1.57 *

Defined by Eq. (4-42)

2.5 (V2i)

1.66 f

* Improvement over RC is 1.4.

t Improvement over RC is 1.51.

* Improvement over RC is 1.4.

t Improvement over RC is 1.51.

As can be seen, the two definitions of TR agree moderately well. The agreement would be even closer for a large number of resistance-coupled stages because of the basis for selecting the constant 27r.

Now we come to the problem of determining the rise time and delay time for a cascade of stages. We do not yet know how the time responses for several stages combine, but we do know that the voltage gains Ai(p) combine as a continued product in a cascade of amplifier stages consisting of ideal pentodes as unilateral coupling elements separating the interstage

1 In this case the response v'it), as well as v(t) and the steady-state amplitude response approaches a gaussian error function; see Valley and Wallman, op. cit., pp. 723-724.

networks. Thus, the gain function for a cascade of n stages (see Fig. 4-26) as a function of the complex frequency variable p is given by

Va{p) i=i where F0(p) = voltage at input of 1st stage Vnip) = voltage at output of nth stage Ai{p) = gain function of xth stage = F,(p)/F,_1(p) The next step is to normalize each of the Ai(p) by dividing by —gmRL, so that the normalized gain for each stage is unity. Then we drive the circuit

1st stage ith stage nth stage

Fig. 4-26 Nomenclature for the stages in a multistage amplifier.

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