Page 178 - Analog and Digital Filter Design

Bandpass Filters 175

with a 6.8 kHz 3dB bandwidth and with 40dB attenuation at flOkHz. In addi-
tion, let the filter have a center frequency, Fo, of 198 kHz. Design a Butterworth
bandpass filter that achieves this specification.

The stopband-to-passband ratio is 20/6.8 = 2.94, as explained in the previous
example. Referring to the attenuation versus frequency curves for Butterworth
filters, you can see that a fifth-order filter will provide the required performance.
Start with a lowpass prototype, as shown in Figure 6.2.

Rs= 1 L2=1.618 L4=1.618

Source
-- -- -- R=l
--
--
--
C1=0.618
C3=2.000
C5=0.618
Figure 6.2
Normalized Fifth-Order Butterworth LowDass Model

The lowpass model must be frequency scaled to have a cutoff frequency of
6.8 kHz. This is done in the same way that lowpass filters are scaled, that is. the
inductors and capacitors are divided by 31rFc, where Fc is the cutoff frequency.
The divisor factor is therefore 42,725.66; results in the component values are
shown in Figure 6.3.

Rs= 1 L2=37.87uH

c3
Source 14.4644~ - c5 F R=l
t - --
46.81 03uF
F
--
14.4644~

Figure 6.3
Scaled Fifth-Order Butterworth Lowpass Filter

To frequency translate the scaled lowpass prototype into a bandpass model yo~~
must resonate each branch of the ladder at the center frequency, Fo. Series
inductors become series LC circuits, and shunt capacitors become parallel tuned
LC circuits. The capacitor and inductor values in the lowpass model are
unchanged.