Coherent DetectionCoherent Detection
1 Transmitted Signal1- Transmitted Signal2- Local Oscillator3 Direct detection3- Direct detection 4- Coherent Detection (3 dB coupler/ Beam Splitter)5 Coherent Detection (Directional coupler)5- Coherent Detection (Directional coupler)
5-1 Single-Branch Coherent Receiver5 2 Balanced Coherent Receiver5-2 Balanced Coherent Receiver
6- Single-Branch IQ Coherent Receiver7 Balanced IQ Coherent Receiver7- Balanced IQ Coherent Receiver
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1- Transmitted Signal
- The complex electric field of the transmitted signal is:( ( ))( ) ( ) ( )s s sj t j t t
s s sE t A t e A t e
( )( ) is the complex amplitude ( ) ( ) sj ts s sA t A t A t e
is the angular frequency( ) is the phase
s
s t
- The real electric field is:
( ) Re{ ( )}s st E t
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- The signal power is:
*2 2( ) ( ) ( ) ( ) ( )2 2 2s s s s sC C CP t E t E t E t A t 2 2 2s s s s s
S
0
effSC
Z
Seff is the effective beam areaZ0 the impedance of the free space
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2- Local Oscillator
- The complex electric field of the local oscillator is:
( ( ))( ) OL LO LOj t j t tLO LO LOE t A e A e
( ) is the complex amplitude ( ) LOj tLO LO OLA A t A e
is the angular frequency( ) is the phase
LO
LO t
- The real electric field is:
( ) Re{ ( )}LO LOt E t
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- The local oscillator power is:
2
*( ) ( ) ( ) LOLO LO LO
ACP t E t E t C ( ) ( ) ( )2 2LO LO LO
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3- Direct detection
biasV
phI( )sE t
LRph
( )V t
R C 2( ) ( ) ( )2
Lph s s
R CI t P t A t
R C
2( ) ( ) ( ) ( )2
LL ph L s s
R CV t R I t R P t A t
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4- Coherent Detection (3 dB coupler/ Beam Splitter)( p p )
( )E t biasV( )sE t
( )LOE t( )I
( )E t
VLR( )I t
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3 dB C l / B litt3 dB Coupler / Beam splitter
ca
a c
b
b
1 ( )2c a bE E E 2
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( ( )) ( ( ))1 1( ) ( ) ( ) ( ( ) )j t t j t tE E E A A ( ( )) ( ( ))1 1( ) ( ) ( ) ( ( ) )2 2
s s OL LOj t t j t ts LO s LOE t E t E t A t e A e
*C
*1 1
2 2
( ) ( ) ( )2CP t E t E t
C
2 2 ( ( ) 2 ( ) cos ( ) ( ( ) ( ))2
( ) 2 ( ) cos ( ( ) ( ))
s LO s LO s OL s LOC A t A A t A t t t
P t P P t P t t t
( ) 2 ( ) cos ( ( ) ( ))
H t d
s LO s LO IF s LOP t P P t P t t t
0HeterodynIF s LO
e 0Homodyne 0
IF
IF
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( ) ( ( ) ( ))IF s LOt t t t
( ) ( ) 2 ( ) ( ( ) ( ))I P P P P
( ) ( ) 2 ( ) cos ( ( ) ( ))2
( ) 2 ( ) ( )
s LO s LO IF s LOI t P t P P t P t t t
P P P P
( ) 2 ( ) cos ( )2 s LO s LOP t P P t P t
( )2 s LOI P t P
( ) 2 ( )2peak s LO s LOI P t P P t P
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5- Coherent Detection (Directional coupler)
( )E tbiasV
( )E( )sE t
( )LOE tV
phI1( )E t
VLR
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5-1 Single-Branch Coherent Receiver5 1 Single Branch Coherent Receiver
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( ( )) ( ( ))1
1 1( ) ( ) ( ) ( ( ) )2 2
