Ch t 5Chapter Angle Modulation EEEF311 (2014-2015) NITIN Sharma 1 FM Illustration The frequency of the carrier is varied around c in relation with the g signal. g message i(t)= c + kf m(t) EEEF311 (2014-2015) NITIN Sharma 2 Instantaneous Frequency The argument of a cosine function represents an angle. angle The angle could be constant [cos(300)], or varying with time, cos [(t)] The instantaneous angular frequency (in rad/sec) is the rate of change of the angle. That is: i (t) = d (t)/dt . For cos(c t +), i (t)= c as expected. t (t ) i ( )d . EEEF311 (2014-2015) NITIN Sharma 3 ). g FM (t ) A cos c t k f m ( )d t For Phase Modulation ((PM). the phase p of the carrier is varied in relation to the message signal: (t) = kp m(t) g PM (t ) A cos c t k p m (t ) EEEF311 (2014-2015) NITIN Sharma 4 .Representation of Angle Modulation in Time Domain For F an FM signal: i l i (t) = c + kf m(t) (t) t t FM (t ) i ( )d ct k f m( )d . Relation Between FM and PM PM (t ) c t k p m (t ). dm (t ) i (t ) c k p c k p m (t ). dt m(t) m(t) () t FM Modulator gFM(t) t ()d m (t )d PM M Modulator d l gPM(t) d () dt EEEF311 (2014-2015) NITIN Sharma dm (t ) dt 5 . Which is Which? EEEF311 (2014-2015) NITIN Sharma 6 . FM and PM Modulation kf = 2×105 rad/sec/volt =105 Hz/Volt = 105 V-11·sec-11 kp = 10 rad/Volt = 5 v-1 fc = 100 MHz FM: fi = fc + kf m(t) 108 -105 < fi < 108 +105 99.9 < fi < 100.1 MHZ PM: fi = fc + kp dm(t)/dt 108 -105 < fi < 108 -105 99.9 < fi < 100.1 MHZ Power ((FM or PM)) = A2/2 EEEF311 (2014-2015) NITIN Sharma 7 Frequency Modulation The image cannot be display ed. Your computer may not hav e enough memory to open the image, or the image may hav e been corrupted. Restart y our computer, and then open the file again. If the red x still appears, y ou may hav e to delete the image and then insert it again. Δf c sin ωmt may be expressed as Bessel The equationvs t = Vc cos ωc t + fm series (Bessel ( l ffunctions)) The image cannot be display ed. Your computer may not hav e enough memory to open the image, or the image may hav e been corrupted. Restart y our computer, and then open the file again. If the red x still appears, y ou may hav e to delete the image and then insert it again. v s t = Vc J β cosω n= n c + nωm t where Jn() are Bessel functions of the first kind. Expanding the equation for a few terms we have: v s (t ) Vc J 0 ( ) cos( c )t Vc J 1 ( ) cos( c m )t Vc J 1 ( ) cos( c m )t Amp fc fc fm Amp Amp fc fm Vc J 2 ( ) cos( c 2 m )t Vc J 2 ( ) cos( c 2 m )t Amp fc 2 fm Amp EEEF311 (2014-2015) NITIN Sharma fc 2 f m 8 FM Signal Spectrum. The amplitudes drawn are completely arbitrary, since we have not found any value for Jn() – this sketch is only to illustrate the spectrum. spectrum EEEF311 (2014-2015) NITIN Sharma 9 we will make some assumptions and work on simple modulating messages. particularly interested in finding the bandwidth occupied by an FM/PM signal. Modulation it is not straightforward to relate the spectrum of the FM/PM modulated signal to that of the modulating signal m(t).Spectrum of FM/PM Unlike Amplitude Modulation. We can deal with i on a case-by-case it b b i basis. We are. however. EEEF311 (2014-2015) NITIN Sharma 10 . we will do the analysis for FM and extend it to PM. For that purpose. Because of the close relation between FM and PM. tables of ‘Bessel functions of the first kind’. preferably. The