20 votes
Accepted

Stability of input filter in SMPS - Theoretical explanation

It is an extremely complicated subject. I have taught an APEC seminar in 2017 and tried to explain the interaction between a filter and a switching converter. First, you need to understand that a ...
user avatar
14 votes
Accepted

Fourier vs. Laplace

The Fourier and the Laplace transform are not the same. First of all, note that when we talk about the Laplace transform, we very often mean the unilateral Laplace transform, where the transformation ...
user avatar
  • 3,603
14 votes
Accepted

Meaning of Sigma in Laplace transform

As most folk know, \$s=\sigma+j\omega\$ (where \$j\omega\$ is the frequency along the x-axis in a bode plot or spectrum analysis). However, in a bode plot, \$\sigma\$ has no apparent meaning but it is ...
user avatar
  • 378k
11 votes

Under what conditions does jw equal the laplace variable s in an electrical circuit?

The Laplace variable \$s\$ relates to Fourier's \$j\omega\$ as follows: $$ s = \sigma + j\omega $$ Fourier transform can be seen as a Laplace transform when \$\sigma=0\$. The \$\sigma\$ allows the ...
user avatar
11 votes
Accepted

how the area is exactly zero?

The dirac-delta function has an area of 1 when integrated. The red area and the delta function have the same area. When integrated from t = (0-) to t -> inf the total area is 0.
user avatar
  • 1,786
8 votes

Laplace of \$f(t)\cos(\omega t)\$

First, note that: \$\small cos(\omega t) = \dfrac{e^{j\omega t}+e^{-j\omega t}}{2} \normalsize\$ The s-shifting property of the Laplace Transform is: \$\small\mathscr{L}[f(t).e^{at}]=F(s-a)\...
user avatar
  • 7,138
7 votes

Relation and difference between Fourier, Laplace and Z transforms

I will try to explain the difference between Laplace and Fourier transformation with an example based on electric circuits. So, assume we have a system that is described with a known differential ...
user avatar
7 votes

Why do we use this particular approximation for the bilinear transform?

The Forward Euler Transform $$z=e^{sT}\approx1+sT\leftrightarrow s\approx(z-1)/T=\frac{1-z^{-1}}{Tz^{-1}}$$ is easy to understand in that it is a direct translation and scaling from the \$s\$-domain ...
user avatar
  • 4,089
6 votes

Solving transient circuit with serial RLC using Laplace Transform

I have tabulated and plotted my solution given below in Excel (fully general/universal solution, i.e. all 3 cases, see below; I can provide an interested person with it via e-mail; I'm Czech as the ...
user avatar
  • 632
6 votes
Accepted

What is an "origin pole"?

The "origin pole" is indeed the \$1/s\$ term in the transfer function \$H(s)\$. In the bode plot it results in a first order transfer that does NOT flatten out for low frequencies. Your Bode plot is ...
user avatar
  • 78.7k
6 votes

is it possible to design a complex analog circuit through a predetermined laplace equation?

Write the Laplace TF equation in controller canonical form, then draw the primitive block diagram (in your case there will be five blocks in the forward path, as you have a 5th order equation). Each ...
user avatar
  • 7,138
6 votes

Transfer function of electrical network

A quick look at the fast analytical techniques or FACTs gives you the transfer function of this guy in the blink of an eye. First, turn the stimulus off or reduce \$V_{in}\$ to 0 V: replace the source ...
user avatar
5 votes

Fourier vs. Laplace

Ok, so you bang a black box made of RLC components and you measure the response - the impulse response. Now you want to know the frequency response, meaning the response to any sinusoidal. First of ...
user avatar
  • 8,229
5 votes
Accepted

What is the transfer function for a first order active high-pass filter

Your expression for \$H(s)\$ is correct: $$H(s)=\frac{RCs}{1+RCs}$$ where \$\tau=RC\$ is the time constant of the high pass filter. The most important features of this transfer function are the ...
user avatar
  • 3,603
5 votes

Finding the laplace transform of a wave?

The easiest way is to define \$f(t)\$ as a piecewise function $$f(t)=\begin{cases}\frac{100}{0.002}\cdot t,&0\le t\le 2\cdot 10^{-3}\\ 100-\frac{100}{0.002}\cdot (t-2),&2\cdot 10^{-3}<t\le ...
user avatar
  • 3,603
5 votes

Standard form of 2nd order transfer function (Laplace transform)?

