Questions tagged [laplace-transform]
Questions regarding or involving Laplace Transforms with respect to Electrical Engineering.
213
questions
1
vote
1answer
67 views
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 ...
1
vote
0answers
37 views
Input impedance of a buck converter
I found the control to output transfer function and the line to output control transfer function and verify it by simulation. It fits :) (all this work is coming essentially from what I have learnt in ...
3
votes
0answers
111 views
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. ...
0
votes
2answers
53 views
Finding transfer function by linear system
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
$$\begin{cases}
h_1(t)=\exp(-3t)u(t-t_0) \text{, with $t_0$ positive} \\
h_2(t)=...
2
votes
2answers
78 views
Justification For Dropping Real Part of s in Transfer Functions, \$F(s)=F(j\omega)\$
Transfer functions always seem to take the form $$F(s) = F(j\omega)$$
However, going back to the original Laplace Transform used to obtain the transfer function, \$s\$ is said to be a complex number, \...
0
votes
0answers
26 views
Laplace transform to Z-transform for filter design
I was given an answer to the following question I can't understand, that how is the Impulse Invariance transformation of
$$\frac{(s+a)}{(s+a+jb)(s+a-jb)}$$ is
$$\frac{(1-e^{-aT} cos(bT) z^{-1})}{(1-e^{...
0
votes
0answers
41 views
Integration of exponential function and square-wave
How do I evaluate,
\begin{equation}
\int_{0}^{t} e^{c\tau}sqw(\frac{\tau}{T})d\tau
\end{equation}
where $$c < 0$$ and \$sqw(\cdot)\$ is a periodic function over \$t\in[0,T)\$,
\begin{equation}
sqw(...
3
votes
1answer
68 views
How to stabilize this system?
I'm trying to understand system stability basics. Let us say I have a system
$$
G(s) = \frac{500}{s^2 - 500}
$$
Since it has two poles in the right half s-plane, it is unstable.
How can I ...
0
votes
1answer
84 views
Why is my zero and pole frequency of this transfer function wrong?
So I have this transfer function:
$$\begin{align}
\dfrac{g_m-sC_{gd}}{s(C_{gs}+C_{gd})}=\dfrac{-C_{gd}\left(s-\dfrac{g_m}{C_{gd}}\right)}{(C_{gd}+C_{gs})\left(s-\dfrac{0}{C_{gd}+C_{gs}}\right)}=-\...
0
votes
1answer
61 views
How would the pole and zero frequency expression look like for this transfer function I derived?
This is a practice problem in deriving the transition frequency function for mos and part of the set of questions is to determine the pole and zero frequency expression but this transfer function i ...
0
votes
1answer
51 views
Could somebody clarify the phase angle and gain of this transfer function?
Suppose a circuit with a transfer function of the form \$A(\omega)=\displaystyle\frac{A_0}{1-\frac{j\omega}{\omega_0}}\$ has \$A_0=-10\; V/V\$ and \$\omega_0=100\;rad/sec.\$
We were asked for the gain ...
4
votes
2answers
160 views
Relation between Fast Fourier Transform and Laplace/Continuous Fourier representation
I am trying to identify a system by means of its differential equation (i.e., Lapace representation). I put together a rather straightforward regression algorithm (similar to Proni's method for ARMA) ...
2
votes
1answer
55 views
When use As+B in partial fraction expansion
I'm trying to solidify my knowledge around using partial fraction expansion. In this specific case, when to use
$$ f(s) = \frac{As+B}{s^2+cs+d}$$
instead of using
$$ f(s) = \frac{A}{s+e}+\frac{B}{s+f}$...
1
vote
1answer
37 views
Inverse laplace with undefined variable
I have the following information in a problem: an input $$r(t) = 60u(t)$$, with u(t) being the unit step function, and a transfer function $$H(s) = \frac{k_1}{s^{2} + s + k_{1}}$$, where k1 is a ...
1
vote
1answer
123 views
s-domain to z-domain conversion in MATLAB
I want to convert a transfer function from s-domain to z-domain. But, by keeping variable i.e without assigning values to variables.
I tried to do it with s2z command but it demands numeric input, not ...
