ANLOG COMMUNICATION Lecture 06

Amplitude Modulation

Lesson 6 EEE352 Analog Communication Systems Mansoor Khan

Amplitude Modulation • Amplitude Modulation is the process of changing the amplitude of a relatively high frequency carrier signal in proportion with the instantaneous value of the modulating signal (information). • Use in commercial broadcasting of both audio and video signals.

• Also used for communications.

two-way

mobile

radio

AM Waveforms

Time Domain Signal

time

Carrier

time

time

Detection of Signal

time

time

Susceptible to Noise

time

Frequency Domain Unmodulated

watts

Carrier Signal

frequency Baseband

watts

Modulated

Carrier Signal

frequency Baseband

Baseband

AMPLITUDE MODULATION: DOUBLE SIDE BAND (DSB) • Modulating signal, base band signal, information signal

m(t )

M ( )

• Carrier signal:

c(t )  cos(ct  c )

• with Spectrum

C ( )    (  c )   (  c )

DSB (cont) • Modulation is the product of the base band with the carrier 1 m(t ) cos(c t )  M (  c )  M (  c ) 2

DSB (cont) • DSB-SC modulation simply shifts the frequency contents of m(t) to the carrier frequency

USB & LSB

Demodulation • To demodulate we multiply the signal by a

cos(wct )

1 1  m(t ) cos(wct )cos(wct )  m(t ) cos (wct )  m(t )  cos(2wct ) 2 2  2

• Therefore the FT of this signal is 1 1 1 1  m(t )   cos(2wct )  M ( w)  M ( w  2wc )  M (  2wc ) 2 4 2 2 

• If we lowpass filter this signal we recover 1 m(t ) 2

Demodulation (cont) • We need a carrier of exactly the same frequency and phase as the carrier used for modulation: Synchronous Detection or Coherent Detection

Demodulation (cont)

Modulators • Multiplier Modulators • Nonlinear Modulators • Switching Modulators • Ring Modulator

Nonlinear Modulators • Let the IO characteristic of a system to be

y(t )  ax(t )  bx (t ) 2





z(t )  y1 (t )  y2 (t )  ax1 (t )  bx1 (t )  ax2 (t )  bx2 (t ) 2

• Substituting the two inputs

x1 (t )  cos wct  m(t )

x2 (t )  cos wct  m(t )

• We obtain

z (t )  2am(t )  4bm(t ) cos wct

2



Nonlinear Modulators (cont) • If we pass the signal though a BPF centered at wc we will get the modulated signal

z (t ) AFTER THE BPF  4bm(t ) cos wct

Switching Modulators • In this case we multiply the modulating signal by any periodic signal of frequency wc • The fourier series of a square pulse train is (Eq. 2.75)

1 2 1 1  w(t )    cos wct  cos 3wct  cos 5wct.... 2  3 5 

• then m(t ) w(t ) 

m(t ) 2  m(t ) m(t )    m(t ) cos wct  cos 3wct  cos 5wct.... 2  3 5 

Switching Modulators (cont) • If this signal is passed trough a BPF centered at wc we get our modulated signal

m(t ) w(t ) AFTER THE BPF 

2



m(t ) cos wct.

Series/Shunt bridge diode modulator

Ring Modulator • This is the second kind of switching modulators, in this case the square wave is bipolar • The fourier series of this pulse train will be given by (Eq. 2.76B.P. Lathi)

• then

4 1 1  w(t )   cos wct  cos 3wct  cos 5wct....  3 5 

4 m(t ) m(t )  m(t ) w(t )   m(t ) cos wct  cos 3wct  cos 5wct....  3 5 

Ring Modulator (cont) • The desired signal after the BPF is

m(t ) w(t ) AFTER THE BPF 

4



m(t ) cos wct.

• The input of the BPF does not contain any of the original input signals, therefore this is an example of a double balanced modulator

Frequency Mixer or converter • We wanted to change the modulated signal from wc to wI • The product x(t) is

x(t )  2m(t ) cos c t cos mix t

x(t )  m(t )cosc  mix t  cosc  mix t  • Down conversion if we select

mix  c   I

x(t )  m(t )cosc  (c   I )t  cosc  c   I t  x(t )  m(t )cos I )t  cos2c   I t 

Frequency Mixer (cont) • Up conversion if we select

mix  c  I x(t )  m(t )cosc  (c  I )t  cosc  c  I t 

x(t )  m(t )cos I )t  cos2c   I t 

Frequency Mixer (cont)

AMPLITUDE MODULATION (Transmitted Carrier DSB-TC) • In this case we send the carrier with the signal

 AM (t )  A cos ct  m(t ) cos ct

    Carrier

Sidebands

• We can think as the modulating signal to be

   cos ct  AM (t )   A  m(t )    mod ulating  signal with a DC  

AM (cont) • The spectrum of this signal is  AM ( w) 

1 M (w  wc )  M (w  wc )  1 A (w  wc )   (w  wc ) 2   2   DSB SC spectrum

Carrier spectrum

EEE 352

AM (cont) • A is large enough that A  m(t )  .0The demodulation can be achieved by a simple envelope detector • Let’s consider the peak value of m(t )to be m p. Then the condition for envelope detection of AM signal is

A  m(t )  0 • Which is equivalent to

A  mp

Modulation Index • We define the modulation index as



mp A

• Therefore we can see that if we want to maintain the condition A  m p • We have

0   1

Example 4.4

Example 4.4 (cont)

Percentage Modulation

Under modulated (100%)

Envelope Detector

Envelope Detector

Can be used

Gives Distorted signal