Amplitude Modulation: Single Sideband (SSB) - Mangoud

Amplitude Modulation:Single Sideband (SSB)

10/25/20EENG 372: Topic 1: Amplitude Modulation Dr. Sana Almansoori1


Single Side Band AMQ: What is Single Side Band AM? Looking at the power spectrum of an DSB we notice that:

PAV

f

Power Spectrum

fc fc + fmfc - fm

8

2mV

One side band may be removed because

they both contain the same information


Single Side Band AMQ: What is Single Side Band AM? This is the power spectrum of an AM SSB signal:

PAV

f

Power Spectrum

fc fc + fmfc - fm

8

2mV

One side band is removed because

they both contain the same information

Single Side Band AM


Q: What is SSB in the Time Domain?In the Frequency Domain:

In the time domain:

[ ] [ ])()(4

)()(4

)( LSBLSBm

USBUSBm

SCDSB ffffVffffVfV ++-+++-=- dddd

)2cos(2

)( tfVtv USBm

SSB p=

[ ])()(4

)( USBUSBm

SSB ffffVfV ++-= dd

))(2cos(2

)( tffVtv mcm

SSB += p


Single Side Band AMQ: What is Single Side Band AM in the Time Domain?

For tone modulation:

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-4

-2

0

2

4modulating (message) signal

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-4

-2

0

2

4Carrier and AM SSB signal

Amplitude Modulation:Generation DSB-TC


Generation DSB-TC


)2cos()()2cos()( tftVtfVtv cmccAM pp +=

X S

)(tvAM)(tvm

)(tvc

Generation DSB-TC


Q: How is a DSB-TC signal generated?Using a modulator system.In general to modulate mean mixing frequencies to get a different frequency.A linear system will not do that for us:

We need nonlinear systems to modulate

LTI

Generation DSB-LC


Q: What is an AM modulator?

Square Law Modulator



Q: What is a square law modulator?

Non-linear Device

BPF

)(tvm

)(tvc

)(tvAM

)(1 tv )(2 tv



Q: What is a square law modulator?The input to the Nonlinear Devices (NLD) is equal to:

The output of the NLD is:

We consider only second order terms:

)()()(1 tvtvtv cm +=

)2cos()()(1 tfVtvtv ccm p+=

.....)()()()( 313

2121102 ++++= tvatvatvaatv

)()()( 2121102 tvatvaatv ++»



Q: What is output of the nonlinear device?Substituting:

[ ] [ ]22102 )2cos()()2cos()()( tfVtvatfVtvaatv ccmccm pp ++++»

[ ] )2(cos)()2cos()(2

)2cos()()(22

22

22

1102

tfVatvatfVtva

tfVatvaatv

ccmccm

ccm

pp

p

+++

++»

[ ] [ ])4cos(12

)()2cos()(2

)2cos()()(2

2222

1102

tfVatvatfVtva

tfVatvaatv

cc

mccm

ccm

pp

p

++++

++»



Q: What is output of the nonlinear device in the frequency domain? Taking the Fourier Transform:

[ ]

[ ] ( ) [ ])2()2(4

)(*)()()(2

*)(2

)()(2

)()(2

)(

22

22

11

22

02

ccc

mmccc

m

ccc

mc

ffffVafVfVaffffVfVa

ffffVafVafVaafV

++-++++-+

++-++úû

ùêë

é+=

dddd

ddd

[ ]

[ ] ( ) [ ])2()2(4

)(*)()()(

)()(2

)()(2

)(

22

22

11

22

02

ccc

mmcmcmc

ccc

mc

ffffVafVfVaffVffVVa

ffffVafVafVaafV

++-++++-+

++-++úû

ùêë

é+=

dd

ddd

Q: Assuming the spectrum of the information signal, draw the V2(f).



