Questions tagged [laplace-transform]

Questions regarding or involving Laplace Transforms with respect to Electrical Engineering.

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Impact of PFC output impedance on the regulation of a converter

I have determined the transfer function of my converter operating in closed loop configuration. Nevertheless I saw on the web that the transfer function is not the same if my converter follows a PFC. ...
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Laplace analysis of coupled circuit confusion

So i solved this by first finding differential equations and then by taking laplace transform of them here are my working- for left loop $$5i_{1}\left( t\right) +4.9\dfrac{d}{dt}i_{1}\left( t\right) -...
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Representation of Fourier transform

I have a problem interpreting 2 different representations of Fourier transform and proving their property. In some texts Fourier transform is represented as: $$ \begin{align*} x(t) = \frac{1}{2\pi} &...
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Laplace tranfsorm of capacitor functions and initial conditions

I may be asking something trivial, but unfortunately, I could not find an answer so far. Suppose an AC circuit. The voltage of the capacitor is given by $$v_C(t)=Q(t)/C = 1/C [ \int_0^t i_C(τ)dτ + v_C(...
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Problem understanding transfer functions of second order filters

The transfer function of any second order filter can be found by analyzing the circuit using the Laplace transform. For example the transfer function of a second order low pass passive RLC filter ...
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Inverse Laplace Transform isn't A Contour Integral

I've learned about and used the Laplace transform in several signal processing classes and the inverse transform has always been defined as an integral like this: $$ \mathcal{L}^{-1}\{F(s)\} = \frac{...
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Equations governing the impedance of a generalised constant-phase element in the time domain?

I apologize in advance for the large wall of text, but I feel like to properly ask this question, some background information is in order. I've been recently working on modelling the impedance of a ...
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1 answer
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Type-2 compensator transient response

I'm looking to find the transient response to a step impulse of a type-2 compensator. I already found the transfer function, but when it comes to finding the transient response by using the inverse ...
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What is up with this series/parallel calculation? Inverse Laplace looks strange

I'm trying to find an analytic solution for this circuit. If the cap is inverted (series resistor to ground) the solution is straightforward. In this case I ended up with a strange cos term that makes ...
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1 answer
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Differential equation of a LC circuit in series with a parallel RLC circuit

I have the following RLC circuit. I am having trouble finding an expression for the natural response of this circuit. I found a similar question, but I was unable to simplify exactly like was done in ...
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What can I conclude about the ROC of a transfer function in discrete time

I have a discrete system with transfer function $$ H\left(z\right)=\frac{a_{2}b_{2}z^{-2}+\left(b_{2}a_{1}+b_{1}\right)z^{-1}+\left(b_{0}+b_{2}\right)}{a_{2}z^{-2}+a_{1}z^{-1}+1} $$ Where \$ a_1,a_2,...
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Conceptual question regarding the Laplace transformation

In preparation for an exam in linear signals and system my instructed handed us a couple of conceptual questions that should prepare us. I ran into the following: Which statements regarding the ...
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Have I correctly solved this RLC problem?

Now I needed to find the transfer function as well as impulse response $$\\ R=14\Omega \\ L=2H \\ \\ C=\frac{1}{12}F \\ In \ s-domain \\ R=14\Omega \\ L=sL=s\cdot 2=2s \\ \\ C=\frac{1}{sC}=\frac{1}{s\...
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Is the region of convergence of Laplace transforms of a right-sided signal right of the rightmost pole?

I know that the ROC of a right-sided signal with a rational Laplace transform is right of the rightmost pole. Does it apply to any right-sided signal?
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how LTspice integrates Laplace in the time domain?

I modeled two different PID controllers with Laplace and with the same control parameters in LTspice, but the results show me the same behavior of the two PID controllers in ...
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How to do Transient analysis?

Consider the above example earlier I used to form a differential equation and then do its solution using Laplace,but for this example the differential equation comes out to be non-ordinary. Please ...
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Circuit analysis - laplace transform

So i have a circuit where R1 = 5 W, R2 = 2 Ω, L = 1 H, C = 1/6 F ja E = 2 V. And i need to figure out what is iL when t=0.5s with laplace transform. Switch opens when t=0 When t<0 i got ...
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Why the driving point functions have the condition that the degree of numerator and denominator only at most differ by one?

I do not understand the logic behind this restriction. What would go wrong if this condition is not fulfilled? E.g, in frequency domain \$\dfrac{1}{(s+1)^2}\$ which has an inverse Laplace of \$t \...
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How to measure a DC motor's inertia

I want to measure the inertia of a DC motor. However, I have no idea how to measure or calculate this. I need the inertia to determine the numeric transfer function for voltage to angular velocity. ...
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2 answers
63 views

How do I find Vo in the circuit?

