Questions tagged [laplace-transform]

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

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44 views

How to calculate damping ratio and natural frequency of a high order system?

To calculate the rate of damping and the natural frequency of second-order systems is easy, third order as well. How do I calculate the damping rate, natural frequency, overshoot for systems of order ...
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53 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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40 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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1answer
53 views

Phasors and Fourier Transform

I have always been told that for a sinusoidal variable (for instance a voltage signal), the fourier transform coincides with the phasor definition, and this is the reason why the analysis of ...
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2answers
71 views

Is the following op-amp-circuit-in-the-Laplace-domain analysis correct?

I am relatively new to analyze circuits in the Laplace domain. So I decided to solve some problems as an exercise. Below presented a problem and my solution to it and I have two questions: ...
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40 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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2answers
87 views

Solving capacitor voltage with Laplace

I saw this example and I got confused. The example shows: \$V_{C}(s)=\dfrac{R\parallel\frac{1}{sC}}{sL+R\parallel\frac{1}{sC}}V_{in}(s)\$ . Isn't it enough to express \$V_{C}(s)\$ with the voltage ...
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49 views

What is difference between natural response and zero-input response of a system and how to find natural response?

In most books it is said that natural response is another name to zero-input response while in some resources is is mentioned that the classification is based on poles of transfer function and input....
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71 views

Filter transfer function

I've the following filter circuit: simulate this circuit – Schematic created using CircuitLab The transfer function can be written as follows (I think): $$\frac{\frac{1}{\text{sC}}}{\frac{1}{\...
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1answer
31 views

determine the Laplace domain of this RL circuit

I am currently learning control system design. I have a lot of confusion about the initial conditions of the inductor in the circuit. Could someone please correctly solve this by getting the ...
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1answer
181 views

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
60 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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34 views

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
86 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
54 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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58 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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61 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
124 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
79 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
83 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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1answer
55 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
109 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
71 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
111 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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88 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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98 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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197 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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374 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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213 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
231 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
167 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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90 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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125 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
166 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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4answers
145 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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113 views

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
239 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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145 views

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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94 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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119 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
361 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
115 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
2k 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
161 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
319 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
1k 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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415 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
2k views

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
56 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 ...