UPM-Coherentes-Matriz.ppt [Modo de compatibilidad]

Coherent Detection

Miguel A MurielMiguel A. Muriel

Miguel A. Muriel - Coherent Detection - 1

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


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


- 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


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


- The local oscillator power is:

2

*( ) ( ) ( ) LOLO LO LO

ACP t E t E t C ( ) ( ) ( )2 2LO LO LO


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


4- Coherent Detection (3 dB coupler/ Beam Splitter)( p p )

( )E t biasV( )sE t

( )LOE t( )I

( )E t

VLR( )I t


3 dB C l / B litt3 dB Coupler / Beam splitter

ca

a c

b

b

1 ( )2c a bE E E 2


( ( )) ( ( ))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


( ) ( ( ) ( ))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


5- Coherent Detection (Directional coupler)

( )E tbiasV

( )E( )sE t

( )LOE tV

phI1( )E t

VLR


Directional Coupler

a

b

c

d

1112

c a

d b

E EjE Ej

2d bj


5-1 Single-Branch Coherent Receiver5 1 Single Branch Coherent Receiver


( ( )) ( ( ))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


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


5-2 Balanced Coherent Receiver5 2 Balanced Coherent Receiver

Removes the dc components and maximizes the beating term


( ) 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


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


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


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


2x2 90º Hybridy

a c

b db d

2

1 11E E 1 1112

c a

d b

E EE Ej


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


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


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


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


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


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


( ( ))( ) ( ) ( ) ( )IF LOj t tI t I t jI t P E t ( ( ))

Electronic processing

( ) ( ) ( ) ( )2

IF LOj t tI Q LO sI t I t jI t P e E t


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