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Questions tagged [laplace-transform]

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

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ROC of Laplace Transform of a time shifted impulse signal

If x(t) is of finite duration and is absolutely integrable, then the ROC is the entire s-plane. This is stated and proved formally in the book of signals and systems by Oppenheim in the context of ...
aditya siroutiya's user avatar
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Unilateral laplace transform of rect(t/2)

What would be the unilateral laplace transform of rect(t/2)? We know that rect(t/2) can be written as u(t+1)-u(t-1).So what would be its unilateral laplace transform? Should it be (exp(s)/s)-(exp(-s)/...
Abrar Fahim's user avatar
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How can I do inverse Laplace of this transfer function to get the step response of the RLC circuit?

I have found this to be my transfer function for the circuit. I have tried doing partial fraction decomposition, but I end up with an s on top which I don't understand what to do with.
Even's user avatar
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How to compute Vgs(t) for circuit below?

Does anyone know how to compute the Laplace and inverse Laplace transform to find vgs(t) for turn on transient for circuit below? Zener diode is of 6.1V.
User691's user avatar
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How to derive Laplace and Inverse Laplace equation for RCD level shifter for SiC MOSFET?

Does anyone know how to get Equation 7 from Equation 5 and 6, shown in the picture? Or any other method for the circuit analysis on getting Eqn 7? Attached also the schematic diagram of the process ...
User691's user avatar
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Nyquist stability criterion in discrete time domain

I've been transforming systems from the s-domain to the z-domain, and looking at the Nyquist plots I get in the z-domain. So far I've assumed that the Nyquist stability criterion that applies in the s-...
Mr Phase Locked Loop's user avatar
2 votes
1 answer
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Electrical network transfer function

I am trying to solve this problem, and my answer is wrong. I suspect that I messed up the Laplace transform of the voltage source. However, I saw this in the book and thought I could simply use it. ...
spinachpizza_'s user avatar
3 votes
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Using Laplace transform to solve integrator circuit

I need to find Vout in time domain for below circuit. Here's my attempt, using Laplace transform. $$V_{in}(t) = V_0 \sin(\omega t)$$ From the above equation, Vin in s-domain is then: $$V_{in}(s)=V_0\...
user97662's user avatar
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What is the differential equation that relates input and output voltage of a circuit?

I have the transfer function of this circuit, which is I am being asked to find the differential equation that represents the relationship between input and output voltage. Since the transfer ...
newbie's user avatar
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How to find poles and zeroes in this kind of transfer function?

How do I find poles and zeroes from this complex transfer function? $$ H(s) = \frac{2959}{100\,s} - \frac{ 171\, \Gamma\left( \frac{7447}{10000} \right)} {200\, s^{7447/10000}} $$ I used the ...
igor's user avatar
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Find R, L and C in RLC series circuit given voltage over capacitor and current through inductor

I have a couple of exercises in my textbook (Fundamentals of Electric Circuits 6th edition) that look like the following: To solve this problem, my first idea was to transform it into the laplace ...
Tom Cajot's user avatar
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Using impedance to get RLC Transfer Function

I am trying to get the transfer function G(s)=Vo(s)/VI(s) of this circuit and I am lost. I know that in the s domain, L=sL and C=1/sC. I tried to calculate it already and got R+(Ls)/((Ls^2)*C+1). But ...
newbie's user avatar
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How to do Laplace transforms?

The above image is just an example of a piecewise function. From the image you have to write the function and then move things around until you can use some of those Laplace transform equations from ...
JohnnyB's user avatar
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Initial conditions in a circuit with two ideal transformers [closed]

I don't know how to determine initial conditions in Laplace transform for a circuit or a system of circuits with ideal transformers with neither mutual inductance nor coupling coefficient is given. I ...
Mertlious1's user avatar
1 vote
1 answer
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PLL Theory - Laplace Transform

[Design of Analog CMOS inteagrtaed circuits by Razavi] Can someone explain what Lapalce transform rules states that this is possible? They have a function of excess output phase / excess input phase ...
muosac's user avatar
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Different answers from mesh analysis and voltage division

This is a problem solving for the voltage across a capacitor with initial conditions. After finding initial conditions and transforming into s-domain, the circuit looks like this: So, the voltage we ...
SunriZe225's user avatar
8 votes
3 answers
653 views

Trouble with filter using Laplace transfer function in LTSpice

I would like to introduce an ideal 5th-order Bessel filter to my simulation. My initial thought is to use a voltage-dependent voltage source and Laplace transform. I copied the Bessel filter ...
Wintermute's user avatar
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Confusion about the initial condition for Laplace transform

I was trying to solve this question with Laplace transform, but I am confused in this question. My confusion is that whether we have to include the initial condition of the capacitor or not. Because ...
Preet's user avatar
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Why is the voltage across a capacitor in the Laplace domain equals I(s) / s?