FM signal spectrum may be determined from v s (t ) Vc J n n ( ) cos( c n m )t The values for the Bessel coefficients. Jn() may be found from graphs or.FM Spectrum – Bessel Coefficients. EEEF311 (2014-2015) NITIN Sharma 11 . e. EEEF311 (2014-2015) NITIN Sharma 12 . frequency fc. with modulation index .Vc J 0 ( ) cos( c t ) hence the n = 0 curve shows how the component at the carrier frequency. varies in amplitude. Jn() = 2.4 =5 In the series for vs(t).FM Spectrum – Bessel Coefficients. n = 0 is the carrier component. i. Hence for a given value of modulation index . A further way to interpret these curves is to imagine them in 3 dimensions EEEF311 (2014-2015) NITIN Sharma 13 . the values of Jn() may be read off the graph and hence the component amplitudes (VcJn()) may be determined.FM Spectrum – Bessel Coefficients. J1(2. i.Examples from the graph = 0: When = 0 the carrier is unmodulated and J0(0) = 1.e.2 EEEF311 (2014-2015) NITIN Sharma 14 . = 2.45 and J3(2.4) = 0.4) = 0.4) = 0. J2(2.4) = 0. 1 all other Jn(0) = 0.4: From the graph (approximately) J0(2.5. 7652 0 4400 0.0196 0.0002 Amplitude 0. In FM the sidebands are considered to be significant if Jn() 0.0196Vc Insignificant Insignificant Frequency fc fc+fm fc . S t As may y be seen from the table of Bessel functions. for values of n above a certain value. Although g the bandwidth of an FM signal g is infinite.0025 0. n 0 1 2 3 4 5 Jn(1) 0.01 (1%). for which Jn() < 0. Example: A message signal with a frequency fm Hz modulates a carrier fc to produce FM with a modulation index = 1.01 are deemed to be insignificant and may be ignored..1149Vc 0. the values of Jn() become progressively smaller.44V 0.fm fc+2fm fc .1149 0.Si ifi t Sidebands Significant Sid b d – Spectrum.7652Vc 0 44Vc 0.2fm fc+3fm fc -3 fm 15 .. components p with amplitudes VcJn().4400 0. Sketch the spectrum. Significant Sidebands – Spectrum. As shown. for = 1. 1 EEEF311 (2014-2015) NITIN Sharma 16 . the bandwidth of the spectrum containing significant components is 6fm. 16 sidebands (8 pairs).0 10.1 0. g for = 5..Significant Sidebands – Spectrum.0 No of sidebands 1% of unmodulated carrier 2 4 4 6 8 16 28 Bandwidth 2fm 4fm 4fm 6fm 8fm 16fm 28fm e. The table below shows the number of significant sidebands for various modulation indices () and the associated spectral bandwidth.g.0 2. 0. EEEF311 (2014-2015) NITIN Sharma 17 .5 1.3 0.0 5. Carson’s Rule for FM Bandwidth. An approximation for the bandwidth of an FM signal is given by BW = 2(Maximum frequency deviation + hi h t modulated highest d l t d ffrequency)) Bandwidth 2(f c f m ) Carson’s Rule EEEF311 (2014-2015) NITIN Sharma 18 . EEEF311 (2014-2015) NITIN Sharma 19 . Wideband FM WBFM For > 0.3 is referred to as narrowband FM (NBFM) (Note.3 F 0 3 there th are more than th 2 significant i ifi t sidebands. BW = 2fm. This is referred to as wideband FM (WBFM). FM with 0. i.3) there is only the carrier and 2 significant sidebands.e. the bandwidth is the same as DSBSC).Narrowband and Wideband FM Narrowband FM NBFM From the graph/table of Bessel functions it may be seen that for small . ( 0. id b d As A increases i the number of sidebands increases. EEEF311 (2014-2015) NITIN Sharma 20 .VHF/FM VHF/FM (Very High Frequency band = 30MHz – 300MHz) radio transmissions. Applying Carson’s Rule BW = 2(75+15) = 180kHz.g. music) fm 15kHz