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Invulnerable Filters 381
40
t
L mill
30 dB
20
10
0
.2 .5 1. 2. 5. 10.
Figure 9.46.
Three-pole invulnerable filter selectivity.
Example 9.5.
A conventional. doubly terminated bandpass filter tuned to I
MHz and having a 10% Butterworth passband width will be compared to its
invulnerable counterpart. For the conventional Butterworth filter. the lowpass,
lossless prototype network, normalized to I-ohm terminations and a 3-dB
passband edge of I radian, has element values C= IF and L=2H. This leads
to the network in Figure 9.47 when R = O. The values indicated were obtained
by frequency and impedance scaling and resonating each lowpass prototype
element according to Section 6.5.1. The Butterworth response is obtained
between 50-ohm terminations. The second harmonic on the prototype frequency
scale is w= IS radians; selectivity curves or (9.24) show that the
second-harmonic (2-MHz) attenuation is 7\ dB.
The value of R must be selected to design the invulnerable filter with the L
and C values fixed as above. One choice is to obtain the maximum possible
value of L min
at the second harmonic. For the invulnerable lowpass network,
(9.93) yields the normalizing frequency WI = 1/fi. The optimum decrement
was shown to be d= I/w. Using the calculated WI value and w= IS in (9.94)
and (9.95), it is found that R= 1/15 in the lowpass network. Therefore,
159.16pH 159.16pF
R'
R'
.79575
~H EACH
Figure 9.47. Three-pole Butterworth/invulnerable filter in Example 9.5.