Questions tagged [laplace-transform]

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

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8 views

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 ...
0 votes
1 answer
69 views

Who was the first person to use Laplace transforms for circuit analysis?

I am an electrical engineering student and I have been using Laplace transforms for circuit analysis. I would like to know: who was the first person to use Laplace transforms for the analysis of ...
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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 ...
0 votes
0 answers
41 views

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. ...
2 votes
1 answer
421 views

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(...
-1 votes
1 answer
98 views

How can I determine the circuit from a transfer function [closed]

I have identified a couple of transfer functions, which fit well to measured data, using MATLAB system identification toolbox. How can I determine a circuit diagram from these transfer functions? $$\...
1 vote
1 answer
1k 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 ...
1 vote
2 answers
80 views

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 ...
3 votes
4 answers
992 views

Why is a capacitor to ground a low frequency pole, instead of a high frequency zero?

In building my intuition about how analog circuits relate to the s-plane, I am wondering why a pole emerges from a capacitor to ground, for example in a simple lowpass filter consisting of only a ...
0 votes
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?
0 votes
2 answers
348 views

why transfer function of derivative controller is \$s\$ while Laplace of derivative is not only \$s\$?

For derivative controller transfer function, it's \$K_ds\$ but the Laplace Transform of \$\frac{df(x)}{dx}\$ is \$sF(s)-f(0)\$. For example if $$f(x) = \frac{dg(x)}{dx}$$ hence its Laplace will be $$...
7 votes
1 answer
363 views

Q: Homework - Past exam solution Is this the right solution?

I am trying to find Vo but I am not sure If this solution right? Is there a shorter path to find Vo? solution
1 vote
1 answer
63 views

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 ...
1 vote
1 answer
163 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=...
2 votes
1 answer
447 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 ...
0 votes
1 answer
235 views

How to determine the transient response of a circuit to causal periodic inputs?

As you know, analyzing a circuit with phasors provides only the steady-state response, and is only useful for sinusoidal signals and DC signals. Fourier series allow us to analyse a circuit with ...
0 votes
0 answers
55 views

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 ...
2 votes
3 answers
83 views

I am trying to find equations for i1(t) and i2(t) using laplace transform for this step input

The place that I am confused is that for \$i_1(t)\$ im trying to use the loop method to develop the first equation which is $$v(t)-L_1\frac{di}{dt}-(R_1+R_2)i_1(t)=0$$ and then use \$i_2(t)\$ for the ...
1 vote
1 answer
33 views

Inverse of \$e^{as}F(s)\$; t-axis translation rule

t-axis translation rule is easy to prove using the definition of laplace transform; the rule is: $$\mathcal{L\{u(t-a)f(t-a)\} = e^{-as}F(s)} $$ I know this works only when we shift the function to the ...
3 votes
2 answers
343 views

Laplace and time domain transform confusion with respect to RC low pass filter

I am a bit confused with Laplace domain and its equivalent time domain conversion Consider the s-domain of first order LPF filter which is $$\frac{V_o(s)}{V_i(s)}=\frac{1}{1+sRC}$$ Now for a second ...
2 votes
0 answers
41 views

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) -...
1 vote
4 answers
1k views

Why should an electronic circuit system be linear in order to use Fourier and Laplace transforms?

What I understood is, if we need to analyze a data from a system (such as damped oscillation or an output of an electronic circuit), the system must act in linear fashion to employ Fourier and Laplace ...
2 votes
2 answers
315 views

Time Reversal Operation for discrete time signals

For a discrete time unit step signal \$u(n)\$ , if time reversal operation is performed then it becomes \$u(-n-1)\$. Is it true for any discrete time signal \$x(n)\$ such that time reversal operation ...
1 vote
1 answer
69 views

Find \$v_0(t), t>0\$

In the circuit given below: $$v_s(t)=4e^{-2t}u(t), i(0)=1, v_0(0)=2$$ Find $$v_0(t), t>0$$ I assumed the current through capacitor is \$i_1\$. By KVL in first loop we have: $$v_s(t)-2(i(t)+i_1(t))-...
1 vote
1 answer
199 views

Transfer Function of 2 Loop RLC Circuit

simulate this circuit – Schematic created using CircuitLab For a problem I am tasked with finding the transfer function \$G(s) = \frac{V_o(s)}{V_i(s)}\$. I am having trouble defining the 2nd ...
0 votes
2 answers
99 views

Laplace of third-order lead-lag filter

For Butterworth low-pass filters, the Laplace function of the third-order filter is $$ H(s)= \frac {1}{\left(1+\frac{s}{\omega_c}\right)\left(1+\frac{s}{\omega_c}+\frac{s^2}{\omega_c^2}\right)} $$ ...
1 vote
3 answers
370 views

