2/2/01

Amplitude Modulation “AM” with Envelope Detector Large S/N limit

[ ]= = + ω + ω + ωc c c c s ci y(t) A 1 ( t n ( t n ( in t

<m 1� ≅ ω ≤m) sin t 1

{ }ω= cj t(t)e slowly varying

“overmodulation” = distortion (“undermodulation = wasted power)

T1

y, low-pass filtered (envelope)

Lec 16b.6-1

Rece ved m s t) cos t)cos t)s

s(t

Re Y

2/2/01

Amplitude Modulation “AM” with Envelope Detector

T2

[ ]= = + ω + ω + ωc c c c s ci y(t) A 1 ( t n ( t n ( in t

{ }ω= cj t(t)e slowly varying

0

2W

f0 fc

= o kTN 2

){ }(t)

)

n(t) ns(t)

{ }eR Y(t) nc(t)Ac

Lec 16b.6-2

Rece ved m s t) cos t)cos t)s

Re Y

Y(f Im Y

Y(t

[1 + m s(t)]

2/2/01

Amplitude Modulation “AM” with Envelope Detector

0

2W

f0 fc

= o kTN 2

){ }(t)

)

n(t) ns(t)

{ }eR Y(t) nc(t)Ac

N [ ]≅ + +c cY(t) A 1 (t) n (t) envelope = detected signal + noise

= ω + ω =2 2 2 2 2 o c c s c cn cos t n sin t n

≅ = 2 2 2

2 2 2 2out c c c

out o

S s (t)s ( (t)N T3

Lec 16b.6-3

Y(f Im Y

Y(t

[1 + m s(t)]

m s

Note: 4WN

A m A m t) n 4WN

2/2/01

Amplitude Modulation “AM” with Envelope Detector

T4

≅ = 2 2 2

2 2 2 2out c c c

out o

S s (t)s ( (t)N

( ) ( )+ ≅ =

22 c 2in

in signalin o

A 2 1S y (t)N

∆ ++ = = ≥ = ⇒ ≥ 2 2

i iAM AM2 2o o

S N 1 m s (t)i FS N 12m s � �

provided that Ac >> nc (large S/N limit)

Lec 16b.6-4

A m A m t) n 4WN

m s(t) where S 4WN

1 1 2 No se figure F 3 2 3 2

2/2/01

AM Performance (small S/N limit)

c n c nY(t) n(t) A (t) ( (t)≅ + φ + φ � multiplicative noise!

{ }

)

φn (t) [ ]+cA 1 (t)

φn (t) { }eR Y

[ ]≅ + φc nA 1 ( (t)

≥ ⇒in inN ly i ligibl�

( )( )+ >c 1 (t) (t)�

T5 Lec 16b.6-5

cos A m s t)cos ��

Im Y

n(t

m s

m s t) cos

Want S 10 for ful ntel e AM "AM threshold"

i.e. A m s 3 n

2/2/01

Frequency and Phase Modulation (FM, PM) [ ]= c citted: ) A t (t)

( )

∆

∆

φ =

φ = π < φ = ∫t-1

(t) (t)

d (t) (t) for s(t) (t) s( )ddt

V1

FM signal

+Ac

-Ac

0 t

x(t)

discriminatorfilter, limiter

low pass filter, DC block

v(t)

output

envelope detector

vo

ωc ω

vo frequency-sensitive discriminator output function

Lec 16b.6-6

ω + φ Transm x(t cos

= ∆ω τ τ

Phase Modulation ("PM"): K'sFrequency Modulation ("FM"):

2 K s r s 1 , or

receiver: y(t)

2/2/01

FM Bandwidth Expansion Factor β*

-1d (t) (t) r s s(t) 1dt φ ⎡ ⎤= π <⎣ ⎦

K W∆∗β =

S(f)

0-W W f

0 f B ≅ 2K

Y(f ) intrinsic bandwidthP( )B , B W∗≅ < ≤ +

( )' (≅ + ( )if 1∗β >>

V2 Lec 16b.6-7

2 K s for = ∆ω

2W 1 so 2W 2K + β

For PM: B 2 K 1 W not proven here)

