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