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ANALOG MODULATION PART II: ANGLE MODULATION What is Angle Modulation? In angle modulation, information is embedded in the angle of the carrier. We define the angle of a modulated carrier by the argument of... st Ac cos t 1999 BG Mobasseri 2 Phasor Form In the complex plane we have t=3 Phasor rotates with nonuniform speed t=1 t=0 1999 BG Mobasseri 3 Angular Velocity Since phase changes nonuniformly vs. time, we can define a rate of change di (t) i dt This is what we know as frequency d i st Ac cos2fct c 2fc i t dt 1999 BG Mobasseri 4 Instantaneous Frequency We are used to signals with constant carrier frequency. There are cases where carrier frequency itself changes with time. We can therefor talk about instantaneous frequency defined as 1 di t fi t 2 dt 1999 BG Mobasseri 5 Examples of Inst. Freq. Consider an AM signal d i st 1 km(t)cos2fc t c 2fc i t dt Here, the instantaneous frequency is the frequency itself, which is constant 1999 BG Mobasseri 6 Impressing a message on the angle of carrier There are two ways to form a an angle modulated signal. – Embed it in the phase of the carrier Phase Modulation(PM) – Embed it in the frequency of the carrier Frequency Modulation(FM) 1999 BG Mobasseri 7 Phase Modulation(PM) In PM, carrier angle changes linearly with the message st Ac cos i t Ac cos fct k pmt 2 Where – 2πfc=angle of unmodulated carrier – kp=phase sensitivity in radians/volt 1999 BG Mobasseri 8 Frequency Modulation In FM, it is the instantaneous frequency that varies linearly with message amplitude, i.e. fi(t)=fc+kfm(t) 1999 BG Mobasseri 9 FM Signal We saw that I.F. is the derivative of the phase 1 di t fi t 2 dt Therefore, t i t 2fc t 2k f mt 0 t st Ac cos fc t 2k f m(t)dt 2 0 1999 BG Mobasseri 10 FM for Tone Signals Consider a sinusoidal message m(t) Am cos2fmt The instantaneous frequency corresponding to its FM version is fi t fc k f m(t) fc k f Am cos2 fmt resting frequency 1999 BG Mobasseri 11 Illustrating FM 1 FM Inst.frequency message 0.8 Moves with the 0.6 Message amplitude 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 1999 BG Mobasseri 12 Frequency Deviation Inst. frequency has upper and lower bounds given by fi t fc f cos2fmt where f frequency deviation k f Am then fi max fc f fi min fc f 1999 BG Mobasseri 13 FM Modulation index The equivalent of AM modulation index is which is also called deviation ratio. It quantifies how much carrier frequency swings relative to message bandwidth f f or W fm baseband tone 1999 BG Mobasseri 14 Example:carrier swing A 100 MHz FM carrier is modulated by an audio tone causing 20 KHz frequency deviation. Determine the carrier swing and highest and lowest carrier frequencies f 20KHz frequency swing 2f 40KHz frequency range : fhigh 100MHz 20KHz 100.02MHz flow 100MHz 20KHz 99.98MHz 1999 BG Mobasseri 15 Example: deviation ratio What is the modulation index (or deviation ratio) of an FM signal with carrier swing of 150 KHz when the modulating signal is 15 KHz? 150 f 75KHz 2 f 75 5 fm 15 1999 BG Mobasseri 16 Myth of FM FM was initially thought to be a bandwidth efficient communication because it was thought that FM bandwidth is simply 2f By keeping frequency deviation low, we can use arbitrary small bandwidth Not so! 1999 BG Mobasseri 17 FM bandwidth Deriving FM bandwidth is a lot more involved than AM and it can barely be derived for sinusoidal message There is a graphical way to illustrate FM bandwidth 1999 BG Mobasseri 18 Piece-wise approximation of baseband Look at the following representation Baseband bandwidth =W 1/2W 1999 BG Mobasseri 19 Corresponding FM signal FM version of the above is an RF pulse for each square pulse. The frequency of the kth RF pulse at t=tk is given by the height of the pulse. i.e. fi fc k f mtk 1999 BG Mobasseri 20 Range of frequencies? We have a bunch of RF pulses each at