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Questions tagged [laplace-transform]

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

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How do you reduce this simple system diagram for the sake of doing algebraic manipulation?

My guess is that since H(s) is parallel with 1(s) we'd do A(H - 1)? But this is my first ...
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1answer
90 views

What is the practical use of Laplace Transform?

I am trying to understand the electrical model of 3-phase Induction Model. The rotor of the motor is modeled as a variable resistor in s-domain. I fail to understand how that works practically. Can ...
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52 views

Analyzing circuit with dirac delta current source without using Laplace transformation

At \$t=0\$ the switch is closed and \$v_o(0)= -5 V\$. The problem asks for \$v_o(t)\$. I did it using Laplace method and get $$v_o(t)=5+10\,e^{-2t}$$ which does not even satisfy the initial condition,...
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2answers
70 views

Meaning of transfer function in s evaluated at a complex number

From the pole-zero plot, you can compute the system frequency response by assuming a locus of test points along the \$j\omega\$ axis. Figure from: http://web.mit.edu/2.14/www/Handouts/PoleZero.pdf \...
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34 views

Solving a RLC circuit with a charged L and C

I've the following circuit: The input current is given by (the pules endures \$1/20\$ seconds and starts at \$t=0\$): $$\text{I}_{\space\text{in}}\left(t\right)=\max\left\{\mathcal{L}_\text{s}^{-1}\...
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1answer
33 views

RC circuit with pulse input voltage; finding the time constants

I've the following circuit: Question: What are the time constants of the voltage at node \$\text{Y}_2\$ when the up part of the puls comes and when the down part of the puls comes? MY WORK: The ...
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2answers
77 views

Confusion about Laplace and frequency response of a electrical circuit

I have a confusion between the Laplace transform of a circuit and the frequency domain AC analysis. Suppose we have a series RLC resonant circuit connected to an ideal sinusoidal voltage source. We ...
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1answer
51 views

RLC bandpass filter

I am working on a circuit: simulate this circuit – Schematic created using CircuitLab My goal is to find \$ \omega_0, \beta, \$ and \$\varrho \$ The way I approached this problem was to ...
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1answer
40 views

Problem related to the transfer function of RC low pass filter

I have the following question: For the passive RC low pass filter shown below: $$V_S(t)=\cos(t)+\cos(100t)$$ $$V_0(t)=\alpha\cos(t+\theta)+\beta\cos(100t+\phi)$$ (where \$\alpha\$, \$\beta\...
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2answers
65 views

Why inverse of time delay is non causal

Please explain the following statement "If \$P(s)\$ contains a time delay term, \$P^{-1}(s)\$ is non-causal". Here '\$s\$' is Laplace variable. Can someone please explain the reason of non causality?
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2answers
86 views

Combining two ideal voltage sources with an impedance between them

Solving a problem, I came across the following source transformation:        My question is: I know that I can do the following:       &...
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156 views

Degenerate circuit concept and its theoretical and practical implications

I came across with the term "degenerate circuit" when I was studying solving linear differential equations with Laplace transform. I have learned that a system is called degenerate when the ...
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151 views

Laplace transforms for transient analysis

simulate this circuit – Schematic created using CircuitLab For t<0 the switch is opened. Att=0 the switch is closed. ...
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60 views

Laplace with source before and after t=0

In my course, there is the following excersise that I should transform to Laplace. I understand that the initial conditions are 3V for the capacitor. For DC current, the capacitor is open-circuited ...
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118 views

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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3answers
163 views

Why do we use Laplace transforms to analyse transient circuits?

I just learned transient circuits and we solved them both in the time domain and the Laplace domain and I can't understand why we would use the Laplace domain as it seems it is a lot more simple to ...
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2answers
115 views

How do I calculate the current in this circuit using Laplace transforms, with a time shift?

In this exercise I have to calculate i(t) and the switch occurs when t=0.01 s, I tried doing it using Laplace but I always get the wrong answer. I did an exercise that is exactly like this one except ...
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84 views

What is the physical meaning of the voltage across an inductor in the Laplace domain?

In my Electrical Engineering degree I recently learned how to analyse circuits using Laplace transforms and I know that the Laplace transform of the voltage across an inductor is \$V_L(s) =s*L*I(s) - ...
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2answers
116 views

Transfer Function: Trying to understand the Laplace analysis of this circuit

I am trying to do the transfer function of this circuit and also trying to understand the frequency domain thing of the Laplace transform. I want to do a transfer function of VA/V1, considering B to ...
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3answers
115 views

What is the time derivative at t=0 for a second order low-pass step response?

For a first order system like an RC filter you have something like $$y(t)=1-e^{-\frac{t}{\tau}}\\ y'(t)=\frac{1}{\tau}e^{-\frac{t}{\tau}}\\ y'(0)=\frac{1}{\tau}$$ But for a second order system there ...
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Applying Laplace and Tension Divisors

INTRODUCTION The question asks for acquiring, in the time domain, the output when \$V_i(t) = t * u(t)\$ from a given circuit (image below); First, you need to transform the simple circuit into it's ...
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4answers
137 views

How to find the system response given the transfer function without using Laplace transforms?

The given transfer function is: $$\frac{6p+100}{p^2+12p+100}$$ and inputted into the system is a unit step response: $$r(t) = \left\{\begin{array} f0 & t < 0\\1 & t > 0 \end{array}\...
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3answers
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Why is there a sudden change in current between \$t=0^{-}\$ and \$t=0^{+}\$ when an active inductor is connected in series with a relaxed inductor?

