High-Speed Circuit Design Principles:Time Constant Methods in High-Speed Analog Design

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Time Constant Methods in High-Speed Analog Design

Analog circuits, with the exception of power amplifiers, operate in the small-signal regime. Thus, the device small-signal transconductance is used in analysis, and the device capacitances are evaluated at a single bias point.

The OCTC methodology described above was originally used for estimating high-frequency performance of analog circuits. In these applications, both frequency and time domain responses are important. Properties of bandwidth, gain peaking and phase margin in frequency domain and risetime, ringing, and overshoot in time domain can be predicted by the tools described above. And, most importantly, the method provides guidance on what parameters must be changed to avoid signal distortion.

First, assume that the circuit transfer function, F(s), is a low-pass with only poles in the denominator. If there are zeros present, the result will be modified somewhat. Then, rewrite the denominator in the standard form typically used in control theory textbooks

High-Speed Circuit Design Principles-0034

For a well-behaved frequency or transient response, the system should be overdamped (z > 1) to minimize ringing or gain peaking. This will help to provide a flatter group delay and hence less pulse distortion. This condition applies to the case where the poles are both on the negative real axis. Table 74.7 presents equations that can be used to predict the frequency and time domain behavior of a circuit subject to the restrictions indicated in the table.

The second pole frequency can be estimated by the separated pole approximation

High-Speed Circuit Design Principles-0035

High-Speed Circuit Design Principles-0036

Here, it is assumed that the third-order coefficient, b3, and higher terms are small, and that b1 » b2/b1. If the latter condition is not met, then the quadratic formula should be used instead. Note that the second pole must be much higher in frequency than the dominant pole to maintain a reasonably well-damped circuit.

When feedback is used, the method is still applicable in many cases. Feedback zeros will not affect the response. But the predictions of the response in Table 74.7 will not be valid if there are zeros in the forward path, sometimes used for compensation purposes. In this case, use of a tool such as MATLAB [12] can be used to gain intuition. The final analysis will in any case require the use of a circuit simulator such as SPICE or ADS [13].

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