4: Amplitude Modulation - ArraytoolIntroductionDSB-SC ModulationAmplitude ModulationBandwidth...

Introduction DSB-SC Modulation Amplitude Modulation Bandwidth Efficient Modulations FDM AM Receivers Noise Summary

4: Amplitude Modulation

Y. Yoganandam, Runa Kumari, and S. R. Zinka

Department of Electrical & Electronics EngineeringBITS Pilani, Hyderbad Campus

August 14, 17, 19, 21, 24 & 26, 2015

4: Amplitude Modulation Communication Systems, Dept. of EEE, BITS Hyderabad


Outline

1 Introduction

2 DSB-SC Modulation

3 Amplitude Modulation

4 Bandwidth Efficient Modulations

5 FDM

6 AM Receivers

7 Noise

8 Summary



Outline

1 Introduction

2 DSB-SC Modulation



5 FDM

6 AM Receivers

7 Noise

8 Summary



Modulation

To alter or adapt (the voice) according to the circumstances, one’s listener, etc.

Baseband signals produced by various information sources are not alwayssuitable for direct transmission over a given channel. These signals are

usually further modified to facilitate transmission. This conversion process isknown as modulation.



Modulation






Modulation






Modulation

Carrier Signal:Ac cos (ωct + θ)

Amplitude Modulation:AAM = f (m (t))

Frequency Modulation:ωFM = g (m (t))

Phase Modulation:θPM = h (m (t))



Modulation







Modulation







Modulation







Modulation







Amplitude Modulation

Time

Amplitude

0

−1.5

1.5

−0.5

0.5

Message wave envelopeCarrier wave



Amplitude Modulation

Time

Amplitude

0

−1.5

1.5

−0.5

0.5

Message wave envelopeCarrier wave



Why Modulation?

• Ease of radiation

• Simultaneous transmission of several signals

• Effecting the exchange of SNR with bandwidth



Why Modulation?






Why Modulation?






Why Modulation?






Basic Terminology

• Modulation

• Modulating Signal

• Carrier Signal

• Modulated Signal

• Sidebands

• Aliasing

• Demodulation



Basic Terminology

• Modulation


• Carrier Signal


• Sidebands

• Aliasing

• Demodulation



Basic Terminology

• Modulation


• Carrier Signal


• Sidebands

• Aliasing

• Demodulation



Basic Terminology

• Modulation


• Carrier Signal


• Sidebands

• Aliasing

• Demodulation



Basic Terminology

• Modulation


• Carrier Signal


• Sidebands

• Aliasing

• Demodulation



Basic Terminology

• Modulation


• Carrier Signal


• Sidebands

• Aliasing

• Demodulation



Basic Terminology

• Modulation


• Carrier Signal


• Sidebands

• Aliasing

• Demodulation



Basic Terminology

• Modulation


• Carrier Signal


• Sidebands

• Aliasing

• Demodulation



Baseband Communication

The term baseband is used to designate the band of frequencies of the signaldelivered by the source or the input transducer.

In telephony, the baseband is the audio band of (voice signals) of 0 to 3.5 kHz.

In television, the baseband is the video band occupying 0 to 4.3 MHz.

For digital data or PCM using bipolar signaling at a rate of Rb pulses per sec-ond, the baseband is 0 to Rb Hz.

Usually, baseband signals cannot be transmitted over a radio link but are suit-able for transmission over a pair of wires , coaxial cables, or optical fibers.











































Carrier Communication

Communication that uses modulation to shift the frequency spectrum of asignal is known as carrier communication.

In this mode, one of the basic parameters (amplitude, frequency, or phase) of asinusoidal carrier of high frequency ωc is varied in proportion to the basebandsignal m (t). This results in amplitude modulation (AM), frequency modula-tion (FM), or phase modulation (PM), respectively.

Modulation is used to transmit both analog as well as digital baseband signals.





















Outline

1 Introduction

2 DSB-SC Modulation



5 FDM

6 AM Receivers

7 Noise

8 Summary



DSB-SC Modulation

m(t)(Modulating signal)



DSB-SC Modulation




DSB-SC Modulation


cosωct(Carrier)



DSB-SC Modulation

m(t)(Modulating signal) (Modulated signal)

m(t) cosωct

cosωct(Carrier)



DSB-SC Modulation


m(t) cosωct

cosωct(Carrier)

t

m(t)



DSB-SC Modulation


m(t) cosωct

cosωct(Carrier)

t

m(t) cosωctm(t)

-m(t)

t

m(t)



DSB-SC Modulation


m(t) cosωct

cosωct(Carrier)

t

m(t) cosωctm(t)

-m(t)

t ω

m(t)

0 2πB-2πB

2A



DSB-SC Modulation


m(t) cosωct

cosωct(Carrier)

t ω

m(t) cosωctm(t)

-m(t)

-ωc +ωc

4πB

LSB USBLSBUSB

t ω

m(t)

0 2πB-2πB

2A

ωc≥2πB

A



DSB-SC Demodulation

m(t) cosωct



DSB-SC Demodulation

m(t) cosωct

cosωct(Carrier)



DSB-SC Demodulation

m(t) cosωct

cosωct(Carrier)

e(t)



DSB-SC Demodulation

m(t) cosωct

cosωct(Carrier)

e(t)

ω+2ωc-2ωc 0



DSB-SC Demodulation

m(t) cosωct

cosωct(Carrier)

Low-pass filtere(t)

m(t)12

ω+2ωc-2ωc 0

A

A/2A/2



Theoretical Explanation of DSB-SC

Modulation:

m (t)⇐⇒ M (ω)

m (t) cos ωct⇐⇒ 12[M (ω + ωc) + M (ω−ωc)] (1)

Demodulation:

e (t) = m (t) cos2 ωct =12[m (t) + m (t) cos 2ωct]

e (t)⇐⇒ 12

M (ω) +14[M (ω + 2ωc) + M (ω− 2ωc)] (2)




Modulation:

m (t)⇐⇒ M (ω)


Demodulation:


e (t)⇐⇒ 12

M (ω) +14[M (ω + 2ωc) + M (ω− 2ωc)] (2)




Modulation:

m (t)⇐⇒ M (ω)


Demodulation:


e (t)⇐⇒ 12

M (ω) +14[M (ω + 2ωc) + M (ω− 2ωc)] (2)



DSB-SC Modulators – 1: Nonlinear Modulator

m(t)




m(t)




m(t)

cosωct




m(t) Σ

cosωct

x1(t)




m(t) Σ

cosωct

x1(t) NLy1(t)




m(t)

Σ

Σ

cosωct

x1(t)

NL

NL

x2(t)

y1(t)

y2(t)

-1




m(t)

Σ

Σ

cosωct

x1(t)

z(t)Σ

NL

NL

x2(t)

y1(t)

y2(t)

-1




m(t)

4bm(t) cosωct

Σ

Σ

cosωct

x1(t)

z(t) BPF±ωc

Σ

NL

NL

x2(t)

y1(t)

y2(t)

-1




Let input-output characteristics of NL device be approximated by a powerseries:

y (t) = ax (t) + bx2 (t) (3)

Then the summer output z (t) is given by

z (t) = y1 (t)− y2 (t) =[ax1 (t) + bx2

1 (t)]−[ax2 (t) + bx2

2 (t)]

. (4)

Substituting the two input signals x1 (t) = cos ωct + m (t) and x2 (t) =cos ωct−m (t) in the above equation gives

z (t) = 2am (t) + 4bm (t) cos ωct. (5)

From the above equation, it can be said that the circuit acts as a balancedbridge for carrier signal. Do you know what is meant by that?





y (t) = ax (t) + bx2 (t) (3)


z (t) = y1 (t)− y2 (t) =[ax1 (t) + bx2

1 (t)]−[ax2 (t) + bx2

2 (t)]

. (4)


z (t) = 2am (t) + 4bm (t) cos ωct. (5)






y (t) = ax (t) + bx2 (t) (3)


z (t) = y1 (t)− y2 (t) =[ax1 (t) + bx2

1 (t)]−[ax2 (t) + bx2

2 (t)]

. (4)


z (t) = 2am (t) + 4bm (t) cos ωct. (5)






y (t) = ax (t) + bx2 (t) (3)


z (t) = y1 (t)− y2 (t) =[ax1 (t) + bx2

1 (t)]−[ax2 (t) + bx2

2 (t)]