)( fVm

-W W

f

)(2 fV

f

Amplitude Modulation:Generation DSB-SC


Generation DSB-SC


)2cos()()( tftvtv cmSCDSB p=-

X)(tv SCDSB-)(tvm

)(tvc

[ ])()(21*)()( ccmSCDSB fffffVfV -+-=- dd

[ ])()(21)( cmcmSCDSB ffVffVfV -+-=-

Generation DSB-SC


Q: What is a DSB-SC modulator?Balanced Bridge Modulator

Balanced Bridge Modulator


Q: What is a square law modulator for DSB-SC?

Non-linear Device

BPF

)(tvm

)(tvc)(tv SCDSB-

)(1 tx

)(2 tx

Non-linear DeviceS

S

S

-

)(1 ty

)(2 ty

)(tz

-



Q: What is a square law modulator?The inputs to the Nonlinear Devices (NLD) are:

The output of the NLD is:

We consider only second order terms:

)()2cos()()()(1 tvtfVtvtvtx mccmc +=+= p

.....)()()()( 313

2121101 ++++= txatxatxaaty

)()()( 2121101 txatxaaty ++»

)()2cos()()()(2 tvtfVtvtvtx mccmc -=-= p

.....)()()()( 323

2222102 ++++= txatxatxaaty

)()()( 2222102 txatxaaty ++»



Q: What is output of the nonlinear device?Substituting:

[ ] [ ]22102,1 )()2cos()()2cos()( tvtfVatvtfVaaty mccmcc ±+±+» pp

[ ] )2(cos)()2cos()(2

)2cos()()(22

22

22

1102,1

tfVatvatfVtva

tfVatvaaty

ccmccm

ccm

pp

p

++±

+±»

[ ] [ ])4cos(12

)()2cos()(2

)2cos()()(2

2222

1102,1

tfVatvatfVtva

tfVatvaaty

cc

mccm

ccm

pp

p

+++±

+±»



Q: What is output of the nonlinear device?Subtracting:

After BPF:

This is a single balanced bridge circuit

)()()( 21 tytytz -=

)2cos()(4)(2)( 21 tfVtvatvatz ccmm p+=

[ ] [ ])4cos(12

)()2cos()(2

)2cos()()(2

2222

110

tfVatvatfVtva

tfVatvaatz

cc

mccm

ccm

pp

p

+++±

+±» / /

/ /

)2cos()(4)( 2 tfVtvatV ccmSCDSB p=-

Amplitude Modulation:Generation SSB


Generation SSB


Q: What is a SSB modulator?We will study two types:1. Filtering Method2. Phase shift method

Filtering Method


( ) ( ) )cos()2cos()( ttfftv mcmcSSB wwp +=+=

)(tvSSB

f

|VDSB-SC (f)| |VDSB-SC (f)|

f

X

)(tv SCDSB-

)(tvm

)(tvcBPF

Limitations of Filtering Method



)(tvSSB

f

|VDSB-SC (f)| |VSSB-SC (f)|

f

X

)(tv SCDSB-

)(tvm

)(tvcBPF

Phase shift method


Q: Phase shift method generation SSB?Starting with:

Using:cos(α + β) = cos(α) cos(β) – sin(α) sin(β)We get:


( ) ( ) ( ) ( )tttttv mcmcSSB wwww sinsincoscos)( -=

Phase shift method

10/25/20EENG 372: Topic 1: Amplitude Modulation Dr. Sana

Almansoori28

-p/2

)(tvc)(tvm )(tvSSB

X

X

S

-p/2-

+

Amplitude Modulation:VSB

10/25/2029

Vestigial Side Band (VSB


Q: What is Vestigial Side Band Modulation?It is between DSB and SSBIt is used for examples where it is difficult to filter out the LSBbecause the message signal contains frequencies down to DC

f

|VDSB-SC (f)|

f

|Vm (f)|

Vestigial Side Band (VSB)


)(tvSSB

f

|VDSB-SC (f)| |VSSB-SC (f)|

f

X)(tv SCDSB-

)(tvm

)(tvc

ideal BPF

)2cos()()( tftvtv cmSCDSB p=-

)(thBPF



)(tvVSB

f

|VDSB-SC (f)| |VVSB (f)|

f

X)(tv SCDSB-

)(tvm

)(tvc

Non ideal BPF

)(thi)2cos()()( tftvtv cmSCDSB p=-



For SSB:

For VSB:

)()()( fHfVfV BPFSCDSBSSB •= -

)(*)()( thtvtv BPFSCDSBSSB -=

îíì +££

=otherwise

fffffH mcc

BPF 01

)(

)(*)()( thtvtv iSCDSBVSB -=

)()()( fHfVfV iSCDSBVSB •= - [ ] )()()(21 fHffVffV icmcm •-++=



We need to know the value of the filter such that we can recover the message when we demodulate.

