37 votes
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What does a Bode plot represent and what is a pole and zero of a Bode plot?

Bode plot Take a typical 2nd order low pass filter amplitude response bode plot: - 3-D picture introducing pole-zero diagram Here's the bigger picture of that response when combined with a pole ...
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15 votes
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What is the difference between frequency response and transfer function?

A circuit's transfer function is a fully mathematical model that can be used to derive the frequency response and phase response (both together are called the bode plot). However the same isn't true ...
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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 ...
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14 votes
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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 ...
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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(\...
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12 votes
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Deriving 2nd order passive low pass filter cutoff frequency

EDIT: Thanks to hryghr I see that the starting assumptions were incorrect. The transfer function magnitude can't be found that simply. It is more than ten years since I considered my skills sharp on ...
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12 votes
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Poles and Bode Plots

Bode plot is not a graph that plots the transfer function (\$H(s)\$) against \$s\$. \$H(s)\$ is a complex function and its magnitude plot actually represents a surface in Cartesian coordinate system. ...
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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 ...
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11 votes
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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 ...
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10 votes
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What's the Laplace transfer function of a moving average?

$$\frac{y_k}{x_k}=\frac{1+z^{-1}+z^{-2}+z^{-3}+...+z^{-N+1}}{N}$$ can be re-written as $$\frac{y_k}{x_k}=\frac{1}{N}\frac{1-z^{-N}}{1-z^{-1}}$$ That should be straightforward to model in the s-...
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10 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 ...
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  • 314
10 votes
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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 ...
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9 votes
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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)} = \...
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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.
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8 votes

Poles and Bode Plots

When trying to understand transfer functions, I think the "rubber-sheet analogy" is very useful. Imagine an elastic rubber-sheet covering the complex \$s\$-plane, and imagine that at every zero of the ...
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8 votes

Poles and Bode Plots

The graph shows the difference between the natural frequency in the complex \$s\$-plane (infinite) and the corresponding magnitude peak along the \$j\omega\$ axis which can be observed during ...
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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)\...
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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
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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{...
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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 ...
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8 votes
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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 ...
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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 ...
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7 votes

Is there a way to find the transfer function from only your input and the steady state response?

Is there a way to find the transfer function from only your input and the steady state response? Clearly, no. Steady state response means assentially the 0 frequency response. Obviously systems can ...
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7 votes

Deriving 2nd order passive low pass filter cutoff frequency

A lot of people confuse natural frequency with cut off frequency. The natural frequency is the frequency the system wants to oscillate at. The cut off frequency (or ...
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7 votes
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Finding the transfer function of this RC circuit

In order for the \$R\$ and \$C\$ to be in parallel, you would need \$V_{\text{out}} = 0\$ due to a short circuit. But that's not the case. First calculate \$V_{\text{out+}}\$, the voltage at the + ...
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7 votes
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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. ...
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7 votes
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Transfer Function of Bessel Filter

How come that the transfer function in the TI design guide is not a Bessel polynomial. Let's look at the transfer function you have written: - \$H(s) = \dfrac{1}{0.618s^2+1.3617s+ 1}\$ Rearranging: - ...
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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 ...
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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 ...
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7 votes
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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+...
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