26
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 ...
- 21.1k
15
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 ...
- 444k
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 ...
- 2,644
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.
- 2,081
9
votes
Accepted
Trouble with filter using Laplace transfer function in LTSpice
Save some grief: set \$\omega=1\$
Just save yourself some algebra grief and set \$\omega=1\$ when focused on a particular filter shape (like Bessel.) The filter shape can be moved around freely (at ...
- 5,757
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)\...
- 7,506
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 ...
- 71
7
votes
Transfer function of non-inverting op-amp circuit
You forgot to include the high-pass filter at the input. Solve for its transfer function, and then multiply it by 10, which is the gain you calculated for the op-amp transfer function.
EDIT:
In one of ...
- 3,457
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 ...
- 80.5k
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 ...
- 7,506
6
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{...
- 4,800
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 ...
- 21.1k
6
votes
Accepted
Differential equation from a circuit: two methods give different results
The two results don't correspond because there are two different functions being used for \$E\$. In time-domain approach taken in the lecture, it is assumed that \$E\$ is constant for all \$t\$, ...
- 2,632
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}\$...
- 444k
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 ...
- 77.5k
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, ...
- 2,632
5
votes
Why is a capacitor to ground a low frequency pole, instead of a high frequency zero?
I intuitively expect the capacitor to cause a zero for those high
frequencies, not a pole.
It does create a zero but only when the frequency is infinite.
For more normal frequencies (such as the 3 dB ...
- 444k
5
votes
Confusions regarding Laplace transform
First, what is a transformation? A transform is a mapping of a function in one domain into another domain. To go from one domain to another, you need basis-functions (basis-vectors).
In Fourier ...
- 3,891
5
votes
Accepted
Inverse Laplace transform
If you want to confirm your inverse transform with a specific circuit you need to come up with a particular solution. You can't just plug in a general solution. It seems as though you don't realize ...
- 77.5k
5
votes
Transfer function of non-inverting op-amp circuit
Well, notice that in an ideal opamp we know that:
$$\text{V}_+=\text{V}_-\tag1$$
Using the voltage divider formula, we see that:
$$\text{V}_+=\frac{\text{R}_1}{\text{R}_1+\frac{1}{\text{sC}}}\cdot\...
- 7,436
4
votes
Interpretation of Laplace transformed function and Laplace vs Fourier
What are the Fourier transforms for the step and ramp functions?
As well stated by Prof. C.P. Quevedo: "The idea of saying that such functions are periodic, with infinite period, no longer applies (...
- 2,633
4
votes
Accepted
Interpretation of Laplace transformed function and Laplace vs Fourier
The Laplace transform has some nice properties that help to get more insight into the behavior of linear systems.
A very nice property is that the Laplace transform evaluated along the jw-axis is ...
- 8,155
4
votes
why transfer function of derivative controller is \$s\$ while Laplace of derivative is not only \$s\$?
The bilateral Laplace Transform of \$ f(t) \$ is \$ F(s) = sG(s) \$
See: https://en.wikipedia.org/wiki/Two-sided_Laplace_transform#Properties
- 2,506
4
votes
Finding Transfer Function, Poles, Zeros of an RC Circuit
Using impedances (forgive the lack of standard forms along the way) and going long-hand from scratch, I get:
$$\begin{align*}
\frac{V_O}{V_I}&= \frac{R\:\vert\vert\: C_2}{C_1+R\:\vert\vert\: C_2}\...
- 77.5k
4
votes
Laplace transform on simple low pass filter in Python
You're trying to plot in the time domain (ie. the x-axis is in seconds) but your formula is in the frequency domain (s is a complex frequency variable). You would ...
- 3,211
4
votes
How Fourier transform be able to deal with transients?
Check out any reference on Gibbs phenomenon. It essentially says that the Fourier series cannot fully accurately represent any repetitive signal with discontinuities. What one gets when the series is ...
4
votes
Accepted
Question about transient behaviour in op-amp circuit
Obviously, this cannot occur in a real circuit
You have several problems.
You are using derivatives on something that is discontinuous. That usually tends not to work. Also, the opamp's output ...
- 72.2k
4
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\...
- 8,149
4
votes
Accepted
Why do we use Laplace transforms to analyse transient circuits?
It's easy to solve simple filter circuits in the time domain but there becomes a tipping-point where most engineers would prefer to solve problems in the frequency domain and apply (for example) a ...
- 444k
4
votes
Why inverse of time delay is non causal
"Causal" in this case means "A leads to B". The cause is first, then comes the effect.
Example of causality: You hit your finger with a hammer, then it hurts.
Example of non-causality: Your finger ...
- 8,901
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