Page 426 - Analog and Digital Filter Design

423
Design Equations

Boltzmann’s constant, and the temperature. The result of these calculations is
the noise figure.

F=- No when T = 290 K, kT = 4.14 x lo-” W.
GkTB
Obviously, unless the bandwidth B is known, it is not possible to know what the
noise figure is either. The noise bandwidth of a filter is given by:

Butterworth Noise Bandwidth

Note that the l/g term has been removed; this is because Butterworth filters have
a smooth response with a gain of one. Note also that g is the power gain.
According to Carlson’ this equation can be simplified to:

71.B
B,, =
2n .sin(nj?n)
The noise bandwidth of a first-order filter is d2, or 1.570796 times the 3dB
bandwidth.

Table A.3 gives normalized Butterworth filter noise bandwidths.

I
1 Filter Order Bandwidth

1,570796
1. I 10721
1.047198
1.026172
1 .0 16641
1.011515
1.008442
Table A.3 1.006455
1.005095
Noise Bandwidth of Butterworth 1.004 124
Filters