Step Response of Lowpass (Video) Amplifiers: Speed of Rise

Most lowpass amplifiers are required to handle transient signals rather than steady-state sine-wave signals. Hence what one would really like to know is the behavior of the amplifier with an input similar to that which the amplifier must actually amplify. Test data obtained with actual signals may be difficult to interpret or to generalize from, although this method of testing is used with video television amplifiers. Here the test signal might be obtained from a special test pattern, passed through the amplifier, and displayed on a picture tube. More usually, however, the transient test signal is a step voltage or low-frequency square wave. Such a signal would occur in a television system at an abrupt transition from white to black. Since the use of an amplifier is most often to amplify a transient signal, it is logical to design the amplifier on the basis of its transient response rather than its steady-state response. Consequently, we shall consider improvements on the high-frequency response obtained in the analysis of the last chapter on the basis of the transient behavior, rather than merely trying to extend the bandwidth. In some ways the transient behavior is more difficult to deal with, and in very complicated cases we may have to fall back upon steady-state analysis; therefore an additional point of interest is the relationship of the transient response to the steady-state response.

4-1 Pentode Stage—Choice of Tube. Let us begin the transient study with the simplest case: the pentode stage shown in Fig. 3-1 with the equivalent circuit shown in Fig. 3-12a. The response of this stage to a unit step voltage input [«(¿)] may be found by assuming Fj (p) = £bi(/)] = £[u(t)] = 1 /p; then the output voltage of one stage is [see Eq. (3-88)]

The 10 to 90 per cent rise time Tr and ultimate (same as mid-frequency) gain A are

If one sets out to design the resistance-coupled amplifier stage to give both high gain and a small rise time, one is confronted with a contradiction. From Eqs. (4-3) and (4-4) it is seen that for a given tube, i.e., a given gm and C, one can increase Rl to raise the gain but in doing so one lengthens the rise time. This proportionality of gain and rise time can be expressed as a quotient whose magnitude is independent of R and depends primarily upon the tube,

Gain A gm

Rise time Tr 2.2C

The capacitance C includes both input and output capacitances of the tube (on the assumption that both tubes associated with the interstage network are of the same type), together with the stray wiring capacitance. The latter can usually be made small compared with the tube capacitance, and in any case it is apparent that, if two tubes have equal gm but different C, the one with the smaller C will be better. In Table 4-1 are listed the transconductances gm, the total capacitance C (which includes 4 pf for stray

Table 4-1 *


Ci, pf

Co, pf

C, pf

gm, Mmhos

Gain/rise time, usee

0 0

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