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Problems. 383'
corresponding numbers at f = 2fo were 8922.0 and 14.98. The 3-dB bandwidths
were about equal.
9.6.3. Summary of Invulnerable Filters. Lowpass bridged-T and three-pole'
invulnerable filters were described, selectivity curves were derived, and, a
design example with analysis was provided. Both open-circuit z and: shortcircuit
y parameters were utilized when convenient, because maximumefficiency
relationships are valid under a simple change of nomenclature.
These invulnerable filters were shown to have a minimum-possible attenuation
rate of only 6 dB/octave at high frequency. In effect, they are selective,
"pads" that absorh energy on a frequency-selective basis. Like resistive pads,
they reduce the load SWR that appears at the input port, a valuable property
in many critical applications. They may be used in conjunction with reflection
filters to obtain the best characteristics of the two techniques.
Prohlems
9.1. Since commensurate-network selectivity is a function of q2 = cas 2 e, use
cos'9 = cos'('l1- 9) to show that any two frequencies having the same
selectivity are related by Equation (9.5): f\/fo=2-(f 2 /fo).
9.2. Which types of elliptic filters have
(a) The exact elliptic filter response?
(b) A negative element or perfect transformers?
(c) Equal terminating resistances?
(d) (N - 1)/2 traps, where N is the filter degree?
(e) N/2 traps?
9.3. An elliptic filter of what degree is required to produce a O.3-dB-ripple
pass band to 1.2 MHz and a 53-dB stopband shelf starting at 2.4 MHz?
9.4. The circuit below has Z;n=0+j6 ohms and dZ;n/dw=4 at w=2. M\
and K\ are resonant at 2 radians. Find L\, M\, and K\.
L,
M,
L,
I
:.
1