a different frequency. Inst.freq corresponding to square pulses lie in the following range fi max fc k f mmax fi min fc k f mmin mmax mmin 1999 BG Mobasseri 21 A look at the spectrum We will have a series of RF pulses each at a different frequency. The collective spectrum is a bunch of sincs lowest highest f 4W 1999 BG Mobasseri 22 So what is the bandwidth? Measure the width from the first upper zero crossing of the highest term to the first lower zero crossing of the lowest term lowest highest f 1999 BG Mobasseri 23 Closer look The highest sinc is located at fc+kfmp Each sinc is 1/2W wide. Therefore, their zero crossing point is always 2W above the center of the sinc. f 2W 1999 BG Mobasseri 24 Range of frequenices lowest highest f Above range lies <fc-kfmp-2W,fc+kfmp+2W> 1999 BG Mobasseri 25 FM bandwidth The range just defined is one expression for FM bandwidth. There are many more! BFM=4W+2kfmp Using =∆f/W with ∆f=kfmp BFM=2(+2)W 1999 BG Mobasseri 26 Carson’s Rule A popular expression for FM bandwidth is Carson’s rule. It is a bit smaller than what we just saw BFM=2(+1)W 1999 BG Mobasseri 27 Commercial FM Commercial FM broadcasting uses the following parameters – Baseband:15KHz – Deviation ratio:5 – Peak freq. Deviation=75KHz BFM=2(+1)W=2x6x15=180KHz 1999 BG Mobasseri 28 Wideband vs. narrowband FM NBFM is defined by the condition – ∆f<<W BFM=2W – This is just like AM. No advantage here WBFM is defined by the condition – ∆f>>W BFM=2 ∆f – This is what we have for a true FM signal 1999 BG Mobasseri 29 Boundary between narrowband and wideband FM This distinction is controlled by – If >1 --> WBFM – If <1-->NBFM Needless to say there is no point for going with NBFM because the signal looks and sounds more like AM 1999 BG Mobasseri 30 Commercial FM spectrum The FM landscape looks like this 25KHz guardband carrier FM station A FM station B FM station C 150 KHz 200 KHz 1999 BG Mobasseri 31 FM stereo:multiplexing First, two channels are created; (left+right) and (left-right) Left+right is useable by monaural receivers Left channel + mono Right channel + + - 1999 BG Mobasseri 32 Subcarrier modulation The mono signal is left alone but the difference channel is amplitude modulated with a 38 KHz carrier Left channel + Composite baseband mono + Right channel + + DSB-SC fsc=38 kHz - fsc= freq 38KHz divider 1999 BG Mobasseri 33 Stereo signal Composite baseband signal is then frequency modulated Composite baseband Left channel + FM mono + transmitter Right channel + + DSB-SC fsc=38 kHz - fsc= freq 38KHz divider 1999 BG Mobasseri 34 Stereo spectrum Baseband spectrum holds all the information. It consists of composite baseband, pilot tone and DSB-SC spectrum Left+right DSB-SC 19 KHz 38 KHz 15 KHz 1999 BG Mobasseri 35 Stereo receiver First, FM is stripped, i.e. demodulated Second, composite baseband is lowpass filtered to recover the left+right and in parallel amplitude demodulated to recover the left-right signal Left+right DSB-SC 19 KHz 38 KHz 15 KHz 1999 BG Mobasseri 36 Receiver diagram + lowpass Left+right + left + filter(15K) coherent detector 15 KHz bandpass - + right 19 KHz 38 KHz X lowpass at 38KHz FM + receiver PLL X lowepass Divide 2 VCO 1999 BG Mobasseri 37 Subsidiary communication authorization(SCA) It is possible to transmit “special programming” ,e.g. commercial-free music for banks, department stores etc. embedded in the regular FM programming Such programming is frequency multiplexed on the FM signal with a 67 KHz carrier and 7.5 KHz deviation 1999 BG Mobasseri 38 SCA spectrum Left+right DSB-SC SCA signal 19 KHz 38 KHz 59.5 67 74.5 f(KHz) 15 KHz 1999 BG Mobasseri 39 FM receiver FM receiver is similar to the superhet layout RF IF Discrimi- mixer limiter deemphasis nator AF power LO amp 1999 BG Mobasseri 40 Frequency demodulation Remember that message in an FM signal is in the instantaneous frequency or