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Questions tagged [laplace-transform]

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

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Impedance calculation from voltage and current (exponential) waveforms

If we want to find the impedance across two terminals (a port) at a frequency \$\omega_0\$ using the voltage waveform across \$v(t)\$) and current through (\$i(t)\$) the terminal, general intuition is ...
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1answer
52 views

How do I calculate this inverse Laplace Transform

I have this transfer function and input, and I have to manually calculate what the systems response will be. The transfer function is: and the input is: I multiplied the two functions and used ...
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0answers
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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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2answers
83 views

How to tackle circuit containing time variable resistor?

simulate this circuit – Schematic created using CircuitLab For instance above schematic find current as function of time in circuit above I studied it about months before and am not able to ...
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1answer
45 views

Using laplace transform to find the expression for voltage in the circuit

Let's say we have the following circuit: Generator in the circuit has sinusoidal waveform \$u_g(t)=\sin\omega t\$. Other known values: \$ L=0.25H\\ R=1\Omega \\ C=0.5F \\ \omega=1 \frac{rad}{s} \\ k=...
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2answers
56 views

Time to Frequency Transform - Where are the Initial Conditions?

In a circuit with sinusoidal source and charged capacitors and inductors we have initial conditions: $$u_{C}=u(0)+\frac{1}{C} \int_{t_{0}}^{t}i(\tau)d\tau$$ $$i_{L}=i(0)+\frac{1}{L} \int_{t_{0}}^{t}...
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2answers
39 views

Frequency Response Function Estimate via FFT Question

I want to estimate the FRF of a dynamic LTI system given experimental input and output data. I know generally the approach is to use a chirp as an input to make sure enough frequency content is ...
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42 views

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
108 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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1answer
59 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
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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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1answer
37 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
95 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
61 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
72 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
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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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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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1answer
172 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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231 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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0answers
61 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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174 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
195 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
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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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2answers
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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
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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
127 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
143 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
174 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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1answer
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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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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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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
320 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
98 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
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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
153 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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1answer
274 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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1answer
979 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
349 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
55 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
456 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
46 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
109 views

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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1answer
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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
120 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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0answers
561 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
773 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
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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 ...