)(*)2cos()()( thtftvtv ocVSBo p=

X)(tvo)(tvVSB

)2cos( tfcp

Non ideal LPF

)(tho

[ ] )()()(21)( fHffVffVfV ocVSBcVSBo •++-=



Q: What is the relationship between Ho(f) and Hi(f)?We will assume the output of the LPF is:

We know that:

Substituting:

[ ] )()()(21)( fHffVffVfV ocVSBcVSBo •++-=

[ ] )()()(21)( fHffVffVfV icmcmVSB •-++=

[ ][ ] )(

)()()()()()(

41)(

fHffHfffVfffV

ffHfffVfffV

fV

ociccmccm

ciccmccm

o

•úû

ùêë

é+•+-++++

-•--+-+

=



Q: What is HV(f)?

For Vo(f) = k . Vm(f):

[ ][ ] )(

)()()2()()2()(

41)( fH

ffHfVffVffHffVfV

fV ocicmcm

cicmcmo •ú

û

ùêë

é+•+++

-•-+=

[ ] )()()()()(41)( fHffHfVffHfVfV ocimcimo •+•+-•=

[ ] )()()()(41)( fHffHffHfVfV ocicimo •++-=

[ ])()(1)(

cicio ffHffHfH

++-=



Exercise: The carrier for a VSB signal is 20kHz and the message signal is 6kHz. The VSB shaping filter Hi(f)if shown below. Find the output low pass filter Ho(f).

f

|Hi (f)|

18 22 26

1

0.5

Amplitude Modulation:QAM

10/25/2038

Quadrature Amplitude Modulation (QAM)


Q: What is QAM?It is an AM technique that overcomes the BW issue of DSB-SC.It is basically transmitting 2 information signals on the same carrier frequency.


10/25/20EENG 372: Topic 1: Amplitude Modulation Dr. Sana

Almansoori40

-p/2

)(tvc

)(1 tvm

)(tvQAM

)(2 tvm

X

X

S

-p/2

)(2)(_ tvtv cdemc =

X LPF1

X LPF2

)(1 tvm

)(2 tvm

)(' tvc

)(1 tx

)(2 tx



The carrier frequency

After the -90 phase shift

Upper arm (in-phase or I channel):

Lower arm (quadrature or Q channel)

Output of the transmitter:

)cos()( ttv cc w=

)sin()(' ttv cc w=

)sin()()cos()()( 21 ttvttvtv cmcmQAM ww +=

)cos()(1 ttv cm w

)sin()(2 ttv cm w



At the receiver: Upper arm:

After LPF 1:

[ ] )cos(2.)sin()()cos()()( 211 tttvttvtx ccmcm www +=

)2sin()()2cos()()()( 2111 ttvttvtvtx cmcmm ww ++=

)()( 11 tvtx mLPF =

)cos(2).()().()( _1 ttvtvtvtx cQAMdemcQAM w==

)cos(2)(_ ttv cdemc w=



Lower arm:

After LPF2:

[ ] )sin(2.)sin()()cos()()( 212 tttvttvtx ccmcm www +=

)()( 22 tvtx mLPF =

)sin(2).()(').()( _2 ttvtvtvtx cQAMdemcQAM w==

)sin(2)(' _ ttv cdemc w=



Exercise: QAM must be total synchronous. To see this, check what happens if the carrier in the demodulator is out of phase from the modulator by q:

)cos(2)(_ qw += ttv cdemc

)cos()( ttv cc w=

Amplitude Modulation: Single Sideband (SSB) - Mangoud

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