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Add a zero to this RC transfer function

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bonzer:
This is what I mean. Therefore it looks like the resistor version has a more complicated formula. Anyway from the physical/engineer point of view which solution is better in your opinion? (compare it to the one at reply #17)

Also: from the bode diagram analysis their overshoot is at the same level. There's no difference at the critical point between them. But phase margin is bigger when adding the capacitor so it looks more stable but there's little difference anyway (like between 40 and 50°).

MrAl:

--- Quote from: bonzer on January 12, 2019, 08:52:10 pm ---This is what I mean. Therefore it looks like the resistor version has a more complicated formula. Anyway from the physical/engineer point of view which solution is better in your opinion? (compare it to the one at reply #17)

Also: from the bode diagram analysis their overshoot is at the same level. There's no difference at the critical point between them. But phase margin is bigger when adding the capacitor so it looks more stable but there's little difference anyway (like between 40 and 50°).

--- End quote ---

Hi again,

Here are the two idealized time responses:

First circuit:
0.078431373*e^(-754.71698*t)-108.07843*e^(-20000*t)

Second Circuit:
0.0034894227*e^(-754.71698*t)-129.00349*e^(-24319.066*t)

They are almost the same.  One is just a little faster.

bonzer:
So in theory there's no big difference. But finding a cap with a precise value would cost more as they usually have much bigger tollerance in value than resistors. So I suppose that If anyone had to build them, he would add the resistor.

MrAl:

--- Quote from: bonzer on January 13, 2019, 09:18:42 am ---So in theory there's no big difference. But finding a cap with a precise value would cost more as they usually have much bigger tollerance in value than resistors. So I suppose that If anyone had to build them, he would add the resistor.

--- End quote ---

Hi,

Well for that you would do a sensitivity analysis.  Just how sensitive is the response to a small change in cap value for some particular capacitor.  There is a chance that the response does not change much for a small change in cap value.  Most likely the time constant changes a little and could be in proportion to the cap value.  So for say a 0.010uf cap changing to a 0.015uf cap we probably see a 50 percent change in time constant, which for this would probably equate to settling time.  There also could be a change in amplitude, probably the max would follow the same rule.

Usually you pick a standard cap value then pick a suitable resistor.  That's probably because you can get lots of resistor values and you probably have them on hand already anyway.

The Electrician:
I get the exact same time responses as MrAl did in reply #26.  If we plot the frequency responses for those same two cases, we get this:

The blue curve is for the first circuit and the red curve is for the second circuit:



The frequency responses are significantly different, so we would expect different time responses.  If Rd4 is changed to 193 ohms, and Cd2 is changed to 260 nF, we get these frequency responses; they're practically coincident:



With these changes, the time response of the second circuit becomes:

0.0790072*e^(-754.717*t) - 107.706*e^(-19928.3*t)

Compare this to the time response of the first circuit--it's very similar as we would expect given the similarity of the frequency responses.

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