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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)
OrderEqNBW
11.5708
21.1107
31.0472
41.0262
51.0166
61.0115
71.0084
81.0065
91.0051
101.0041
Ripple0.01 dB0.1 dB0.25 dB0.5 dB1.0 dB
Order
23.66722.14441.74491.48891.2532
31.96421.44181.28251.16661.0411
41.50391.23261.14051.06560.9735
51.31141.14171.07801.02080.9433
61.21201.09371.04480.99700.9272
71.15371.06531.02510.98280.9175
81.11661.04711.01250.97360.91133
91.09141.03471.00380.96740.9071
101.07361.02580.99770.96290.9041
OrderEqNBW
11.57
21.56
31.08
41.04
51.04
61.04

Reference: Filter Design, by Steve Winder


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