CMOS Optical Preamplifier Design Using Graphical Circuit Analysis

5.2 Developing an Analytic Circuit Model 124
To demonstrate the accuracy of Equation (5.24), we apply the equation to the
same four preamplifier designs used earlier to verify the accuracy of our frequency
response. Figure 5.15 plots the results obtained using Equation (5.24) together with
the simulation results from SPICE. An excess noise factor of γ = 2 ⁄ 3 was used.
The results are close within the passband of the designs, with the error increasing at
high frequencies as expected because of our simplifying assumption that the tran-
simpedance gain is flat. Within the passband, however, we confirm that our analytic
results are no greater than 3dB off from the simulated results.
Input−referred Noise Current (pA/Hz 1/2 )
10 3
10 2
10 1
10 0
10 0
5.2.3 Design Optimization
Analytic vs Simulated Input−Referred Noise Current
10 1
80MHz
frequency (MHz)
70MHz
60MHz
160MHz
Figure 5.15 Plot of analytic vs. simulated input-referred noise of 4 designs. Vertical
bars mark 3dB cut-off frequencies of preamplifiers.
As is typical in analog circuits, the design of an optical preamplifier involves
addressing conflicting goals and making trade-offs. Bandwidth, gain, and sensitivity
are three important design specifications, and each is affected by circuit parameters
such as the supply voltage and the input capacitance. Design trade-offs are often
better understood with the aid of analytic models of the circuit. The following equa-
tions represent our analytic model of the preamplifier:
10 2
10 3
solid — analytical
dashed — simulated
Scale:
3dB