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If one cascades these lters the phase shifts can

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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 op-amp 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 op-amp circuits themselves, this is almost impossible to eliminate. Most manufacturers of op-amps confront this issue by intentionally reducing the open-loop gain at high frequency. This is called compensation. It is carried out by bypassing one of the internal ampli er stages with a high-pass lter. The e ect of this is illustrated in Fig. 37. It is a so-called Bode plot", log10A vs log10f , showing how the intrinsic gain of a compensated op-amp 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 op-amp open-loop gain, A, is unity, is called fT , and gives a good indication of how fast the op-amp is. Compensation accounts for why op-amps 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 op-amp compensation. 43...
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