what information can we get from phase response of a filter?

phase response low pass filter

How to understand the phase response of a simple low pass filter?
What does it represent? stability of the system?
How do we know if the system is stable?

phase response of filter

snee said:

How to understand the phase response of a simple low pass filter?
What does it represent? stability of the system?
How do we know if the system is stable?

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What do you mean with "simple low pass" ? Just an RC unit of 1st order ?
Your question can´t be answerd in this general form. Please, be more specific.
Stability issues can be discussed only with respect to a specific active circuit (with feedback).

why we need phase response of system

For analog filters with poles and zeros, the amplitude and phase response are related by the Hilbert transform. The phase response differentiated gives group delay which can be used to predict degrading of digitally modulated signals.

phase respons sine

snee said:

How to understand the phase response of a simple low pass filter?
What does it represent?

Click to expand...

The phase response is the phase difference between the input and the output if you use a sin signal as input. https://en.wikipedia.org/wiki/Phase_response
To understand whaat happens, think in a sin out of phase by 90º, what you get? a cos. For the diagram attached, with a frecuency of 10^-2 you get the same input and output, a sin; but with a frecuency of 10^2 you use a sin as a input, and get a cos. The problem is that in this case the output for a frecuency of 10^2 is 100 times (-40dB) smaller than the input.

One information you get from the phase response is the phase distort. In general audio applications you don't worry about the phase distort because we can't detect (hear) a phase distort. But in other types of systems it can be a problem. If the phase varyes linear with the frecuency you don't get phase distort

snee said:

stability of the system?
How do we know if the system is stable?

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To study the stability of a circuit (with feedback, like LvW says) you need both the phase response, and the gain response of the open loop system. The method is the Nyquist plot, and with it you can find if a system is stable or not, and how much close of unstability (phase and gain margin) it is. You can search in study books of linear systems, to see the complete method.

In the figure is the amplitude and phase response of a simple first order system, like an RC low pass filter.

I hope this help, and if i made any mistake please correct me.
Regards, Diego.

phase response plot filter

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

phase response sin cos

system stability can be seen by pole zero filters,it tells u the phase shift in ur input it shows it is worth while in case of all pass filter where poles n zeros are on complex conjugates of each other,we cann't find any thing by its amplitude response.

2nd order phase response

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

Click to expand...

1.) Plotting of phase response is not important for active filters because it has a close and fixed relationship with the magnitude response. But in simulation it can give you a feeling about stability (because the magnitiude response looks good also for instable systems).
2.) For non-inverting low-pass filters there should be a smooth decrease of phase down to -180 deg.(2nd order) or -270 deg (3rd order) and so on.
3.) The 2nd graph looks good . Your program cannot show phase shifts larger than -180 deg and switches to +180 deg. (Remember: -270deg=+90 deg.)

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

Click to expand...

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.

what we can get form phase response

diegobb said:

The first order systems are always stable (because the phase is always less than +-90º, so the nyquist plot can't make a turn around the (-1,0) value, for any amplitude value), this is not true for second order system, this is an important thing, because those systems can get a phase of +-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.
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I can agree to (nearly) everything diegobb has mentioned, except one point:

In principle, also a 2nd order low pass cannot be unstable as the (ideal) phase approaches -180 deg. only at infinity. But I know, that real opamp behaviour introduces more phase shift - however, as the pole Q of low pass filters is mostly in the range of 2.0 or less (Butterworth: 0.707) there is no danger that the Q will approach infinity due to parasitics. The problem is more severe for bandpass filters with desired pole Q values of 20...50 or even larger.

filter amplitude and phase relationship

I can agree to (nearly) everything diegobb has mentioned, except one point:

In principle, also a 2nd order low pass cannot be unstable as the (ideal) phase approaches -180 deg. only at infinity. But I know, that real opamp behaviour introduces more phase shift - however, as the pole Q of low pass filters is mostly in the range of 2.0 or less (Butterworth: 0.707) there is no danger that the Q will approach infinity due to parasitics. The problem is more severe for bandpass filters with desired pole Q values of 20...50 or even larger.

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Yes, you are 100% right, the ideal systems of second order are stable, the third order systems can be unstable.

Sometimes my memory fails, thanks for your correction. I've edited my previous post to correct the mistake.

Regards, Diego.

second order filters phase response

thanks to everyone, your information really did help me. ;-)

filter phase response

diegobb said:

Yes, you are 100% right, the ideal systems of second order are stable, the third order systems can be unstable.
Sometimes my memory fails, thanks for your correction. I've edited my previous post to correct the mistake.
Regards, Diego.

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Hi Diego !
Your memory did fail ? Well, this also applies to me. Sorry.
Of course, a second order system can be unstable under certain circumstances.

Thus, I have to correct my statement as follows:
1.) A second order system which only incorporates NEGATIVE feedback is always stable.
2.) If there is some POSITIVE feedback (in combination with neg. feedback) the system may become unstable when both feedbacks cancel each other.
This could be the case, for example, for the non-inverting SALLEN-KEY-equal-value-lowpass which can be very sensitive to gain tolerances, and will be unstable (oscillate) for G=3.

Regards (and sorry for the late correction)

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