ece 4710: lecture #20 1 dsb-sc am tx signal also called dsb-lc double side band - large carrier ...

ECE 4710: Lecture #20 1

DSB-SC

AM Tx signal Also called DSB-LC Double Side Band - Large Carrier

AM Tx signal spectrum

Discrete delta functions represent sinusoidal carrier Delta functions provide DC term when s(t) is shifted to

baseband DSB-SC is also an amplitude modulated signal but

the carrier term present in AM is suppressed Double Side Band – Suppressed Carrier

tftmAts cc 2cos)](1[)(

)]()()()([)( 21

ccccc ffMffffMffAfS


DSB-SC

DSB-SC Tx signal m(t) must have zero DC component for SC

DSB-SC signal spectrum is identical to AM except the delta functions (LC) are removed

Modulation Efficiency = 100% since no power used on carrier» Best case AM efficiency was 50%

Sideband power is four times that of AM signal for same peak level for Tx output signal 10 log (4) = 6 dB difference

tftmAts cc 2cos)()(

)]()([)( 21

ccc ffMffMAfS


DSB-SC Power

Let peak Tx output signal power be the same for AM and DSB-SC

Same peak Tx output so

For demonstration let MAM = 1 then MDSB-SC = 2

Sideband power M 2 and

SCDSBcSCDSBc

ccSCDSB

MAtmAts

tftmAts

)](max[ ])(max[ so

2cos)()(

]1[)](1max[ ])(max[so

2cos)](1[)(

AMcAMc

ccAM

MAtmAts

tftmAts

SCDSBcAMc MAMA ]1[

)(2 tmdB 6or 4

14

2

2

AM

SCDSB

M

M


DSB-SC Tx

˜

Antenna

AnalogInput

CarrierOscillator

Mixer

DSPfc

cos(2fct)

PowerAmplifier

BasebandLPF

BasebandAmplifier

DigitalInput

Encoding, Pulse Shaping,Error Coding, DAC, etc.

tftmAts cc 2cos)()(

)(tsGain = Ac)(tm


DSB-SC Rx

˜

Antenna

Low NoiseRF Amp

LPFBasebandAmplifier

Digital orAnalogOutput

LocalOscillator

Mixer = Product Detector

NOTE: SuperHeterodyne Rx often used but Zero-IF is shown

for simplicity

DSP

fc

tftmAtr c2cos)()(

)(tr)(tm~


DSB-SC Spectrums

f

|)(| fS

fc

2A

fc

2A

|)(| fR

2fc

2A

2fc

4A

4A

Desired Baseband Signal

BandpassSignal

Frequency Doubled Signal


BandpassSignal

LPF

NOTE: No LC present!!


Product Detector or Mixer: converts bandpass signal s(t) back into a baseband signal via another frequency translation

Product Detector multiplication of r (t) with cos(2fc t)

» Product = multiplication & Detector = result is original m(t)

Envelope Detector normally not possible» Only possible if m(t) is always > 0 e.g. unipolar line code

If m(t) is polar or bipolar then it will have + and values 180° phase change occurs in carrier when m(t)

transitions from + to » r (t) = A m(t) cos(2fc t) so for m(t) > 0 cos(2fc t)

and for m(t) < 0 cos(2fc t) = cos(2fc t + 180°)

DSB-SC Product Detection



)(tm )2cos()()( tftmts c)2cos( tfc

1. Envelope of s(t) = | s(t) | m(t) cannot use envelope detector!!

2. For m(t) > 0 +cos(2fc t) & for m(t) < 0 cos(2fc t)

3. 180° phase change between + m(t) & m(t)

4. Sign of m(t) is stored in phase of carrier

5. Must have phase information from carrier to recover m(t) coherent detection mixer is a coherent detector

+cos -cos +cos



tftftmAtftstm ccc 2cos2cos)(2cos)()(~

Product Detection

xx 2cos1)(cos2 :identity tric trigonomeUsing 2

tftmAtmAtm

tftmAtftmAtm

c

cc

4cos)()()(~

4cos1)(2cos)()(~

21

21

212

Desired Baseband

SignalAfter LPF then frequency doubled signal is eliminated and )()(~

21 tmAtm




What happens if there is a phase or frequency error in cosine supplied by local oscillator in Rx?