. (4)


z (t) = 2am (t) + 4bm (t) cos ωct. (5)






y (t) = ax (t) + bx2 (t) (3)


z (t) = y1 (t)− y2 (t) =[ax1 (t) + bx2

1 (t)]−[ax2 (t) + bx2

2 (t)]

. (4)


z (t) = 2am (t) + 4bm (t) cos ωct. (5)




DSB-SC Modulators – 2: Switching Modulators

t

m(t)




t

m(t)




t

m(t)

ω0




t

w(t)

t

m(t)

ω0




t

w(t)

t

m(t)w(t)

t

m(t)

ω0




t

w(t)

t

m(t)w(t)

ω0

t

m(t)

ω0




t

w(t)

t

m(t)w(t)

ω0

t

m(t)

ω0

BPF±ωc




t

w(t)

t

m(t)w(t)

ω0

t

m(t)

ω0

BPF±ωc t

m(t) cosωct2π



DSB-SC Modulators – 3: Diode Bridge Switch

a

b

c d

D1 D3

D4D2

Acosωct




a

b

c d

D1 D3

D4D2

Acosωct




a

b

c d

D1 D3

D4D2

Duringpositive

cycle




a

b

c d

D1 D3

D4D2

Duringnegative

cycle




a

b

c d

D1 D3

D4D2

a b

+−

Bandpassfilterm(t) km(t) cosωct

+

−

+−

a

b

Bandpassfilterm(t) km(t) cosωct

+

−



DSB-SC Modulators – 4: Ring Modulator

Bandpassfilter km(t) cosωct

a

b

c

d

m(t)

Acosωct

D1

D3

D4

D2

+

−vi





a

b

c

d

m(t)

Acosωct

D1

D3

D4

D2

+

−vi





a

b

c

d

m(t)

Acosωct

D1

D3

D4

D2

+

−vi





a

b

c

d

m(t)

Acosωct

D1

D3

D4

D2

+

−vi





a

b

c

d

m(t)

Acosωct

D1

D3

D4

D2

+

−vi

t

w0(t)





a

b

c

d

m(t)

Acosωct

D1

D3

D4

D2

+

−vi

t

w0(t)

t

m(t)





a

b

c

d

m(t)

Acosωct

D1

D3

D4

D2

+

−vi

t

w0(t)

t

vi=m(t)w0(t)

t

m(t)



Impact of Asynchronous Carrier

m(t) cosωct

cosωct(Carrier)

Low-pass filtere(t)

m(t)12

ω+2ωc-2ωc 0

A

A/2A/2

Demodulation process is similar to that of modulation except that we use alowpass filter instead of bandpass filter. Thus all the circuits used for modu-lation can be used for demodulation also.

But having a synchronous carrier at the receiver end is a must. This compli-cates the receiver design.




m(t) cosωct

cosωct(Carrier)

Low-pass filtere(t)

m(t)12

ω+2ωc-2ωc 0

A

A/2A/2






m(t) cosωct

cosωct(Carrier)

Low-pass filtere(t)

m(t)12

ω+2ωc-2ωc 0

A

A/2A/2






m(t) cosωct

cosωct(Carrier)

Low-pass filtere(t)

m(t)12

ω+2ωc-2ωc 0

A

A/2A/2






Let the local carrier with phase and frequency offset be 2 cos [(ωc + ∆ω) t + δ] .

Then the product at the receiver is given as

e (t) = 2m (t) cos ωct cos [(ωc + ∆ω) t + δ]

= m (t) {cos [(2ωc + ∆ω) t + δ] + cos [(∆ω) t + δ]} .

After lowpass filtering,

e0 (t) = m (t) cos [(∆ω) t + δ] . (6)









e0 (t) = m (t) cos [(∆ω) t + δ] . (6)









e0 (t) = m (t) cos [(∆ω) t + δ] . (6)









e0 (t) = m (t) cos [(∆ω) t + δ] . (6)




So, after lowpass filtering,

e0 (t) = m (t) cos [(∆ω) t + δ] .

If ∆ω = 0,e0 (t) = m (t) cos δ. (7)

If δ = 0 and ∆ω 6= 0,e0 (t) = m (t) cos (∆ωt) . (8)

Even if ∆f is 1 Hz, the effect is very annoying.





e0 (t) = m (t) cos [(∆ω) t + δ] .

If ∆ω = 0,e0 (t) = m (t) cos δ. (7)







e0 (t) = m (t) cos [(∆ω) t + δ] .

If ∆ω = 0,e0 (t) = m (t) cos δ. (7)







e0 (t) = m (t) cos [(∆ω) t + δ] .

If ∆ω = 0,e0 (t) = m (t) cos δ. (7)







e0 (t) = m (t) cos [(∆ω) t + δ] .

If ∆ω = 0,e0 (t) = m (t) cos δ. (7)





Ensuring Synchronous Carrier at the Receiver

To ensure identical carrier frequencies at the transmitter and the receiver, wecan use quartz crystal oscillators, which are very stable (at least at low carrierfrequencies).

At very high frequencies, a carrier, or pilot, is transmitted at a reduced level(usually about -20dB) along with the sidebands. After separating the pilotsignal using a very narrow-band filter, it is amplified and used to synchronize(with the help of a phase-locked loop or PLL) the local oscillator.













Phase-Locked Loop (PLL)

A sin (ωct+θi)




A sin (ωct+θi)




VCO

A sin (ωct+θi)

B cos (ωct+θo)




VCO

x(t)A sin (ωct+θi)

B cos (ωct+θo)




Loopfilter

VCO

eo(t)x(t)A sin (ωct+θi)

B cos (ωct+θo)




Loopfilter

VCO


B cos (ωct+θo)Phase Detector




Loopfilter

VCO


B cos (ωct+θo)ω = ωc + ceo(t)




Loopfilter

VCO


B cos (ωct+θo)

eo

θe

a

θe

eo

ω = ωc + ceo(t)

θe = θi-θo

eo = sinθe




Let the input to the PLL be A sin (ωct + θi), and let the VCO output beB cos (ωct + θo). Then

x (t) = AB sin (ωct + θi) cos (ωct + θo)

=AB2

[sin (2ωct + θi + θo) + sin (θi − θo)] .

After filtering, error signal eo (t) is given as

eo (t)=AB2

sin (θi − θo) =AB2

sin θe, (9)

where θe = θi − θo.






=AB2



eo (t)=AB2


sin θe, (9)







=AB2



eo (t)=AB2


sin θe, (9)




Signal-Squaring Method

BPF±2ωc

x(t)( )2 PLL 2:1 Frequency

dividerk cosωctm(t) cosωct c cos 2ωct

Narrow-bandfilter

The squarer output x (t) is

x (t) = [m (t) cos ωct]2 =12

m2 (t) +12

m2 (t) cos 2ωct.

Since m2 (t) is a non-negative signal, it can be written as

12

m2 (t) = k + φ (t) .

Thenx (t) =

12

m2 (t) + k cos 2ωct + φ (t) cos 2ωct. (10)




BPF±2ωc



Narrow-bandfilter


x (t) = [m (t) cos ωct]2 =12

m2 (t) +12

m2 (t) cos 2ωct.


12

m2 (t) = k + φ (t) .

Thenx (t) =

12





BPF±2ωc



Narrow-bandfilter


x (t) = [m (t) cos ωct]2 =12

m2 (t) +12

m2 (t) cos 2ωct.


12

m2 (t) = k + φ (t) .

Thenx (t) =

12





BPF±2ωc



Narrow-bandfilter


x (t) = [m (t) cos ωct]2 =12

m2 (t) +12

m2 (t) cos 2ωct.


12

m2 (t) = k + φ (t) .

Thenx (t) =

12





BPF±2ωc



Narrow-bandfilter


x (t) = [m (t) cos ωct]2 =12

m2 (t) +12

m2 (t) cos 2ωct.


12

m2 (t) = k + φ (t) .

Thenx (t) =

12




Costas Loop

m(t) cos (ωct+θi)

The mechanism is very similar to that of PLL except that

eo (t) ∝ sin 2θe.



