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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

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:

VCOm(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 tLC LC L Cm t

Cm t O t

CLC

f C

Modern VCOs are usually implemented as PLL IC

Why VCO generates FM signal?

00

0

0

( )2

( )

f Cf m t

C

f f m t

m(t) L s(t)C

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 nfm(t) v(t) s(t)

multiplier

NBFM nfim(t) v(t) s(t)

f1Crystal ControlledOscillator

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 PhaseShift

m(t) v(t)

NBFM

A csin(2 f1t)π

A c cos(2 f 1 t)

multiplier

NBFM nfim(t) v(t) s(t)

f1Crystal ControlledOscillator

frequency

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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)

DeviceNonlinear Bandpass

Filter(nf 1 )

s(t)v(t) vo

|S(f)|Bandpass filter

ff1−f1B1

|V(f)|right lefti if n f

f

f

|S(f)|Bandpass filter

−fc 1=nfc

Analysis of Indirect FMAnalysis of Indirect FM

1 01. Input: ( ) cos 2 2 ( ) ,

max | ( ) |where ( ) ( ) 1

t

c f

f

v t A f t k m d

k m tf t f k m t

1

21 2

2. Nonlinear device outputs frequencies: ( )

( ) ( ) ( ) ( )

f

no n

nf nk m t

v t a v t a v t a v t

1 where ( ) ( ), 1i ff t f k m tW

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 tf t nf nk m t

W

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:1N914L2:.22μH, L3:1.8μH, L4:330μHC2:120pF, 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)

NBFMModulator

m(t)(W<15kHz)

200 kHzc1(t)

filter #1Bandpass frequency

multiplierx72

c2(t)13.15 MHz

BandpassFilter #2

FrequencyMultiplierX72

s(t)carrier

1.44 MHz

carrier1.25MHz

carrier90 MHz

(a) (b) (c)

200 kHzcarrier(crystal)

13.15 MHzcarrier(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

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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)

ddt

s(t) x(t)

H(f)=j2 fπS(f)X(f)

outputvoltage

|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

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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)

slopecircuit 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 frequencyresponse of transformer BPF.

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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

)(5cos5

)(3cos3

)(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%

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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

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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) +

−+

freqencydevidedby N

LP r(t)

FilterLoop

VCO

s(t) e(t) v(t)

by N

Reference Carrier

r(t)VCO

Phase and Frequency Acquisition Phase and Frequency Acquisition

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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

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Electronic Amplifier

52

A: low powerB: high distortionC: 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

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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.

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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 compatibleFor non-stereo receiver

TV FM broadcastingTV FM broadcasting

fm=15KHz, f=25KHz, =5/3, B=2(fm+f)=80kHz

Center fc+4.5MHz

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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