Suppose, a simple second order notch filter has pass band gain -1 dB and attenuation at notch frequency is -37 dB (this is the maximum attenuation). Then which shall determine the band width? The -4 dB line or the -34 dB line? Or is it that unlike resonator, for Notch the Q-factor is not that important, compared to its stop band attenuation?
Ideally, the suppression is endless and not a function of the quality factor
In real circuits they play a significant role properties of the actual amplifier, and passive components. See for example
https://www.researchgate.net/publication/281437561_Band_stop_filters_with_real_operational_amplifier
Article Band stop filters with real operational amplifier
Dear Researcher
please refer to this attachments if it is helpful for you.
Regards
http://www.sengpielaudio.com/calculator-bandwidth.htm
https://en.wikipedia.org/wiki/Q_factor
Ideally, the suppression is endless and not a function of the quality factor
In real circuits they play a significant role properties of the actual amplifier, and passive components. See for example
https://www.researchgate.net/publication/281437561_Band_stop_filters_with_real_operational_amplifier
Article Band stop filters with real operational amplifier
I enclose for you the following helpful papers that shows how the Q-factor of the notch filter is determined.
Good luck
Prof. S. EL-Rabaie
There will be, certainly the option to determine the Q factor from the phase response of the circuit.
For a bandpass circuit I know that Q is related directly to the phase slope at the mid frequency: Q=(wo/2)dphi/dw.
Therefore, we can expect that a similar relationship does exist also in case of a band stop filter. But I have no formula for this case.
Thank you all, for your responses. As much as I understand from the documents provided, Notch filter's Q-factor is to be determined from -3 dB point from input magnitude. Actually I have made a fractional order notch filter, and I need to measure its Q-factor from its voltage output data. Thanks again for your help.
U. Dreher
Your analogy to OpAmp Active BandStop
makes things much clearer at the student level.
Results = Q of notch is -3 dB from V(siginput).
Seems so standard now.
Avishek,
You are invited to check my website
for innovative Active Filter designs,
which may help you expand your view
of the Active OpAmp Filter world.
http://www.geocities.ws/glene77is/
Hi U. Dreher,
thank you, you are right . I should have known. And, of course, we must not ake into account the sign of the phase slope.
Here is the math background of the answer:
Bandpass: Numerator s*T always imaginary with no contribution to d(phi)/dw.
Band stop: Numerator (1-s/wp)² always real (imag. part zero).
In both cases, it is the denominator only (identical for band pass and band stop) that contributes to the phase slope at w=wp. Hence, we can show that in both cases: Q=0.5*wp*|d(phi)/dw|.
Thanks Adam,
I also had the same notion in mind. That Q-factor may be a more applicable term for resonator not for filter. Then that pops up two new questions as follows,
1. How will Q-factor be defined for a parallel resonator (for anti-resonance)?
2. What is the parameter by which Notch filters' sharpness is determined?
According to my knowledge - while speaking about the Q factor of a second-order filter we always refer to the "pole Q" which is clearly defined based on the position of the complex pole pair in the left half of the s-plane. If this Q factor is a good/helpful parameter for describing the most important properties of a filter is another question.
Dear Lutz,
Can you please explain the "pole Q" or can give any reference document on this?
Thanks Avishek
Dear Lutz,
I got your points. Thanks a lot. Yet if you can send me any reference that will be highly helpful.
@Avishek Adhikary, here is the definition you were asking for:
Q=1/2cos(phi)=wp/2|Re(wp)|
Legende:
* Angle phi is the angle between the real axis of the s-plane and the pointer to the pole.
* wp is the pole frequency (magnitude of the pointer to the pole)
* Re(wp) is the real part (sigma) of the pole in the s-plane.
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