Deviation 75kHz Modulation Index 5 f c Vm f c fm For = 5 there are 16 sidebands and the FM signal bandwidth is 16fm = 16 x 15kHz= 240kHz. in the band 88MHz to 108MHz have the following parameters: Max frequency input (e. as do all the other components and none may be suppressed .v s (t ) Vc J n n ( ) cos( c n m )t • In FM we refer to sideband pairs not upper and lower sidebands.Comments FM • The FM spectrum contains a carrier component and an infinite number of sidebands at frequencies fc nfm (n = 0. …) FM signal signal. FM • The relative amplitudes of components in FM depend on the values Jn(). 2. where V m fm thus the component at the carrier frequency depends on m(t). EEEF311 (2014-2015) NITIN Sharma 21 . 1. C i or other Carrier th components t may nott be b suppressed d in i FM. When m(t) is a band of signals.01. EEEF311 (2014-2015) NITIN Sharma 22 . E.3 0 3 or less) only J0() and J1() are significant. (impossible?) Calculations usually assume a single tone frequency equal to the maximum input frequency. similar to DSBSC in terms of bandwidth . The principle of superposition does not apply.e. only a carrier and 2 sidebands. speech or music the analysis is very difficult (impossible?). e.called NBFM.g. • Large modulation index f c fm means that a large bandwidth is required – called WBFM • The FM process is non-linear. i. fm = 15kHz is used.g. m(t) band 20Hz 15kHz.Comments FM • Components are significant if Jn() 0. 0 01 For <<1 ( 0. Bandwidth is 2fm. Power in FM Signals. the total power in the infinite spectrum is (Vc J n ( )) 2 Total power PT 2 EEEF311 n (2014-2015) NITIN Sharma 23 . From the equation for FM v s (t ) Vc J n n ( ) cos( c n m )t we see that the p peak value of the components p is VcJn() for the nth component. 2 V pk (V RMS ) 2 Then the nth component Single normalised average power is= 2 V J ( ) Vc J n ( ) c n 2 2 2 2 Hence. (2014-2015) 24 NITIN Sharma 2 . considering the waveform. the peak value is V-c.Power in FM Signals. V pk Vc Since we know that the RMS value of a sine wave is 2 2 2 Vc J n ( ) V V c c 2 P and power = (VRMS) then we may deduce that T 2 2 n 2 2 Hence. By this method we would need to carry out an infinite number of calculations to find PT. we can find the total power PT for the infinite spectrum with a simple EEEF311calculation. But. which is constant. if we know Vc for the FM signal. EEEF311 (2014-2015) NITIN Sharma 25 . We can think of the signal spectrum as a ‘train’ and the channel bandwidth as a tunnel – obviously we make the train slightly l h l less l wider d than h the h tunnell iff we can. user Only a limited bandwidth is available for any particular signal. this implies that we require an infinite bandwidth channel.g. Thus we have to make the signal spectrum fit into the available channel bandwidth. However. if we wish to transfer this signal. over a radio or cable.Power in FM Signals. it will contain an infinite number of sidebands. e. Now consider – if we generate an FM signal. Even if there was an infinite channel bandwidth it would not all be allocated to one user. many y signals g ((e... digital g signals) g ) contain an infinite number of components. If we put an infinitely wide train through a tunnel.. the train would come out distorted. EEEF311 (2014-2015) NITIN Sharma 26 .g. g FM. spectral components decrease in amplitude as we move away y from the spectrum p ‘centre’. we will lose some of the components and the output signal will be distorted.Power in FM Signals. square q waves. If we transfer such a signal via a limited channel bandwidth. However. distorted the question is how much distortion can be tolerated? Generally speaking. e. Hence. In general distortion may be defined as D Power in total spectrum . a = 8 pairs (16 components). 