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Old 31st January 2006, 08:00 PM   #1
percy is offline percy  United States
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Default What is pole analysis ?

I understand that pole analysis is typically done to find out where and why there is an anomaly in the frequency response of an amplifier. But I'd like to know how exactly is pole analysis done ?
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Old 31st January 2006, 08:12 PM   #2
poobah is offline poobah  United States
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BBBBBBBBBIIIIIIIIIIIIIIGGGGGGGGGGGGG subject.

Think of a pole as a low pass filter (or an integrator). Think of a zero as a high pass filter (or a differentiator).

When you talk about transfer functions; poles are terms in the denominator of the equation, zeroes are in the numerator.

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Old 31st January 2006, 11:36 PM   #3
clem_o is offline clem_o  Philippines
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In other words, you have to model or get the mathematical equivalent of the real-world transfer function of the amplifier. With this equation, you look at the denominator (usually a polynomial), do factorization and figure out the values that will zero-out the equation. These are your poles, and their values tell you if the amp is stable or not... I left this behind when I realized you can't figure out the math equation without measuring the amp - and if you do 'measure up' the amp, you may as well find out if its stable or not from there...

Cheers!
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Old 1st February 2006, 03:52 PM   #4
percy is offline percy  United States
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thanks both.
its a good start but please help me put this in first gear.


Quote:
you have to model or get the mathematical equivalent of the real-world transfer function of the amplifier
how exactly(practically) is that done ? I realize its a extensive subject but could you point me to some good resources(links, books,..) also.


Quote:
you can't figure out the math equation without measuring the amp

what measurment is needed ? frequency response, noise, thd, etc..??


Quote:
you may as well find out if its stable or not from there
maybe the answer to my previous question might help understand this too.


Also, can pole analysis help identify what part of the circuit is causing the poles or zeros ? for example specifically which coupling capacitor is undervalued to cause the low frequency rolloff ?
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Old 1st February 2006, 04:10 PM   #5
kevinkr is offline kevinkr  United States
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Pole/zero pairs are quite useful in the theoretical domain for modeling amplifier stability and phase/amplitude responses. I find them extremely tedious to interprete and hardly ever use them and I am a full time analog design engineer. They will tell you quickly whether or not the circuit is stable based on what plains the poles, and zeroes inhabit, beyond that it is somewhat difficult to interprete.

I recommend instead that you download spice and learn how to use that instead, you will much more quickly arrive at results that you can use. LTspice/SWcadIII is an excellent choice as you can add competing device models and tubes as well quite easily.

Kevin
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Old 1st February 2006, 04:27 PM   #6
poobah is offline poobah  United States
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Maybe it would help if you state your purpose more precisely.

You should know a lot of calculus to further into poles and zeros.

Let's look at a simple lowpass filter. A resistor in series followed by a capacitor to ground. The transfer function is:

Vo/Vi = Xc / [Xc + R]

Vo/Vi = [1/(2*pi*f*C)] / [(1/(2*pi*f*C)) + R]

Vo/Vi = 1 / [ 1 + (2*pi*f*C*R) ]

At DC, f = 0, the transfer function equals 1. As f increases, the value of the transfer function decreases... where 2*pi*f*R*C equals one in the botton of the equation; this is location of the pole... the -3dB point.

You can solve for the frequency by using this formula:

1 = 2*pi*f*C*R

solve this for f:

f = 1 / [ 2*pi*R*C]



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Old 1st February 2006, 08:10 PM   #7
percy is offline percy  United States
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Quote:
Maybe it would help if you state your purpose more precisely.
Here's what I am trying to do...

Below is the frequency response of the "electronics" of the popular radioshack sound level meter(digital). My goal is to extend the high and low frequency rolloffs further out, without adversely affecting the gain (and hence the calibration of absolute spl) of the meter.
Click the image to open in full size.


If you would like to take a look at the schematic of the meter which another enthusiast has drawn up then its here -


Click the image to open in full size.

Now how do I identify which networks, and components within those networks, are causing the rolloffs ? I can look at the schematic and identify some networks right away especially in the input section that the coupling caps are undervalued but how can I make sure I covered them all ? and thats where pole analysis came in.

It could also be the IC (LM324) that is rolling off but someone in the chipamp forum said that its not likely and I dont want to go about replacing ICs without really making sure it will help. So baiscally I just want to sort out the areas which are causing this rolloffs. Hope that helps.

Generally math(algebra, trig) doesn't intimidate me. Now calculus is something I wasn't really friends with but that was at a time when I didn't have access to calculators that could do calculus!
I am still encouraged to try it though.
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Old 1st February 2006, 09:55 PM   #8
poobah is offline poobah  United States
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OK,

c2, c5, c6, c7, c11, c12 are poles these could all stand to increased by a factor of 3 or more... in nearly all cases the method for arriving the value of R is different. Google Thevinen equivalents and find the AC resistance of the node the caps is hooked to.

c4, c9, c12 are zero's and you must do the same thevinenthing but there are op-amps involved so "AC grounds" are less clear.

C13 and its network does something whacky but I don't know what.

C18 is the filter for the peak detector and should left as is.

I would start by just working on the poles and then measure it again.

Kevinkr's idea about getting LTspice is a good one two.

Most of the BS hanging "below" the op-amps is for bias and can be ignored.
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Old 1st February 2006, 11:31 PM   #9
clem_o is offline clem_o  Philippines
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Howdy!

I agree with kevinkr, just plug the circuit into LTSPICE and start modifying the capacitors. Put two versions of the circuit on one schematic page, so that you'll always have a reference output to compare against.

The C13 network seems to be an output coupling network (to a jack?) so I think that can be ignored...

Cheers!
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Old 2nd February 2006, 02:53 AM   #10
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I will just interject that I am 50% of Pole-ish descent and my wife (50% of Italian descent) has never been able to analyze me -- we always revert to the cavalry.
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