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From the circuit composition structure of the basic feedback circuit, the closed-loop transfer function is obtained  . The open-loop gain of the circuit is a function of the parameters of each transistor and capacitor, so it is also a function of frequency, so the closed-loop gain can be written as  . The stability of the feedback circuit is related to the loop gain A(w). When the amplitude of the loop gain is unity 1 and the phase angle is 180 degrees, A(w)=-1, then the closed-loop gain is infinite, which results in the output signal not being 0 when the input signal is 0, which means that the circuit is oscillating.
The basis for judging the stability of the system: Nyquist criterion can not only determine whether the system is stable, but also determine the degree of system stability. To use this criterion, you must first draw the Nyquist curve, which is the trajectory of the loop gain in the polar coordinate system.
The Nyquist criterion for judging the stability of a circuit can be expressed as follows: When the Nyquist curve surrounds or passes through the point (-1, 0), the amplifier is unstable. When the Nyquist curve surrounds or passes through this point, the amplitude-frequency gain is -1, the phase-frequency gain is 0, and the input and output of the system are originally 180 degrees apart. Then the system oscillates at a gain of -1, and the output signal and the input signal are superimposed.
Using this basis, we can get a simpler stability test method in many cases. That is, when the frequency is -180 degrees, if |A(w)|>1, the amplifier is unstable. I don't quite understand this sentence. Does it mean that when the phase gain of the system is -180 degrees, the system gain is greater than 1, then the amplifier circuit can be judged to be unstable?
By checking the loop gain, you can determine whether the feedback system is stable. The loop gain is a function of frequency. Here we introduce two concepts, phase margin and gain margin:
1. Phase margin: At the frequency where the loop gain is 1, if the absolute value of the loop gain phase is less than 180 degrees, the system is stable. The difference (absolute value) between the phase angle of the loop gain and 180 degrees at the next frequency is called the phase margin. The typical value of the designer's phase margin is 45-60 degrees. There are two questions. Why do we need to make a judgment when the loop gain is 1? Is it because the circuit must maintain the amplification characteristics and the amplitude gain must be greater than 1? In addition, the phase difference between the input and output in the open loop is already 180 degrees, plus the phase difference of the closed-loop branch, that is to say, the phase difference of the entire loop gain must be far away from -180 degrees. Generally, because the circuit is capacitive, the phase margin must be greater than 225 degrees to 240 degrees, so that the loop input and output can be stable and will not overlap?
2. Gain margin: It indicates the size of the loop gain |A(w)| at the frequency when the phase is -180 degrees, reflecting the extent to which the loop gain can be increased while the system remains stable. This means that when the loop input and output have already differed by 0 degrees, since the amplitude gain at this frequency point is not greater than or equal to 1, the system will reach stability after a period of balance. This gain margin refers to the frequency difference between the frequency point at the phase of -180 degrees and the frequency point at which the gain is 1, right?
3. Will the phase gain exceed -180 degrees? Two sine waves of the same frequency have a maximum phase difference of 180 degrees. If the capacitance of the circuit is taken into account, the maximum phase difference is no more than 360 degrees. The circuit signal is delayed by a capacitor by a maximum of 90 degrees. Is the delay so large due to the multi-stage capacitive load?
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