leo_o2 said:I think complex poles will lead to 180 degree phase shift instead of 90 degree.
tyassin said:Hi
The complex poles will start at -90 degree phase shift at the pole frequency. Then the asymtotic behaivior will reach 0 degrees at lower frequencies. It will reach 180 degree at higher frequencies.
This link explains something: https://www.swarthmore.edu/NatSci/e...odeHow.html#A Complex Conjugate Pair of Poles
Regards
ee484 said:Hi, all.
Thank you all for your reply.
Let me clear my question...
How does RHHP occur with capacitor and active device (e.g. MOS) - without inductor!?
How does a complex pole pair occur with capacitor with active devices - again without inductor?
Of course, I can derive all tedios transfer function to find out RHHP and complex pole pair. However, do you have any intuitive explanation or a way to find those?
BTW, I can answer some of question in the reply. Let me know if my explanations are wrong.
1) Why always complex pole are in pair?
--> This is because a real number that has frequency associated with (e.g. sinusoid) in complex plane in math should be "in pair". For example, to represent 3 in real number (for example, this number 3 is coming from sinusoidal function, meaning associated with frequency), we can write 3+jb. To represent this number in complex plane, there should be 3-jb. With these two numbers 1/2(3+jb + 3-jb) = 3. In conclusion, to represent a real number in complex domain requires to have complex conjugate pair!!!
(NOTE) if you are dealing with imaginary number, yes, a complex number can exit alone, not in a pair.
2) Inductor with capacitor = two reactive components will give you complex poles.
Associating with 1), if you have real value of L and C, you will have a complex pole IN pair. The poles cannot be alone.
However, with R and C only....you will have only real poles (I am not 100% sure, but very sure)
For example, if you have two RC lowpass filter cascaded with no buffer between and find the transfer function, you can make sure that two poles must be real and all in the LHP.
3) tyassin answered complex pole gives us -40dB/dec in magnitude and -90degree/dec in phase.
I agree with -40dB/dec in magnitude at high frequency, but phase respone is in doubt.
If you think simple LC lowpass filter (Here, R is omitted), magnitude response is -40dB/dec drop where f>>f0, where f0 = 1/(2*pi*sqrt(LC)), which is resonant frequency. Now, if you solve phase response, you will have 0 on both sides where f<fo and f>0. If you assume +/-delta f, now you can find the phase change occurs 180 degree. However, this phase response occurs instantly and its slope cannot be -90degree/dec. It is more likey infinity at that resonant frequency. Thus, simple LC filter phase respone cannot be -90degree/dec in general.
I understand this is little tricky.
Reply me if you have different viewpoints or you don't agree.
B
I think complex poles will lead to 180 degree phase shift instead of 90 degree.
would u plz explain why ?
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