15
votes
Accepted
Why do we use step response?
Step response and transfer function are interchangeable via Laplace transform (step response -> differentiate to get impulse response -> laplace -> transfer function), but you can't run a Laplace ...
- 72k
14
votes
Accepted
Determine transfer function from circuit
When you deal with a circuit whose transfer function must be determined, you must try to rearrange the components and sources in a friendlier way so that things become clearer. For instance, in your ...
- 21k
13
votes
Accepted
over and critically damped systems settling time
TL;DR: NO, you can't use the underdamped settling time formula to find out the settling time of an overdamped system. And you can't use it for a critically damped system either.
LONG FORM answer ...
- 5,751
13
votes
Significance of cut-off frequency in a low-pass filter
H(w) =1/ (square root of 2) That sounds a bit confusing, we usually refer to the cutoff point as the -3 dB point.
That is the same though, -3 dB is half the power.
Let me explain: take your \$H(\...
- 80.5k
12
votes
How to find phase angle from transfer function
It is just a matter of manipulating complex numbers.
$$ \angle H(\omega) = \tan^{-1} \left( \frac{\Im\{H(\omega)\}}{\Re\{H(\omega)\}} \right)$$
Where \$\Re \{ \cdot \} \$ is the real part and \$ \Im ...
- 334
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
Exciting an RC Circuit at its TRUE Pole on the Sigma (Real) Axis in the Left-Half Plane
Good question, here's my attempt. You still have to convert your input signal from the time domain to s domain, then do the math, then convert the result back to the time domain. That pole just tells ...
- 2,001
10
votes
Accepted
Calculating magnitude of a transfer function
First off, we transform the s domain to frequency domain with \$s=j\omega \$
which gives us:
$$T(j\omega) = \frac{1}{(j\omega+1)((j\omega)^2+j\omega+1)} = \frac{1}{(j\omega+1)(j\omega+1-\omega^2)} = \...
- 140
10
votes
Accepted
Is every linear circuit equivalent to a single RLC series circuit?
Is every linear circuit equivalent to a single series RLC circuit?
No. All passive linear circuits can be reduced to an order that is dependent on the number of independant storage elements. They can ...
- 13.6k
9
votes
Accepted
Understanding in-loop compensation for capacitive-loaded OpAmp
I believe the authors used fast analytical circuits techniques or FACTs but I am not sure about their results. The principle is based on the generalized Extra-Element Theorem or EET from Dr. ...
- 21k
9
votes
Is there an English word for the output response of a non-minimum phase system?
I've always heard that being called undershoot. And, in this Control Systems magazine article on Nonminimum-Phase Zeros they also call it initial undershoot.
- 2,537
8
votes
Laplace of \$f(t)\cos(\omega t)\$
First, note that: \$\small cos(\omega t) = \dfrac{e^{j\omega t}+e^{-j\omega t}}{2} \normalsize\$
The s-shifting property of the Laplace Transform is: \$\small\mathscr{L}[f(t).e^{at}]=F(s-a)\...
- 7,506
8
votes
Real device with derivative transfer function
You can build such a device with limitations from an OP-amp, 1 resistor and 1 capacitor.
simulate this circuit – Schematic created using CircuitLab
- 3,876
8
votes
Accepted
Second order all-pass filter using a single op-amp
One option for a second order all-pass filter with one OpAmp is the Delyiannis structure, as shown here (p.2):
The transfer function of this filter is given by
$$H(s)=\frac{R_4}{R_3+R_4}\cdot \frac{...
- 3,651
8
votes
Accepted
How can I build a circuit with this transfer function, using only resistors?
There are two problems with your design.
A voltage divider only produces it's notional output voltage when unloaded.
Your second stage forms an averaging circuit not a sum.
Bottom line is that your ...
- 21.7k
8
votes
Accepted
Is there an English word for the output response of a non-minimum phase system?
I think the correct term in English would be “initial inverse response”.
The system initially does the opposite of what is commanded. For example, in this book. So it’s even worse than a dead time ...
- 384k
8
votes
Accepted
I'm confused a bit on basic control stuff for a PID controller
Your control is quite good despite if you feel in other way. I do think that a P-control with feed forward LUT (Look Up Table) would solve 98% of your need.
Try this way:
For each temperature ...
- 23.7k
8
votes
Accepted
What is the definition of phase margin?
It's not the definition of phase margin. It's the way that "gain" in a control loop is defined. There's two systems of thought jostling together in the world of control theory, and neither ...
- 45.4k
7
votes
Accepted
Resonance frequency of an RLC circuit
KCL: (\$v_o\$ over your output, \$v_i\$ over voltage source and \$v\$ over the internal node:
$$ \frac{v_o}{R_3} + \frac{v_o-v}{Z_{C1}}+\frac{v_o-v_i}{R_2} = 0 \\
\frac{v}{Z_L} + \frac{v-v_i}{Z_{C2}} ...
- 1,305
7
votes
Resonance frequency of an RLC circuit
It is important to realize that the resonance frequency (i.e., the frequency at which the circuit resonates if the damping is sufficiently low) of a second-order RLC circuit never equals \$\frac{1}{\...
- 3,651
7
votes
Transfer function of Bessel filter
A Bessel filter has, as you correctly show in your first formula, \$\omega_0=\sqrt{3}\$. It's not unusual if you think that, normally, a Bessel filter is used for its flat group delay, rather than its ...
- 21.2k
7
votes
Why do we use step response?
An impulse, i.e. hit it with a hammer, is not very friendly, particularly in systems that have mechanical bits and pieces.
A perfect impulse cannot be generated, so you have to tailor the pulse ...
- 7,506
7
votes
Accepted
How to sketch the Bode diagram of the output filter of a Buck converter?
Background
Starting with your result and proceeding:
$$\begin{align*}
H\left(s\right)&=\frac{R}{R\,L\,C\,s^2+L\,s+R}\\\\
&=\frac{1}{L\,C\,s^2+\frac LR\,s+1}\\\\
&=\frac{\frac 1 {L\,C}}{s^2+...
- 77.4k
7
votes
Pole zero plot of band reject filter
Perhaps this is where the confusion starts: 's' is complex (re + j*im, or sigma + jw), not just imaginary. Those two terms are often accidentally used interchangeably, and they shouldn't be.
G is ...
- 3,117
7
votes
Accepted
What are the final steps to arrive at the transfer function for this RCL circuit?
Your schematic is as follows:
simulate this circuit – Schematic created using CircuitLab
Above, you can see that \$R_2\$ and \$Z_2\$ form a voltage divider that divides \$V_Y\$ into \$V_\text{...
- 77.4k
7
votes
How to find transfer function of this filter?
Early on, perhaps the best approach to solving complex-looking schematics is to figure out some way to divide them up into things you do recognize and can solve. Then break down each piece, repeating ...
- 77.4k
7
votes
Accepted
Transfer function of an RLC filter
Your numerator in this:
$$
v_{o}=v_{oi}\frac{R}{Ls+R_{L}+\frac{R(\frac{1}{Cs})}{R+\frac{1}{Cs}}}
$$
Should be \$Z_R || Z_C\$. That is,
$$
v_{o}=v_{oi}\frac{R || Z_C}{Z_L+R_{L}+(R||Z_C)}
$$
- 4,917
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