Analysis of the automatic frequency control in heterodyne optical receivers

Abstract

control loop can be done for the three modulations considered. Design guidelines are given that account for the presence of the AFC loop by properly using some performance results derived in the assumption of perfect frequency tracking.

System Performance of Optical Heterodyne CPFSK Receivers with AFCs

“…[18] one can find the power spectral density (PSD) of e(t) aŝ S niF +(k c k d )S n |FH| 2 |l + (k c k d ) 2 FH| 2 (9) where F and H represent the transfer functions of the loop filter and the bandpass filter, respectively kj is the conversion coefficient of the limiter-discriminator and both S", F and S n are PSD's defined as s - (10) By assuming F and H, respectively, as and H(s) = one can obtain [18] one can find the power spectral density (PSD) of e(t) aŝ S niF +(k c k d )S n |FH| 2 |l + (k c k d ) 2 FH| 2 (9) where F and H represent the transfer functions of the loop filter and the bandpass filter, respectively kj is the conversion coefficient of the limiter-discriminator and both S", F and S n are PSD's defined as s - (10) By assuming F and H, respectively, as and H(s) = one can obtain…”

Optical Phase-Locked Loops

“…If we include the laser's tuning constant, , we can write the laser's output frequency for the gain-only loop filter as It can be shown for this simple loop that stable frequency control is available only over the range [35] In general, the dynamic loop transfer function of the loop in Figure 12 This simple analysis does not consider the noise transformed by the frequency discriminator. Our more detailed analysis is similar to that of Bononi,et.al.,[32]. Refer to Figure 12.15 for the position of the various signals to be computed.…”

“…Assuming the dual-detector mixer discussed previously, the IF signal to the frequency discriminator can be written as [32] The amplitude A, is a function of the photodetector's response and the input power of the two signals (see . Clearly the IF frequency is the difference,…”

“…The derivative in Equation 12-45 represents the phase noise of the two optical sources. (Recall We assume that the discriminator's characteristic is centered at frequency Bononi et al represent the phase noise in the frequency domain as From Figure 12.13, we define the closed loop frequency error as [32] When the AFC loop is in track, the nominal output frequency will be , the center frequency of the discriminator, plus a frequency error term due to the phase noise (t) and the transformed shot noise, N(t). We can write the discriminator output as…”

“…Computing the power spectral density of both sides provides [32] Assuming that the loop filter G( f ) is a lowpass filter, the first term of Equation 12-53 is a highpass function. Hence, the high frequency components of the phase noise appear in the frequency error.…”