The "standard" form you believe you have is in fact a low-pass 2nd order filter. Here's a picture that might explain things: - The standard form listed above applies to all types of 2nd order filter ...
user avatar
  • 378k
5 votes
Accepted

Euler's relation (e^(j*pi/4)

I don't know how you managed to get cos(pi/4) = 0.5 because cos(45) = 0.7071 and sin(45) = 0.7071 too. (These errors were subsequently edited out of the question). Hence \$\sqrt{0.7071^2 + 0.7071^2}\$...
user avatar
  • 378k
5 votes

Does an impulse function at t=0 go to infinity, or 1?

The \$\delta(t)\$ is defined as positive infinite amplitude and infinitesimal width with an area of 1 at \$\delta(0)\$, and 0 otherwise. As Wikipedia states: \$\int^\infty_{-\infty}\delta(t)~dt = 1\...
user avatar
5 votes
Accepted

How to find the system response given the transfer function without using Laplace transforms?

I assume you are permitted to perform partial fractions, even if you aren't supposed to use \$\mathscr{L}^{-1}\$. The roots of your denominator are \$p_1=-6+j\:8\$ and \$p_2=-6-j\:8\$ and the root of ...
user avatar
  • 68.8k
5 votes
Accepted

How can I design a low pass filter using Z transform in Microcontroller?

The usual method to design an IIR filter is to start with a frequency response we want, for example. $$A(s)= \dfrac{1}{1+\dfrac{s}{\omega_p}}$$ Where \$ \omega_p \$ is the pole frequency in \$ \text{...
user avatar
  • 4,670
5 votes
Accepted

Finding impulse response by a non-Laplace-transform method

Great question. Of course, transforms are the best way to solve this, which you already know. But maybe when you start with a bunch of numbers from an oscilloscope instead of a nice, neat formula, ...
user avatar
  • 2,487
4 votes
Accepted

How to get the crossover frequency from a Laplace oquasion

Cross-over frequency, in the context of control / signal-systems, is defined as the frequency where the magnitude of transfer function crosses the 0 dB axis (amplification = 1). For the first-order ...
user avatar
4 votes
Accepted

What is the significance of the standard form of 1st and 2nd order transfer functions?

What is the physical meaning of "first" and "second order"? ... How do I know if a system is first or second order? A 1st order system has one energy storage element and requires just one initial ...
user avatar
4 votes

What is the significance of the standard form of 1st and 2nd order transfer functions?

The order of a transfer function is determined by the highest order of the denominator. This order gives the number of poles and - thus - determines the roll-off characteristics of the transfer ...
user avatar
  • 22.5k
4 votes

For a first order system, what type of response to a sine wave?

A first order system will produce an output which is also a sine, but with a different amplitude and phase. Because the differential of a sine is also a (phase shifted) sine of the same period, and ...
user avatar
  • 1,926
4 votes
Accepted

Steady state response and transfer function

Not quite, \$H(s)X(s)\$ is the response to the signal \$X(s)\$ if the system is initially at rest, i.e. with "zero" initial conditions. You can understand this in the following way. A LTI system can ...
user avatar
4 votes
Accepted

How to easily calculate transfer function of an LC filter

A simple (mathematical!) way to compute a transfer function for a circuit is to find the voltage at the output using the impedances of the components. For a simple \$L\$-\$C\$ circuit (i.e. if you ...
user avatar
  • 654
4 votes

why transfer function of derivative controller is \$s\$ while Laplace of derivative is not only \$s\$?

The bilateral Laplace Transform of \$ f(t) \$ is \$ F(s) = sG(s) \$ See: https://en.wikipedia.org/wiki/Two-sided_Laplace_transform#Properties
user avatar
  • 2,341
4 votes
Accepted

Interpretation of Laplace transformed function and Laplace vs Fourier

The Laplace transform has some nice properties that help to get more insight into the behavior of linear systems. A very nice property is that the Laplace transform evaluated along the jw-axis is ...
user avatar
  • 7,955
4 votes

Interpretation of Laplace transformed function and Laplace vs Fourier

What are the Fourier transforms for the step and ramp functions? As well stated by Prof. C.P. Quevedo: "The idea of saying that such functions are periodic, with infinite period, no longer applies (...
user avatar

Only top scored, non community-wiki answers of a minimum length are eligible