2/2/01

Vector Signal Analysis of PM/FM

V3

( ) { }cj t ci i l y(t) x(t) n(t) r( t (t) Y(t)e ω = + = ω =

( )n n c s c(t) (t) r (t)sin A (t) ) A∆ψ + = φ +

s cv(t) (t) (t) (t) ) ) A= ψ = φ = +

s cv(t) (t) 2 ) ) d∆= ψ π = + π ψ�� �

PM:

FM:

Discriminator output:

2 2) n (t)>>

{ }Im (t)Y

{ }(t)0

r(t)

η(t)

φ(t) Ac

ψ(t)

ns(t) φn

φn - φ(t)

) rn(t)

Lec 16b.6-8

Rece ved s gna t)cos Re + ψ

n (t≅ φ φ − φ

K ' s(t n (t+ η

Ks(t n (t 2 A where dt ψ =

x (t

Re Y

Y(t

2/2/01

Calculation of PM Sout/Nout

s cv(t) (t) (t) (t) ) ) A= ψ = φ = +PM:

V4

c c s cll n(t) n ( t n ( in t= ω − ω

slowlyvarying

slowlyvarying

2 2 2 c s o) ) )= = =

RkT 2 B

N(f)

0 f

RkT 2

output

22 2 2 2 c

o out 2 2 os c

A 2K ' s (t)N K ' s (t) 2 ) A

⎡ ⎤ = = • ⎢ ⎥⎡ ⎤ ⎢ ⎥⎣ ⎦⎣ ⎦

o o≅ CNR2 2 s (t), )

Lec 16b.6-9

K ' s(t n (t+ η

Reca t) cos t) s

n (t n (t n (t 2N B

Therefore PM: S 2N W n (t2N B 4N W

for case B = 2W(K´<<1) (want large K ' but approaches FM

2/2/01

Calculation of FM Sout/Nout

s cv(t) (t) 2 ) ) d∆= ψ π = + π ψ�� �FM:

V5

ss s) N (f ) )↔ �

2 soN N∆

= snR ( )τ� ↔

↔ sj )ω

22 2 s o) Nω

↓ ↓ ↓

( )22 2 2 out out cN K s (t) n (t)= π⎡ ⎤

⎣ ⎦�

( ) W2 3 o

o 2 c 0 c

4N1 W)2 A 3A

π = • π ∫

0 W4 segments

2W

f

Sout

⇒

Lec 16b.6-10

Ks(t n (t 2 A where dt ψ =

n (t n (t N (f

N (f = ω

FM : S 2 A

4 (2 f 2N df

2/2/01

out/Nout

FM

2 2 2 3c

out out o A

N K s 2

= • • ⎡ ⎤ ⎢ ⎥ ⎣ ⎦

2 2 3 2c

o

3P s 6[ ] s ∗ ∗ = β = β

c o c o( i i P P ∗ = = β

(K/W)2

Pc

o out

o

S"Wi ) S N N ⎛ ⎞= ⎜ ⎟⎝ ⎠

2 c oP s

5 ( ( 1)W ); ∗ ∗β ≅ ≅ 23 ∗

V6

• 3β*2

Lec 16b.6-11

Calculation of FM S

Therefore S 3 2N W

CNR2N W

where CNR Carr er-to-No se Ratio) 2N B 2N 2W

WBFM out DSBSC

de-band FM" (WBFM

2N W

FM advantage for FM radio, 2 200 kHzβ +

19 dB! β ≅

2/2/01

out/Nout

V7

FM pre-emphasis & de-emphasis filters

0 f

Since FM noise →

Pre-emphasis signal ∝ f2 pre-transmission and de-emphasize signal + noise at receiver; this can yield ~10 dB improvement (depending…)

2 s )

2f∝

Lec 16b.6-12

Calculation of FM S

N (t

2/2/01

“FM Threshold” – (low SNR limit) { }(t)

rn(t)

) ψ(t)

φn(t)

φn(t) -φ(t)

Ac

{ }(t)

( )c n n

n

A(t) l

r ψ ⇒

π

Therefore must have Ac >> rn

10 20 30

10 20 30 40 50 60

baseband 1 2 5

(analogous to coding gain via bandwidths)

(baseline) (dB)

typical FM thresholds

0

40

FM

t

SNROUT for automobile

dropouts in nulls, spaced ~λ/2

V8 Lec 16b.6-13

Im Y

Y(t

Re Y

sin signa obliteration ≅ φ + φ − φ

ranges over 2

to avoid multiplicative noise

S/N in threshold

Issues In Choosing Modulation Type

1) Desired output SNR2) Cost of bandwidth ($, availability) (for communications or

storage) 3) Standards imposed on channel, inexpensive equipment 4) Potential for source coding 5) Characteristics (noise, fading), potential for channel coding 6) Cost, power, weight, size, thermal constraints on system

