phase second order low pass filter
snee said:
For an active 2nd order low pass filter.
Why is it important to have phase response?
For example, the attachment below which i done simulation for the active low pass filter for temperature -49degree Celcius and 27degree Celcius.
What can i say about the system from the graph that i obtained from simulation?
The 2nd graph is weird to me.
RED line is for -49degree Celcius
GREEN line for 27degree Celcius
The first order systems,
and most of the second order systems, are always stable (because the phase is always less than +-180º, so the nyquist plot can't make a turn around the (-1,0) value, for any amplitude value), this is not true for
third order system, this is an important thing, because those systems can get a phase
bigger than +-180º, so the nyquist plot can make a turn around the (-1,0) value, depending on the amplitude value for that specific frecuency, so the system
can be unstable.
In the second graph (the phase response graph), you must take care of a very important thing, it jumps from -180º to +180º, this is a 360º jump (or 2*pi). In this cases due to the nature of the functions involved (complex functions, that are expressed in terms of sin and cos) the jump is not "true", i mean, a jump of 2*pi is like you have a continuos line.
To do the Nyquist plot, you must use vectors, the amplitude response is the amplitude of the vector and the phase response is the angle of the vector (Like in polar plots). The plot goes from 0 to 2*pi, so for your diagram it will looks like this:
The system, is stable, because it doesn't go around (-1,0).
This is based on Nyquist analysis, you can find a lot of books on stability, but right now i don't remember wich one i've used at university, it was something like "Linear Systems".
This is just an image i've searched in google, so it doesn't reflect the real values in your graph. For a 0 frecuency, the magnitude must be 1, not 0.5, because you get an amplitude of 0dB for a small frecuency.
I've not made the graph, so i can't take the credit. I've searched with google, for something similar, i'm at work right now. 8O
Regards, Diego.
(I apologise, my english is not very good)
The text in Blue was edited to correct a mistake Thanks to LvW.