Costas Loop

VCOm(t) cos (ωct+θi)

2 cos (ωct+θo)

2 sin (ωct+θo)

−π/2





Costas Loop

VCOm(t) cos (ωct+θi)

2 cos (ωct+θo)

2 sin (ωct+θo)

−π/2





Costas Loop

Lowpassfilter

VCO

Lowpassfilter

m(t) cos (ωct+θi)

2 cos (ωct+θo)

2 sin (ωct+θo)

m(t) cos θe

m(t) sin θe

−π/2





Costas Loop

Lowpassfilter

VCO

Lowpassfilter

m(t) cos (ωct+θi)

2 cos (ωct+θo)

2 sin (ωct+θo)

m(t) cos θe

m(t) sin θe

m2(t) sin 2θe12

−π/2





Costas Loop

Lowpassfilter

Lowpassfilter

(narrow band)VCO

Lowpassfilter

m(t) cos (ωct+θi)

2 cos (ωct+θo)

2 sin (ωct+θo)

m(t) cos θe

m(t) sin θe

K sin 2θe

m2(t) sin 2θe12

−π/2





Costas Loop

Lowpassfilter

Lowpassfilter

(narrow band)VCO

Lowpassfilter

m(t) cos (ωct+θi)

2 cos (ωct+θo)

2 sin (ωct+θo)

m(t) cos θe

m(t) sin θe

K sin 2θe

m2(t) sin 2θe12

−π/2





Costas Loop

Lowpassfilter

Lowpassfilter

(narrow band)

Output

VCO

Lowpassfilter

m(t) cos (ωct+θi)

2 cos (ωct+θo)

2 sin (ωct+θo)

m(t) cos θe

m(t) sin θe

K sin 2θe

m2(t) sin 2θe12

−π/2





Outline

1 Introduction

2 DSB-SC Modulation



5 FDM

6 AM Receivers

7 Noise

8 Summary



Amplitude Modulation (with Carrier)

DSB-SC receivers are expensive as they have to maintain the synchronismwith that of the transmitter.

The solution is to send the carrier along with the signal. This implies that thetransmitter has to transmit extra power in the high power carrier.

So, amplitude modulated signal is given by

ϕAM (t) = m (t) cos ωct + A cos ωct = [A + m (t)] cos ωct. (11)
























Under Modulation

Time

Amplitude

0

−0.5

0.5



Under Modulation

Time

Amplitude

0

−0.5

0.5



Under Modulation

Time

Amplitude

0

1.5

−0.5

0.5



Under Modulation

Time

Amplitude

0

−1.5

1.5

−0.5

0.5



Under Modulation

Time

Amplitude

0

−1.5

1.5

−0.5

0.5



Over Modulation

Time

Amplitude

0−0.5

0.5



Over Modulation

Time

Amplitude

0−0.5

0.5



Over Modulation

Time

Amplitude

0

2.5

−0.5

0.5



Over Modulation

Time

Amplitude

0

−2.5

2.5

−0.5

0.5



Over Modulation

Time

Amplitude

0

−2.5

2.5

−0.5

0.5



Modulation Index (µ)

From the previous slides, the condition for envelope detection of an AM signalis

A + m (t) ≥ 0. (12)

The above equation is equivalent to

A ≥ mnp, (13)

where mnp is the absolute negative peak amplitude.

From the above discussion, we define modulation index (µ) as

µ =mnp

A. (14)

When µ > 1 (over-modulation), envelop detection is not possible and onlyoption available is synchronous detection.





A + m (t) ≥ 0. (12)


A ≥ mnp, (13)



µ =mnp

A. (14)






A + m (t) ≥ 0. (12)


A ≥ mnp, (13)



µ =mnp

A. (14)






A + m (t) ≥ 0. (12)


A ≥ mnp, (13)



µ =mnp

A. (14)






A + m (t) ≥ 0. (12)


A ≥ mnp, (13)



µ =mnp

A. (14)




Power Efficiency (η)

ϕAM (t) = m (t) cos ωct︸︷︷︸side−bands

+A cos ωct︸︷︷︸carrier

Pc =A2

2and Ps =

12

m2 (t)

The sideband power is the useful power and the carrier power is the powerwasted for convenience. So, η, the power efficiency is defined as

η =useful powertotal power

=Ps

Pc + Ps=

m2 (t)

m2 (t) + A2× 100%. (15)

For the special case of tone modulation, m (t) = µA cos ωmt. So, m2 (t) =

(µA)2 /2 and

η =µ2

2 + µ2 × 100%. (16)






Pc =A2

2and Ps =

12

m2 (t)



=Ps

Pc + Ps=

m2 (t)

m2 (t) + A2× 100%. (15)


(µA)2 /2 and

η =µ2

2 + µ2 × 100%. (16)






Pc =A2

2and Ps =

12

m2 (t)



=Ps

Pc + Ps=

m2 (t)

m2 (t) + A2× 100%. (15)


(µA)2 /2 and

η =µ2

2 + µ2 × 100%. (16)






Pc =A2

2and Ps =

12

m2 (t)



=Ps

Pc + Ps=

m2 (t)

m2 (t) + A2× 100%. (15)


(µA)2 /2 and

η =µ2

2 + µ2 × 100%. (16)



AM Modulators

AM signals can be generated by any DSB-SC modulator if the modulatingsignal is A + m (t) instead of just m (t).

But because there is no need to suppress the carrier in the output, the modu-lating signal do not have to be balanced. This results in a considerably simplermodulator for AM.



AM Modulators





AM Modulators





AM Modulators

+−

+−

BPF±ωc

m(t)

c cosωct

a b

a' b'

c

c'

vo(t)

When c� m (t), the voltage across terminals bb′ is

vbb′ = [c cos ωct + m (t)]w (t)

= [c cos ωct + m (t)][

12+

2π

(cos ωct− 1

3cos 3ωct +

15

cos 5ωct− · · ·)]

=c2

cos ωct +2π

m (t) cos ωct︸︷︷︸AM

+ other terms.



AM Modulators

+−

+−

BPF±ωc

m(t)

c cosωct

a b

a' b'

c

c'

vo(t)




12+

2π

(cos ωct− 1

3cos 3ωct +

15

cos 5ωct− · · ·)]

=c2

cos ωct +2π


+ other terms.



AM Modulators

+−

+−

BPF±ωc

m(t)

c cosωct

a b

a' b'

c

c'

vo(t)




12+

2π

(cos ωct− 1

3cos 3ωct +

15

cos 5ωct− · · ·)]

=c2

cos ωct +2π


+ other terms.



AM Modulators

+−

+−

BPF±ωc

m(t)

c cosωct

a b

a' b'

c

c'

vo(t)




12+

2π

(cos ωct− 1

3cos 3ωct +

15

cos 5ωct− · · ·)]

=c2

cos ωct +2π


+ other terms.



AM Modulators

+−

+−

BPF±ωc

m(t)

c cosωct

a b

a' b'

c

c'

vo(t)




12+

2π

(cos ωct− 1

3cos 3ωct +

15

cos 5ωct− · · ·)]

=c2

cos ωct +2π


+ other terms.



AM Modulators

+−

+−

BPF±ωc

m(t)

c cosωct

a b

a' b'

c

c'

vo(t)




12+

2π

(cos ωct− 1

3cos 3ωct +

15

cos 5ωct− · · ·)]

=c2

cos ωct +2π


+ other terms.



AM Demodulation

The AM signal can be demodulated coherently by a locally generated carrier.However, this defeats the very purpose (i.e., using non-coherent demodula-tion) of AM.

