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Optical Receivers 237

2 × 4 90° hybrid
PD1
1
q out I Q+
I = I Q+ −I Q−
Q
+
Σ
DC 1 ESP
Received signal
2 ‒
q out I Q−
PS
PD2
LO PS

π
Phase-shifter
2
PD3
3
q out I I+
I = I −I I−
I+
I
+
DC 2 Σ ESP
4 ‒
q out I I−
PD4
Figure 5.38 Block diagram of a balanced IQ receiver. DC = directional coupler, PS = power splitter, LO = local
oscillator, PD = Photodetector.

5.6.4 Balanced IQ Receiver

It is straightforward to modify the block diagram of Fig. 5.36 to obtain the balanced IQ receiver, shown in
Fig. 5.38. The inputs of DC1 are
q
in r
q = √ , (5.127)
1
2
q LO
in
q = √ . (5.128)
2
2
The transfer function of DC1 is given by Eq. (5.106),
[ ]
1 1 −i
T . (5.129)
DC = √ −i 1
2
Therefore, the output of DC1 is
in
q out = T q , (5.130)
dc
1
out
q = [q − iq LO ], (5.131)
r
1 2