Unformatted text preview: an RC lter introduces a phase shift between 0 and =2. If one cascades these
lters, the phase shifts can accumulate, producing at some frequency ! the possibility of
a phase shift of . This is dangerous for opamp circuits employing negative feedback, as
a phase shift of converts negative feedback to positive feedback. This in turn tends to
42 compound circuit instabilities and can lead to oscillating circuits as we do on purpose for
the RC relaxation oscillator.
So it is perhaps easy to simply not include such phase shifts in the feedback loop. However, at high frequencies f 1 MHz or more, unintended stray capacitances can become
signi cant. In fact, within the opamp circuits themselves, this is almost impossible to
eliminate. Most manufacturers of opamps confront this issue by intentionally reducing the
openloop gain at high frequency. This is called compensation. It is carried out by bypassing
one of the internal ampli er stages with a highpass lter. The e ect of this is illustrated
in Fig. 37. It is a socalled Bode plot", log10A vs log10f , showing how the intrinsic
gain of a compensated opamp like the 741 or 411 decreases with frequency much sooner
than one without compensation. The goal is to achieve A 1 at ! , which is typically at
frequencies of 5 to 10 MHz. One other piece of terminology: The frequency at which the
opamp openloop gain, A, is unity, is called fT , and gives a good indication of how fast the
opamp is.
Compensation accounts for why opamps are not very fast devices: The contribution of
the higher frequency Fourier terms are intentionally attenuated. However, for comparators,
which we turn to next, negative feedback is not used. Hence, their speed is typically much
greater.
Log 10 G
5 Compensated 3
Uncompensated
1
Log
1 3 5 7 10 f Figure 37: Bode plot showing e ect of opamp compensation. 43...
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 Fall '12
 Soujanu
 Cybernetics, Positive feedback, de nition Zin

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