So, we shall consider here the following non-coherent demodulation schemes:

1 Rectifier detection

2 Envelop detection



AM Demodulation




2 Envelop detection



AM Demodulation




2 Envelop detection



Rectifier Detector

+−[A+m(t)] cosωct



Rectifier Detector




Rectifier Detector




Rectifier Detector


[A+m(t)]



Rectifier Detector


[A+m(t)]/π



Rectifier Detector

+−

Lowpassfilter[A+m(t)] cosωct

[A+m(t)]/π



Rectifier Detector

+−

Lowpassfilter[A+m(t)] cosωct

[A+m(t)]/π



Rectifier Detector

+−

Lowpassfilter[A+m(t)] cosωct vo(t)



Rectifier Detector

+−

Lowpassfilter[A+m(t)] cosωct vo(t)



Envelop Detector

+−[A+m(t)] cosωct RC Capacitor

discharge vo(t)



Envelop Detector


discharge vo(t)



Envelop Detector


discharge vo(t)



Envelop Detector


discharge vo(t)



Envelop Detector


discharge vo(t)



Envelop Detector


discharge vo(t)



Envelop Detector


discharge vo(t)



Outline

1 Introduction

2 DSB-SC Modulation



5 FDM

6 AM Receivers

7 Noise

8 Summary



Bandwidth Efficient Modulation Schemes

• Single Side-Band Modulation (SSB)

• Vestigial Side-Band Modulation (VSB)

• Quadrature Amplitude Modulation (QAM)





















SSB-SC Modulation



SSB-SC Modulation

ω0



SSB-SC Modulation

ω-ωc +ωc

LSB USBLSBUSB

ω0



SSB-SC Modulation

ω-ωc +ωc

LSB USBLSBUSB

ω-ωc +ωc

ω0



SSB-SC Modulation

ω-ωc +ωc

LSB USBLSBUSB

ω-ωc +ωc

ω-ωc +ωc

ω0



SSB-SC Modulation

ω-ωc +ωc

LSB USBLSBUSB

ω-ωc +ωc

ω-ωc +ωc

ω0

ω0-2ωc +2ωc



Time-Domain Representation of SSB Signals

ω0

M(ω)




ω0

M(ω)




ω0

M(ω)

ω

M+(ω)

ω

M−(ω)




ω0

M(ω)

ω

M+(ω)

ω

M−(ω)

ω-ωc +ωc

M+(ω−ωc)M−(ω+ωc)

ω-ωc +ωc

M−(ω−ωc)M+(ω+ωc)




M+ (ω)⇐⇒ m+ (t)M− (ω)⇐⇒ m− (t)

Since M+ (ω) and M− (ω) are conjugates, m+ (t) and m− (t) are also conju-gates. Also, because m+ (t) + m− (t) = m (t), we can express

m+ (t) =12[m (t) + jmh (t)]

m− (t) =12[m (t)− jmh (t)]

where mh (t) is unknown.

From the above set of equations, it follows that

M+ (ω) =12[M (ω) + jMh (ω)] (17)

M− (ω) =12[M (ω)− jMh (ω)] .




M+ (ω)⇐⇒ m+ (t)M− (ω)⇐⇒ m− (t)


m+ (t) =12[m (t) + jmh (t)]

m− (t) =12[m (t)− jmh (t)]



M+ (ω) =12[M (ω) + jMh (ω)] (17)

M− (ω) =12[M (ω)− jMh (ω)] .




M+ (ω)⇐⇒ m+ (t)M− (ω)⇐⇒ m− (t)


m+ (t) =12[m (t) + jmh (t)]

m− (t) =12[m (t)− jmh (t)]



M+ (ω) =12[M (ω) + jMh (ω)] (17)

M− (ω) =12[M (ω)− jMh (ω)] .




M+ (ω)⇐⇒ m+ (t)M− (ω)⇐⇒ m− (t)


m+ (t) =12[m (t) + jmh (t)]

m− (t) =12[m (t)− jmh (t)]



M+ (ω) =12[M (ω) + jMh (ω)] (17)

M− (ω) =12[M (ω)− jMh (ω)] .




Since M+ (ω) = M (ω) u (ω),

M+ (ω) =12

M (ω) [1 + sgn (ω)]

=12

M (ω) +12

M (ω) sgn (ω) . (18)

Comparing (18) and (17) gives

Mh (ω) = −jM (ω) sgn (ω) = [M (ω)] [−jsgn (ω)] .

Since, 1/πt⇐⇒ −jsgn (ω), taking inverse Fourier transform on both sides ofthe above equation gives

Mh (ω) =12

ˆ ∞

−∞

m (τ)

t− τdτ =

12

ˆ ∞

−∞

m (α)

t− αdα. (19)

The right-hand side of the above equation defines the Hilbert transform ofm (t).





M+ (ω) =12

M (ω) [1 + sgn (ω)]

=12

M (ω) +12

M (ω) sgn (ω) . (18)




Mh (ω) =12

ˆ ∞

−∞

m (τ)

t− τdτ =

12

ˆ ∞

−∞

m (α)

t− αdα. (19)






M+ (ω) =12

M (ω) [1 + sgn (ω)]

=12

M (ω) +12

M (ω) sgn (ω) . (18)




Mh (ω) =12

ˆ ∞

−∞

m (τ)

t− τdτ =

12

ˆ ∞

−∞

m (α)

t− αdα. (19)






M+ (ω) =12

M (ω) [1 + sgn (ω)]

=12

M (ω) +12

M (ω) sgn (ω) . (18)



Since, 1/πt⇐⇒ −jsgn (ω),

taking inverse Fourier transform on both sides ofthe above equation gives

Mh (ω) =12

ˆ ∞

−∞

m (τ)

t− τdτ =

12

ˆ ∞

−∞

m (α)

t− αdα. (19)






M+ (ω) =12

M (ω) [1 + sgn (ω)]

=12

M (ω) +12

M (ω) sgn (ω) . (18)




Mh (ω) =12

ˆ ∞

−∞

m (τ)

t− τdτ =

12

ˆ ∞

−∞

m (α)

t− αdα. (19)





SSB signal ΦUSB (ω) can be expressed as

ΦUSB (ω) = M+ (ω−ωc) + M− (ω + ωc) .

Taking inverse transform of the above equation gives

ϕUSB (t) = m+ (t) ejωct + m− (t) e−jωct.

Substituting m+ (t) and m− (t) values gives

ϕUSB (t)= m (t) cos ωct−mh (t) sin ωct. (20)

Similarly, it can be shown that

ϕLSB (t)= m (t) cos ωct + mh (t) sin ωct. (21)





ΦUSB (ω) = M+ (ω−ωc) + M− (ω + ωc) .











ΦUSB (ω) = M+ (ω−ωc) + M− (ω + ωc) .











ΦUSB (ω) = M+ (ω−ωc) + M− (ω + ωc) .











ΦUSB (ω) = M+ (ω−ωc) + M− (ω + ωc) .









Hilbert Transform – Physical Interpretation

ω0

|H(ω)|

1

ω0

θh(ω)+π/2

−π/2

Mh (ω) = [M (ω)]× [−jsgn (ω)]




ω0

|H(ω)|

1

ω0

θh(ω)+π/2

−π/2

Mh (ω) = [M (ω)]× [−jsgn (ω)]




ω0

|H(ω)|

1

ω0

θh(ω)+π/2

−π/2

Mh (ω) = [M (ω)]× [−jsgn (ω)]



SSB-SC Modulators

• Selective-Filtering Method

• Phase-Shift Method



SSB-SC Modulators

• Selective-Filtering Method

• Phase-Shift Method



Selective-Filtering Method

0 1000 2000 3000 4000Frequency f, Hz

Rela

tive

PSD




0 1000 2000 3000 4000Frequency f, Hz

Rela

tive

PSD




0 1000 2000 3000 4000Frequency f, Hz

Rela

tive

PSD

ω-ωc +ωc




0 1000 2000 3000 4000Frequency f, Hz

Rela

tive

PSD

ω-ωc +ωc



Phase-Shift Method

cos ωct

m(t)

ϕUSB (t) = m (t) cos ωct−mh (t) sin ωct



Phase-Shift Method

cos ωct

m(t)




Phase-Shift Method

cos ωct

m(t)




Phase-Shift Method

DSB-SCmodulator

cos ωct

m(t)

m(t) cos ωct




Phase-Shift Method

−π/2

DSB-SCmodulator

−π/2

cos ωct

m(t)

mh(t)

m(t) cos ωct

sin ωct




Phase-Shift Method

−π/2

DSB-SCmodulator

DSB-SCmodulator−π/2

cos ωct

m(t)

mh(t) mh(t) sin ωct

m(t) cos ωct

sin ωct




Phase-Shift Method

−π/2 Σ

DSB-SCmodulator

DSB-SCmodulator−π/2

SSB signal

cos ωct

m(t)

mh(t) mh(t) sin ωct

m(t) cos ωct

+

−+

sin ωct




SSB-SC Demodulation

SSB signal is given by

ϕSSB (t) = m (t) cos ωct∓mh (t) sin ωct.