After LPF term the frequency doubled term is gone and

whereas for no errors we had !!

tfftftmAtftstm ccc )(2cos2cos)(2cos)()(~

error phase anderror frequency Let f

)]cos()[cos(coscos :identity tric trigonomeUsing 21 BABABA

tfftmAtftmAtm c )(4cos)(2cos)()(~21

21

tftmAtm 2cos)()(~21

)()(~21 tmAtm



Phase Error

Non-linear distortion of information signal m(t) For always < 20° then error is small since cos(20°) =

0.94 For = ±90° then Rx signal is completely eliminated For random the performance is not acceptable

channel propagation distance is unknown so received signal phase is random!

0 and 0 f

cos)()(~then 21 tmAtm



Frequency Error

m(t) is modulated by time-varying cos(2f t)!!

Low frequency cosine (assuming f <<< fc) distorts m(t) and periodically eliminates signal

Completely unacceptable

0 and 0 f tftmAtm 2cos)()(~then 2

1

** DSB-SC requires perfect knowledge of frequency and phase of Tx carrier must be present in the Rx **


DSB-SC Synchronization

Frequency and phase synchronization required between Tx and Rx in DSB-SC Coherent Detection

Product Detector = Coherent Detector if oscillator is completely synchronized

How do we synchronize Tx and Rx? Radar System pass copy of Tx carrier to Rx

» Not possible for vast majority of communication systems

Pilot Carrier transmit copy of carrier outside spectrum for carrier recovery in Rx

Carrier Recovery PLL or Squaring Loop for carrier recovery in Rx

0 & 0 f


Pilot Carrier

f

|)(| fS

fc fc

|)(| fR

2fc2fc

Desired Baseband Signal

Pilot Carrier


Pilot Carrier

LPF

-0.5fc 0.5fc

BPF to get 0.5 fc and then

2 multiply to recover carrier for local oscillator


Squaring Loop Recovery

Square Law Device Full wave diode rectifier


Costas PLL Recovery


DSB-SC Detection

Complicated circuitry added to Rx for coherent detection of DSB-SC signals Good performance for low S/N at Rx input No distortion in recovered baseband signal spectrum

» Allows for data signals with non-zero power near DC in PSD

Significant cost added to Rx design and manufacturing for coherent detection

Squaring loop and Costas PLL have a 180° phase ambiguity» At initial start up of loop either type can lock on wrong polarity for

carrier phase ambiguity between +m(t) and –m(t)


DSB-SC Detection

180° phase ambiguity Not a problem for audio signal

» no auditory difference for +m(t) vs. –m(t) tone not affected by sign!!

Problem for polar data signal Ambiguity solutions:

Send test signal with a priori known phase to lock phase of recovery

Use differential encoding so that “1” and “0” stored in phase change rather than absolute phase value


DSB-SC Data Signal

If m(t) is digital data signal like polar NRZ we have

Binary Phase Shift Keying = BPSK Special case of DSB-SC for a Polar NRZ

m(t) Must have coherent detection for BPSK to

measure absolute phase Can use non-coherent detection with DBPSK

)2cos( tfc

)(tm

+1

-1

+1

-1

)2cos()()( tftmts c

180° Carrier Phase

Transitions:

cos(2fct)

cos(2fct)


AM vs. DSB-SC

ModulationType

Advantages Disadvantages

AM(DSB-LC)

DSB-SC

1. Envelope Detection

2. Simple & Cheap Rx’s

1. Inefficient use of power2. Poor performance forlow S/N 3. High power & expensiveTx for good S/N @ Rx4. Can’t use for most datasignals

1. Good performanceat low S/N2. Can use for all datasignals3. Power efficient

1. Synchronization of fand for coherentdetection2. Complicated andexpensive Rx’s

ece 4710: lecture #20 1 dsb-sc am tx signal also called dsb-lc double side band - large carrier ...

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