ECE 4371, Fall, 2017 Introduction to Telecommunication Engineering/Telecommunication Laboratory Zhu Han Department of Electrical and Computer Engineering Class 4 Sep. 13th, 2017 FM Modulator and Demodulator Review of FM 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 Project 1 Review of last class

PLL and math Instantaneous frequency 1 di (t ) fi (t ) 2 dt FM and PM LPF s (t ) Ac cos 2 f c t 2 k f VCO

t m ( ) d 0 s (t ) Ac cos 2 f ct k p m(t ) Modulation index

Narrow band FM characteristics Carsons rule max | ka m(t ) | , 1 max | k f m(t ) | FM (frequency): fm AM (envelope): BT 2f 2 f m 2( 1) f m FM 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. Direct method is simple, low cost, but lack of high stability & accuracy, low power application, unstable at the carrier frequency Capacitance changes with the applied voltage: C (t ) C0 Cm(t ) LC oscillator frequency: 1

1 f i (t ) 2 LC 2 LC0 LCm(t ) C 2 1 m ( t ) O ( t

) 2C0 f 0 C f0 m(t ) 2C0 1 2 LC0 f 0 f m(t ) Modern VCOs are usually implemented as PLL IC

Why VCO generates FM signal? Indirect FM Generate NBFM first, then NBFM is frequency multiplied for targeted f. 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. First, generate NBFM signal with a very small 1 v(t ) Ac cos(2 f1t ) 1 Ac sin(2 f1t ) sin(2 m(t) f mt ) Indirect FM cont.

Then, apply frequency multiplier to magnify Instantaneous frequency is multiplied by n So do carrier frequency, f, and What about bandwidth? fi right n f i left Analysis of Indirect FM t 1. Input: v(t ) Ac cos 2 f1t 2 k f m( )d ,

0 max | k f m(t ) | where f i (t ) f1 k f m(t ), 1 W 2. Nonlinear device outputs frequencies: nf1 nk f m(t ) vo (t ) a1v(t ) a2v 2 (t ) an v n (t ) 3. Bandpass filter select new carrier f c nf1 t s(t ) Ac cos 2 nf1t 2 nk f m( ) d 0 where new f i (t ) nf1 nk f m(t ),

max | nk f m(t ) | W Armstrong FM Modulator Invented by E. Armstrong, an indirect FM A popular implementation of commercial level FM Parameter: message W=15 kHz, FM s(t): f=74.65 kHz.

Can you find the f at (a)-(d)? Solution: (a) f 14.4 Hz. (b) f 72 14.4 1.036 kHz. (c) f 1.036 kHz. (d) f 72 1.036 74.65 kHz. FM 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 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) 10 Hz

20 Hz voltage in x(t) j 20 j 40 FM Slope Demodulator cont. Block diagram of direct method (slope detector = slope circuit + envelope detector) t s (t ) Ac cos 2 f ct 2 k f m( )d , where f i (t ) f c k f m(t )

0 Let the slope circuit be simply differentiator: t s1 (t ) Ac 2 f c 2 k f m(t ) sin 2 f ct 2 k f m( )d 0 so (t ) Ac 2 f c 2 k f m(t ) so(t) linear with m(t) Slope Detector Magnitude frequency response of transformer BPF.

Bandpass 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 of bandpass limiter Bandpass filter 4 1 1 vo (t ) cos (t ) cos 3 (t ) cos 5 (t ) 3 5 t 4 eo (t ) cos(wc t k f m(a )da )

Remove the amplitude variations Ratio 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 Detector FM 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 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) Superheterodyne Receiver Radio receivers 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. Advantage 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 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. Block diagram and spectrum Relation of stereo transmission and monophonic transmission FM Stereo Multiplexing

Fc=19KHz. (a) Multiplexer in transmitter of FM stereo. (b) Demultiplexer in receiver of FM stereo. Backward compatible For non-stereo receiver TV FM broadcasting fm=15KHz, f=25KHz, =5/3, B=2(fm+f)=80kHz Center fc+4.5MHz Eye cells structure

XM vs. Sirus Frequency Allocation ECE 4371 Fall 2008 Project 1 Project 1 AM/FM/Real voice Due 10/1/17