The original transfer function is I(s) over V(s) for a basic circuit that contains a resistor, inductor and a capacitor with a voltage source (Basic RLC circuit) where R is the resistance of the ...
SwiftEnthusiast's user avatar
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How can I find the transfer function with Laplace in the (s) domain?

How can I find the transfer function for this circuit with laplace in the (s) domain?
genci_andonihotmailcom's user avatar
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Why does MATLAB show a pole in bode plot of an underdamped second order system at natural frequency?

I am using the sisotool in MATLAB to obtain the bode plot of the following transfer function: MATLAB marks a pole at wo which is approximately 11.18 What is the meaning of this? How would you even ...
needbrainscratched's user avatar
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Integral Controller design

For this system, what method do I use to select a value of Ki? Gh and Gt are first-order blocks with time constants Th and Tt-
diode's user avatar
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Find the range of variables based on the steady-state response

I have a transfer function as below: $$ G(s) = \dfrac{s(s+2)}{s^2+(b+2)s+ab} $$ Now with input as $$ u(t) = \sin{t} $$ The maximum steady-state response of y(t) is less than 1, I would like to ...
Sonamu's user avatar
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Laplace transform of multiple sources in a circuit

I came across this circuit and couldn't solve it. From what I know the Laplace transform of a DC source would be the constant divided by the \$s\$ variable. However, does this only applies to sources ...
Alex Lim's user avatar
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Is the Laplace transform of an integral the same as the Laplace transform of a constant?

I was analyzing the circuit of an amplifier to know its response, the schematic is the following: What I did is the following: I considered \$(v_{in}\$ as the input signal; \$v_{out}\$ as the output ...
ThreeNamesGrace's user avatar
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1 answer
344 views

Transfer function of capacitor and resistor connected in series and one resistor connected in parallel with the capacitor

I have been trying to derive the transfer function H(s) of the circuit diagram. I know how to derive CR circuit, but I'm stock on connecting another resistor with the capacitor. Can anyone help me ...
juneymoon's user avatar
1 vote
3 answers
261 views

Find the transfer function H(s) assuming a signal input i,in(t) and signal output, i,out(t)

I am having trouble answering this question for my Signals and Systems class and would appreciate any assistance. Find the transfer function, \$H(s)\$, assuming a signal input \$i_{in}(t)\$ and signal ...
Jordan Stanley's user avatar
1 vote
0 answers
68 views

How to separate Transient and Steady-State Expression from Periodic Summation Response?

Background My question comes from here, it's a response of 1st order LPF RC circuit from an arbitrary periodic input. How to determine the transient response of a circuit to causal periodic inputs? ...
Unknown123's user avatar
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2 answers
391 views

Solving an RLC circuit with two voltage sources using Laplace transforms

What is the Laplace transform for an RLC circuit with two voltage sources? I tried to find I(s), but the calculation gets complicated.
S.alhaider's user avatar
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1 answer
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Laplace inverse transform of an exponential multiplying another function

I was trying to understand the inverse transform of \$Y(s)=F(s)e^{-as}\$, but on different sources I found three different answers (H being the step): \$f(t-a)\$, \$H(t)f(t-a)\$ and \$H(t-a)f(t-a)\$. ...
Mauro's user avatar
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Knowing the transfer function of a system and the output, how can I get the input?

I have a system composed by k-thermocouple + metal handpiece, the thermocouple is drowned into the handpiece. If I manage to estimate a transfer function of the system so-made, for example trough ...
jaster's user avatar
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1 vote
1 answer
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Sources remaining in the open part of the circuit after the switch is closed

Below there is a circuit from the book Nilsson & Riedel Electrical Circuits 9th Edition. The switch in the circuit been in position x for a long time. At t = 0, the switch moves instantaneously ...
emrexx's user avatar
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1 vote
1 answer
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Laplace transform of some functions

What would be the Laplace transform of these functions? \$f(t) = [5u(t)]^{2} - u(t)\$ \$f(t) = tu(2t)\$ As for the first function, it is like multiplying two unit step functions which is not ...
Amit M's user avatar
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2 votes
2 answers
303 views

Solving for current in RLC circuit with Laplace and steady-state solution

The following parallel RLC circuit is example 8.8 in Fundamentals of Electric Circuits by Charles Alexander. In the example in this text, the current through the inductor i(t) is found to be: $$i(t) =...
EElmo's user avatar
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2 votes
2 answers
204 views