s s OL LOj t t j t ts LO s LOE t E t jE t A t e j A e
*1 1 1( ) ( ) ( )2CP t E t E t
2 2 ( ( ) 2 ( ) sin ( ) ( ( ) ( ))2 s LO s LO s OL s LOC A t A A t A t t t
( ) 2 ( ) sin ( ( ) ( ))s LO s LO IF s LOP t P P t P t t t
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1( ) ( ) 2 ( ) sin ( )2 s LO s LOI t P t P P t P t 2
( )2 s LOI P t P
( ) 2 ( )2peak s LO s LOI P t P P t P
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5-2 Balanced Coherent Receiver5 2 Balanced Coherent Receiver
Removes the dc components and maximizes the beating term
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( ) is the same as the Single Branch Coherent ReceiverE t
1
( ( )) ( ( ))2
- ( ) is the same as the Single-Branch Coherent Receiver1 1- ( ) ( ) ( ) ( ( ) )2 2
s s LO LOj t t j t ts LO s OL
E t
E t jE t E t j A t e A e 2 2
*2 2 2( ) ( ) ( )2CP t E t E t 2 2 2
2 2
( ) ( ) ( )2
( ( ) 2 ( ) sin ( ) ( ( ) ( )2 s LO s LO s LO s LOC A t A A t A t t t )2
( ) 2 ( ) sin ( ( ) ( ))s LO s LO IF s LOP t P P t P t t t
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1( ) ( ) 2 ( ) sin ( )2 s LO s LOI t P t P P t P t
2
2 ( ) ( ) 2 ( ) sin ( )2 s LO s LOI t P t P P t P t
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1 2( ) ( ) ( ) 2 ( ) sin ( )s LOI t I t I t P t P t
0
2 ( )
I
I P P
2 ( )peak s LOI P t P
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6- Single-Branch IQ Coherent Receiver
( )sE t ( )IE t ( )II t
( )E t ( )E t ( )QI t
2( )LOE t ( )QE t ( )QI t
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2x2 90º Hybridy
a c
b db d
2
1 11E E 1 1112
c a
d b
E EE Ej
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1
1( ) ( ) ( )2I s LOE t E t E t
( ) ( ) 2 ( ) cos ( )2I s LO s LOI t P t P P t P t
1
1( ) ( ) ( )2Q s LOE t E t jE t
( ) ( ) 2 ( ) sin ( )2Q s LO s LOI t P t P P t P t
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( ( ))( ) ( ) ( ) ( )IF LOj t tI t I t jI t P e E t ( ( ))
Electronic processing
( ) ( ) ( ) ( )IF LOjI Q LO sI t I t jI t P e E t
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7- Balanced IQ Coherent Receiver
( )E t 1( )IE t 1( )II t( )sE t 1( )I
2 ( )IE t1I
2 ( )II t( )II t
( )E1( )QE t 1( )QI t
( )QI t2( )LOE t
2 ( )QE t 2 ( )QI t( )Q
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2x4 90º Hybrid
a c
d
b
e
fb 2 f
1 11
c
d
EE Ej j
1
121
d a
e b
E Ej jE EjE j
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1fE j
1( ) ( ) ( )E t E t E t
1( ) ( ) ( )2
( ) ( ) 2 ( ) cos ( )
I s LOE t E t E t
I t P t P P t P t
1( ) ( ) 2 ( ) cos ( )
4I s LO s LOI t P t P P t P t
21( ) ( ) ( )2I s LOE t j E t E t
2( ) ( ) 2 ( ) cos ( )
4I s LO s LOI t P t P P t P t
( ) ( ) ( ) ( ) cos ( )I t I t I t P t P t 1 1 2( ) ( ) ( ) ( ) cos ( )2I I I s LOI t I t I t P t P t
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1( ) ( ) ( )E t j E t jE t
1( ) ( ) ( )2
( ) ( ) 2 ( ) sin ( )
Q s LOE t j E t jE t
I t P t P P t P t
1( ) ( ) 2 ( ) sin ( )
4Q s LO s LOI t P t P P t P t
21( ) ( ) ( )2Q s LOE t E t jE t
2( ) ( ) 2 ( ) sin ( )
4Q s LO s LOI t P t P P t P t
( ) ( ) ( ) ( ) sin ( )I t I t I t P t P t 1 1 2( ) ( ) ( ) ( ) sin ( )2Q Q Q s LOI t I t I t P t P t
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