1
vote
1answer
82 views
Laplace Analysis of Step Response of a Parallel RC Circuit
simulate this circuit – Schematic created using CircuitLab
My KCL Equation:
$$\frac{Cdv}{dt} + iĪ(t) = \frac{Vo}{10k} + iĪ $$
My laplace transform is:
$$\frac{Vo(s)}{s} = \frac{sVc(s)}{20} - 0....
0
votes
2answers
48 views
Find the initial value of the signal from its Laplace transform?
Given
My answer:
.
,
Since there is an impulse at the origin, the initial value theorem cannot be applied. Is this conclusion correct?
2
votes
1answer
47 views
Initial value generator in a circuit (Anfangswertgenerator)
I am preparing for my electrical engineering exam and I saw this in my script.
I have this first circuit and the requirement is to draw the circuit in Laplace with initial value generator where t > ...
6
votes
1answer
295 views
Stability of input filter in SMPS - Theoretical explanation
I read the Application note Wurth Electronics ANP008c about negative resistance of a SMPS input and how to avoid oscillation when using an input LC filter. I'm asking for a theorethical clarification ...
1
vote
1answer
63 views
Time shifted Laplace of a resistor
Is a usable Laplace function possible with a time shifted resistor, e.g. r = R + Re^-2s? For instance what is the Z(s) of a series RC circuit: 1/Cs + R + Re^-2s. (???)
1
vote
0answers
51 views
Have I correctly solved this RLC problem?
Now I needed to find the transfer function as well as impulse response
$$\\ R=14\Omega \\ L=2H \\ \\ C=\frac{1}{12}F \\ In \ s-domain \\ R=14\Omega \\ L=sL=s\cdot 2=2s \\ \\ C=\frac{1}{sC}=\frac{1}{s\...
0
votes
3answers
68 views
Could you please find the Laplace transform?
I can use the table directly, but I am struggling how to make the combination. This equation will help me to work on my gyroscope sensor equations ( magnetic based ) , My pain point is at the ...
1
vote
0answers
50 views
Is the region of convergence of Laplace transforms of a right-sided signal right of the rightmost pole?
I know that the ROC of a right-sided signal with a rational Laplace transform is right of the rightmost pole. Does it apply to any right-sided signal?
0
votes
1answer
37 views
Is there any Laplace transform whose ROC contain a pole?
While I was reading "Signals& Systems" by Oppenheim, I read that "For rational Laplace transforms, the ROC does not contain any poles". So, I was wondering is there any non-...
0
votes
2answers
101 views
Derivation of y(t)=H(s)x(t)
\$x(t)=e^{st}\$ is the input to the system. \$x(t)\$ is not going to present in this question anything else than the exponential \$e^{st}\$ where t is time and s is a complex valued parameter.
\$H(s)\$...
1
vote
0answers
86 views
how LTspice integrates Laplace in the time domain?
I modeled two different PID controllers with Laplace and with the same control parameters in LTspice, but the results show me the same behavior of the two PID controllers in ...
0
votes
0answers
100 views
how to simulate a Laplace function of a PID controller in the time domain with LTspice
I tried to simulate a Laplace function of a PID controller with LTspice in the time domain, but an error message appears "The laplacian is singular at DC".
cs1 is the controller, so I just ...
-2
votes
1answer
217 views
Sinusoidal steady-state analysis
Find the Transfer function of the given circuit in the frequency domain.The problem here is that the equations of this circuit become complicated by finding equal Z of R,C,L (right side of the circuit)...
4
votes
3answers
630 views
Transfer function of electrical network
I need help with this problem. The transfer function that I found is ((RCS+1)/(2RCS+1)) , but then I cannot go further because the form of T.S is untypical. The typical form of this question is RC ...
0
votes
0answers
32 views
Laplace transform - How to determine the initial conditions of the derivative functions
I m trying to get the transfer function of this circuit. I do it essentially for fun. I clearly a newbie about Laplace's transformation. Nevertheless here is the circuit :
Here is the differential ...
0
votes
1answer
39 views
Negative Freqs from FFT in Laplace Circuit Analysis
Do I use the absolute-value of the FFT frequencies when using the Laplace equations for calculating the impedance of an RLC circuit?
