About transfer function

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About transfer function [Copy link]

Recently, I was reading about circuit principle analysis. Regarding the transfer function, I introduced an exponential sine wave excitation to analyze the steady-state response, and finally introduced the concept of complex frequency S. Why do we need to introduce the exponential sine function? Is it a further description of the actual natural signal? What is the specific physical meaning of complex frequency S=a+jw?

jimtien

Laplace transform is developed based on Fourier transform. Fourier transform requires that the signal function is absolutely integrable in an infinite interval, so many signals cannot be Fourier transformed, so Laplace transform is processed like this: multiplying the function by an attenuation factor makes the originally non-integrable function integrable. This attenuation factor is e^a, s=a+jw. You will find that when a=0 (no attenuation treatment), Laplace transform becomes Fourier transform.

xjtburden

Any waveform can be decomposed into a superposition of sine waves of different frequencies. The transfer function is analyzed in the frequency domain or S domain, which is more convenient than analyzing in the time domain.

se7ens

Exponential sine wave, what signal is it?

javnson

First of all, s-domain analysis can be directly used as a mathematical tool to perform frequency domain analysis of signals or circuits. The calculation of the connection relationship between each link is very simple, and there are generally only a few fixed ones.

Another value of it is that as you said, we only need to let s=j\omega to get the amplitude-phase-frequency curve of the circuit. From this perspective, we have bypassed the relatively difficult knowledge of differential equations and provided a simple method to perform amplitude-phase-frequency analysis of the circuit.

In addition, there is a large set of logic that can be used to analyze closed-loop characteristics through open-loop transfer functions, which is difficult or impossible to do with many other methods. It has a wide range of applications in control and stability analysis.

One more thing to add is that through such transfer function design, combined with bilinear transformation, it is also easy to design the corresponding discrete control system and compare and analyze its performance, so as to comprehensively evaluate whether this part of the control function is more suitable to be implemented in a digital system or an analog system.

As for adding exponents, we usually joke that this is a very clever mathematical method to solve convergence problems, which can greatly expand the range of problems that Fourier analysis can solve.

15272693963

javnson posted on 2022-4-30 23:20 First of all, s-domain analysis can be directly used as a mathematical tool to perform frequency domain analysis of signals or circuits. The connection relationship between each link is very simple to calculate...

Thank you so much