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[Moved]: What are the general guidelines to quickly identifying poles and zeroes?

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jaydnul

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Without deriving the transfer function, what is the general method of identifying poles and zeroes of an arbitrary circuit? As I understand so far, to find a pole you short the voltage source and calculate the total resistance to ground and the total capacitance to ground. Then the time constant is 1/RC. If that is correct, I have a few more questions:

1. What is the method to calculate a zero? Because if you use the same method and short the voltage source, you will end up getting the same values for R and C as the pole.
2. Basically poles and zeroes are low pass and high pass circuits made by the capacitance in the circuit, right? Wouldn't that mean all of the phase changes are lags? How does a RHP pole or LHP zero manifest itself?
3. How do you tell if a pole or zero calculated with these methods is LHP or RHP? Or is the only way by deriving the transfer function?
4. How do you know when you need to use the resistance R to calculate the time constant 1/RC or the transistor gm to calculate the time constant gm/C? How do you know which gm to use?

Thanks a bunch!
 

Re: What are the general guidelines to quickly identifying poles and zeroes?

Without deriving the transfer function, what is the general method of identifying poles and zeroes of an arbitrary circuit? As I understand so far, to find a pole you short the voltage source and calculate the total resistance to ground and the total capacitance to ground. Then the time constant is 1/RC.
Time constant is R*C. I should mention that that works only for single-time-constant circuits (only caps + resistors OR only inductors + resistors, no mixing).
So, it is not so general as you think.

1. What is the method to calculate a zero? Because if you use the same method and short the voltage source, you will end up getting the same values for R and C as the pole.
You test what is the output of the circuit when ω->∞ or ω=0.
When ω=0 and the output =0, then High pass circuit with G(s)=s*tau/(1+s*tau), otherwise, low pass circuit with real LHP pole.
Only works for single-time-constant circuits.

3. How do you tell if a pole or zero calculated with these methods is LHP or RHP? Or is the only way by deriving the transfer function?
LHP..generally
Another way is to graphically draw the bode plot by inspection... then, you realize where are the poles or zeros by looking at it.
 
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Re: What are the general guidelines to quickly identifying poles and zeroes?

If a pole can be found as 1/RC, then why do you sometimes see (like in a 2 stage op amp) the poles represented as gm/C? That suggests that they are multiplying the original pole by the gain (since Av/RC = gm/C). But why?
 

Re: What are the general guidelines to quickly identifying poles and zeroes?

gm/C might represent the pole ω for specific feedback circuits. You need to perform detailed circuit analysis.
 

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