Assuming that we have a synchronized local carrier at the receiver end, wecan demodulate the signal as shown below:

ϕSSB (t) cos ωct =12

m (t) (1 + cos 2ωct)∓ 12

mh (t) sin 2ωct

=12

m (t) +12

m (t) cos 2ωct∓ 12

mh (t) sin 2ωct︸︷︷︸can be filtered out using an LPF

. (22)



SSB-SC Demodulation





m (t) (1 + cos 2ωct)∓ 12

mh (t) sin 2ωct

=12

m (t) +12



. (22)



SSB-SC Demodulation





m (t) (1 + cos 2ωct)∓ 12

mh (t) sin 2ωct

=12

m (t) +12



. (22)



SSB-SC Demodulation





m (t) (1 + cos 2ωct)∓ 12

mh (t) sin 2ωct

=12

m (t) +12



. (22)



SSB-SC Demodulation





m (t) (1 + cos 2ωct)∓ 12

mh (t) sin 2ωct

=12

m (t) +12



. (22)



Envelope Detection of SSB+C Signal

SSB signal with a carrier (SSB+C) can be expressed as

ϕSSB+C (t) = A cos ωct + [m (t) cos ωct + mh (t) sin ωct]= [A + m (t)] cos ωct + mh (t) sin ωct

=√[A + m (t)]2 + m2

h (t)×[A + m (t)] cos ωct + mh (t) sin ωct√

[A + m (t)]2 + m2h (t)

=√[A + m (t)]2 + m2

h (t) cos (ωct + θ) . (23)

So, the envelope of the SSB+C signal is given by

E =√[A + m (t)]2 + m2

h (t)

= A

√1 +

2m (t)A

+m2 (t)

A2 +m2

h (t)A2

≈ A[

1 +m (t)

A

]= A + m (t). ( Assuming A� m (t)) (24)






=√[A + m (t)]2 + m2


[A + m (t)]2 + m2h (t)

=√[A + m (t)]2 + m2

h (t) cos (ωct + θ) . (23)


E =√[A + m (t)]2 + m2

h (t)

= A

√1 +

2m (t)A

+m2 (t)

A2 +m2

h (t)A2

≈ A[

1 +m (t)

A

]= A + m (t). ( Assuming A� m (t)) (24)





ϕSSB+C (t) = A cos ωct + [m (t) cos ωct + mh (t) sin ωct]

= [A + m (t)] cos ωct + mh (t) sin ωct

=√[A + m (t)]2 + m2


[A + m (t)]2 + m2h (t)

=√[A + m (t)]2 + m2

h (t) cos (ωct + θ) . (23)


E =√[A + m (t)]2 + m2

h (t)

= A

√1 +

2m (t)A

+m2 (t)

A2 +m2

h (t)A2

≈ A[

1 +m (t)

A

]= A + m (t). ( Assuming A� m (t)) (24)






=√[A + m (t)]2 + m2


[A + m (t)]2 + m2h (t)

=√[A + m (t)]2 + m2

h (t) cos (ωct + θ) . (23)


E =√[A + m (t)]2 + m2

h (t)

= A

√1 +

2m (t)A

+m2 (t)

A2 +m2

h (t)A2

≈ A[

1 +m (t)

A

]= A + m (t). ( Assuming A� m (t)) (24)






=√[A + m (t)]2 + m2


[A + m (t)]2 + m2h (t)

=√[A + m (t)]2 + m2

h (t) cos (ωct + θ) . (23)


E =√[A + m (t)]2 + m2

h (t)

= A

√1 +

2m (t)A

+m2 (t)

A2 +m2

h (t)A2

≈ A[

1 +m (t)

A

]= A + m (t). ( Assuming A� m (t)) (24)






=√[A + m (t)]2 + m2


[A + m (t)]2 + m2h (t)

=√[A + m (t)]2 + m2

h (t) cos (ωct + θ) . (23)


E =√[A + m (t)]2 + m2

h (t)

= A

√1 +

2m (t)A

+m2 (t)

A2 +m2

h (t)A2

≈ A[

1 +m (t)

A

]= A + m (t). ( Assuming A� m (t)) (24)






=√[A + m (t)]2 + m2


[A + m (t)]2 + m2h (t)

=√[A + m (t)]2 + m2

h (t) cos (ωct + θ) . (23)


E =√[A + m (t)]2 + m2

h (t)

= A

√1 +

2m (t)A

+m2 (t)

A2 +m2

h (t)A2

≈ A[

1 +m (t)

A

]= A + m (t). ( Assuming A� m (t)) (24)






=√[A + m (t)]2 + m2


[A + m (t)]2 + m2h (t)

=√[A + m (t)]2 + m2

h (t) cos (ωct + θ) . (23)


E =√[A + m (t)]2 + m2

h (t)

= A

√1 +

2m (t)A

+m2 (t)

A2 +m2

h (t)A2

≈ A[

1 +m (t)

A

]= A + m (t). ( Assuming A� m (t)) (24)






=√[A + m (t)]2 + m2


[A + m (t)]2 + m2h (t)

=√[A + m (t)]2 + m2

h (t) cos (ωct + θ) . (23)


E =√[A + m (t)]2 + m2

h (t)

= A

√1 +

2m (t)A

+m2 (t)

A2 +m2

h (t)A2

≈ A[

1 +m (t)

A

]= A + m (t). ( Assuming A� m (t)) (24)



Vestigial Sideband (VSB) Modulation

ω0




ω0




ω-ωc +ωc

LSB USBLSBUSB

ω0

DSB




ω-ωc +ωc

LSB USBLSBUSB

ω-ωc +ωc

ω0

DSB

SSB




ω-ωc +ωc

LSB USBLSBUSB

ω-ωc +ωc

ω0

ω-ωc +ωc

DSB

SSB

VSB




m(t)

2 cosωct




m(t)

2 cosωct




m(t)

2 cosωct

BPFHi(ω)

VSB signal




m(t)

2 cosωct

BPFHi(ω)

VSB signal

2 cosωct

VSB signal e(t)




m(t)

2 cosωct

BPFHi(ω)

VSB signal

Lowpasfilter Ho(ω)

2 cosωct

VSB signal m(t)e(t)




ΦVSB = [M (ω + ωc) + M (ω−ωc)]Hi (ω)

e (t)⇐⇒ [ΦVSB (ω + ωc) + ΦVSB (ω−ωc)]

M (ω) = [ΦVSB (ω + ωc) + ΦVSB (ω−ωc)]Ho (ω)

= M (ω) [Hi (ω + ωc) + Hi (ω−ωc)]Ho (ω)

HenceHo (ω) =

1[Hi (ω + ωc) + Hi (ω−ωc)]

, |ω| ≤ 2πB (25)








HenceHo (ω) =

1[Hi (ω + ωc) + Hi (ω−ωc)]

, |ω| ≤ 2πB (25)








HenceHo (ω) =

1[Hi (ω + ωc) + Hi (ω−ωc)]

, |ω| ≤ 2πB (25)








HenceHo (ω) =

1[Hi (ω + ωc) + Hi (ω−ωc)]

, |ω| ≤ 2πB (25)








HenceHo (ω) =

1[Hi (ω + ωc) + Hi (ω−ωc)]

, |ω| ≤ 2πB (25)



Quadrature Amplitude Modulation (QAM)

m1(t)




m1(t)




m1(t)

m2(t)




m1(t)

m2(t)

cos ωct




m1(t)

m2(t)

cos ωct

−π/2

sin ωct




m1(t)

m2(t)

cos ωct

−π/2

sin ωct




ΣQAM signal

m1(t)

m2(t)

cos ωct

−π/2

sin ωct

m1(t) cos ωct + m2(t) sinωct




Σ

m1(t)

m2(t)

cos ωct

−π/2 −π/2

2cos ωct

sin ωct 2sin ωct

x1(t)

x2(t)

QAM signal





Σ

m1(t)

m2(t)

m1(t)

m2(t)

cos ωct

−π/2 −π/2

2cos ωct

sin ωct 2sin ωct

Lowpassfilter

Lowpassfilterx1(t)

x2(t)

