Questions tagged [laplace-transform]
Questions regarding or involving Laplace Transforms with respect to Electrical Engineering.
170
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Is it possible to sketch a bode plot for a discrete-time transfer function?
For a regular s-domain transfer function, there are simple rules you can use to draw an asymptotic bode graph, basically by taking a slope of +/-20dB per decade and a phase shift of +/-90 degree for ...
0
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1answer
38 views
Learning process automation starting from general engineering background [closed]
I'd like to study process automation by myself, could you suggest a good entry-level book to start with?
I have engineering college math level and I remember a bit of Laplace transforms to model ...
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25 views
Solving for the current/charge across the elements of this RLC circuit?
I have a circuit which is composed of an inductor (L), capacitor (C), and two identical resistors (R1=R2):
This represents an equivalent electrical circuit to a guitar pick or piano hammer as an "...
0
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1answer
69 views
Laplace transform in a block system
I'm trying to understand the resolution of the problem 5.11, but I can't understand how she gets the expression in the rectangle:
$$\dot{x}_1=-x_1+2u$$
How can I get the expression in the rectangle?
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1answer
30 views
Getting different impulse responses by solving with Laplace transform and plugging delta-dirac
If I know that the output of a system $$y(t) = 2e^{-3t} \cdot u(t)$$
and it's specified that the input is $$ x(t) = u(t) $$
I was trying to find the impulse response h(t).
So I solved it using ...
0
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1answer
68 views
Laplace Transform
can anyone help in finding the expression for the voltage at the output of the circuit if the input is a step function with 1V amplitude.
simulate this circuit – Schematic created using ...
4
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1answer
142 views
Closed Loop System
Why is RC circuit considered closed loop system with negative feedback? Is it because it has a differential equation due to which current 'I' through capacitor 'C' will be C*(dVo/dt) = C*{Vo(t)-Vo(t-h)...
3
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3answers
189 views
How does Laplace transform include the transient response?
When we provide a sinsusoidal input, the evaluation of the solution of the differential equation head-on becomes horrendous. So we give an imaginary, complex exponential input and solve the ...
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47 views
Laplace Transform Question
looking at laplace transform for electrical applications, I don't understand how the provided answer works? Like how did they get the e^(-sT), through using the laplace conversion table? And also, ...
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27 views
Analysing an s-domain circuit with multiple sources
So I am working on the following circuit:
I have already worked my initial conditions and the next step is to perform analysis of the charged up circuit. My charged circuit is shown below:
The ...
2
votes
1answer
68 views
Final Value Theorem yielding the wrong result?
C1 has an impedance of 1/0.1s Ohm in S-domain. Its impedance together with R1's is 100/(10s+10) Ohm
The transfer function is:
$$\frac{V_2}{V_1}=\frac{5}{\frac{100}{10s+10}+5}=\frac{50s+50}{50s+150}$$
...
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1answer
41 views
Calculating steady state output using Laplace transform
I've tried to obtain the the steady state output with the help of final value theorem and multiplication properties of Laplace transform.But I'm not sure whether I've solved the problem correctly or ...
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3answers
170 views
Inconsistency in Values of Laplace Transformed Current when Changing Units
I was trying to convert the units of the following current in Time Domain and Complex Frequency domain (s-domain):
$$
i(t)=20\cdot e^{-t}H(t)\,\,\,\,\,\text{[mA,ms]}
$$
Where \$\text{[mA, ms]}\$ ...
0
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2answers
132 views
Transfer Function Derivation
Where did the following transfer function come from?
\$H(s) = -H_o\frac{\frac{\omega_o}{Q}s}{s^2 +\frac{\omega_o}{Q}s + \omega_o^2}\$
\$H_o\$ is the gain at resonant frequency.
I'm told it ...
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0answers
74 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
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1answer
84 views
If I look at a signal in its frequency domain, are there some guidelines by which I can tell how that signal looks in the time domain?
I was studying the Laplace transform and the Fourier transform, and I can't figure out if there is some intuitive way of finding out how a signal looks in the time domain if we know its frequency ...
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1answer
101 views
Laplace Transforms and the imaginary input
When we get an exponential on the RHS of our differential equation (or if we give an exponential input) it's quite easy to solve the equation, but if we provide a sinsusoidal or cosinusoidal input, ...
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49 views
How to do Transient analysis?
