ECE4371, Fall, 2009

Zhu Han

Department of Electrical and Computer Engineering

Class 6

Sep. 10th, 2007

                                                           

                                                           

FM Modulator and DemodulatorFM Modulator and Demodulator

FM modulator– Direct FM

– Indirect FM

FM demodulator– Direct: use frequency discriminator (frequency-voltage

converter)

– Ratio detector

– Zero crossing detector

– Indirect: using PLL

Superheterodyne receiver

FM broadcasting and Satellite radio

                                                           

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

Modern VCOs are usually implemented as PLL IC

Why VCO generates FM signal?

0

Capacitance changes with

the applied voltage:

( ) ( )C t C Cm t 0

2

00

00

0

0

LC oscillator frequency:

1 1( )

2 2 ( )

1 1 ( ) ( )

22

( )2

( )

if tLC LC L Cm t

Cm t O t

CLC

f Cf m t

C

f f m t

                                                           

Indirect FMIndirect FM Generate NBFM first, then NBFM is frequency multiplied for

targeted Δf.

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

                                                           

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)

                                                           

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?

right lefti if n f

                                                           

Analysis of Indirect FMAnalysis of Indirect FM

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 0

1

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

max | ( ) | where ( ) ( ), 1

t

c f

fi f

v t A f t k m d

k m tf t f k m t

W

1

1 0

3. Bandpass filter select new carrier

( ) cos 2 2 ( )

c

t

c f

f nf

s t A nf t nk m d

1

max | ( ) |where new ( ) ( ), f

i f

nk m tf t nf nk m t

W

… …

                                                           

C1:100pF, L1:2.7μH. D:1N914L2:.22μH, L3:1.8μH, L4:330μHC2:120pF, C3:10pF.

30 MHz output. X3 (x5)

A simple electronic implementation of frequency multiplierA simple electronic implementation of frequency multiplier

                                                           

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)?

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

                                                           

FM DemodulatorFM Demodulator

Four primary methods– 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)

                                                           

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

freqency in s(t) voltage in x(t)

10 20

20 40

Hz j

Hz j

                                                           

FM Slope Demodulator cont.FM Slope Demodulator cont. Block diagram of direct method (slope detector = slope circuit +

envelope detector)

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

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.

                                                           

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

Bandpass filter

Remove the amplitude variations

))(cos()()(cos)()( t

fci daamktwtAttAtv

))(cos(4

)( t

fco daamktwte

)(5cos

5

1)(3cos

3

1)(cos

4)( 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 provide 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%

                                                           

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 signal 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

                                                           

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

                                                           

Phase and Frequency Acquisition Phase and Frequency Acquisition

                                                           

(a) Block diagram for a PLL FM demodulator; (b) PLL FM demodulator using the XR-2212 PLL(a) Block diagram for a PLL FM demodulator; (b) PLL FM demodulator using the XR-2212 PLL

Phase-Locked Loop Demodulator

32-38

                                                           

1.Strong nonlinearity, e.g., square-law modulators ,

hard limiter, frequency multipliers.

2.Weak nonlinearity, e.g., imperfections

Nonlinear input-output relation

An FM system is extremely sensitive to phase nonlinearity.

Common types of source: AM-to-PM conversion

)()()()(32

3210 tvatvatvatv iii

Nonlinear Channel (device)

vi(t) v0(t)

52

Nonlinear Effects in FM Systems

                                                           

52

Electronic Amplifier

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 station

– 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

                                                           

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 transmission and reducing them by a corresponding amount in the receiver.

                                                           

Fc=19KHz.Fc=19KHz.((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.

FM Stereo MultiplexingFM Stereo Multiplexing

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

                                                           

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