Questions tagged [laplace-transform]

Questions regarding or involving Laplace Transforms with respect to Electrical Engineering.

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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 ...
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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 ...
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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. ...
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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)=...
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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, \...
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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^{...
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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(...
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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 ...
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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)}=-\...
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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 ...
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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 ...
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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) ...
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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}$...
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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 ...
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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 ...
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1answer
82 views

Laplace Analysis of Step Response of a Parallel RC Circuit

simulate this circuit – Schematic created using CircuitLab My KCL Equation: $$\frac{Cdv}{dt} + iΔ(t) = \frac{Vo}{10k} + iΔ $$ My laplace transform is: $$\frac{Vo(s)}{s} = \frac{sVc(s)}{20} - 0....
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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?
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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 > ...
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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 ...
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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. (???)
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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\...
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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 ...
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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?
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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-...
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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)\$...
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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 ...
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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 ...
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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)...
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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 ...
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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 ...
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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 ...
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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(τ)dτ + v_C(...
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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 ...
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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 "...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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-...
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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 ...
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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 ...
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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 ...
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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)\$ ...
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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 ...
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1answer
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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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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?
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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 ...
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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 ...

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