A filter's equivalent noise bandwidth (EqNBW) is the bandwidth that an ideal filter
(infinite rejection in the
stopband) of the same bandwidth would have. EqNBW is calculated by integrating the total available noise power under
the response curve from 0 Hz to infinity Hz. In practice, integration only needs to be carried out to about the
point of thermal noise. The steeper the filter skirts (higher order), the narrower the range of integration needed
to get an acceptable approximation. Integration needs to be done in linear terms of power (mW, W, etc.) rather than
in dB.
The values in the following table are for normalized lowpass filter functions with infinite Q and exact conformance
to design equations. If you need a better estimation than what is presented here, then a sophisticated system simulator
is necessary.
Butterworth (fco = 3 dB) 
Chebyshev (fco = ripple) 
Bessel (fco = 3 dB) 
Order 
EqNBW 
1 
1.5708 
2 
1.1107 
3 
1.0472 
4 
1.0262 
5 
1.0166 
6 
1.0115 
7 
1.0084 
8 
1.0065 
9 
1.0051 
10 
1.0041 

Ripple 
0.01 dB 
0.1 dB 
0.25 dB 
0.5 dB 
1.0 dB 
Order 
2 
3.6672 
2.1444 
1.7449 
1.4889 
1.2532 
3 
1.9642 
1.4418 
1.2825 
1.1666 
1.0411 
4 
1.5039 
1.2326 
1.1405 
1.0656 
0.9735 
5 
1.3114 
1.1417 
1.0780 
1.0208 
0.9433 
6 
1.2120 
1.0937 
1.0448 
0.9970 
0.9272 
7 
1.1537 
1.0653 
1.0251 
0.9828 
0.9175 
8 
1.1166 
1.0471 
1.0125 
0.9736 
0.91133 
9 
1.0914 
1.0347 
1.0038 
0.9674 
0.9071 
10 
1.0736 
1.0258 
0.9977 
0.9629 
0.9041 

Order 
EqNBW 
1 
1.57 
2 
1.56 
3 
1.08 
4 
1.04 
5 
1.04 
6 
1.04 

Reference: Filter Design, by Steve Winder