2 n a a EEEF311 (2014-2015) NITIN Sharma 27 .Power in FM Signals.. For a bandlimited FM spectrum. let a = the number of sideband p pairs.Power in Bandlimited spectrum Power in total spectrum PT PBL D PT With reference to FM the minimum channel bandwidth required would be just wide enough to pass the spectrum of significant components.g. g for = 5. power in the bandlimited spectrum PBL is (Vc J n ( )) 2 PBL = carrier power + sideband powers. p . e. Vc2 Since PT 2 Vc2 Vc2 a ( J n ( )) 2 a 2 2 n a 2 1 ( J ( )) Distortion D n Vc2 n a 2 Also. it is easily seen that the ratio a Power in Bandlimited spectrum PBL D ( J n ( )) 2 = 1 – Distortion PT Power in total spectrum n a a i. proportion pf power in bandlimited spectrum to total power = EEEF311 (2014-2015) NITIN Sharma (J n a n 28 ( )) 2 .Power in FM Signals. 99or 99% of the total power 50 EEEF311 (2014-2015) NITIN Sharma 29 36 .e.995 i e the carrier + 2 sidebands contain i.Example Consider NBFM. The total power in the infinite a Vc2 2 spectrum = 50 Watts. ( Amp A )2 Power = 2 49.5 Watts 49.2) (0 2) Amp = VcJn(0.90 0.005 0.0995 9.2.2) (0 2) 0 1 0. i.e.4950125 PBL = 49.5 0. with = 0.9900 0. 2 n a From the table – the significant components are n Jn(0. Let Vc = 10 volts. ( J n ( )) = 50 Watts. 01 or 1%.01 2 2 1 PBL ( J n ( )) 2 1 D 0.e. i.Example PT PBL 50 49. don’t ’t need d tto know k Vc.99 Ratio PT n 1 EEEF311 (2014-2015) NITIN Sharma 30 . i alternatively lt ti l Distortion = 1 1 (J n 1 n (0.5 0.99) (0.0995) 0.2)) 2(a = 1) D =1 (0. Distortion = 50 PT A t ll we d Actually. which turns out to be wrong.What is NOT the bandwidth of FM! O One may ttendd to t believe b li th thatt since i th the modulated d l t d signal instantaneous frequency is varying between by ff around fc. What Wh t was missing i i from f the th picture i t off bandwidth? b d idth? EEEF311 (2014-2015) NITIN Sharma 31 . False! In fact. then the bandwidth of the FM signal g is 2f. the motivation behind introducing FM was to reduce the bandwidth compared to that of Amplitude Modulation. and wiggling it back and forth to modulate the carries in response to some message.FM Visualization Think of holding the frequency knob of a signal generator. There are two wiggling gg g parameters: p How far you deviate from the center frequency (f) How fast you wiggle (related to Bm) The rate of change of the instantaneous frequency was missing! EEEF311 (2014-2015) NITIN Sharma 32 . BFM ≈ 2(( +1)) Bm The same rule applies to PM bandwidth. BPM ≈ 2(f+Bm) = 2( +1) Bm where (f )PM = kp |dm(t)/dt|max EEEF311 (2014-2015) NITIN Sharma 33 .Carson’s Rule BFM ≈ 2(f+Bm) where f = frequency deviation = kf |m(t)|max Bm = bandwidth b d id h off m(t) () Define the deviation ratio = f / Bm. the deviation h bandwidth b d id h off the h modulated signal does not get smaller than 2Bm. BNBFM ≈ 2Bm (same ( f NBPM) for Therefore. no matter how small we make the d i i aroundd fc . NBPM). <<1) the th scheme h is i called Narrow Band (NBFM.Narrow Band and Wide Band FM Wh When f << Bm (or ( <<1). EEEF311 (2014-2015) NITIN Sharma 34 . 