At each pole, the gain is attenuated by -3db and shifted by -45 degrees. The gain after the pole drops by 20db every ten times, and the zero point is opposite to the pole. At each zero, the gain is increased by 3db and shifted by 45 degrees. After the zero point, the gain increases by 20db every ten octaves.
Closed-loop gain A0: A/ 1+AB = 1/B (when a is large), where a is the open-loop gain and b is the feedback factor, which can be understood as the ratio of feedback to output. When the open-loop gain approaches infinity, the closed-loop gain is the reciprocal of the feedback coefficient.
Loop gain: T=a*b
For operational amplifiers, the zero point of the closed-loop gain (1/b) transfer function is the pole of the loop gain (ab) transfer function; The pole of the closed-loop gain transfer function is the zero point of the loop gain transfer function; When we feed back, we want the loop gain to be greater than 1 before the phase drops to 180 degrees, so we need to eliminate the pole of a loop gain function (that is, the closed-loop gain zero) to avoid oscillation.
Pole influence
A pole is the point where the denominator of the transfer function of a linear time-invariant system is zero. For Laplace transform, the system with poles in the left half plane is stable. For linear discrete systems, the system is stable when the poles are in the unit circle. According to the position of the zero pole of the system, the amplitude-frequency characteristics of the system can be analyzed
Similar to Laplace transform, the basic characteristics of the system can also be analyzed by using the zero pole of the system function in Z transform. The system function of discrete-time system is completely determined by its poles and zeros, and the system function is the Z transform of impulse response. Therefore, a predictable result is that there must be some internal relationship between the zero pole of the system function and the impulse response. The system function of discrete-time system can be expressed as a partial fractional expansion of this formula, and assuming that all poles of ⅱ (z) are first-order poles, there is (6.82), from which the impulse response of the system can be obtained (6.83). Comparing equations (6.82) and (6.83), we can see that the impulse response of the system is determined by the poles of the system function.
Therefore, the basic characteristics of the system impulse response will be different for different pole positions. For a discrete sequence, the so-called basic features usually refer to the changing trend and frequency of the sequence envelope. As mentioned above, these basic characteristics are completely determined by the pole position of the system function, while the zero position only affects the amplitude and phase of the impulse response.
On the Z plane, the poles of the system function may be located in, above or outside the unit garden. Obviously, it can be seen from equations (6.82) and (6.83) that for a causal system, if the poles are located in the unit garden, the envelope of the impulse response will decay with the increase of n value; If the pole is on the unit circle, [3] the envelope of the impulse response will not change with the value of n, and it is an envelope with constant amplitude; If the pole is outside the unit circle, the envelope of the impulse response will increase with the increase of n value.
It is not difficult to understand that the radius of the pole determines the changing trend of the sequence envelope, while the amplitude angle of the pole determines the changing frequency of the sequence envelope. Because, on the Z plane, the meaning of amplitude angle is the envelope frequency of the sequence, and amplitude angle can directly map the envelope frequency.