Electronics > Beginners
Poles and Zeros
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b_force:

--- Quote from: IconicPCB on June 15, 2018, 08:29:53 pm ---Without a through understanding of maths, graphical solutions and rules of thumb would not come into existence.

Bode plots , stability circles. Smith Charts. various nomographs are a product of thorough understanding of maths describing a particular condition.

Don't be scared by the problem...understand and appreciate it.

--- End quote ---
One of my best teachers on my university for control theory had a much easier approach.
He just showed us a controlled valve system, what happens when it's underdamped, what happens if it's over damped and what happens when these "poles and zeros" are placed wrong.
Understanding a problem doesn't mean you need to know all the math behind it.
It means that you understand why it happens and what needs to be done to fix it.
Some people think in theoretical math equations, other people think in physics.

When a system is unstable you only need to use always the same equations to get it fixed.
Where are these equations are coming from is maybe nice for a Sunday afternoon reading, but you are never gonna think of it ever again
npelov:

Here is what I think about mathematics in electronics. I'm not that good at math, but it never stopped me before. I try to learn the absolute minimum to keep me going. I like to do the math when I can, but I know my limits and I when I reach them I learn more or I just find a shortcut. For practical engineering I this the truth is in the middle. There are people smarter than me who will do the theoretical part.

So I always try to simplify the problem. Do I need to know how to use poles and zeroes to make a feedback work - no. I know that an opamp can't immediately drive a capacitive load. It takes time to charge the capacitor. So when I see the solutions I have a basic idea why they put a resistor on the output and/or a capacitor in the feedback. If I overcompensate the opamp it'll still work. Maybe I don't need such a fast response. But I still want to try and learn as much as I can for cases when I need a faster response and tweaking doesn't do the job.

And in the real word you still need some experimenting and tweaking anyway. Theoretical part relies too much on you knowing every single detail about your parts. You may know the series resistance of a capacitor or the DC resistance of inductor but if you build a complex schematic with many active elements - opamps, transistors etc, the calculations are just the beginning, you may still have to measure, teak or adjust your calculations.

So, back to the poles and zeros.

@rstofer - I've stumbled upon some these videos (Control Course) before. I'll watch the whole series when I have the time. Thanks!

@rbola35618 Thanks for the video it is helpful. I'll have to watch it few more times.

In the link rstofer suggested  Tolga Soyata says that the transfer function can be the impedance of a filter. When I first heard of transfer function I thought  it's the relation of a output voltage to the input - Vout = F(Vin). The impedance is just a part of this relation and in this case it forms a divider with the input/output impedances of connected circuits. That confused me a bit. So the impedance goes to zero or infinity, but the output voltage. How do we choose what is the transfer function?
Benta:

--- Quote from: npelov on June 16, 2018, 02:57:13 pm ---In the link rstofer suggested  Tolga Soyata says that the transfer function can be the impedance of a filter. When I first heard of transfer function I thought  it's the relation of a output voltage to the input - Vout = F(Vin). The impedance is just a part of this relation and in this case it forms a divider with the input/output impedances of connected circuits. That confused me a bit. So the impedance goes to zero or infinity, but the output voltage. How do we choose what is the transfer function?

--- End quote ---

I don't agree with Soyata here. The transfer function describes which output you can expect from a certain input. This can be:
Po/Pi, Uo/Ui, Io/Ii, Uo/Ii, Io/Ui, Po/Ui etc., you can combine whatever you want.
Normally you compare apples with apples, meaning voltage/current/power input-to-output transfer functions.

Bringing impedance into play relates to two-port network analysis, which then can be transformed to a transfer function.

jmw:
As a non-EE (software engineer) who has strayed into power electronics and had to start from zero on this same subject, I must agree with Cerebus and say there is no running away from this mathematical subject if you want to design circuits that have feedback loops. You may be able to skate by, but you will be mostly limited to copying reference designs or making small tweaks to one. I've found it to be an illuminating way to understand circuits and well worth the effort to do things that aren't a straightforward application of a datasheet example.
IanB:
Since this is a question I have had for a long time and not seen any clear answers (including in this thread), I would like to echo the question from the first post, and try to pose the question more clearly:

If you have a transfer function and you can locate the poles and zeros in this function (take that as a given), how do you use the location of these poles and zeros to interpret the behavior of the circuit? So for example, maybe there is a pole at 100 kHz. What, practically, does this mean for the circuit and for stability analysis?

Lots of suggested answers explain how you can find the location of poles and zeros, but this is just the application of mathematics, it does nothing to answer the question.

Can anyone point to a resource, maybe like a "3blue1brown" video that really explains what the poles and zeros mean, what you should deduce from them, and what your goal should be when you try to shift their position or eliminate them?
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