0 n even The 5th harmonic onward can be neglected. BFM =130 KHz EEEF311 (2014-2015) NITIN Sharma 35 .5 v-1 fc = 1000 MHz First estimate the Bm.Estimate BFM and BPM kf = 2×105 rad/sec/volt =10 105 Hz/Volt = 105 V-1·sec-1 kp = 5 rad/Volt = 2. Cn = 8/2n2 for n odd. BFM =230 KHz For PM: f = 50 kHz. Bm = 15 kHz For FM: f = 100 kHz. BFM = 430 KHz For PM: f = 100 kHz. BFM = 230 KHz Doubling the signal peak has significant effect on both FM and PM bandwidth 2 -2 2 EEEF311 (2014-2015) NITIN Sharma 40.5 v-1 fc = 1000 MH MHz For FM: f = 200 kHz.000 .Repeat if m(t) is Doubled kf = 2×105 rad/sec/volt =105 Hz/Volt = 105 V-1·sec-1 kp = 5 rad/Volt = 2. 36 .000 -40. 000 . This has significant effect on PM.5 kHz For FM: f = 100 kHz. BFM = 65 KHz Expanding the signal varies its spectrum.5 v-1 fc = 1000 MH MHz Bm = 7. 37 .000 -10. BFM = 215 KHz For PM: f = 25 kHz.Repeat if the period of m(t) is Doubled kf = 2×105 rad/sec/volt =105 Hz/Volt = 105 V-1·sec-1 kp = 5 rad/Volt = 2. 4x10-44 EEEF311 (2014-2015) NITIN Sharma 10. Spectrum of NBFM (1/2) g FM (t ) A cos c t k f a (t ) where h t a (t ) m ( )d j t k a (t ) gˆ FM (t ) A e c f A cos c t k f a (t ) jA sin c t k f a (t ) gˆ FM (t ) A e j c t j 2 k f2a 2 (t ) j 3 k f3a 3 (t ) j 4 k f4a 4 (t ) 1 jk f a (t ) 2! 3! 4! 2 2 3 3 4 4 j t k a ( t ) jk a ( t ) k a (t ) j c t j c t j c t j c t f f f c A e jk f a (t )e e e e 2! 3! 4! g FM (t ) Re gˆ FM (t ) k f2a 2 (t ) k f3a 3 (t ) k f4a 4 (t ) A cos(c t ) k f a (t ) sin(c t ) cos(c t ) sin(c t ) cos(c t ) 2! 3! 4! EEEF311 (2014-2015) NITIN Sharma 38 . Spectrum of NBFM (2/2) For NBFM. NBFM |kf a(t)|<< 1 g FM ( Narrowband ) (t ) A cos(c t ) k f a (t ) sin(c t ) Bandwidth of a(t) is equal to the bandwidth of m(t). expected) Similarly for PM (|kp m(t)|<< 1 ): g PM ( Narrowband ) (t ) A cos(c t ) k p m (t ) sin(c t ) BNBPM ≈ 2 2· Bm EEEF311 (2014-2015) NITIN Sharma 39 . BNBFM ≈ 22· Bm (as expected). Bm. NBFM Modulator g FM ( Narrowband ) (t ) A cos(c t ) k f a (t ) sin(c t ) t ()d EEEF311 (2014-2015) NITIN Sharma 40 . NBPM Modulator g PM ( Narrowband ) (t ) A cos(c t ) k p m (t ) sin(c t ) EEEF311 (2014-2015) NITIN Sharma 41 . Immunity of FM to Non-linearities q (t ) a1A cos c t k f m ( ) d a A cos c t k f 2 a3 A cos c t k f m ( ) d 3 m ( )d a2 A a1A cos c t k f m ( )d 1 cos 2c t 2k f 2 aA 3 2 2 1 cos 2c t 2k f ( ) d cos c t k f m m ( )d m ( ) d a2 A 3a3 A a2 A t k m d t k m d a1A cos ( ) cos 2 2 ( ) c f c f 2 4 2 DC Around c with k f k f Around 2c with k f 2 k f aA 3 cos 3c t 3k f m ( )d 4 Around 3c with k f 3 k f EEEF311 (2014-2015) NITIN Sharma 42 . Frequency Multipliers g FM (t ) A cos c t k f m ( ) d q (t ) contains the followingg cos c t k f m ( ) d cos 2c t 2k f m ( ) d cos P c t Pk f m ( ) d g FM (output ) (t ) B cos P c t Pk f m ( )d EEEF311 (2014-2015) NITIN Sharma 43 . Generation of WBFM: Indirect Method Usually. This way. EEEF311 (2014-2015) NITIN Sharma 44 . In the indirect method. we generate a NBFM with small then use a frequency multiplier to scale to the required value. We may need a frequency mixer to adjust fc. fc will also b scaled be l d by b the th same factor. we are interested in generating an FM signal of certain bandwidth (or f or ) and certain fc. f1 = 35 Hz.Example: From NBFM to WBFM A NBFM modulator