Questions tagged [transfer-function]

Anything related to transfer functions, i.e. those complex-valued functions of a complex variable used to model mathematically the I/O relationship of linear time-invariant initially-at-rest system using Laplace transform.

Anything related to transfer functions, i.e. those complex-valued functions of a complex variable (typically named s, a.k.a. complex frequency) used to model the I/O relationship of linear time-invariant (LTI) initially-at-rest systems using Laplace transform.

Given an LTI analog system whose impulse response is \$h(t)\$, its transfer function is $$ H(s)=L[h(t)] $$ Where L indicates the Laplace transform. It turns out that the zero-state response \$y(t)\$ of the system to the input signal \$x(t)\$ can be easily obtained in the s-domain by the formula: $$ Y(s) = H(s) X(s) $$ where uppercase letters indicate the Laplace transform of the signals involved.

See also Wikipedia on transfer functions.

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Poles and Bode Plots

I have three questions that have been troubling me for a long while: We say that, in a Bode plot, there is a drop in gain of 20 dB per decade whenever a pole is encountered. But aren't poles defined as the values of \$s\$ which make the transfer…
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Difference between natural response and forced response?

Reference Second post on EdaBoard.com Time response of a system is the time evolution of the variables. In circuits, this would be the waveforms of voltage and current versus time. Natural response is the system's response to initial conditions…
bluejamesbond
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Signal Flow Graph for electrical circuits

I am a student and my question is about finding the signal flow graph for a simple circuit. I found the above formula for a \$k\$ node having \$U_k\$ potential. In the book it is said that this is a base for building the signal flow graph using…
NumLock
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What is the difference between frequency response and transfer function?

I would like to understand the difference between frequency response and transfer function. I know the former can be obtained by substituting \$s = j\omega\$. But what is the difference in information I can get from both representations? What are…
luis
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What is causing this long tail in the transient reponse?

I have a fifth order transfer function for which I designed a controller using pole-zero cancellation technique on a root locus. I am targeting \$<5%\$ overshoot and \$<2s\$ settling time. Currently, the overshoot criteria are satisfied. Note I know…
rrz0
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Why do we use step response?

We tend to identify systems more often by using the step response. Why? Especially when the impulse response is directly related to the transfer function?
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Meaning of zeros in transfer function

Can someone please explain, provide a link or cite a book where the properties of the zeros for continuous and discrete time systems are explained? I know that the zeros are the frequencies where the numerator of a transfer function becomes…
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What does a Bode plot represent and what is a pole and zero of a Bode plot?

I studied Bode plots and the author of my book is somehow relating zeros of transfer functions to Bode plots. What is the relation between zeros or poles of a Bode plot and transfer function? We usually take zeros at \$s=-a\$ (let's say) but how…
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Transfer function with current source

I have been trying this exercise for a while and I can't solve it. What they ask me to find is $$\frac{V_2\left(s\right)}{V_s\left(s\right)}=?$$ My best attempt has been the following \begin{array}{l}\left[1\right]\…
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Finding the Transfer Function of Spring Mass Damper System

I have been going through Ogata Modern Control Engineering book and working through several exercises to improve my understanding of basic control principles. I came across the following example which I am struggling to solve. I need to come up with…
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Significance of cut-off frequency in a low-pass filter

My question is: why do we choose cut-off frequency to satisfy that the magnitude of transfer function \$ H(\omega) = \frac{1}{\sqrt{2}} \$? Therefore I am not asking how cut-off frequency is calculated as \$ \sqrt{\frac{R}{L}}\$, but I am asking why…
Binary Yildirim
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What is the significance of the standard form of 1st and 2nd order transfer functions?

A standard form of a first order differential equation is: (1) $$\tau \frac{dy}{dt} + y = k * x(t)$$ The laplace transform of this: (2) $$G(s) = \frac{Y(s)}{X(s)} = \frac{k}{\tau s+1}$$ but sometimes it is given as (3) $$H(s) = \frac{1}{\tau s +1} =…
Blue7
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Is every linear circuit equivalent to a single RLC series circuit?

Is every linear circuit equivalent to a single series RLC circuit? If not, can one determine from the transfer function of the linear circuit whether or not it is equivalent to a single series RLC circuit; that is to say, what form (zeroes and…
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What do the poles and zeros of a system physically represent?

I've been working with transfer functions and control models for a while, but I never really have gotten an intuitive understanding of what the poles and zeros of a system really represent. I was wondering if anyone would be kind enough to offer an…
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Is there an English word for the output response of a non-minimum phase system?

I've noticed in some French language control courses they have a word for the initial part of the response of a non-minimum phase system. They say it has "un départ malin". I looked up malin and it means different things in English, for…
Bill
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