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# Filter Equivalent Noise Bandwidth

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