QAM signal




Outline

1 Introduction

2 DSB-SC Modulation



5 FDM

6 AM Receivers

7 Noise

8 Summary



A Simple FDM Example




Channel 3

12 kHz300-3400 Hz




Channel 3

12 kHz300-3400 Hz




Mixer 3Channel 3

12 kHz300-3400 Hz




Mixer 3Channel 3

12 kHz300-3400 Hz

8.6 − 11.7 kHz




Mixer 3Channel 3

12 kHz300-3400 Hz

8.6 − 11.7 kHz




Mixer 2

Mixer 3

Channel 2

Channel 3

12 kHz

16 kHz300-3400 Hz

300-3400 Hz

8.6 − 11.7 kHz

12.6 − 15.7 kHz




Mixer 1

Mixer 2

Mixer 3

Channel 1

Channel 2

Channel 3

12 kHz

16 kHz

20 kHz300-3400 Hz

300-3400 Hz

300-3400 Hz

8.6 − 11.7 kHz

12.6 − 15.7 kHz

16.6 − 19.7 kHz




Mixer 1

Mixer 2

Mixer 3

Channel 1

Channel 2

Channel 3

12 kHz

16 kHz

20 kHz300-3400 Hz

300-3400 Hz

300-3400 Hz

8.6 − 11.7 kHz

12.6 − 15.7 kHz

16.6 − 19.7 kHz

8.6 kHz 19.7 kHz

Output

Common bus




Mixer 1

Mixer 2

Mixer 3

Channel 1

Channel 2

Channel 3

12 kHz

16 kHz

20 kHz300-3400 Hz

300-3400 Hz

300-3400 Hz

8.6 − 11.7 kHz

12.6 − 15.7 kHz

16.6 − 19.7 kHz

8.6 kHz 19.7 kHz

Output

Common bus



A More Complicated FDM Modulation Plan

Input

Voice channels(0.3 - 3.4 kHz)

0.3 kHz

3.4 kHz




Input


0.3 kHz

3.4 kHz




Input


Channelcarriers

0.3 kHz

3.4 kHz

104 kHz

96 kHz

88 kHz

80 kHz

72 kHz

64 kHz




Input

Chan 11

Chan 12


Channelcarriers

0.3 kHz

3.4 kHz

104 kHz

96 kHz

88 kHz

80 kHz

72 kHz

64 kHz

60 kHz




Input

Chan 1

Chan 2

Chan 3

Chan 4

Chan 5

Chan 6

Chan 7

Chan 8

Chan 9

Chan 10

Chan 11

Chan 12


Channelcarriers

0.3 kHz

3.4 kHz

104 kHz

96 kHz

88 kHz

80 kHz

72 kHz

64 kHz

60 kHz




Input

Chan 1

Chan 2

Chan 3

Chan 4

Chan 5

Chan 6

Chan 7

Chan 8

Chan 9

Chan 10

Chan 11

Chan 12


Channelcarriers

Basic12 - channel

group(60 - 108 kHz)

0.3 kHz

3.4 kHz

104 kHz

96 kHz

88 kHz

80 kHz

72 kHz

64 kHz

60 kHz




Input

Chan 1

Chan 2

Chan 3

Chan 4

Chan 5

Chan 6

Chan 7

Chan 8

Chan 9

Chan 10

Chan 11

Chan 12


Channelcarriers

Basic12 - channel

group(60 - 108 kHz)

Groupsubcarriers

0.3 kHz

3.4 kHz

104 kHz

96 kHz

88 kHz

80 kHz

72 kHz

64 kHz

612 kHz

468 kHz

584 kHz

516 kHz

420 kHz

60 kHz




Input

Chan 1

Chan 2

Chan 3

Chan 4

Chan 5

Chan 6

Chan 7

Chan 8

Chan 9

Chan 10

Chan 11

Chan 12

Gr 5

Gr 4

Gr 3

Gr 2

Gr 1


Channelcarriers

Basic12 - channel

group(60 - 108 kHz)

Groupsubcarriers

0.3 kHz

3.4 kHz

104 kHz

96 kHz

88 kHz

80 kHz

72 kHz

64 kHz

612 kHz

468 kHz

584 kHz

516 kHz

420 kHz

552 kHz

504 kHz

408 kHz

456 kHz

360 kHz

312 kHz

60 kHz




Input

Chan 1

Chan 2

Chan 3

Chan 4

Chan 5

Chan 6

Chan 7

Chan 8

Chan 9

Chan 10

Chan 11

Chan 12

Gr 5

Gr 4

Gr 3

Gr 2

Gr 1


Channelcarriers

Basic12 - channel

group(60 - 108 kHz)

Groupsubcarriers

0.3 kHz

3.4 kHz

Basic60 - channelsupergroup

(312 - 552 kHz)

104 kHz

96 kHz

88 kHz

80 kHz

72 kHz

64 kHz

612 kHz

468 kHz

584 kHz

516 kHz

420 kHz

552 kHz

504 kHz

408 kHz

456 kHz

360 kHz

312 kHz

60 kHz



Outline

1 Introduction

2 DSB-SC Modulation



5 FDM

6 AM Receivers

7 Noise

8 Summary



Tuned Radio Frequency (TRF) Receiver










Receiverantenna




Receiverantenna




Antennacouplingnetwork

Receiverantenna





RF stage

Receiverantenna





RFamp.

RFamp.

RFamp.

RF stage

Receiverantenna





RFamp.

RFamp.

RFamp.

RF stage

Receiverantenna





RFamp.

RFamp.

RFamp.

RF stage Detectorstage

Receiverantenna





RFamp.

RFamp.

RFamp.

Audiodetector


Receiverantenna





RFamp.

RFamp.

RFamp.

Audiodetector


Audiostage

Receiverantenna





RFamp.

RFamp.

RFamp.

Audiodetector

Audioamplifiers

Speaker


Audiostage

Receiverantenna



Multistage Amplifiers

0

1.0

0.5

0.7 1.0 1.3

n = 1




0

1.0

0.5

0.7 1.0 1.3

n = 1




0

1.0

0.5

0.7 1.0 1.3

n = 1n = 2




0

1.0

0.5

0.7 1.0 1.3

n = 1n = 2n = 3




0

1.0

0.5

0.7 1.0 1.3

n = 1n = 2n = 3n = 4




0

1.0

0.5

0.7 1.0 1.30

1.0

0.5

0.7 1.0 1.3

n = 1n = 2n = 3n = 4




0

1.0

0.5

0.7 1.0 1.30

1.0

0.5

0.7 1.0 1.3

n = 1n = 2n = 3n = 4



TRF Receiver – Disadvantages

• Bandwidth is inconsistent and varies with center frequency (due to skineffect)

• High-frequency, multi-stage amplifiers are susceptible to breaking intooscillations

• Gains are not uniform over a very wide frequency range

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�With the development of the superheterodyne receiver, TRF receivers are

seldom used except for special-purpose, single-station receivers.







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Superheterodyne AM Receiver






Edwin Howard Armstrong (1890 – 1954)

• Inventor of regenerative andsuper-regenerative circuits

• Invented superheterodynereceiver

• Armstrong was also the inventorof modern frequency modulation(FM) radio transmission

The most prolific and influential inventor in radio history










































RF amplifierwith bandpassfilters tubanleto desired ωc

Localoscillator

ωc+ωIF





Localoscillator

ωc+ωIF

[A+m(t)] cos ωct





Frequencyconverter(mixer)

Localoscillator

ωc+ωIF

[A+m(t)] cos ωct






IFamplifier

Localoscillator

ωc+ωIF

[A+m(t)] cos ωct






IFamplifier

Localoscillator

ωc+ωIF

[A+m(t)] cos ωct [A+m(t)] cos ωIFt






IFamplifier Detector

Localoscillator

ωc+ωIF







IFamplifier Detector

Audioamplifier

Speaker

Localoscillator

ωc+ωIF


fIF = 455 KHz



Outline

1 Introduction

2 DSB-SC Modulation



5 FDM

6 AM Receivers

7 Noise

8 Summary



Noise in Baseband Systems

Inputm(t)

TransmitterST

Channel

Channel noisen(t)

ReceiverSi Ni,

So No,Output

so(t) no(t),

Sn(ω)

ω2πB-2πB

Assuming that the filters are ideal and channel is distortion-less,

No = 2ˆ B

0Sn (ω) df = 2

ˆ B

0

N2

df = NB. (26)




Inputm(t)

TransmitterST

Channel

Channel noisen(t)

ReceiverSi Ni,

So No,Output

so(t) no(t),

Sn(ω)

ω2πB-2πB


No = 2ˆ B

0Sn (ω) df = 2

ˆ B

0

N2

df = NB. (26)




Inputm(t)

