Summary of the concepts of turning frequency, cutting frequency, cutoff frequency, poles and zeros

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Summary of the concepts of turning frequency, cutting frequency, cutoff frequency, poles and zeros [Copy link]

The textbooks seem to have a very poor understanding of the definition of this aspect, at least that was the case when I was learning the principle of automatic control. I have summarized it here for the benefit of future generations. —————————————————————————————————————— Transition frequency: that is, the transition line of the AF logarithmic coordinate axis, the asymptote of the high frequency part is a straight line with a slope of -20dB/dec. When the frequency of the input signal increases by ten times, the amplitude of the corresponding output signal decreases by 20dB. Cut-off frequency: a special frequency used to illustrate the frequency characteristic index of a circuit. When the amplitude of the circuit input signal remains unchanged, the frequency is changed to make the output signal drop to 0.707 times the maximum value. The frequency response characteristic is expressed as -3dB point is the cut-off frequency. or a certain special rated value, this frequency is called the cut-off frequency.In fact, it is the turning frequency.Turning frequency=Cut-off frequency Cut-off frequency:The angular frequency corresponding to the amplitude A(w)=1 (that is, 20lg|A(w)|=0) on the open-loop logarithmic frequency characteristic is called the cut-off frequency, usually represented by Wc. Crossover frequency: An indicator used to describe the frequency characteristics of a system, also known as the shear frequency. It is defined as the frequency at which the amplitude-frequency crosses 0dB. The phase on the phase-frequency curve corresponding to the crossover frequency reflects the relative stability of the system. The phase margin is defined as the phase +180° corresponding to the crossover frequency. A phase margin greater than 0 indicates a stable system, and a phase margin less than 0 indicates an unstable system (as shown in the "angular frequency Wc" in the figure below). Crossover frequency == Shear frequency = fc; f0 indicates the starting feedback oscillation frequency. f_{0[/sub], = is the frequency when the phase frequency crosses -180°, that is, the proper frequency for self-excitation.} Pole: The point where the X-axis coordinate of the turning frequency corresponds to each -3db drop; After the pole, the gain drops by 20db for every decade of frequency. The zero point is the opposite of the pole. Zero point: It is the point that makes the numerator of the transfer function zero or The starting point of each turning line. At the zero point, the gain increases by 3db and the phase shifts by 45 degrees. After the zero point, the gain increases by 20db for every decade of frequency. Zero state response:refers to the response to the input when the initial state is zero, similar to the constant voltage source charging the capacitor. Stability margin:It is seen from the Bode diagram when judging stability. There are two forms of expression, phase margin and amplitude margin. When the phase angle is 180 degrees, the difference between the corresponding response and the actual response corresponding to the cutoff frequency. 1. The physical meaning of zeros and poles in transfer functions: Zero: When the system input amplitude is not zero and the input frequency makes the system output zero, this input frequency value is the zero. Pole: When the system input amplitude is not zero and the input frequency makes the system output infinite (the system stability is destroyed and oscillation occurs), this frequency value is the pole. For example: Sometimes your stereo or TV case emits a series of sharp hissing noises. You will know that the screws of the case are loose. Tighten the screws and the noise problem will be solved. In fact, what you have done is pole compensation. Tighten the screws - you have greatly reduced the pole frequency of the system. Of course, the system here refers to the mechanical vibration system, not the circuit system, but the system principle is the same. I am just throwing out some ideas. I hope there will be more answers. (This paragraph needs to be discussed) 2. At each pole, the gain is attenuated by -3db and the phase is shifted by -45 degrees (which can be understood as each turning point). After the pole, the gain decreases by 20db for every decade. The zero point is opposite to the pole. At the zero point, the gain increases by 3db and the phase is shifted by 45 degrees. After the zero point, the gain increases by 20db for every decade of frequency. The Bode plot is as follows: The zero point plot is not suitable, but it is the opposite of the pole plot. The following is the pole plot. Pole zeros are generally used for loop stability analysis. [url=][img=495,311]http://cdn13.21dianyuan.com/attachments/jpg/2012/10/23/1350923024508573105aa08.jpg[/im g][/url] [url=][/url] The following content is excerpted from a certain brother's blog, extracting the key points and adding some comments. In CMOS, the capacitance Cgs from the gate terminal to the ground is generally large, so people usually take this pole, The input signal frequency makes the impedance from the node to the ground infinite (that is, the so-called 1/RC). R is the resistance to the ground, and C is the capacitance to the ground (parallel connection produces a pole) In CMOS, the zero point is often caused by the capacitance in the signal path, which makes the impedance of the signal to the ground zero; in Miller compensation, not only the main pole is pushed inward and the secondary pole is pushed outward (increasing the capacitance), but also a zero point is generated (close to the frequency of the third pole), but people generally only care about the former. In experience, high-impedance nodes in amplifier circuits should be paid attention to, even if the capacitance at this point is very small, a large pole will be generated. Zero points are generally not so intuitive. Usually, if two out-of-phase signals intersect, a zero point will be generated, but this cannot explain all zero points. I personally think that zeros and poles are just auxiliary methods abstracted from circuit analysis. Circuit action characteristics can be analyzed through zeros and poles. However, since there is abstraction, there must be its physical manifestation. From the Bode diagram, poles have two functions: delay (frequency increases but my gain will decrease) and gain reduction. In the feedback system, the function is to reduce the amplitude of the feedback signal and delay the time for the feedback signal to return to the input point. Therefore, if there is a capacitance to ground at a certain node, the capacitor will inevitably be charged. At the same time, there is a voltage divider between the capacitor and the output resistor of the previous stage, so this capacitor will produce a pole (think about the signal from the sampling voltage divider resistor, and a capacitor filter is added). Zeroes can increase gain, and poles reduce gain. When we give feedback, we hope that the gain will be reduced to one before the phase drops to 180 degrees, so we need to eliminate a zero to avoid oscillation.

10jolin123

Thanks for sharing

luck_gfb

Thanks for sharing

ypy321

My textbook knowledge: Cut-off frequency = Amplitude crossover frequency = Frequency corresponding to phase margin Crossover frequency = Phase crossover frequency = Frequency corresponding to amplitude margin I want to know what the cut-off frequency is. After reading your explanation, I am getting more and more confused.