Environmental Engineering Reference
In-Depth Information
4.2 TWO-POLE FEEDBACK AMPLIFIERS
The loop-gain transfer function of real amplifiers includes more than one
single pole. In the absence of suitable compensation, this can cause
instability phenomena even under negative feedback. To demonstrate these
instability problems, and the related importance of a sufficiently large
separation between the two lowest poles of the loop-gain transfer function,
consider now an open-loop amplifier with two real negative poles. As
already mentioned, and as will be further explained in the following
chapters, it is more convenient to analyse the loop gain instead of the
amplifier open-loop gain.
Assume that the amplifier operating within the given feedback network
gives rise to the following two-pole loop-gain function
It should now be observed that for second-order and higher-order transfer
functions, the gain-bandwidth product, does not necessarily
coincide with the unity-gain frequency However, this is still a good
approximation if the second pole is greater than This observation is
graphically explained in Fig. 4.4, where two loop-gain functions (with
different pole separation) are plotted.
Note that hereinafter and unless differently indicated, we will denote the
gain-bandwidth product of the loop-gain transfer function with
Using (3.la), the closed-loop transfer function becomes
where and are the parameters called pole frequency and damping
factor, respectively, and are expressed as functions of the loop-gain poles by
[SS91]
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