Time Constant Methods: Complications

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Time Constant Methods: Complications

As attractive as the time constant delay and risetime estimates are computationally, the user must beware of complications that will degrade the accuracy by a large margin. First, consider that both methods depend on a restrictive assumption regarding monotonic risetime. In many cases, however, it is not unusual to experience complex poles. This can occur owing to feedback which leads to inductive input or output impedances and emitter or source followers which also have inductive output impedance. When combined with a predominantly capacitive input impedance, complex poles will generally result unless the circuit is well damped. The time constant methods ignore the complex pole effects which can be quite significant if the poles are split and s « j w. In this case, the circuit transient response will exhibit ringing, and time constant estimates of bandwidth, delay, and risetime will be in serious error. Of course, the ringing will show up in the circuit simulation, and if present, must be dealt with by adding damping resistances at appropriate locations.

An additional caution must be given for circuits that include zeros. Although Elmore’s equations can modify the estimates for TD and TR when there are zeros, the OCTC method provides no help in finding the time constants of these zeros. Zeros often occur in wideband amplifier circuits that have been modified through the addition of inductance for shunt peaking, for example. The addition of inductance, either intentionally or accidentally, can also produce complex pole pairs. Zeros are intentionally added for the optimization of speed in very high-speed digital ICs; however, the large area required for the spiral inductors when compared with the area consumed by active devices tends to discourage the use of this method in all but the simplest (and fastest) designs where transmission lines can be used as inductors [5].

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