d l t iis modulating d l ti a message signal i l m(t) with bandwidth 5 kHz and is producing an FM signal g with the following g specifications p fc1 = 300 kHz. f 2 = 77 kHz. g to ggenerate a WBFM We would like to use this signal signal with the following specifications fc2 = 135 MHz. f 2 77 *103 2200 f 1 35 f c 2 135*106 450 3 f c 1 300*10 EEEF311 (2014-2015) NITIN Sharma 45 . From NBFM to WBFM: System 1 EEEF311 (2014-2015) NITIN Sharma 46 . From NBFM to WBFM: System 2 EEEF311 (2014-2015) NITIN Sharma 47 . bili Requires R i feedback to stabilize it. EEEF311 (2014-2015) NITIN Sharma 48 .Generation of WBFM: Direct Method H Has poor ffrequency stability. FM Demodulator Four F primary i methods th d Differentiator with envelope detector/Slope detector FM to AM conversion Phase-shift discriminator/Ratio detector Approximates the differentiator Zero-crossing detector Frequency feedback Phase lock loops (PLL) EEEF311 (2014-2015) NITIN Sharma 49 . FM Demodulation: Signal Differentiation g FM (t ) A cos c t k f m ( )d dg FM (t ) A c k f m (t ) sin c t k f dt m ( )d EEEF311 (2014-2015) NITIN Sharma 50 . FM Demodulation: Signal Differentiation d () dt d () dt A c k f m (t ) sin c t k f m ( ) d dm (t ) A c k f sin c t k p m (t ) d dt dm (t ) dt t ()d EEEF311 (2014-2015) NITIN Sharma 51 . EEEF311 (2014-2015) NITIN Sharma 52 .Frequency Discriminators A Any system t with ith a transfer function of the form ||H(()| = a + b over the band of the FM signal can be used for FM ddemodulation d l ti The differentiator is just one example example. Slope Detectors (Demodulators) A c Ck f m (t ) cos ct k f m ( ) d EEEF311 (2014-2015) NITIN Sharma 53 . Example: filters. differentiator s(t) S(f) x(t) d dt H(f)=j2 πf |H(f)| X(f) output voltage range X(f) freqency in s(t) voltage in x(t) 10 Hz 20 Hz j 20 j 40 f Input frequency range in S(f) EEEF311 (2014-2015) NITIN Sharma 54 .FM Slope Demodulator Principle: use slope detector (slope circuit) as frequency discriminator. which implements frequency to voltage conversion (FVC) Slope circuit: output voltage is proportional to the input frequency. 0 where fi (t ) f c k f m(t ) Let the slope circuit be simply differentiator: t s1 (t ) Ac 2 f c 2 k f m(t ) sin 2 f c t 2 k f m( )d 0 so (t ) Ac 2 f c 2 k f m(t ) so(t) linear with m(t) EEEF311 (2014-2015) NITIN Sharma 55 . Block diagram g of direct method ((slope p detector = slope p circuit + envelope detector) s(t) slope circuit s1(t) (FM AM) (FVC) envelope detector so(t) (AM demodulator) t s (t ) Ac cos 2 f c t 2 k f m( )d .FM Slope Demodulator cont. Slope Detector Magnitude frequency response of transformer BPF BPF. EEEF311 (2014-2015) NITIN Sharma 56 . Hard Limiter A device that imposes hard limiting on a signal and contains a filter that suppresses the unwanted products (harmonics) of the limiting process. Input Signal t vi (t ) A(t ) cos (t ) A(t ) cos( wc t k f m(a)da) Output O off hhard d li limiter i vo (t ) 4 1 1 cos ( t ) cos 3 ( t ) cos 5 (t ) 3 5 Bandpass filter e (t ) 4 cos( w t k t m(a )da ) o c f Remove the amplitude EEEF311 variations (2014-2015) NITIN Sharma 57 . These amplitude variations are rectified to provide a DC output voltage which varies in amplitude and polarity with the input signal frequency. AM but b t 50% EEEF311 (2014-2015) NITIN Sharma 58 . di i i t nott response to t AM.Ratio Detector Foster