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It can be generated by current mirror in differential amplifier... also in the case of pole-zero cancellation, when components are not perfectly matched.
The effect of pole-zero doublet could be not clearly seen in the amplitude and phase response, especiaqlly if the case if they are closed together, but relativlly small mismatch can have high impact on time response.
For step response in the case of zero-pole doublet (especially in area around unity gain frequency) is typical one fast part and one much slower (undershoot), which can significantly degrade settling time.
In the case of pole-zero doublet there is an overshoot with also slow settling time.
It can be generated by current mirror in differential amplifier... also in the case of pole-zero cancellation, when components are not perfectly matched.
The effect of pole-zero doublet could be not clearly seen in the amplitude and phase response, especiaqlly if the case if they are closed together, but relativlly small mismatch can have high impact on time response.
For step response in the case of zero-pole doublet (especially in area around unity gain frequency) is typical one fast part and one much slower (undershoot), which can significantly degrade settling time.
In the case of pole-zero doublet there is an overshoot with also slow settling time.
It is true for standard two pole system until Q factor reach value of 0.7(Butterworth response). For higher peaking you would have faster rise time, but slower settling time(approx Q periodes of osillations).
Here are two unity gain closed-loop response plots for pole-zero (wz=2wp), and zero pole (wz=0.5wp), where N is number of decades from unity gain frequency. You could se that the biggest problem is around unity gain frequency, and that overshoot does not mean fast settling time.
(1) What is the relation between phase margin and settling time? From rajavi (page 354), I can concldue that better the phase margin, slower is the response or settling time is more. Correct me if I am wrong!
(2) Now if we are talking about pole-zero doublet, we should specify whether it is right half or left half plane zero. In diode connected load, it is a left half plane zero. As I know, left half plane zero increases the phase margin.
Is this the reason why you are saying that doublet causes large settling time?
(3) If it the reason, then pole-zero or zero-pole both will result in good phase margin (bad settling time), but zero-pole doublet will be worse in terms of settling time. Correct me if I am wrong!
(1) What is the relation between phase margin and settling time? From rajavi (page 354), I can concldue that better the phase margin, slower is the response or settling time is more. Correct me if I am wrong!
(2) Now if we are talking about pole-zero doublet, we should specify whether it is right half or left half plane zero. In diode connected load, it is a left half plane zero. As I know, left half plane zero increases the phase margin.
Is this the reason why you are saying that doublet causes large settling time?
(3) If it the reason, then pole-zero or zero-pole both will result in good phase margin (bad settling time), but zero-pole doublet will be worse in terms of settling time. Correct me if I am wrong!
1. Circuits with smaller phase margin have faster rising time. Settling time is equal with rise time just until peaking is produced. If phase PM is low, ringing is produced, and settling time is worse. Aproximattely for known Q factior you need Q ringing cycles to settle... which makes settling time worse.
Optimal value should be around butterworth response (Q=0.707, PM=63)
2.RHP zero makes different response of this drawn. For fast impulse its shorts inverting amplifier which makes positive loop, and because of that your signal shortly goes in first in one direction (same as input because of positive feedback), and than in other when negative feedback becomes active...
>Is this the reason why you are saying that doublet causes large settling time?
No,
phase margin can be same as forButterworth response, but you can have higher settling time than expected... because of that doublet can be dangerous...
For doublet is most valid transient response...
This is a very good point that settling time is equal to settling time until peaking occurs.
That means, lower the phase margin, lower is the rising time. (is it true for any number of pole system? someone told me that these theories work only for two pole system)
Now settling requirements may depend upon the user. So the question comes who decides the amount of overshoot. Can you suggest some good paper where I can see these calculations.
B.Y ESHWANT KAMATH,"Relationship Between Frequency Response and Settling Time of Operational Amplifiers"
meghna said:
This is a very good point that settling time is equal to settling time until peaking occurs.
That means, lower the phase margin, lower is the rising time. (is it true for any number of pole system? someone told me that these theories work only for two pole system)
Now settling requirements may depend upon the user. So the question comes who decides the amount of overshoot. Can you suggest some good paper where I can see these calculations.
It is true for standard two pole system until Q factor reach value of 0.7(Butterworth response). For higher peaking you would have faster rise time, but slower settling time(approx Q periodes of osillations).
Here are two unity gain closed-loop response plots for pole-zero (wz=2wp), and zero pole (wz=0.5wp), where N is number of decades from unity gain frequency. You could se that the biggest problem is around unity gain frequency, and that overshoot does not mean fast settling time.
So what's the difference between the pole-zero doublet and zero-pole doublet?
If Wz>Wp,is it called pole-zero doublet,and vice versa?
Other question is that in my impression,Q factor is a factor to describe AC frequency response.But for settling time,it is a time domain response, so is it reasonable? Thanks
So what's the difference between the pole-zero doublet and zero-pole doublet?
If Wz>Wp,is it called pole-zero doublet,and vice versa?
Other question is that in my impression,Q factor is a factor to describe AC frequency response.But for settling time,it is a time domain response, so is it reasonable? Thanks
1.) In short: We have an "doublet" if we introduce a zero Fz1 and a pole Fp2 with the aim to cancel another pole Fp1 - and if Fz1 does not meet Fp1 exactly !
If Fz1>Fp1 the step response will have a "long tail" slightly above the final value and if Fz1<Fp1 the tail will be slightly below the final value.
2.) The Q factor of a pole pair is a measure for the ac response in the transition region around the pole frequency - and at the same time Q detrermines the step response in the time domain. For Q>0.5 we will have a an overshoot which increases and turns into ringing for higher Q values.
So what's the difference between the pole-zero doublet and zero-pole doublet?
If Wz>Wp,is it called pole-zero doublet,and vice versa?
Other question is that in my impression,Q factor is a factor to describe AC frequency response.But for settling time,it is a time domain response, so is it reasonable? Thanks
1.) In short: We have an "doublet" if we introduce a zero Fz1 and a pole Fp2 with the aim to cancel another pole Fp1 - and if Fz1 does not meet Fp1 exactly !
If Fz1>Fp1 the step response will have a "long tail" slightly above the final value and if Fz1<Fp1 the tail will be slightly below the final value.
2.) The Q factor of a pole pair is a measure for the ac response in the transition region around the pole frequency - and at the same time Q detrermines the step response in the time domain. For Q>0.5 we will have a an overshoot which increases and turns into ringing for higher Q values.
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