Lec 16b.6-14 2/2/01

X1

2/2/01

Output SNR Requirements CD-quality audio:

say 40 dB dynamic range (loudest power/“quiet” power) +55 dB SNR ⇒ 95 dB so 20 LOG10L ≅ 95

Therefore L l l l l= < ⇒�

FM-quality audio: say β* = 5 ⇒ ~50 dB (~35 dB available above ~15-dB threshold)

Video:

Video:

Intelligible speech: 10dB>�

X2 Lec 16b.6-15

56,000 eve s of 32,000 digital eve s, 15-bits σ⇒

studio-quality ~40 + dB

home-quality ~20 - 35 + dB

Nominal Bandwidth Requirements

1) Voice: ~3 kHz (6kHz excellent)

2) Music ~15 + kHz

3) Video ~6 MHz (NTSC), 20 MHz (HDTV)

4) Data ~10 – 109→7 bits/sec; 104 OK often

Lec 16b.6-16 2/2/01

X3

2/2/01

State-Of-The-Art Source Coding

X4

2)

1) Voice →good

↑

~ 58 dB SNR

3) Video 2 pixels (lip-read

threshold) and artifacts (moving details) 384 kbps good video conference quality 1.5 Mbps ⇒ 6 Mbps ⇒ good NTSC TV 20 Mbps ⇒ HDTV

4) Data Lec 16b.6-17

Music 128 – 256 kbps for ~ CD quality, stereo

~1.2, 2.4, 4.8, 9.6 kbps; OK32 – 64 kbps ~ uncompressed

e.g. 8 kHz at 8 bits

10 kbps jerky, blurred, or little change

56 – 128 kbps ~10 fps, 256

“VCR” NTSC TV

divide by 2 – 4 for typical miscellaneous data, lossless coding

2/2/01

FM Hybrid Analog Communication System

bandwidth, βY1

Laser Example 1 FM Modulation

x(t)

s(t)

t

t0

∼ (t)ω

s(t)

x(t) Laser 0

( )2 3 OUTS / N [ ] B /∗ ∗ = β β =

↑

Lec 16b.6-18

Optical superheterodynes are limited by photon noise that fluctuates with S(t), so the expression here is approximate. Since optical links have great

* can be very large.

OUT CNR 6 s where 2W

Baseband

Here we use the standard definition of CNR for a superheterodyne receiver.

2/2/01

AM Hybrid Analog Communication System

Y2

Laser Example 2

within the passband of the detector output corresponding tothe spectrum of the signal s(t). This CNR must be above the AM threshold of ∼10 dB in order for

to apply.

2 2S / N [ ]=

AM Modulation

x(t)

t Laser

1 )

x(t) 0

Lec 16b.6-19

The CNR applies to the unmodulated laser and its detector

OUT OUT CNR m s

S (t

2/2/01

FM/AM Analog Communication System

Y3

Laser Example 3

[ ] 2 2 2 3 OUT 1 2 2

AM S / N 6s (t)∗ ∗⎡ ⎤≅ β = β⎣ ⎦

( ) ( )

2 D

APD s 22 s L s

g P[CNR] P / 1G P R P

∗ ⎛ ⎞⎛ ⎞

⎡ ⎤ ⎜ ⎟= η β + +⎜ ⎟⎣ ⎦ ⎜ ⎟η⎝ ⎠⎝ ⎠ 2 2

D 1 AM

0 O

P (W) ]

to yi iS / N (

∗

⎡ ⎤ ⎣ ⎦

≅ β

FM/AM Modulation

t Laser

s2(t) [FM] f1

s1(t) 0

2 1s (t) ⇒

1 1f (t) ies with s ( ]

Sm

Lec 16b.6-20

OUT FM

CNR m s where B 2W for s ⎤ ⎡ ⎦ ⎣

Assume avalanch photo diode:

2kThf hf 2W eG

= dark current + background power . Want [CNR m s

to be over FM threshold 15 dB; then choose eld des red say 50 dB total)

AM near f Hz

var t) [FM