Consider the above example earlier I used to form a differential equation and then do its solution using Laplace,but for this example the differential equation comes out to be non-ordinary.
Please ...
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1answer
227 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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67 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 ...
0
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1answer
54 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 ...
1
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1answer
228 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
101 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:
...
0
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1answer
42 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
116 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 ...
0
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1answer
114 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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1answer
74 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):
$$\frac{\frac{1}{\text{sC}}}{\frac{1}{\...
0
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1answer
41 views
determine the Laplace domain of this RL circuit
I am currently learning control system design. I have a lot of confusion about the initial conditions of the inductor in the circuit. Could someone please correctly solve this by getting the ...
3
votes
1answer
210 views
Impedance calculation from voltage and current (exponential) waveforms
If we want to find the impedance across two terminals (a port) at a frequency \$\omega_0\$ using the voltage waveform across \$v(t)\$) and current through (\$i(t)\$) the terminal, general intuition is ...
2
votes
1answer
62 views
How do I calculate this inverse Laplace Transform
I have this transfer function and input, and I have to manually calculate what the systems response will be.
The transfer function is:
and the input is:
I multiplied the two functions and used ...
2
votes
0answers
37 views
Inverse Laplace Transform isn't A Contour Integral
I've learned about and used the Laplace transform in several signal processing classes and the inverse transform has always been defined as an integral like this:
$$ \mathcal{L}^{-1}\{F(s)\} = \frac{...
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2answers
93 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
73 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=...
1
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2answers
64 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:
$$u_{C}=u(0)+\frac{1}{C}
\int_{t_{0}}^{t}i(\tau)d\tau$$
$$i_{L}=i(0)+\frac{1}{L}
\int_{t_{0}}^{t}...
1
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2answers
81 views
Frequency Response Function Estimate via FFT Question
I want to estimate the FRF of a dynamic LTI system given experimental input and output data. I know generally the approach is to use a chirp as an input to make sure enough frequency content is ...
0
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1answer
42 views
How do you reduce this simple system diagram for the sake of doing algebraic manipulation?
My guess is that since H(s) is parallel with 1(s) we'd do A(H - 1)? But this is my first ...
1
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1answer
153 views
What is the practical use of Laplace Transform?
I am trying to understand the electrical model of 3-phase Induction Model. The rotor of the motor is modeled as a variable resistor in s-domain.
I fail to understand how that works practically. Can ...
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1answer
109 views
Analyzing circuit with dirac delta current source without using Laplace transformation
At \$t=0\$ the switch is closed and \$v_o(0)= -5 V\$.
The problem asks for \$v_o(t)\$. I did it using Laplace method and get
$$v_o(t)=5+10\,e^{-2t}$$
which does not even satisfy the initial condition,...
2
votes
2answers
132 views
Meaning of transfer function in s evaluated at a complex number
From the pole-zero plot, you can compute the system frequency response by assuming a locus of test points along the \$j\omega\$ axis.
Figure from: http://web.mit.edu/2.14/www/Handouts/PoleZero.pdf
\...
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1answer
90 views
RC circuit with pulse input voltage; finding the time constants
I've the following circuit:
Question: What are the time constants of the voltage at node \$\text{Y}_2\$ when the up part of the puls comes and when the down part of the puls comes?
MY WORK:
The ...
0
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2answers
147 views
Confusion about Laplace and frequency response of a electrical circuit
I have a confusion between the Laplace transform of a circuit and the frequency domain AC analysis.
Suppose we have a series RLC resonant circuit connected to an ideal sinusoidal voltage source.
We ...
0
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1answer
167 views
RLC bandpass filter
I am working on a circuit:
simulate this circuit – Schematic created using CircuitLab
My goal is to find \$ \omega_0, \beta, \$ and \$\varrho \$
The way I approached this problem was to ...
0
votes
1answer
155 views
Problem related to the transfer function of RC low pass filter
I have the following question:
For the passive RC low pass filter shown below:
$$V_S(t)=\cos(t)+\cos(100t)$$
$$V_0(t)=\alpha\cos(t+\theta)+\beta\cos(100t+\phi)$$
(where \$\alpha\$, \$\beta\...
1
vote
2answers
120 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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2answers
129 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:
&...
3
votes
1answer
268 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 ...
0
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1answer
564 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. ...
0
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0answers
287 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 ...
0
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3answers
387 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 ...
0
votes
2answers
218 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 ...
