What is pole analysis ?

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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.

:)
 
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!
 
thanks both.
its a good start but please help me put this in first gear.


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.


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


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


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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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
 
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]



;)
 
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.
An externally hosted image should be here but it was not working when we last tested it.



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


An externally hosted image should be here but it was not working when we last tested it.


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.
 
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.
 
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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One simple thing no one here has apparently considered is the response of the microphone at low frequencies, certain patterns can exhibit a strong proximity effect boost at low frequencies. Also the roll off in the response may be quite deliberate based on one of several psychoacoustic weighting curves used for measuring spl. I would recommend leaving it alone for this reason.

I checked one of rat shack analog meters against a B&K (model forgotten it was long ago) and the calibration was quite close on both A and C weighting. (within a dB or so from about 100Hz up)
 
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The wallin mods defeat the weighting applied in these meters which is exactly what you need if you are trying to measure spkr frequency response or unweighted spls, or particularly in order to determine the flatness of the speaker/room response. If you are trying to correlate what sounds loud to human hearing you do need the weighting, so in the end it depends on what the meter will be used for.

;)
 
Let me provide some more info...

kevinkr said:
One simple thing no one here has apparently considered is the response of the microphone at low frequencies

The RMAA response posted above does NOT include the mic. The mic was removed and signal was applied straight to the pads where the mic goes. So that response is only of the 'electronics' of the meter.


NetRunner said:
Do you have to do it yourself? Eric Wallin has done much the same previously: Radio Shack SPL Meter mods.

True but like I mentioned earlier I also want to find out if its worth changing the IC or not. And I also wanted to find out more about pole analysis and how its done.

kevinkr said:
T..if you are trying to measure spkr frequency response or unweighted spls, or particularly in order to determine the flatness of the speaker/room response.


...and that is the purpose.


Look at these two charts. These are of a woofer and a tweeter measured with a PC based speaker measurement setup (BLUE). Setup is a ECM8000 mic, UB802 mixer/preamp, Turtle Beach Santa Cruz soundcard and Speaker Workshop. Then the mic+preamp was simply swapped for the radioshack meter (RED). The meter has an rca/phono out so it could be essentially used as a mic+preamp.

Both measurements are nearfield (very close to the cone/dustcap).

I would have expected the shape of curves(not the amplitude for now, just the shape) to be same atleast in the frequency range where the meter electronics is flat. Notice the rise in response between 2k-5khz. My guess is that this behaviour could be because of the mic capsule used because that is the only thing different between the RMAA and acoustic tests.

First the Woofer -


An externally hosted image should be here but it was not working when we last tested it.



...and the tweeter..


An externally hosted image should be here but it was not working when we last tested it.



..
 
Do multiple poles (or zeros) add up to a net result or are they all independent of each other ?
for example if there are two or three poles in a circuit that have -3db points of say 8hz, 16hz and 6hz then will they somehow interact or add up to some final pole frequency ? or just the pole with the highest frequency(16hz in this case) simply becomes the most restrictive pole ?
 
In the case of poles the lowest valued one tends to be considered the dominant one... the converse applies to zeros.

A 3rd order low pass filter with poles at 10, 100, and 1000 Hz would be considered a 10 HZ low pass filter.

A 3rd order high pass filter with poles at 10, 100, and 1000 Hz would be considered a 1000 HZ high pass filter.

This is somewhat of a word game though... and in the course belittles the real math behind it all.
 
Greetings from Norfolk

Having in the distant past worked closely with engineers developing special microphones, I would say that the difference between the red and blue curves could be explainable just by the different microphones used. Mics do vary considerably, even between samples of the same type, especially near their 'limits' of frequency operation.

A plot of the ACTUAL performance of each of the mics would be very illuminating. This needs to hbe done very carefully, under controlled conditions.

Whilst the actual size of the mic capsule is a guide to its low and high frequency limits, the actual internal design modifies the detailed frequency performance - the type of damping and pressure equalisation material used for example.

Plot the curves for the two mics under identical conditions, using, ideally, a flat amplifier, with the correct loads on the mics.

Richard
 
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