Questions tagged [laplace-transform]
Questions regarding or involving Laplace Transforms with respect to Electrical Engineering.
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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 ...
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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-
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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 ...
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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 ...
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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 ...
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Barkhausen stability criterion and poles location in s domain
For studying stability, I am actually working with 2 methods :
Here is the Barkhausen stability criterion :
The loop gain is equal to unity in absolute magnitude, that is,
$$|\beta A|= 1 $$
and the ...
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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 ...
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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 ...
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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?
...
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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.
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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)\$.
...
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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 ...
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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 ...
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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 ...
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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:
$$i(t) =...
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How to find driving point impedance of non-inverting op-amp circuit
I have this circuit:
And I am asked to find the driving point impedance.
I know that a driving-point impedance relates the voltage and current at a pair of terminals. The formula for the driving-...
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Transfer function of non-inverting op-amp circuit
I have this circuit:
I am asked to show that the transfer functions of the circuit is:
I know that for non-inverting op-amps:
\$ Z_{in}=\infty \$
\$ Z_{out}=0 \$
\$ H(s)=\frac{V_{out}(s)}{V_{in}(s)} ...
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Inverse Laplace transform not giving correct result
How does one calculate the inverse Laplace transform of \$V(s) = \frac{1}{(s+α)(s+β)} \$? Laplace transform of function $$V(t) = \frac{1}{β-α}(e^{-αt} - e^{-βt})$$ is $$V(s) = \frac{1}{(s+α)(s+β)}$$...
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Transfer function h(t) of a positive feedback system
I want to find the transfer function h(t) of the below positive feedback system. I came out till this.
How can i get the inverse laplace of this function? say β = 1 and γ = 1.
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What is the best method for solving this circuit analysis problem in the S-domain?
I'm just curious what the best method for solving for voltage across the capacitor might be.
My initial idea was to use nodal analysis but I ran into a roadblock in that I am not entirely sure how the ...
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Converting Laplace to CTFT to find solution
Let us take a system where the input is \$V_{i}(t)\$ and output is \$V_{o}(t)\$ and the impulse response of the system be \$I(t)\$ where \$t\$ represents time domain and \$w\$ be frequency. we get \$\...
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laplace- second order
We were told to solve this using the series equivalent circuit for the inductor and the parallel equivalent circuit for the capacitor. However, I am not sure how that will look like. Could someone ...
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Solving a circuit problem using Laplace
Why is the iL(0-) here 0? wouldn't the 2e^-t u(t) cause current to flow?
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Inverse Laplace transform
I found the transfer function of the RC circuit (Figure 1).
$$
G(s)=\frac{V_{out}(s)}{I_{in}(s)}=\frac{R_2}{R_2sC_1+1}=\frac{50}{50*10^{-9}s+1}
$$
I can check if the transfer function is correct or ...
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What is the correct way of replacing the value of a step voltage source in Laplace?
I'll be presenting two ways to reach the same answer. I would like to hear which way is the correct way to get there. I am not interested in the result, it's the same in both cases, I'm interested in ...
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Matlab calculation with laplace analysis is different from what I got in LTspice
Here is the circuit diagram.
Waveform for the current passing through voltage source.
The code I use for Matlab .
...
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Colpitts oscillator with a series inductance π-network
In a Colpitts oscillator, the feedback occurs via a series inductance π-network. An, based on a common-emitter BJT amplifier, is shown in the circuit below.
Here below is a simplified version.
This ...
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Differential equation from a circuit: two methods give different results
I saw an example problem from a lecture note and tried to solve it by a different method. Then I got confused as the results are different.
Here is the example:
It's not some web site as I know so I'...
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Rewriting piecewise voltage function using Heaviside?
Recently I've had an idea to create an assignment where we have low-pass filter connected to the voltage source which is described by piecewise function. I've already dealt with periodic functions ...
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Laplace transform for circuit analysis gives me different result from LTSpice Simulation
Here is a simple circuit I want to simulate with LTSpice. I make everything to be 1 for easy arithmetic. The source is $$V_1 = cos(t) u(t)$$
$$H(s) = \frac{R} {R + \frac{1} {s C} + s L}$$
Substitute ...
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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 ...
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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 denominator.
How can this be proven rigorously?
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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 ...
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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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Order of RC circuit
In the given RC circuit, there are 3 capacitors, out of which the voltages of 2 capacitors can be uniquely determined.
This implies that it is a second-order circuit. But when I found the expression, ...
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Bode plot from s-domain singularities
Considering any transfer function H(s), is there any meaningful way to use the s-variable singularities to obtain the f-variable ones to trace the Bode plot?
I know direct conversion with \$ s = \...
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Settling time from change in plant
I have an electrical circuit as shown below:
I would like to formulate an equation for the settling time for the voltage on the capacitor node given a change in resistance on R2. I have calculated ...
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Confusions regarding Laplace transform
We know that Laplace transform has two parts, \$\sigma \$ and \$ j\omega\$.
\$\sigma\$ is the real part
while \$ j\omega\$ is the imaginary part.
Is it okay to say that the term \$\sigma \$ is a ...
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Unclear relationship between s domain and frequency domain
I’m trying to brush up on some things I left behind, let’s consider the usual RC parallel circuit, I’m trying to get the bode plot of its impedance.
The equivalent impedance is obviously \$ Z = \frac{...
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Type-2 compensator transient response
I'm looking to find the transient response to a step impulse of a type-2 compensator.
I already found the transfer function, but when it comes to finding the transient response by using the inverse ...
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Who was the first person to use Laplace transforms for circuit analysis?
I am an electrical engineering student and I have been using Laplace transforms for circuit analysis. I would like to know: who was the first person to use Laplace transforms for the analysis of ...
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How to measure a DC motor's inertia
I want to measure the inertia of a DC motor. However, I have no idea how to measure or calculate this. I need the inertia to determine the numeric transfer function for voltage to angular velocity. ...
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How can I determine the circuit from a transfer function [closed]
I have identified a couple of transfer functions, which fit well to measured data, using MATLAB system identification toolbox.
How can I determine a circuit diagram from these transfer functions?
$$\...
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What is up with this series/parallel calculation? Inverse Laplace looks strange
I'm trying to find an analytic solution for this circuit. If the cap is inverted (series resistor to ground) the solution is straightforward. In this case I ended up with a strange cos term that makes ...
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Why is a capacitor to ground a low frequency pole, instead of a high frequency zero?
In building my intuition about how analog circuits relate to the s-plane, I am wondering why a pole emerges from a capacitor to ground, for example in a simple lowpass filter consisting of only a ...
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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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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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