of sidebands.-As Mf increases, so does the value of a particular J coefficient. mf is inversely proportional to the modulating frequency; we see that the relative amplitude of distinct sidebands increases when the modulation frequency is lowered.-In AM, increased depth of modulation increases the sideband power and therefore the total transmitted power. In Fm , the total transmitted power always remains constant, but with an increased depth of modulation, the required bandwidth is increased. To be quite specific, what increases is the bandwidth required to transmit a relatively undistorted signal. This is because an increased depth of modulation means an increased deviation and therefore an increased modulation index so that more distant sidebands acquired significant amplitudes.-The theoretical bandwidth required in FM is infinite. In practice, the bandwidth used is one that has been calculated to allow all significant amplitudes of sideband components under the most exacting conditions. This means ensuring that, with a maximum deviation by the highest modulating frequency, no significant sideband components are lopped off.In FM, unlike in Am, the amplitude of the carrier component does not remain constant. Its J coefficient is J0, which is a function of mf. Keeping the overall amplitude of the Fm wave constant would very difficult if the amplitude of the carrier were not reduced when the amplitude of the various sidebands is increased.It is possible for the carrier component of the FM wave to disappear completely. This happens in certain values of the modulation index called eigen values. The graph shows that these are approximately 2.4,5.5,8.6,11.8 and so on. These disappearances of the carrier for specific values of mf form a handy basis for measuring deviation.Advantages of FM over AM-Better Noise immunity-Rejection of interfering signals because of capture effect-Better Transmitter efficiencyDisadvantages of FM over AM-Large Bandwidth -More complex and expensive circuits-Limited receptionFM Varactor ModulatorFM receiver CircuitPre Emphasis Circuit (High Pass Filter)-A circuit that boosts the high audio frequencies in modulation at the transmitter, used to improve the signal to noise ratio.Audio in----(R1+capacitor)-----(resistor to ground)------------Audio OutTau= R1*C=75 micro seconds (10x-6)F1 = ( 1 / 2*(pi)*R1*C ) = 2122Hzf2 = (1 / 2*pi )*( r1+r2/r1*r2*C ) > 15KhzDe-Emphasis Circuit (Lowpass Filter)-A circuit that attenuates the high audio frequencies (at the receiver) in the same amount that if is boosted to compensate for the effect of the emphasis circuit.Pre Emphasized Audio------------------resistor-----capacitor to ground---------Audio outTau=R*C=75 micro seconds (10x-6)7.2 phase Modulation -A form of angle modulation where the phase of the carrier is varied in accordance with the instantaneous value of the modulating signal.Em---------Ec(parallel)--->(phase modulator)---EpmZero slope at peaksMaximum Deviation at peaksAt zeroes no modulation,Zero crossing at x axis -- maximum slope Rest frequency(a) Carrier Signal(b) Modulating Signal(c) FM Signal(d) Pm SignalMathematically, ePM = Ec*sin(wc(t)+mP*sin(wm(t)))where:ePM= instantaneous value of the Pm signal, (V)Ec = peak amplitude of the carrier, (V)wc =carrier angular velocity, (rad/s)mp = modulation index for PM; also, the maximum phase shift caused by the intelligence signalwm = intelligence signal angular velocity (rad/s)Comparison between FM and PM(m & Vm graph) - FM and PM, m & Vm are directly proportional(m & fm graph) - PM is constant, FM inversely proportional(delta(angle) & Vm graph ) PM shows a directly proportionality(delta(f) & Vm graph )FM shows a direct proportionality

Lesson 8 Multiplexing-Multiplexing is the process of combining signals from multiple sources for transmission across a single link.a.) No Multiplexing multiple linksb.) Multiplexing 1 path 4 channels-Path refers to the physical link.-Channel is a portion of the path that carries a transmission between a given pair of devices.Categories of Multiplexing Frequency- division multiplexing (FDM)Wave-Division multiplexing (WDM)Time-Division Multiplexing (TDM)-Synchronous TDM-Asynchronous TDM8.1 Frequency Division Multiplexing- An analog technique that can be applied when the bandwidth of the link is greater than the combined bandwidths of the signals to be transmittedMUX