Foster-Seeley/phase Seeley/phase shift discriminator uses a double-tuned transformer to convert the instantaneous frequency variations of the FM input signal to instantaneous amplitude variations. Example Ratio detector M difi d Foster-Seeley Modified F t S l discriminator. Zero Crossing Detector EEEF311 (2014-2015) NITIN Sharma 59 . patte . the output of the PLL would be following m(t) pattern. When the angles are locked. The error is fed to VCO to adjust the angle.Phased-Locked Loop (PLL) Th The multiplier lti li followed f ll d by the filter estimates the error bewteen the angle of gFM(t) and gVCO(t). EEEF311 (2014-2015) NITIN Sharma Loop Filter VCO 60 . change frequency (or phase) according to inputs PLL can be used for both FM modulator and demodulator Just as Balanced Modulator IC can be used for most amplitude modulations and demodulations EEEF311 (2014-2015) NITIN Sharma 61 . make a signal in fixed phase (and frequency) relation to a reference signal Track frequency (or phase) variation of inputs Or.FM Demodulator PLL Phase Phase-locked locked loop (PLL) A closed-loop feedback control circuit. Sv=Avcos(wct+c(t)) Sp=0.PLL FM Remember the following relations Si=Acos(wct+1(t)).5AA S 0 5AAvsin( i (1-c)=AA ) AAv(1-c) Section 2.14 m(t) + + s(t) VCO − s(t) freqency devided by N LP e(t) r(t) v(t) Loop Filter VCO Reference Carrier EEEF311 (2014-2015) NITIN Sharma 62 .5AAv[sin(2wct+1+c)+sin(1-c)] So=0. Armstrong in 1918.Superheterodyne Receiver Radio receiver receiver’ss main function Demodulation get message signal Carrier frequency tuning select station Filt i remove noise/interference Filtering i /i t f Amplification combat transmission power loss Superheterodyne p y receiver Heterodyne: mixing two signals for new frequency Superheterodyne receiver: heterodyne RF signals with local tuner. 88M 108MHz Midband 10. convert to common IF Invented by E.7MHz 10 7MHz EEEF311 (2014-2015) NITIN Sharma 63 .455MHz FM: RF 88M-108MHz. Midband 0.605 MHz. AM: RF 0.535MHz-1. and power amplification Superheterodyne receiver deals them with different blocks RF bl blocks: k selectivity l ti it only l IF blocks: filter for high signal quality. selectivity signal quality. not a large band EEEF311 (2014-2015) NITIN Sharma 64 . use circuits that work in only a constant IF. and amplification.Advantage of superheterodyne receiver A signal block (of circuit) can hardly achieve all: selectivity. fm=15KHz. system with the effect that noise occurs predominantly at the highest frequencies within the baseband.5 MHz . =5. B=2(fm+f)=180kHz Pre-emphasis and de-emphasis Random noise has a 'triangular' spectral distribution in an FM system.5 to 108. This can be offset. NITIN Sharma .FM Broadcasting The frequency q y of an FM broadcast station is usuallyy an exact multiple of 100 kHz from 87. f=75KHz. by boosting the high frequencies before transmission and reducing them by a corresponding EEEF311 (2014-2015) 65 amount in the receiver. to a limited extent. In most of the Americas and Caribbean only odd multiples are used. FM Stereo Multiplexing Fc=19KHz. (a) Multiplexer in transmitter of FM stereo. Backward compatible For non-stereo receiver EEEF311 (2014-2015) NITIN Sharma 66 . (b) Demultiplexer in receiver off FM stereo. TV FM broadcasting fm=15KHz.5MHz EEEF311 (2014-2015) NITIN Sharma 67 . B=2(fm+f)=80kHz Center fc+4. =5/3. f=25KHz.