488 CHAPTER 10. COHERENT LIGHTWAVE SYSTEMS
Figure 10.4: Block diagram of a synchronous heterodyne receiver.10.3.1 Heterodyne Synchronous Demodulation
Figure 10.4 shows a synchronous heterodyne receiver schematically. The current gen-
erated at the photodiode is passed through a bandpass filter (BPF) centered at the inter-
mediate frequencyωIF. The filtered current in the absence of noise can be written as
[see Eq. (10.1.8)]
If(t)=Ipcos(ωIFt−φ), (10.3.1)
whereIp= 2 R
√
PsPLOandφ=φLO−φsis the phase difference between the local
oscillator and the signal. The noise is also filtered by the BPF. Using the in-phase and
out-of-phase quadrature components of the filtered Gaussian noise [1], the receiver
noise is included through
If(t)=(Ipcosφ+ic)cos(ωIFt)+(Ipsinφ+is)sin(ωIFt), (10.3.2)whereicandisare Gaussian random variables of zero mean with varianceσ^2 given
by Eq. (10.1.9). For synchronous demodulation,If(t)is multiplied by cos(ωIFt)and
filtered by a low-pass filter. The resulting baseband signal is
Id=〈Ifcos(ωIFt)〉=^12 (Ipcosφ+ic), (10.3.3)where angle brackets denote low-pass filtering used for rejecting the ac components
oscillating at 2ωIF. Equation (10.3.3) shows that only the in-phase noise component
affects the performance of synchronous heterodyne receivers.
Synchronous demodulation requires recovery of the microwave carrier at the inter-
mediate frequencyωIF. Several electronic schemes can be used for this purpose, all
requiring a kind of electrical phase-locked loop [36]. Two commonly used loops are
thesquaring loopand theCostas loop. A squaring loop uses a square-law device to
obtain a signal of the form cos^2 (ωIFt)that has a frequency component at 2ωIF. This
component can be used to generate a microwave signal atωIF.
10.3.2 Heterodyne Asynchronous Demodulation
Figure 10.5 shows an asynchronous heterodyne receiver schematically. It does not
require recovery of the microwave carrier at the intermediate frequency, resulting in a
much simpler receiver design. The filtered signalIf(t)is converted to the baseband by