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# Ch4 2 _fm modulator and demodulator15

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### Ch4 2 _fm modulator and demodulator15

1. 1. 1 Chapter 4-2 FM Modulator and Demodulatorp 馮武雄 教授 長庚大學 電子系 FM Modulator and DemodulatorFM Modulator and Demodulator  FM modulator – Direct FM – Indirect FMIndirect FM  FM demodulator – Direct: use frequency discriminator (frequency-voltage converter) – Ratio detector – Zero crossing detectorZero crossing detector – Indirect: using PLL  Superheterodyne receiver  FM broadcasting and Satellite radio
2. 2. 2 FM Direct ModulatorFM Direct Modulator  Direct FM – Carrier frequency is directly varied by the message through voltage-controlled oscillator (VCO) – VCO: output frequency changes linearly with input voltage – A simple VCO: implemented by variable capacitor – Capacitor Microphone FM generator FM Direct Modulator cont.FM Direct Modulator cont.  Direct method is simple, low cost, but lack of high stability & accuracy, low power application, unstable at the carrier frequency LC oscillator frequency: VCO m(t) s(t) 0 Capacitance changes with the applied voltage: ( ) ( )C t C Cm t   0 2 00 1 1 ( ) 2 2 ( ) 1 1 ( ) ( ) 22 if t LC LC L Cm t C m t O t CLC f C                  Modern VCOs are usually implemented as PLL IC  Why VCO generates FM signal? 0 0 0 0 ( ) 2 ( ) f C f m t C f f m t      m(t) L s(t)C
3. 3. 3 Indirect FMIndirect FM  Generate NBFM first, then NBFM is frequency multiplied for targeted Δf.  Good for the requirement of stable carrier frequency Good for the requirement of stable carrier frequency  Commercial-level FM broadcasting equipment all use indirect FM  A typical indirect FM implementation: Armstrong FM  Block diagram of indirect FM NBFM nf m(t) v(t) s(t) multiplier NBFM nfi m(t) v(t) s(t) f1 Crystal Controlled Oscillator frequency Indirect FM cont.Indirect FM cont.  First, generate NBFM signal with a very small β1 1 1 1( ) cos(2 ) sin(2 )sin(2 )c c mv t A f t A f t f t     m(t) π −90o Phase Shift m(t) v(t) NBFM Acsin(2 f1t)π Ac cos(2 f 1 t) multiplier NBFM nfi m(t) v(t) s(t) f1 Crystal Controlled Oscillator frequency
4. 4. 4 Indirect FM cont.Indirect FM cont.  Then, apply frequency multiplier to magnify β – Instantaneous frequency is multiplied by n – So do carrier frequency, Δf, and β – What about bandwidth? (t) Device Nonlinear Bandpass Filter (nf 1 ) s(t)v(t) vo |S(f)|Bandpass filter f f1−f1 B1 |V(f)| right lefti if n f f f |S(f)|Bandpass filter −fc 1=nfc Analysis of Indirect FMAnalysis of Indirect FM 1 0 1. Input: ( ) cos 2 2 ( ) , max | ( ) | where ( ) ( ) 1 t c f f v t A f t k m d k m t f t f k m t                1 2 1 2 2. Nonlinear device outputs frequencies: ( ) ( ) ( ) ( ) ( ) f n o n nf nk m t v t a v t a v t a v t        1where ( ) ( ), 1i ff t f k m t W    13. Bandpass filter select new carrier cf nf   … … 1 0 ( ) cos 2 2 ( ) t c fs t A nf t nk m d         1 max | ( ) | where new ( ) ( ), f i f nk m t f t nf nk m t W   
5. 5. 5 A simple electronic implementation of frequency multiplierA simple electronic implementation of frequency multiplier 30 MHz output. X3 (x5) C1:100pF, L1:2.7μH. D:1N914 L2:.22μH, L3:1.8μH, L4:330μH C2:120pF, C3:10pF. Armstrong FM ModulatorArmstrong FM Modulator  Invented by E. Armstrong, an indirect FM  A popular implementation of commercial level FM  Parameter: message W=15 kHz, FM s(t): Δf=74.65 kHz.  Can you find the Δf at (a)-(d)? (d) NBFM Modulator m(t) (W<15kHz) 200 kHz c1(t) filter #1 Bandpass frequency multiplier x72 c2(t) 13.15 MHz Bandpass Filter #2 Frequency Multiplier X72 s(t) carrier 1.44 MHz carrier 1.25 MHz carrier 90 MHz (a) (b) (c) 200 kHz carrier (crystal) 13.15 MHz carrier (crystal) Solution: (a) 14.4 Hz. (b) 72 14.4 1.036 kHz. (c) 1.036 kHz. (d) 72 1.036 74.65 kHz. f f f f            
6. 6. 6 FM DemodulatorFM Demodulator  Four primary methods – Differentiator with envelope detector/Slope detector FM t AM i FM to AM conversion – Phase-shift discriminator/Ratio detector  Approximates the differentiator – Zero-crossing detector – Frequency feedback h l k l ( ) Phase lock loops (PLL) FM Slope DemodulatorFM 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. Example: filters, differentiator X(f) d dt s(t) x(t) H(f)=j2 fπS(f) X(f) output voltage |H(f)| Input frequency voltage range f range in S(f) freqency in s(t) voltage in x(t) 10 20 20 40 Hz j Hz j    
7. 7. 7 FM Slope Demodulator cont.FM Slope Demodulator cont.  Block diagram of direct method (slope detector = slope circuit + envelope detector) slope envelopes(t) s1(t) so(t) 0 ( ) cos 2 2 ( ) , where ( ) ( ) t c c f i c fs t A f t k m d f t f k m t           L h l i i b i l diff i (AM demodulator) slope circuit detector envelopes(t) s1(t) so(t) (FM AM) (FVC) 1 0 Let the slope circuit be simply differentiator: ( ) 2 2 ( ) sin 2 2 ( ) ( ) 2 2 ( ) t c c f c f o c c f s t A f k m t f t k m d s t A f k m t                         so(t) linear with m(t) Slope DetectorSlope Detector Magnitude frequency response of transformer BPF.