For the above question I drew the corresponding Laplace transform diagram, as follows (didn't draw the switch since it basically open circuit after \$t=0\$): simulate this circuit – Schematic ...
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1answer
127 views

Determine by the order of transfer function what kind of filter

How can I determine by looking at the following tranfer function, that is this the transfer function of a band-pass filter: $$\frac{1}{as^3+bs^2+cs+1}$$
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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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2answers
70 views

How do I compensate for Exponential decay in an op-amp circuit

Using an oscillator, I want to provide a square wave input to the second opamp circuit shown in the provided link(But using IC741 instead), the problem is in s domain: I get a voltage input of 1/(s^s+...
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2answers
116 views

Algebraic way for finding a transfer function of a filter

I've the following filter and I tried to write the transfer function for it: simulate this circuit – Schematic created using CircuitLab And I wrote for the current nodes the following ...
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1answer
272 views

Calculate transfer function H(w) of Schmitt trigger with RC at inverting input

I have got the following Schmitt trigger circuit implemented already on a breadboard. As seen, the input signal at the non-inverting and inverting terminals of the op amp is the same, but with the ...
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2answers
90 views

Transient analysis with Laplace and nodal analysis error

Have the schematic: Solving using MathCAD: There is an error in my equations with nodal analysis but I can't find where? May anyone help me? I also add the solution using approach of series RLC ...
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2answers
800 views

Is low pass filter more commonly used than high pass filter?

I have heard my teacher saying** that low pass filter is more commonly used than high pass filter because in high pass filter, frequency increases with gain and thus noise also increases and thus it ...
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3answers
143 views

Does an impulse function at t=0 go to infinity, or 1?

Impulse function is basically the derivative of the step function u(t): $$ u(t)= \begin{cases} 0 & \text{if $t<0$} \\ 1 & \text{if $t\geq0$} \end{cases} $$ I was taught that in laplace ...
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239 views

Find inductor current with Laplace

I need to find the inductor current for t > 0 and initial conditions as in example below. I think it's enough to divide V1 by 5*s and take the inverse Laplace Transform but my answer 3*e^-2*t - 7*e^-t ...
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817 views

Obtaining Bode plots by using Laplace transform and time domain data from SPICE

An active filter is given as(for this question the filter can be any other filter): In LTspice in time domain, I apply a step function V(in) and obtain V(out) plots as below(I skip initial op. point ...
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1answer
315 views

Convert Current source to Voltage source in Laplace domain

Is it possible, once I've converted the circuit diagram into its Laplace equivalent, to replace a current source which is in parallel with, in this case, a resistor and inductor by the usual V=IR ...
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1answer
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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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1answer
54 views

laplace inverse transformation

So I have have an equation and I need to do laplace inverse transformation $$ I(s)=\frac{s}{7s+6} $$ and then for partial fractions I got $$ I(s)=1/7-\frac{6}{49s+42}$$ and now for inverse transform ...
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1answer
419 views

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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0answers
45 views

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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1answer
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Find the transfer function of the system given by its weight function

I've understood that, to find the transfer function of a system, given its weight function, Laplace transform should be used. I.e. if $$w(t)=50\,\cdot(e^{-5t}\,-\,e^{-10t})\,\cdot\,u(t)$$ then $$W(s)...
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Inverse Laplace via Decomposition Theorem

The original query is to find x(t) with a Laplace transform of X(s) = 4(s+1) / s(s+2)^2. The poles are s_1 = 0 and s_2 = -2 (with a multiplicity of 2). Because the second pole is not simple, its x(t) ...
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2answers
109 views

Question about transient behaviour in op-amp circuit

Consider the following circuit. The switch closes at \$t=0\$. The voltage source is \$V_0e^{-t/t_0}\$. We assume to op is ideal, so there's no voltage difference between the input terminals and no ...
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470 views

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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3answers
682 views

How Fourier transform be able to deal with transients?

Below is what Matt L.said in the thread here. Could anyone clarify how Fourier transform be able to deal with transitents? Reading that thread many times but I couldn't figure it out. Note that ...
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1answer
2k views

Meaning of Sigma in Laplace transform

I found the question below in a forum and I also have same problem. Unfortunately, there is no answer at all so I will post it here hope someone could make it clear. A gain relation in a circuit of ...
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1answer
319 views

Use of Heaviside operator versus Laplace transform in electrical engineering

Is there a significant difference between Heaviside Operator p and Laplace transform operator s? I'm wondering why Laplace transform is more commonly used to solve electrical circuits than using ...
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2answers
2k views

laplace transform on simple low pass filter in python

Looking at the first picture in the link, showing a simple graph of an with- and without bypass filter circuit voltage difference, i wanted to recreate this picture. I have coded the noise and ...
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1answer
133 views

The current I=-10e^-2t,Find the voltage of the source Vs?

This is the Question Attempt: I Solved this circuit with two different method like this Now In the laplace transformation method I am getting an extra term that is first derivation of impulse(...
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Unity negative feedback controller, why does Gain K go on the numerator of the transfer function

I have a system G(s). It has no zeroes, but some poles. When applying unity negative feedback, with a static gain K, why does K remain on the numerator of my transfer function T(s) which describes ...
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1answer
2k views

Laplace of Sinc? [closed]

How can I find the Laplace transform of a sinc function? Inserting \$f(t) = \frac{\sin(t)}{t} \$ into \$F(s) = \int_{0}^{\infty}e^{-st}f(t)dt\$ gives three functions dependent on variable t within ...
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3answers
650 views

Transfer function of a rotary encoder

First of all, I would like to tell you that this is my first question on this forum and I found your topics and your answers very useful during my academic years so thank you all. At the moment I have ...