How to find driving point impedance of non-inverting op-amp circuit

I have this circuit: And I am asked to find the driving point impedance. I know that a driving-point impedance relates the voltage and current at a pair of terminals. The formula for the driving-...
karl karlsen's user avatar
2 votes
2 answers
607 views

Transfer function of non-inverting op-amp circuit

I have this circuit: I am asked to show that the transfer functions of the circuit is: I know that for non-inverting op-amps: \$ Z_{in}=\infty \$ \$ Z_{out}=0 \$ \$ H(s)=\frac{V_{out}(s)}{V_{in}(s)} ...
karl karlsen's user avatar
1 vote
3 answers
74 views

Inverse Laplace transform not giving correct result

How does one calculate the inverse Laplace transform of \$V(s) = \frac{1}{(s+α)(s+β)} \$? Laplace transform of function $$V(t) = \frac{1}{β-α}(e^{-αt} - e^{-βt})$$ is $$V(s) = \frac{1}{(s+α)(s+β)}$$...
Amit M's user avatar
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What is the best method for solving this circuit analysis problem in the S-domain?

I'm just curious what the best method for solving for voltage across the capacitor might be. My initial idea was to use nodal analysis but I ran into a roadblock in that I am not entirely sure how the ...
Thxforhelping's user avatar
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1 answer
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laplace- second order

We were told to solve this using the series equivalent circuit for the inductor and the parallel equivalent circuit for the capacitor. However, I am not sure how that will look like. Could someone ...
jbean's user avatar
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2 votes
2 answers
195 views

Inverse Laplace transform

I found the transfer function of the RC circuit (Figure 1). $$ G(s)=\frac{V_{out}(s)}{I_{in}(s)}=\frac{R_2}{R_2sC_1+1}=\frac{50}{50*10^{-9}s+1} $$ I can check if the transfer function is correct or ...
Antel's user avatar
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1 vote
1 answer
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What is the correct way of replacing the value of a step voltage source in Laplace?

I'll be presenting two ways to reach the same answer. I would like to hear which way is the correct way to get there. I am not interested in the result, it's the same in both cases, I'm interested in ...
a concerned citizen's user avatar
1 vote
2 answers
108 views

Matlab calculation with laplace analysis is different from what I got in LTspice

Here is the circuit diagram. Waveform for the current passing through voltage source. The code I use for Matlab . ...
kile's user avatar
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Colpitts oscillator with a series inductance π-network

In a Colpitts oscillator, the feedback occurs via a series inductance π-network. An, based on a common-emitter BJT amplifier, is shown in the circuit below. Here below is a simplified version. This ...
kile's user avatar
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4 votes
3 answers
671 views

Differential equation from a circuit: two methods give different results

I saw an example problem from a lecture note and tried to solve it by a different method. Then I got confused as the results are different. Here is the example: It's not some web site as I know so I'...
internet's user avatar
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3 votes
2 answers
128 views

Rewriting piecewise voltage function using Heaviside?

Recently I've had an idea to create an assignment where we have low-pass filter connected to the voltage source which is described by piecewise function. I've already dealt with periodic functions ...
tom_ger's user avatar
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1 answer
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Laplace transform for circuit analysis gives me different result from LTSpice Simulation

Here is a simple circuit I want to simulate with LTSpice. I make everything to be 1 for easy arithmetic. The source is $$V_1 = cos(t) u(t)$$ $$H(s) = \frac{R} {R + \frac{1} {s C} + s L}$$ Substitute ...
kile's user avatar
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1 vote
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Why the ROC is all s? (Signals & System)

The problem from mit ocw signals and systems (open for everyone) https://ocw.mit.edu/courses/6-003-signals-and-systems-fall-2011/ Sorry, I tried to write it Latex, but it doesn't work well. Sorry that ...
Jin's user avatar
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3 votes
1 answer
220 views

How to prove property of transfer function for causal LTI system

For causal linear time-invariant systems the degree of denominator must be larger or equal than the degree of the numerator. How can this be proven rigorously?
MichaelW's user avatar
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3 votes
2 answers
264 views

How to solve this problem using transient time-domain analysis?

Find V0(t) in this circuit assuming zero initial conditions. I solved it (refer image above) using frequency-domain analysis using Laplace and found the answer, but I am not able to get the same ...
Bruce Wayne's user avatar
1 vote
1 answer
536 views

Laplace transformations of dependent sources

The following example is from the book Fundamentals of electric circuits by Charles K. Alexander. I don't understand how the dependent current source of 2δ(t) in the question becomes a 2 A current ...
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