October 2017
Intermediate to advanced
592 pages
20h 47m
English
Content preview from Analysis and Design of Transimpedance Amplifiers for Optical Receivers
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Appendix H
Second-Order Low-Pass Transfer Functions
Let us define the second-order low-pass transfer function
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
where
H.3 
As shown in Fig. H.1, this somewhat complicated expression can be bounded by two linear terms:
where the lower bound holds for (none ...
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