8. 8. 8 Hard LimiterHard 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  Output of hard limiter ))(cos()()(cos)()(    t fci daamktwtAttAtv       )(5cos 1 )(3cos 1 )(cos 4 )( ttttv   Bandpass filter  Remove the amplitude variations ))(cos( 4 )(    t fco daamktwte       )(5cos 5 )(3cos 3 )(cos)( ttttvo   Ratio DetectorRatio Detector  Foster-Seeley/phase shift discriminator – uses a double-tuned transformer to convert the instantaneous frequency variations of the FM input signal to instantaneous amplitude variations. These amplitude variations are rectified to id DC t t lt hi h i i lit d d l itprovide a DC output voltage which varies in amplitude and polarity with the input signal frequency. – Example  Ratio detector Modified Foster-Seeley discriminator, not response to AM, but 50%
9. 9. 9 Zero Crossing DetectorZero Crossing Detector FM Demodulator PLLFM Demodulator PLL  Phase-locked loop (PLL) – A closed-loop feedback control circuit, make a signal in fixed phase (and frequency) relation to a reference signalp ( q y) g  Track frequency (or phase) variation of inputs  Or, 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
10. 10. 10 PLL FMPLL FM  Remember the following relations – 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) – Section 2.14 s(t) VCOm(t) + − + freqency devided by N LP r(t) Filter Loop VCO s(t) e(t) v(t) by N Reference Carrier r(t) VCO Phase and Frequency AcquisitionPhase and Frequency Acquisition
11. 11. 11 Phase-Locked Loop Demodulator (a) Block diagram for a PLL FM demodulator; (b) PLL FM demodulator using the XR(a) Block diagram for a PLL FM demodulator; (b) PLL FM demodulator using the XR--2212 PLL2212 PLL 32-38 1.Strong nonlinearity, e.g., square-law modulators , hard limiter, frequency multipliers. 2.Weak nonlinearity, e.g., imperfections Nonlinear Effects in FM Systems Nonlinear input-output relation )()()()( 32 3210 tvatvatvatv iii  Nonlinear Channel (device) vi(t) v0(t) An FM system is extremely sensitive to phase nonlinearity. Common types of source: AM-to-PM conversion Channel (device) 52
12. 12. 12 Electronic Amplifier 52 A: low power B: high distortion C: need a filter but narrow band Superheterodyne ReceiverSuperheterodyne Receiver  Radio receiver’s main function – Demodulation  get message signal – Carrier frequency tuning  select stationq y g – Filtering  remove noise/interference – Amplification  combat transmission power loss  Superheterodyne receiver – Heterodyne: mixing two signals for new frequency – Superheterodyne receiver: heterodyne RF signals with local tuner, convert to common IF – Invented by E. Armstrong in 1918. – AM: RF 0.535MHz-1.605 MHz, Midband 0.455MHz – FM: RF 88M-108MHz, Midband 10.7MHz
13. 13. 13 Advantage of superheterodyne receiverAdvantage of superheterodyne receiver  A signal block (of circuit) can hardly achieve all: selectivity, signal quality, and power amplification  Superheterodyne receiver deals them with different blocks  RF blocks: selectivity only  IF blocks: filter for high signal quality, and amplification, use circuits that work in only a constant IF, not a large band FM BroadcastingFM Broadcasting  The frequency of an FM broadcast station is usually an exact multiple of 100 kHz from 87.5 to 108.5 MHz . In most of the Americas and Caribbean only odd multiples are used.  fm=15KHz, f=75KHz, =5, B=2(fm+f)=180kHz  Pre-emphasis and de-emphasis – Random noise has a 'triangular' spectral distribution in an FM system, with the effect that noise occurs predominantly at the highest frequencies within the baseband. This can be offset, to a limited extent, by boosting the high frequencies before t i i d d i th b di t itransmission and reducing them by a corresponding amount in the receiver.
14. 14. 14 Fc=19KHz.Fc=19KHz. ((aa) Multiplexer in) Multiplexer in FM Stereo MultiplexingFM Stereo Multiplexing ((aa) Multiplexer in) Multiplexer in transmitter of FM stereo.transmitter of FM stereo. ((bb) Demultiplexer in) Demultiplexer in receiver of FM stereo.receiver of FM stereo. Backward compatible For non-stereo receiver TV FM broadcastingTV FM broadcasting  fm=15KHz, f=25KHz, =5/3, B=2(fm+f)=80kHz  Center fc+4.5MHz
15. 15. 15 Satellite RadioSatellite Radio  WorldSpace outside US, XM Radio and Sirius in North America XM Satellite Radio Sirius Company info XMSR, \$2billion, DC SIRI, \$5 billion, NYC Current Subscribers 7,000,000+ 4,000,000+ Monthly rate 12.95/month 12.95/month Total channel 170+, 90+streams of music 165+, 80+streams of music Satellite 2 Boeing geostationary satellites 3 Loral satellites at high- elevation geosynchronous orbit XM vs. SirusXM vs. Sirus