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

Read pg 16 in annex.

Notch = bandstop.

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

how to analzye ECG signals using Wavelets ?

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.

@ Lutz

The formula has to apply to the bandstop as well - except for a minus sign.

The reasoning is quite simple: inserting a bandpass filter in the feedback path of an ideal OpAmp results in 'the whole thing' being a bandstop filter.

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|.

Q-factor is related to a single resonator not a filter.

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.

let fu is the upper frequency, fl is the lower frequency and f0 is the centre frequency.

Where f0 is a geometric mean of fu and fl.

The quality factor Q is defined as the ratio between f0/(fu-fl).

But the centre frequency is not the Notch frequency.

let fN is the Notch frequency and fs is the sampling frequency.

The quality factor Q can be found as:

Q=tan(pi*fN/fs)/[tan(pi*fu/fs) - tan(pi*fl/fs)]