I'm currently working on something where I need to numerically ...
2
votes
1answer
77 views
Laplace tranfsorm of capacitor functions and initial conditions
I may be asking something trivial, but unfortunately, I could not find an answer so far.
Suppose an AC circuit. The voltage of the capacitor is given by $$v_C(t)=Q(t)/C = 1/C [ \int_0^t i_C(Ļ)dĻ + v_C(...
3
votes
1answer
1k views
how the area is exactly zero?
I was reading this PDF which tries to explain the concept of poles and zeros of Laplace transform.
My question is about FIGURE 32-5(b) on page #591.
I don't understand why the area is said to be zero ...
3
votes
2answers
288 views
zero of spring-mass system
I was reading this PDF which tries to explain the concept of poles and zeros of Laplace transform. I started with second paragraph on page #590 and read it up to page #592 before the new section "...
2
votes
0answers
67 views
Problem understanding transfer functions of second order filters
The transfer function of any second order filter can be found by analyzing the circuit using the Laplace transform.
For example the transfer function of a second order low pass passive RLC filter ...
1
vote
1answer
51 views
finding the current in a branch with resistor, capactor and a voltage source
I'm solving a question in Linear circuit analysis 2 class. the question is to analyze a switching circuit with inductors and capacitors. this is the circuit in the time interval drawn in S-domain ...
0
votes
1answer
44 views
Deriving Transfer function from position block diagram
For the system shown below I am trying to get the system function.
I tried putting it into the equation:
$$T(s) = \frac{C_G(s)}{1+C_G(s)\cdot H(s)}$$
where $$ C_G(s) = \frac{K}{s(s+3)(s+4)}$$ and ...
2
votes
2answers
130 views
Time Reversal Operation for discrete time signals
For a discrete time unit step signal 'u(n)' , if time reversal operation is performed then it becomes 'u(-n-1)'.
Is it true for ANY discrete time signal 'x(n)' such that time reversal operation makes ...
4
votes
2answers
223 views
Finding impulse response by a non-Laplace-transform method
The input function is $$x(t)=e^{-t}u(t)$$ and the corresponding output function of a linear system is $$y(t)=10e^{-t}\cos(4t)u(t)$$ where \$u(t)\$ is unit step function.
I understand how to find the ...
2
votes
2answers
138 views
Laplace and time domain transform confusion with respect to RC LPF
I am a bit confused with Laplace domain and its equivalent time domain conversion
Consider the s-domain of first order LPF filter which is \$V_o(s)/V_i(s)=1/(1+sRC)\$. Now for a second order LPF ...
3
votes
2answers
1k views
How can I design a low pass filter using Z transform in Microcontroller?
I have generated a signal which is a mixture of 50 Hz and 250 Hz sine waves using a microcontroller and DAC. Check the screenshot of the excel file:
The values of row 4 (i.e. f1+f2) are feed to an 8-...
0
votes
1answer
79 views
RC Laplace and time domain
Another basic question to understand. It is well known that the transfer function of a low pass RC filter in Laplace domain is \$V_o(s)/V_i(s)=1/(1+sRC)\$. Now sticking to this format and taking ...
1
vote
2answers
132 views
Response of a RC circuit and Frequency Response Theorem
let's consider this important result of control theory for linear systems, called "Frequency Response Theorem" (reference):
Briefly, it says that under the hypotesis of stability and linearity, if ...
0
votes
0answers
45 views
How can I build proper laplace RLC circuit
I think there are two different circuits over the picture. But for equations they are acting same to me. I mean DC source of left circuit look like an initial voltage for C. After inver Laplace I have ...
2
votes
3answers
89 views
Recovering a Differential Equation From the Transfer Function of a Cascaded System
With respect to the below discussion, consider that we are talking about Continuous LTI systems characterized by constant coefficient ODEs.
Consider a cascaded system whose transfer function \$H(s)\$ ...
0
votes
2answers
706 views
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
votes
1answer
43 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 ...
0
votes
1answer
73 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$$
How can I get the expression in the rectangle?
0
votes
1answer
37 views
Getting different impulse responses by solving with Laplace transform and plugging delta-dirac
If I know that the output of a system $$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
votes
1answer
78 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 ...
