Transient Response of Two-Terminal Networks

The maximum possible increase in gain/rise-time for a 2-terminal network with shunt capacitance is shown to be 2.75 compared with the parallel RC case; the overall gain/rise-time figure for a cascade of n such stages is also deduced. As such networks would have a large amount of overshoot, those having a monotonic response to a stepfunction current drive are next considered. Improvement in figure of merit is shown to be greatest with complex poles and zeros, and the case of three poles, two of which are conjugate complex, is discussed in some detail. Finally, modifications are made to a network with three poles having a monotonic response so as to produce improved risetime at the expense of a small amount of overshoot; e.g. a figure of merit of 1.90 can be obtained with 1% overshoot.