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CRC Press - Continuous-Time Active Filter Design by T. Deliyanis, Y. Sun, J. Fidler

By T. Deliyanis, Y. Sun, J. Fidler

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22, a typical step response of a lowpass filter is shown. Characteristic quantities associated with this response are values of the rise time tr, the delay time τo, the settling time ts, and the overshoot. These quantities are defined as follows: • The rise time tr is defined as the time it takes the step response to rise from 10 percent to 90 percent of its final value. • The delay time τo is the time it takes for the step response to rise to 50 percent of its final value. • The settling time ts is the time that elapses between the moment of appearance of the first peak and the moment beyond which the step response does not differ by more that 2 percent from its final value.

However, in practice, both inductors and capacitors have always some loss associated with their values. The effect of this loss is to move the jωaxis poles and zeros out of the jω-axis inside the LHP. In this case, both N(s) and D(s) will be Hurwitz and the passive one-port strictly stable. ©1999 CRC Press LLC On the other hand, any passive termination of the passive one-port will not change the passivity property, since the sum of two positive real functions is also positive real. Therefore, a passive one-port is absolutely stable.

However, contrary to the case of an active one-port, an active two-port may be absolutely stable, because the activity conditions in this case do not violate the passivity conditions. On the other hand, a potentially unstable network will be active. 9 Reciprocity This property of a network is included here for completeness rather than for its usefulness in the development of the material in this book. A network is reciprocal if [2] 1. 25) the current occurring in a short between two nodes α and β due to a voltage between the nodes γ and δ is equal to the current occurring in a short between the nodes γ and δ, if the same voltage as before is applied between the nodes α and β, or 2.

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