Questions tagged [laplace-transform]

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

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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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inverse laplace transform with case distinction

We have to find the missing 2 cases for the inverse laplace transform y(t) of Y(s). Which theorem do we have to use to find these cases? How come the given solution is specifically for case t>=2?
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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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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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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 ...
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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 ...
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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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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))-...
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Laplace of third-order lead-lag filter

For Butterworth low-pass filters, the Laplace function of the third-order filter is $$ H(s)= \frac {1}{\left(1+\frac{s}{\omega_c}\right)\left(1+\frac{s}{\omega_c}+\frac{s^2}{\omega_c^2}\right)} $$ ...
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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 ...
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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 ...
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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 ...
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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 ...
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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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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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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(\...
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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 ...
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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 ...
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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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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 ...
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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 ...
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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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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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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
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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?
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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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2 votes
2 answers
317 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 ...
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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 ...
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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 ...
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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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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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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 )
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How to separate transient and steady state solution when using the Laplace transform?

When we find the solution of a system using the Laplace transform, it gives a complete solution unlike the differential equation approach which gives the transient part the steady state part ...
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Is it possible to syntethize this Voltage Transfer Function?

I have the following voltage transfer function: $$ H(s) = \frac {a s^4 + b s^2 + c}{p s^4 + q s^2 + r} $$ Where \$a, b, c, p, q, r\$ are all real constants. The only method I have been taught to ...
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Why can't you get the transfer function in time by taking inverse laplace of the transfer function in laplace?

In the KD9PDP's answer in the post below why can't you calculate the transfer function in time by taking the inverse Laplace transform of the transfer function in Laplace domain? The original post: ...
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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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Differential Equations vs Phasor vs Laplace

I've just read a book on basic circuit theory and I'd like to understand the pros and cons of each analysis method. Time Domain Usually ends up in differential equations for reactive circuits. Gives ...
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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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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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Application of Laplace Transform to Circuits containing Diodes, etc

Can I use the transform methods and treat the "approximated" diode, say Silicon, as a 0.7 Volts power source and convert it into the S - domain, 0.7/s ? Are there any advance methods for ...
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Laplace and KVL

I was preparing for my exam by solving questions and there is this one question I was stuck on but when I saw its solution provided by book, I think KVL applied is not right or I am not able to ...
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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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Analyzing effects of sixth order transfer function

This question is in relation to this question asked before (Settling time of sixth order denominator transfer function), but formulated in greater details. So I have a transfer function which looks as ...
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When/why is the solution for an RLC circuit differential equation actually useful? [closed]

Maybe it's an obvious answer that I'm missing, but I was trying to apply the Laplace transform to a differential equation for a maths assignment, and an RLC circuit differential equation was one of ...
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Settling time of sixth order denominator transfer function

I have a system whose transfer function is as follows $$ \frac{V_o(s)}{V_i(s)}=\frac {\text{numerator}(s)}{a_1 s^6 + a_2 s^5 + a_3 s^4 + a_4 s^3 + a_5 s^2 +a_6 s + a_7}. $$ I am interested in the ...
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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 Domain Representation for Phase Detector

I am trying to model an LTI system and determine the overall transfer function of the system. The setup consists of a laser signal being fed through some filters, amplifiers, etc. represented by ...
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Time constant of Transfer function

I have a transfer function as follows - $$ G(s) = \frac{320 (1-4s)e^{-3s}}{24s^2+28s+4} $$ I calculated its time delay as 3 sec, gain as 80, but confused in finding the time constant. I know the time ...
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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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Finding transfer function by linear system

Here's the system: $$\begin{cases} z(t)=h_1(t)*x(t) \\ w(t)=z(t)+h_3(t)*y(t) \\ y(t)=h_2(t)*w(t) \end{cases}$$ And $$\begin{cases} h_1(t)=\exp(-3t)u(t-t_0) \text{, with $t_0$ positive} \\ h_2(t)=...
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