Solving RL circuit using Laplace

I've got this RL circuit: simulate this circuit – Schematic created using CircuitLab And the Vin(t): And I'd like to find Vout(t) using Laplace. I cannot figure out what the equation for this ...
4 votes
4 answers
157 views

Voltage calculation with Laplace

I was trying to find the transfer function of the following circuit, given the voltage on the inductor as output, and V as voltage input: simulate this circuit – Schematic created using ...
0 votes
0 answers
37 views

Why do we have two separate transforms for transforming a time domain signal to the frequency domain? [duplicate]

I know that Laplace transform and Fourier transform are not exactly equal; they will be equal when alpha = jω. But according to my understanding, both transforms convert a time domain signal to the ...
5 votes
2 answers
130 views

Determine \$i_L(t)\$of the RLC circuit

I have an RLC circuit that I am supposed to solve using s-domain analysis and I have gotten stuck when trying to transform back into time domain. I utilized node voltage analysis to determine the ...
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33 views

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 $$ \int_{t_{1}}^{t_{2}} |x(t)|e^{-\sigma_{0}}e^{-(\sigma_{1}-\sigma_{0})t}\,dt $$ ...
1 vote
1 answer
112 views

RL-circuit using Laplace

I have a series RL circuit (with zero initial conditions) and I want to find the voltage across the inductor. The formula I got is: $$\text{V}_\text{L}\left(t\right)=\int_0^t\text{V}_\text{in}\left(\...
1 vote
2 answers
63 views

Reverse Engineering Filter Laplacian Equation from Bode Plot

I am dealing with a particular filter that I was told has the response curve shown below in red. I am trying to figure out how quickly this filter could settle to n-bits from a step function input. I ...
0 votes
1 answer
62 views

Laplace transform, How to calculate the output of a system to a infinitely extending signal?

I need to calculate the output of a system given as \begin{align*} H(s) = \frac{s}{(s+1)(s+2)} \end{align*} For an input \begin{align*} e^{3t} \ \ \ \ \forall \ t \end{align*} I currently ...
-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 ...
1 vote
1 answer
84 views

How to calculate inverse Laplace of this response function?

Sorry for my English in terms of control theory - up to now I used only German phrases in that field. There is a controlled process of order 2 with $$F_p(s)=\frac{1}{(1+s)^2} $$ which shall be ...
2 votes
0 answers
72 views

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} &...
0 votes
1 answer
52 views

Discrete \$z\$-transform for deriving transfer function

I have a discrete linear system that reads as follows: $$ x_{i+1} = A x_{i-1} + Bu_{i-1} \\ y_{i} = C x_i + Du_{i} $$ The first equation is supposed to denote the discrete time evolution of some ...
0 votes
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. ...
3 votes
2 answers
234 views

Does the frequency response \$H(j\omega) \$ exist for system with unstable poles?

This question arose from a discussion between me and TimWescott in the comments here. The question is: Does \$H(j\omega) \$ exist for systems with poles in the RHP (unstable poles)? My own answer to ...
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0 answers
48 views

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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1 answer
242 views

Thevenin of DC circuits with inductors and capacitors

Can I use Thevenin's theorem for DC circuits containing an inductor or capacitor upon application of Laplace transform - bringing the entire circuit to the \$s\$ frequency?
1 vote
0 answers
43 views

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,...
2 votes
2 answers
384 views

Zero Order Hold Bode diagram

Here is the transfer function of the Zero Order Hold and its bode diagram: This transfer function is usually used for modelized a Digital to Analog Converter. Do you know why there is sharp roll off ...
0 votes
3 answers
94 views

Can't figure out this PMDC motor model

I was going through a series of experiments on PMDC motor where I found out the following block diagram representing the system: I'm new to this field and I'm trying to get a little ahead of my ...
1 vote
1 answer
43 views

Compensation Loop of a mixed system

I have a system which is a mixed system. The system is an analog and numerical system. I modelized the analog part and I know its transfer function which I do not want to modify. The numerical part is ...
1 vote
2 answers
290 views

Two representations of a circuit, what is the advantage?

Usually a circuit or system can be represented by its transfer function in Lapace domain or differential equations in time domain. For example, for the low pass filter below you could express them as: ...
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1 answer
1k 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....
0 votes
1 answer
130 views

Laplace transform problem

Can you help me with these laplace problems ? I'm having trouble understanding how to do it. ( u(t) is heaviside step function )
1 vote
1 answer
206 views

Is there a more simple and less confusing way of solving laplace-tranformation equations?

The picture I have shared below shows the laplace transform of the circuit. The calculations shown are really simplified. I know how to do laplace transforms but the problem is they are super long and ...

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