Questions tagged [laplace-transform]
Questions regarding or involving Laplace Transforms with respect to Electrical Engineering.
159
questions
0
votes
1answer
33 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 ...
3
votes
3answers
157 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
votes
2answers
106 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 ...
0
votes
0answers
52 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
1answer
79 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 ...
1
vote
1answer
84 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, ...
1
vote
0answers
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 ...
0
votes
1answer
56 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 ...
0
votes
0answers
56 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
votes
1answer
46 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
vote
1answer
58 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 ...
1
vote
2answers
79 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
votes
1answer
40 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 ...
1
vote
2answers
94 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
votes
1answer
58 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
1answer
71 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):
$$\frac{\frac{1}{\text{sC}}}{\frac{1}{\...
0
votes
1answer
32 views
determine the Laplace domain of this RL circuit
I am currently learning control system design. I have a lot of confusion about the initial conditions of the inductor in the circuit. Could someone please correctly solve this by getting the ...
3
votes
1answer
189 views
Impedance calculation from voltage and current (exponential) waveforms
If we want to find the impedance across two terminals (a port) at a frequency \$\omega_0\$ using the voltage waveform across \$v(t)\$) and current through (\$i(t)\$) the terminal, general intuition is ...
2
votes
1answer
60 views
How do I calculate this inverse Laplace Transform
I have this transfer function and input, and I have to manually calculate what the systems response will be.
The transfer function is:
and the input is:
I multiplied the two functions and used ...
2
votes
0answers
34 views
Inverse Laplace Transform isn't A Contour Integral
I've learned about and used the Laplace transform in several signal processing classes and the inverse transform has always been defined as an integral like this:
$$ \mathcal{L}^{-1}\{F(s)\} = \frac{...
-1
votes
2answers
87 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 ...
1
vote
1answer
56 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
vote
2answers
59 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:
$$u_{C}=u(0)+\frac{1}{C}
\int_{t_{0}}^{t}i(\tau)d\tau$$
$$i_{L}=i(0)+\frac{1}{L}
\int_{t_{0}}^{t}...
1
vote
2answers
62 views
Frequency Response Function Estimate via FFT Question
I want to estimate the FRF of a dynamic LTI system given experimental input and output data. I know generally the approach is to use a chirp as an input to make sure enough frequency content is ...
0
votes
1answer
42 views
How do you reduce this simple system diagram for the sake of doing algebraic manipulation?
My guess is that since H(s) is parallel with 1(s) we'd do A(H - 1)? But this is my first ...
1
vote
1answer
130 views
What is the practical use of Laplace Transform?
I am trying to understand the electrical model of 3-phase Induction Model. The rotor of the motor is modeled as a variable resistor in s-domain.
I fail to understand how that works practically. Can ...
-1
votes
1answer
92 views
Analyzing circuit with dirac delta current source without using Laplace transformation
At \$t=0\$ the switch is closed and \$v_o(0)= -5 V\$.
The problem asks for \$v_o(t)\$. I did it using Laplace method and get
$$v_o(t)=5+10\,e^{-2t}$$
which does not even satisfy the initial condition,...
2
votes
2answers
87 views
Meaning of transfer function in s evaluated at a complex number
From the pole-zero plot, you can compute the system frequency response by assuming a locus of test points along the \$j\omega\$ axis.
Figure from: http://web.mit.edu/2.14/www/Handouts/PoleZero.pdf
\...
1
vote
1answer
67 views
RC circuit with pulse input voltage; finding the time constants
I've the following circuit:
Question: What are the time constants of the voltage at node \$\text{Y}_2\$ when the up part of the puls comes and when the down part of the puls comes?
MY WORK:
The ...
0
votes
2answers
116 views
Confusion about Laplace and frequency response of a electrical circuit
I have a confusion between the Laplace transform of a circuit and the frequency domain AC analysis.
Suppose we have a series RLC resonant circuit connected to an ideal sinusoidal voltage source.
We ...
0
votes
1answer
74 views
RLC bandpass filter
I am working on a circuit:
simulate this circuit – Schematic created using CircuitLab
My goal is to find \$ \omega_0, \beta, \$ and \$\varrho \$
The way I approached this problem was to ...
0
votes
1answer
132 views
Problem related to the transfer function of RC low pass filter
I have the following question:
For the passive RC low pass filter shown below:
$$V_S(t)=\cos(t)+\cos(100t)$$
$$V_0(t)=\alpha\cos(t+\theta)+\beta\cos(100t+\phi)$$
(where \$\alpha\$, \$\beta\...
1
vote
2answers
92 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?
1
vote
2answers
105 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
222 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
votes
1answer
453 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
votes
0answers
245 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
votes
3answers
260 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
179 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 ...
1
vote
2answers
93 views
What is the physical meaning of the voltage across an inductor in the Laplace domain?
In my Electrical Engineering degree I recently learned how to analyse circuits using Laplace transforms and I know that the Laplace transform of the voltage across an inductor is \$V_L(s) =s*L*I(s) - ...
1
vote
2answers
127 views
Transfer Function: Trying to understand the Laplace analysis of this circuit
I am trying to do the transfer function of this circuit and also trying to understand the frequency domain thing of the Laplace transform.
I want to do a transfer function of VA/V1, considering B to ...
0
votes
3answers
189 views
What is the time derivative at t=0 for a second order low-pass step response?
For a first order system like an RC filter you have something like
$$y(t)=1-e^{-\frac{t}{\tau}}\\
y'(t)=\frac{1}{\tau}e^{-\frac{t}{\tau}}\\
y'(0)=\frac{1}{\tau}$$
But for a second order system there ...
1
vote
4answers
148 views
How to find the system response given the transfer function without using Laplace transforms?
The given transfer function is:
$$\frac{6p+100}{p^2+12p+100}$$
and inputted into the system is a unit step response:
$$r(t) = \left\{\begin{array} f0 & t < 0\\1 & t > 0 \end{array}\...
3
votes
3answers
113 views
Why is there a sudden change in current between \$t=0^{-}\$ and \$t=0^{+}\$ when an active inductor is connected in series with a relaxed inductor?
For the above question I drew the corresponding Laplace transform diagram, as follows (didn't draw the switch since it basically open circuit after \$t=0\$):
simulate this circuit – Schematic ...
0
votes
1answer
253 views
Determine by the order of transfer function what kind of filter
How can I determine by looking at the following tranfer function, that is this the transfer function of a band-pass filter:
$$\frac{1}{as^3+bs^2+cs+1}$$
2
votes
1answer
162 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
2answers
107 views
How do I compensate for Exponential decay in an op-amp circuit
Using an oscillator, I want to provide a square wave input to the second opamp circuit shown in this TI application note (but using IC741 instead.) The problem lies in the s domain:
I get a voltage ...
5
votes
2answers
123 views
Algebraic way for finding a transfer function of a filter
I've the following filter and I tried to write the transfer function for it:
simulate this circuit – Schematic created using CircuitLab
And I wrote for the current nodes the following ...
1
vote
1answer
380 views
Calculate transfer function H(w) of Schmitt trigger with RC at inverting input
I have got the following Schmitt trigger circuit implemented already on a breadboard. As seen, the input signal at the non-inverting and inverting terminals of the op amp is the same, but with the ...
1
vote
2answers
118 views
Transient analysis with Laplace and nodal analysis error
Have the schematic:
Solving using MathCAD:
There is an error in my equations with nodal analysis but I can't find where? May anyone help me?
I also add the solution using approach of series RLC ...
