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AM DSB-LC A.J.Wilkinson, UCT EEE3086F Signals and Systems II506 P age 3 April 14, 2014

5.3.1 Double Sideband Large arrier !DS"#L $

%m&litude 'odulation and Demodulation

DSB-LC is so$eti$es called /AM0 $odulation, asin AM radio.

To ear an AM radio 1roadcast, tune to /Ca!eTalk0 *23 k4z on t e $ediu$ wa(e radio 1and.

A.J.Wilkinson, UCT AM DSB-LC EEE3086F Signals and Systems II506 P age 4 April 14, 2014

DSB-SC modulation requires a fairly complicated demodulator,involving a mixer and oscillator, which must be synchronised to thetransmitter.

S !"#$ %& 'n alternative approach is to design the modulation suchthat the modulating signal can be recovered purely from the envelope ofthe modulated carrier.#his can be achieved by ensuring that the signal fed into the mixer isalways positive .

(ery simple circuits can be used to perform envelope detection. )arlyradio receivers used this approach.

Standard *edium +ave broadcast '* radio uses this technique. $nSouth 'frica, broadcast '* radio uses a / bandwidth, with radiostations located in the range 012 / 34 5622 / band7.

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A.J.Wilkinson, UCT AM DSB-LC EEE3086F Signals and Systems II506 P age 5 April 14, 2014

A$!litude Modulation" Lar'e Carrier 5DSB-LC6

#he signal fed into the mixer can be made always positive by adding aDC offset to f 8t7&

such that

#he modulated carrier can be re-expressed as&

which is equivalent to adding a carrier component to a DSB-SC signal,hence the name DSB-!C 8large carrier7.

DSB-!C is sometimes referred to as 9'*: as in 9'* radio:.

t At t f t cc AM coscos7878 +=

[ ] t At f t c AM cos7878 +=

278 + At f A min { f t }

A.J.Wilkinson, UCT AM DSB-LC EEE3086F Signals and Systems II506 P age 6 April 14, 2014

DSB-LC in 7re8uenc) Do$ain

;ourier transforming the DSB-!C signal,

we get&

AM =5eneration o% DSB-LC Si'nal

@ractical $mplementations&Chopper 8switch7 type modulators)xploiting non-linear characteristics of devices

i.e.

i t = a 5 e t a < e< t

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A.J.Wilkinson, UCT AM DSB-LC EEE3086F Signals and Systems II506 P age 2 3 April 14, 2014

C o!!er Modulator 5DSB-LC6

Simply chop and pass through c +2F E

#hop

7788 At f +

78t f

A c

78t AM c

+2F E

{ } At f +78F

2

2 2c c F

c c F

+2F

#hop rate

*pectr0% after chopper

A.J.Wilkinson, UCT AM DSB-LC EEE3086F Signals and Systems II506 P age 2 4 April 14, 2014

'nother method Chop and filter.

Gectifier *ethod& also wor s if one replace switch with adiode.

C o!!er Modulator 5DSB-LC6

H

7cos788 t C t f c +

H

c +2F E78t f

t C c cos

c

D 2 t

c

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A.J.Wilkinson, UCT AM DSB-LC EEE3086F Signals and Systems II506 P age 2 5 April 14, 2014

Understandin' C o!!er # :ecti%ier Circuit

(oltage across is

where is square wave, 252525I $n frequency domain

2 T t

f t C cos ct 2

T t = D

t

D ( )= { f (t )+4 cos c t } 2 T ( ) 5

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A.J.Wilkinson, UCT AM DSB-LC EEE3086F Signals and Systems II506 P age 2 7 April 14, 2014

DSB-LC Usin' ?on-Linear De(ices

@assing the sum through a non-linear device8e.g. diode7 generates DSB-!C spectral replicas in frequency

spectrum. Consider Circuit&

D (t )= i (t ) v!

( f (t )+ C cos c t )

i %on-linearDiodecharacteristic

HH +2F

f (t ) 782 t D

v! (t )

78t D i ( t )

#he voltage drop across G is proportionalto current through diode&

C cos c t

2.6(

5.2m'

8' DC bias is also sometimes added in series7

A.J.Wilkinson, UCT AM DSB-LC EEE3086F Signals and Systems II506 P age 2 8 April 14, 2014

DSB-LC Usin' ?on-Linear De(ices

v !

%on-linearDiodecharacteristic

+e shall analy/e the case where the total appliedvoltage is less than, say, 2.66(, and J D

J KK Jv

!

f (t )+ C cos c t 2.66 (

Liven max D ! ? D

) = 2.66(

'ssume D ! = .3 D an! D

= .3. D3

Fro% c0rve9 D ! M 2.6( M4 I

! M5m'.

#his same current flows through .M4 choose M 2.26N5)-F M 62 ohms.

2.6(

5.2m'

8operating range7

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A.J.Wilkinson, UCT AM DSB-LC EEE3086F Signals and Systems II506 P age 2 9 April 14, 2014

DSB-LC Usin' ?on-Linear De(ices

#he non-linear voltage to current relationship is modeled by a power series&

;or 8small voltage drop across G7

v! (t ) f (t )+ C cos c t D KKv ! (t )

i (t )= a 5 v ! (t )+a < v ! < (t )+

t t Cf at C at f at C at f at C t f at C t f at i

ccc

cc

cos78

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A.J.Wilkinson, UCT AM DSB-LC EEE3086F Signals and Systems II506 P age 3 3 April 14, 2014

Carrier and Side1and ower in AM

+ 2 f

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A.J.Wilkinson, UCT AM DSB-LC EEE3086F Signals and Systems II506 P age 3 5 April 14, 2014

?ote

%ote& ere we have developed an expression for the total9signal power: which is defined as the mean square value&

$f the load impedance is 5 ohm, then the total power dissipatedin the 5 ohm load is equal to the total signal power.

$f the signal is a voltage driving a resistive load of ohms,then the power dissipated is

2 t =

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A.J.Wilkinson, UCT AM DSB-LC EEE3086F Signals and Systems II506 P age 3 7 April 14, 2014

ower S!ectral Densit) o% DSB-LC AM

;or power calculations we consider the power spectraldensity shown below&

where is the @SD offor which

* B

* f 78t f

f

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A.J.Wilkinson, UCT AM DSB-LC EEE3086F Signals and Systems II506 P age 3 9 April 14, 2014

=1tainin' t e ower %ro$ t e SD

Carrier @ower

Sideband @ower

#otal @ower 2 t = 5

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A.J.Wilkinson, UCT AM DSB-LC EEE3086F Signals and Systems II506 P age 4 1 April 14, 2014

Trans$ission &%%icienc) %or a Sinusoidal Modulatin' Si'nal

!et f (t )= %Acos %t

AM (t )=

%Acos %

t cos ct +

Acos ct

2 c =5