equivalently derivative of carrier angle t st Ac cos fc t 2k f m(t)dt 2 0 t s t Ac 2fc 2k f mt sin 2fc t 2k f m(t)dt Do envelope detection on s’(t) 1999 BG Mobasseri 41 Receiver components:RF amplifier AM may skip RF amp but FM requires it FM receivers are called upon to work with weak signals (~1V or less as compared to 30 V for AM) An RF section is needed to bring up the signal to at least 10 to 20 V before mixing 1999 BG Mobasseri 42 Limiter A limiter is a circuit whose output is constant for all input amplitudes above a threshold Limiter’s function in an FM receiver is to remove unwanted amplitude variations of the FM signal Limiter 1999 BG Mobasseri 43 Limiting and sensitivity A limiter needs about 1V of signal, called quieting or threshold voltage, to begin limiting When enough signal arrives at the receiver to start limiting action, the set quiets, i.e. background noise disappears Sensitivity is the min. RF signal to produce a specified level of quieting, normally 1999 BG Mobasseri 44 Sensitivity example An FM receiver provides a voltage gain of 200,000(106dB) prior to its limiter. The limiter’s quieting voltage is 200 mV. What is the receiver’s sensitivity? What we are really asking is the required signal at RF’s input to produce 200 mV at the output 200 mV/200,000= 1V->sensitivity 1999 BG Mobasseri 45 Discriminator The heart of FM is this relationship fi(t)=fc+kfm(t) What we need is a device that linearly follows inst. frequency f is at the IF frequency Of 10.7 MHz carrier Disc.output -75 KHz +75 KHz fcarrier f Deviation limits 1999 BG Mobasseri 46 Examples of discriminators Slope detector - simple LC tank circuit operated at its most linear response curve This setup turns an FM signal output into an AM fc fo f 1999 BG Mobasseri 47 Phase-Locked Loop PLL’s are increasingly used as FM demodulators and appear at IF output Output proportional to Difference between fin and fvco fin Phase Error signal Lowpass comparator filter Control signal:constant When fin=fvco fvco VCO input VCO 1999 BG Mobasseri 48 PLL states Free-running – If the input and VCO frequency are too far apart, PLL free-runs Capture – Once VCO closes in on the input frequency, PLL is said to be in the tracking or capture mode Locked or tracking – Can stay locked over a wider range than was necessary for capture 1999 BG Mobasseri 49 PLL example VCO free-runs at 10 MHZ. VCO does not change frequency until the input is within 50 KHZ. In the tracking mode, VCO follows the input to ±200 KHz of 10 MHz before losing lock. What is the lock and capture range? – Capture range= 2x50KHz=100 KHz – Lock range=2x200 KHz=400 KHz 1999 BG Mobasseri 50 Advantages of PLL If there is a carrier center frequency or LO frequency drift, conventional detectors will be untuned PLL, on the other hand, can correct itself. PLL’s need no tuned circuits output If fc drifts detector has no way of Slope detector correcting itself fc fo f 1999 BG Mobasseri 51 Zero crossing detector FM Zero Output Hard Multi- Averaging Crossing limiter vibrator circuot detector FM input Hard limiter more frequent ZC’s means higher inst freq in turn means Larger message ZC detector amplitudes multiV Averaging circuit 1999 BG Mobasseri 52 NOISE IN ANALOG MODULATION AMPLITUDE MODULATION Receiver Model The objective here is to establish a relationship between input and and output SNR of an AM receiver Modulated signal s(t)l BPF detector output filter BT=2W Noise n(t) -fc fc 1999 BG Mobasseri 54 Establishing a reference SNR Define “channel” SNR measured at receiver input (SNR)c=avg. power of modulated signal/ avg. noise power in the message bandwidth 1999 BG Mobasseri 55 Noise in DSB-SC Receiver Tuner plus coherent detection DSB-SC x(t) v(t) BPF LPF s(t) n(t) Cos(2πfct) st Ac m(t)cos2fc t 2 s2 t avg.power Ac 2 m2 (t) / 2 Ac P / 2 P avg. message power 1999 BG Mobasseri 56 Receiver input SNR