TransmitterST

Channel

Channel noisen(t)

ReceiverSi Ni,

So No,Output

so(t) no(t),

Sn(ω)

ω2πB-2πB


No = 2ˆ B

0Sn (ω) df = 2

ˆ B

0

N2

df = NB. (26)




Inputm(t)

TransmitterST

Channel

Channel noisen(t)

ReceiverSi Ni,

So No,Output

so(t) no(t),

Sn(ω)

ω2πB-2πB


No = 2ˆ B

0Sn (ω) df = 2

ˆ B

0

N2

df = NB. (26)



SNR

So, SNR for baseband systems is given as

SNR =So

No=

SiNB

=m2

NB= γ. (27)

• SNR of 5 – 10 dB is barely intelligible• Telephone Quality : 25 – 30 dB• TV Quality : 45 – 55 dB



SNR


SNR =So

No=

SiNB

=m2

NB= γ. (27)




SNR


SNR =So

No=

SiNB

=m2

NB= γ. (27)




QAM – Revisited

Σ

m1(t)

m2(t)

m1(t)

m2(t)

cos ωct

−π/2 −π/2

2cos ωct

sin ωct 2sin ωct

Lowpassfilter

Lowpassfilterx1(t)

x2(t)

QAM signal




QAM – Revisited

Σ

m1(t)

m2(t)

m1(t)

m2(t)

cos ωct

−π/2 −π/2

2cos ωct

sin ωct 2sin ωct

Lowpassfilter

Lowpassfilterx1(t)

x2(t)

QAM signal




Bandpass Noise Representation

ωωc−ωc

4πB

Sn(ω)

n (t) = nc (t) cos ωct + ns (t) sin ωct n2 = n2c = n2

s




ωωc−ωc

4πB

Sn(ω)


s




ωωc−ωc

4πB

Sn(ω)


s




ωωc−ωc

4πB

Sn(ω)

ω2πB

Sns(ω)Snc(ω) or

-2πB

n (t) = nc (t) cos ωct + ns (t) sin ωct

n2 = n2c = n2

s




ωωc−ωc

4πB

Sn(ω)

ω2πB

Sns(ω)Snc(ω) or

-2πB


s



DSB-SC Systems

m(t)

√2 cos ωct



DSB-SC Systems

m(t)

√2 cos ωct



DSB-SC Systems

m(t)

n(t)√2 cos ωct



DSB-SC Systems

m(t)

Si Ni,

n(t)

Bandpassfilter

ωc + 2πB yi(t)

√2 cos ωct



DSB-SC Systems

m(t)

Si Ni,

n(t)

Bandpassfilter

ωc + 2πB yi(t)

√2 cos ωct √2 cos ωct



DSB-SC Systems

m(t)

Si Ni, So No,

n(t)

Bandpassfilter

ωc + 2πB

Basebandfilter

yi(t) yo(t)




DSB-SC Systems

m(t)

Si Ni, So No,

n(t)

Bandpassfilter

ωc + 2πB

Basebandfilter

yi(t) yo(t)


Demodulator



DSB-SC Systems

m(t)

Si Ni, So No,

n(t)

Bandpassfilter

ωc + 2πB

Basebandfilter

yi(t) yo(t)


Demodulator

Receiver



DSB-SC Systems

m(t)

Si Ni, So No,

n(t)

Bandpassfilter

ωc + 2πB

Basebandfilter

yi(t) yo(t)


Demodulator

Receiver

yi =√

2m (t) cos ωct + n (t)

ST = Si = m2 (t)

Ni = 2NB

yo = m (t) +1√2

nc (t)

So = m2 (t)

N0 = NB



DSB-SC Systems

m(t)

Si Ni, So No,

n(t)

Bandpassfilter

ωc + 2πB

Basebandfilter

yi(t) yo(t)


Demodulator

Receiver

yi =√


ST = Si = m2 (t)

Ni = 2NB

yo = m (t) +1√2

nc (t)

So = m2 (t)

N0 = NB



DSB-SC Systems

m(t)

Si Ni, So No,

n(t)

Bandpassfilter

ωc + 2πB

Basebandfilter

yi(t) yo(t)


Demodulator

Receiver

yi =√


ST = Si = m2 (t)

Ni = 2NB

yo = m (t) +1√2

nc (t)

So = m2 (t)

N0 = NB



DSB-SC Systems

m(t)

Si Ni, So No,

n(t)

Bandpassfilter

ωc + 2πB

Basebandfilter

yi(t) yo(t)


Demodulator

Receiver

yi =√


ST = Si = m2 (t)

Ni = 2NB

yo = m (t) +1√2

nc (t)

So = m2 (t)

N0 = NB



SSB-SC Systems

m(t)

2 cos ωct



SSB-SC Systems

m(t)

2 cos ωct

SSBfilter



SSB-SC Systems

n(t)

m(t)

2 cos ωct

SSBfilter



SSB-SC Systems

Si Ni,

n(t)

BandpassfilterLSB yi(t)

m(t)

2 cos ωct

SSBfilter



SSB-SC Systems

Si Ni,

n(t)

BandpassfilterLSB yi(t)

m(t)

2 cos ωct 2 cos ωct

SSBfilter



SSB-SC Systems

Si Ni, So No,

n(t)

BandpassfilterLSB

Basebandfilter

yi(t) yo(t)m(t)


SSBfilter



SSB-SC Systems

Si Ni, So No,

n(t)

BandpassfilterLSB

Basebandfilter

yi(t) yo(t)m(t)


Demodulator

SSBfilter



SSB-SC Systems

Si Ni, So No,

n(t)

BandpassfilterLSB

Basebandfilter

yi(t) yo(t)m(t)


Demodulator

Receiver

SSBfilter



SSB-SC Systems

Si Ni, So No,

n(t)

BandpassfilterLSB

Basebandfilter

yi(t) yo(t)m(t)


Demodulator

Receiver

SSBfilter

yi = [m (t) cos ωct∓mh (t) sin ωct]+n (t)

ST = Si = m2 (t)

Ni = NB

yo = m (t) + nc (t)

So = m2 (t)

N0 = NB



SSB-SC Systems

Si Ni, So No,

n(t)

BandpassfilterLSB

Basebandfilter

yi(t) yo(t)m(t)


Demodulator

Receiver

SSBfilter


ST = Si = m2 (t)

Ni = NB

yo = m (t) + nc (t)

So = m2 (t)

N0 = NB



SSB-SC Systems

Si Ni, So No,

n(t)

BandpassfilterLSB

Basebandfilter

yi(t) yo(t)m(t)


Demodulator

Receiver

SSBfilter


ST = Si = m2 (t)

Ni = NB

yo = m (t) + nc (t)

So = m2 (t)

N0 = NB



SSB-SC Systems

Si Ni, So No,

n(t)

BandpassfilterLSB

Basebandfilter

yi(t) yo(t)m(t)


Demodulator

Receiver

SSBfilter


ST = Si = m2 (t)

Ni = NB

yo = m (t) + nc (t)

So = m2 (t)

N0 = NB



AM Systems – Synchronous Demodulation

Synchronous demodulation is identical to DSB-SC in every respect except forthe addition carrier. So the signal at the input of the receiver is

yi (t) =√

2 [A + m (t)] cos ωct + n (t) .

Hence, the desired signal power is

Si =(√

2)2 [A + m (t)]2

2= A2 + m2 (t) + 2Am (t) = A2 + m2 (t).

The output noise will be exactly the same as that of DSB-SC:

So = m2 (t)No = NB

So,

So

No=

m2 (t)NB

=A2 + m2 (t)NB

m2 (t)

A2 + m2 (t)=

(SiNB

)m2 (t)

A2 + m2 (t). (28)



AM Systems – Synchronous DemodulationSynchronous demodulation is identical to DSB-SC in every respect except forthe addition carrier. So the signal at the input of the receiver is

yi (t) =√

2 [A + m (t)] cos ωct + n (t) .


Si =(√

2)2 [A + m (t)]2

2= A2 + m2 (t) + 2Am (t) = A2 + m2 (t).


So = m2 (t)No = NB

So,

So

No=

m2 (t)NB

=A2 + m2 (t)NB

m2 (t)

A2 + m2 (t)=

(SiNB

)m2 (t)

A2 + m2 (t). (28)




yi (t) =√

2 [A + m (t)] cos ωct + n (t) .


