Analysis and Design of Transimpedance Amplifiers for Optical Receivers

Appendix H

Second-Order Low-Pass Transfer Functions

Let us define the second-order low-pass transfer function

H.1

which plays an important role in the analysis of TIAs (cf. Chapter 6). In the following, we calculate the 3-dB bandwidth, noise bandwidths, and Personick integrals of this transfer function. Then, we specialize the results for the case when the poles are real, relevant for common-gate and common-base TIAs. After that, we discuss four special cases of the transfer function (critically damped, Bessel–Thomson, Butterworth, and ) in the frequency and time domain.

3-dB Bandwidth

The transfer function in Eq. (H.1) has two poles, no zeros, and a low-frequency gain of one. Its 3-dB bandwidth is found by solving , which results in

H.2

where

H.3

As shown in Fig. H.1, this somewhat complicated expression can be bounded by two linear terms:

H.4

where the lower bound holds for (none ...