Also defined as channel SNR: 2 Ac 2 P / 2 Ac P (SNR)c WN o 2WN o noise power in the message bandwidth Flat noise spectrum:white noise No/2 Noise power=hatched area -W W 1999 BG Mobasseri 57 Output SNR Carrying signal and noise through the rest of the receiver, it can be shown that output SNR comes out to be equal to the input. Hence SNRo 1 SNRc Therefore, any reduction in input SNR is linearly reflected in the output 1999 BG Mobasseri 58 (SNR)o for DSB-AM Following a similar approach, SNRo k2P 2 1 SNRc 1 k P k : AM modulation index P : avg. message power Best case is achieved for 100% modulation index which, for tone modulation, is only 1/3 1999 BG Mobasseri 59 DSB-AM and DSB-SC noise performance An AM system using envelope detection needs 3 times as much power to achieve the same output SNR as a suppressed carrier AM with coherent detection This is a result similar to power efficiency of the two schemes 1999 BG Mobasseri 60 Threshold effect-AM In DSB-AM (not DSB-SC) there is a phenomenon called threshold effect This means that there is a massive drop in output SNR if input SNR drops below a threshold For DSB-AM with envelope detection, this threshold is about 6.6 dB 1999 BG Mobasseri 61 NOISE IN ANALOG MODULATION FREQUENCY MODULATION Receiver model FM FM LPF s(t) BFP Limiter detector (W) n(t) Noisy FM signal at BPF’s output is x t st n(t) Ac cos2fct t r(t)cos2fc t t noise where t m(t)dt 1999 BG Mobasseri 63 Phasor model We can see the effect of noise graphically (t) (t) (t) reference The angle FM detector will extract 1999 BG Mobasseri 64 Small noise For small noise, it can be approximated that the noise inflicted phase error is =[r⁄Ac]Sin( So the angle available to the FM detector is + FM Detector computes the derivative of this angle. It will then follow that... 1999 BG Mobasseri 65 FM SNR for tone modulation Skipping further detail, we can show that for tone modulation, we have the following ratio SNRo 3 2 SNRc 2 SNR rises as power of 2 of bandwidth; e.g. doubling deviation ratio quadruples the SNR Bandwidth-SNR exchange 1999 BG Mobasseri 66 Comparison with AM In DSB-SC the ratio was 1 regardless. For commercial FM, =5. Therefore, (SNR)o/(SNR)c=(1.5)x25=37.5 Compare this with just 1 for AM 1999 BG Mobasseri 67 Capture effect in FM An FM receiver locks on to the stronger of two received signals of the same frequency and suppresses the weaker one Capture ratio is the necessary difference(in dB) between the two signals for capture effect to go into action Typical number for capture ratio is 1 dB 1999 BG Mobasseri 68 Normalized transmission bandwidth With all these bandwidths numbers, it is good to have a normalized quantity. Define normalized bandwidth=Bn=BT/W Where W is the baseband bandwidth 1999 BG Mobasseri 69 Examples of Bn For AM: Bn=BT/W=2W/W=2 For FM Bn=BT/W~2 to 3 For =5 in commercial FM, this is a very large expenditure in bandwidth which is rewarded in increased SNR 1999 BG Mobasseri 70 Noise/bandwidth summary AM-envelope detection 2 SNRo SNRc 2 2 Bn 2 1999 BG Mobasseri 71 Noise/bandwidth summary DSB-SC/coherent detection (SNR)o=(SNR)c Bn=2 SSB (SNR)o=(SNR)c Bn=1 1999 BG Mobasseri 72 Noise/bandwidth summary FM-tone modulation and =5 (SNR)o=1.5 2(SNR)c=37.5 (SNR)c Bn~16 for =5 1999 BG Mobasseri 73 Preemphasis and deemphasis High pitched sounds are generally of lower amplitude than bass. In FM lower amplitudes means lower frequency deviation hence lower SNR. Preemphasis is a technique where high frequency components are amplified before modulation Deemphasis network returns the baseband to its original form 1999 BG Mobasseri 74 Pre/deemphasis response Flat up to ~500Hz, rises from 500-15000 Hz 17dB Deemphasis circuit Is between the detector preemphasis And the audio amplifier +3dB -3dB deemphasis -17dB 500 Hz 2120 Hz 15KHz 1999 BG Mobasseri 75 Suggested homework 3.41 5.3 5.7 1999 BG Mobasseri 76