I1 + I2 = I3 I1 = Vi/Z1 ... Z1 = (1+sCR1)/sC I1= Vi(sC)/(1+sCR1) I2= Vi/R1 I3= -Vo/R1 I1 + I2 = I3 Vi[(sc)/(1+sCR1) + (1/R1)] =-Vo/R1 -Vi[(R1sC)/(1+sCR1) + 1] = Vo How do I change back to time domain?
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Why are they called delayed integrators

I'm quite confused as to why we call a system with transfer function $$\frac{1}{s+\alpha}$$ a delayed integrator. It does not seem to be an integrator in the first place since it convolves with an ...
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Trying to prove a property for the region of convergence of a Laplace transform

I've been studying Schaum's outlines for Signals and Systems, and came across this: And I understood the part until $$ \int_{t_{1}}^{t_{2}} |x(t)|e^{-\sigma_{0}}e^{-(\sigma_{1}-\sigma_{0})t}\,dt $$ ...
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Why ROC is important in Laplace transform

For example there is a function 1/s where ROC is Re(s)>0, but why is this important and what we can see from ROC? What is the practical reason we calculate ROC, when it doesn't contain poles?
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Circuit analysis problem involving Fourier series

Please help me with this problem I can not solve this. It is about Fourier series. It is so hard.
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42 views

Laplace Domain Transfer Function for Feedforward System

I am trying to obtain the overall transfer function of this feed-forward system which consists of an oscillating input being mixed with a local oscillator to create a mixed signal as the output. G1 ...
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Laplace transform to Z-transform for filter design

I was given an answer to the following question I can't understand, that how is the Impulse Invariance transformation of $$\frac{(s+a)}{(s+a+jb)(s+a-jb)}$$ is $$\frac{(1-e^{-aT} cos(bT) z^{-1})}{(1-e^{...
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51 views

Integration of exponential function and square-wave

How do I evaluate, \begin{equation} \int_{0}^{t} e^{c\tau}sqw(\frac{\tau}{T})d\tau \end{equation} where $$c < 0$$ and \$sqw(\cdot)\$ is a periodic function over \$t\in[0,T)\$, \begin{equation} sqw(...
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346 views

how to simulate a Laplace function of a PID controller in the time domain with LTspice

I tried to simulate a Laplace function of a PID controller with LTspice in the time domain, but an error message appears "The laplacian is singular at DC". cs1 is the controller, so I just ...
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Laplace transform - How to determine the initial conditions of the derivative functions

I m trying to get the transfer function of this circuit. I do it essentially for fun. I clearly a newbie about Laplace's transformation. Nevertheless here is the circuit : Here is the differential ...
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How can I build proper laplace RLC circuit

I think there are two different circuits over the picture. But for equations they are acting same to me. I mean DC source of left circuit look like an initial voltage for C. After inver Laplace I have ...
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120 views

Laplace Transform

can anyone help in finding the expression for the voltage at the output of the circuit if the input is a step function with 1V amplitude. simulate this circuit – Schematic created using ...
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159 views

Analysing an s-domain circuit with multiple sources

So I am working on the following circuit: I have already worked my initial conditions and the next step is to perform analysis of the charged up circuit. My charged circuit is shown below: The ...
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1 answer
123 views

If I look at a signal in its frequency domain, are there some guidelines by which I can tell how that signal looks in the time domain?

I was studying the Laplace transform and the Fourier transform, and I can't figure out if there is some intuitive way of finding out how a signal looks in the time domain if we know its frequency ...
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134 views

Phase, Frequency and Laplace transform

I have a doubt on the relationship between phase and frequency. We know that the definition of angular frequency is: ω(t) = d(\$phi\$(t) / dt, where \$phi\$(t) is the istantaneous phase of our ...
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2 answers
333 views

How do I refer the transfer function of a system from its Laplace equivalent?

I have a problem, I know how to analyze circuits in Laplace domain to get the transfer Laplace function. However, I don't know how to translate the answer to "real life" Suppose that I have a ...
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1 answer
45 views

AC signal analysis: Voltage dip (amplitude dip) at time = 0

I'm working on a series RLC problem where the input voltage is a sinusoidal function for all time. The catch is, for t < 0, the sinusoidal function is of greater magnitude than t >= 0. There is no ...
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How to get the transfer function of electrical network using nodal method

We have the following circuit: I am trying to get the transfer function using the Mesh Method. The first equation I've got is: (s+1) I1(s) - sI2(s) = Vi(s) The ...
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How to choose coefficients to compute surface LaPlacian filtration of analog sensor data?

Surface LaPlacian filtration is used (among other things, probably) to improve spatial resolution of analog sensor data, particularly in the context of electroencephalogram (EEG) and the ...
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How to make a state space model of en electrical RLC-circuit?

I want to learn how to build a state space model of an electrical RLC-cicuit. I don't know how to do that. So I will try here and check if I have done it right. Focusing on L1: $$ L_1 \dot{I_1} = U -...
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Laplace Transform without given continuity variables

simulate this circuit – Schematic created using CircuitLab So I was trying to solve problems in preparation for an exam regarding Laplace Transforms. I was able to solve some problems and then ...
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1 answer
138 views

2nd Order Differential circuit convert to Laplace domain

The circuit is closed At t = 0 , initial state of capacitor v(0-) = 1v and inductor i(0-) = 0A. My problem is when I convert this circuit into Laplace domain resistor become 2 and inductor become S. ...
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-1 votes
1 answer
126 views

Help with inverse Laplace of a circuit solution in time domain

A part of a circuit has the transfer function in s domain as: H(s) = R / (s×R×C + 1) V(s) = I(s) × H(s) and the input is a pulse current with an area: 1, pulse duration: a and amplitude 1/a. And its ...
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-2 votes
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RLC-circuit, laplace transformation

So i have a circuit where R1 = 5 Ω, R2 = 2 Ω, L = 1 H, C = 1/6 F ja E = 2 V. And i need to figure out what is iL when t=0.5s with laplace transform. Switch opens when t=0 When t<0 i got ...
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  • 23