Si

=(√

2)2 [A + m (t)]2

2= A2 + m2 (t) + 2Am (t) = A2 + m2 (t).


So = m2 (t)No = NB

So,

So

No=

m2 (t)NB

=A2 + m2 (t)NB

m2 (t)

A2 + m2 (t)=

(SiNB

)m2 (t)

A2 + m2 (t). (28)




yi (t) =√

2 [A + m (t)] cos ωct + n (t) .


Si =(√

2)2 [A + m (t)]2

2

= A2 + m2 (t) + 2Am (t) = A2 + m2 (t).


So = m2 (t)No = NB

So,

So

No=

m2 (t)NB

=A2 + m2 (t)NB

m2 (t)

A2 + m2 (t)=

(SiNB

)m2 (t)

A2 + m2 (t). (28)




yi (t) =√

2 [A + m (t)] cos ωct + n (t) .


Si =(√

2)2 [A + m (t)]2

2= A2 + m2 (t) + 2Am (t)

= A2 + m2 (t).


So = m2 (t)No = NB

So,

So

No=

m2 (t)NB

=A2 + m2 (t)NB

m2 (t)

A2 + m2 (t)=

(SiNB

)m2 (t)

A2 + m2 (t). (28)




yi (t) =√

2 [A + m (t)] cos ωct + n (t) .


Si =(√

2)2 [A + m (t)]2

2= A2 + m2 (t) + 2Am (t) = A2 + m2 (t).


So = m2 (t)No = NB

So,

So

No=

m2 (t)NB

=A2 + m2 (t)NB

m2 (t)

A2 + m2 (t)=

(SiNB

)m2 (t)

A2 + m2 (t). (28)




yi (t) =√

2 [A + m (t)] cos ωct + n (t) .


Si =(√

2)2 [A + m (t)]2

2= A2 + m2 (t) + 2Am (t) = A2 + m2 (t).


So = m2 (t)No = NB

So,

So

No=

m2 (t)NB

=A2 + m2 (t)NB

m2 (t)

A2 + m2 (t)=

(SiNB

)m2 (t)

A2 + m2 (t). (28)




yi (t) =√

2 [A + m (t)] cos ωct + n (t) .


Si =(√

2)2 [A + m (t)]2

2= A2 + m2 (t) + 2Am (t) = A2 + m2 (t).


So = m2 (t)No = NB

So,

So

No=

m2 (t)NB

=A2 + m2 (t)NB

m2 (t)

A2 + m2 (t)=

(SiNB

)m2 (t)

A2 + m2 (t). (28)




yi (t) =√

2 [A + m (t)] cos ωct + n (t) .


Si =(√

2)2 [A + m (t)]2

2= A2 + m2 (t) + 2Am (t) = A2 + m2 (t).


So = m2 (t)No = NB

So,

So

No=

m2 (t)NB

=A2 + m2 (t)NB

m2 (t)

A2 + m2 (t)

=

(SiNB

)m2 (t)

A2 + m2 (t). (28)




yi (t) =√

2 [A + m (t)] cos ωct + n (t) .


Si =(√

2)2 [A + m (t)]2

2= A2 + m2 (t) + 2Am (t) = A2 + m2 (t).


So = m2 (t)No = NB

So,

So

No=

m2 (t)NB

=A2 + m2 (t)NB

m2 (t)

A2 + m2 (t)=

(SiNB

)m2 (t)

A2 + m2 (t). (28)



AM Systems – Envelop Detection

In case of envelop detection, signal at the input of the receiver is

yi (t) = [A + m (t)] cos ωct + n (t)= [A + m (t) + nc (t)] cos ωct + ns (t) sin ωct. (29)


Si =[A + m (t)]2

2= A2 + m2 (t) + 2Am (t) =

A2 + m2 (t)2

. (30)

Since we are using envelop detection, output of the demodulator is given as

yo = Ei (t) =

√[A + m (t) + nc (t)]2 + n2

s (t). (31)

Depending upon whether A + m (t) � n (t) or A + m (t) � n (t), we can usedifferent approximations. We will discuss only small-noise noise case. Forfurther explanation, see B. P. Lathi’s book.







Si =[A + m (t)]2

2= A2 + m2 (t) + 2Am (t) =

A2 + m2 (t)2

. (30)


yo = Ei (t) =

√[A + m (t) + nc (t)]2 + n2

s (t). (31)








Si

=[A + m (t)]2

2= A2 + m2 (t) + 2Am (t) =

A2 + m2 (t)2

. (30)


yo = Ei (t) =

√[A + m (t) + nc (t)]2 + n2

s (t). (31)








Si =[A + m (t)]2

2

= A2 + m2 (t) + 2Am (t) =A2 + m2 (t)

2. (30)


yo = Ei (t) =

√[A + m (t) + nc (t)]2 + n2

s (t). (31)








Si =[A + m (t)]2

2= A2 + m2 (t) + 2Am (t)

=A2 + m2 (t)

2. (30)


yo = Ei (t) =

√[A + m (t) + nc (t)]2 + n2

s (t). (31)








Si =[A + m (t)]2

2= A2 + m2 (t) + 2Am (t) =

A2 + m2 (t)2

. (30)


yo = Ei (t) =

√[A + m (t) + nc (t)]2 + n2

s (t). (31)








Si =[A + m (t)]2

2= A2 + m2 (t) + 2Am (t) =

A2 + m2 (t)2

. (30)


yo

= Ei (t) =

√[A + m (t) + nc (t)]2 + n2

s (t). (31)








Si =[A + m (t)]2

2= A2 + m2 (t) + 2Am (t) =

A2 + m2 (t)2

. (30)


yo = Ei (t)

=

√[A + m (t) + nc (t)]2 + n2

s (t). (31)








Si =[A + m (t)]2

2= A2 + m2 (t) + 2Am (t) =

A2 + m2 (t)2

. (30)


yo = Ei (t) =

√[A + m (t) + nc (t)]2 + n2

s (t). (31)








Si =[A + m (t)]2

2= A2 + m2 (t) + 2Am (t) =

A2 + m2 (t)2

. (30)


yo = Ei (t) =

√[A + m (t) + nc (t)]2 + n2

s (t). (31)




AM Systems – Envelop Detection (Small Noise Case)


yi (t) = [A + m (t)] cos ωct + n (t)= [A + m (t) + nc (t)] cos ωct + ns (t) sin ωct.

For small noise case, envelope Ei can be approximated as

yo = Ei (t) =√[A + m (t) + nc (t)]2 + n2

s (t) ≈ A + m (t) + nc (t) . (32)

ST = Si =A2 + m2 (t)

2

Ni = n2 (t) = 2NB

So = m2 (t)

N0 = 2NB







yo = Ei (t) =√[A + m (t) + nc (t)]2 + n2

s (t) ≈ A + m (t) + nc (t) . (32)

ST = Si =A2 + m2 (t)

2

Ni = n2 (t) = 2NB

So = m2 (t)

N0 = 2NB







yo = Ei (t) =√[A + m (t) + nc (t)]2 + n2

s (t) ≈ A + m (t) + nc (t) . (32)

ST = Si =A2 + m2 (t)

2

Ni = n2 (t) = 2NB

So = m2 (t)

N0 = 2NB







yo = Ei (t) =√[A + m (t) + nc (t)]2 + n2

s (t) ≈ A + m (t) + nc (t) . (32)

ST = Si =A2 + m2 (t)

2

Ni = n2 (t) = 2NB

So = m2 (t)

N0 = 2NB







yo = Ei (t) =√[A + m (t) + nc (t)]2 + n2

s (t) ≈ A + m (t) + nc (t) . (32)

ST = Si =A2 + m2 (t)

2

Ni = n2 (t) = 2NB

So = m2 (t)

N0 = 2NB




So, signal to noise ratio is given as

So

No=

m2

2NB=

m2

A2 + m2 (t)

A2 + m2 (t)2NB

=

(SiNB

)m2

A2 + m2 (t). (33)




So, signal to noise ratio is given as

So

No=

m2

2NB=

m2

A2 + m2 (t)

A2 + m2 (t)2NB

=

(SiNB

)m2

A2 + m2 (t). (33)





Outline

1 Introduction

2 DSB-SC Modulation



5 FDM

6 AM Receivers

7 Noise

8 Summary


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