download searchable PDF of Circuit Design book - IEEE Global ...

Invulnerable Filters 377
9.6. Invulnerable Filters
Microwave literature contains descriptions of a number of waveguide and
other devices connected to a dissipative medium by frequency-selective
means. One implementation is to have side-coupling holes that excite chambers
containing resistance sheets. These devices usually are designed to absorb
unwanted stopband energy, especially in high-power circuits, where the source
cannot tolerate unwanted reflected energy. At frequencies above 400 MHz, it
is common practice to use three-port circulators to dissipate the reflected
energy in a load attached to the extra port. Another application occurs in
oscillators when stopband reactive terminations cause unwanted oscillations.
Circulators are too large at low frequencies, and many dissipative designs have
been ad hoc and difficult to model and adapt.
This section describes an organized approach to the design of filters that
absorb energy rather than reflect it; i.e., the reflection basis described in
Section 3.2.3 is not employed. Instead, the concept of designing a filter having
a limited maximum efficiency is exploited by direct design techniques. Two
specific filters will be described, and the basis for designing other absorptive
filters will be evident. The invulnerable part of the filter capability comes from
the fact that maximum efficiency may be achieved for only one unique load
impedance; any other load impedance will result in lower efficiency. In this
sense, the designer need not have any information whatever about the load
impedance; indeed, this is precisely the case in power lines and many other
environments.
The only additional development is the expression of the minimum loss
associated with the maximum efficiency. This is
L min
= IOI0g_l_dB. (9.91)
""max
Using (9.83) and Equation (G.4) in Appendix G, a surprisingly simple expression
for L min may be obtained:
L min = 8.6858 sinh -1ft.[ dB, (9.92)
where'Jl is defined by (9.81). Open-circuit impedance parameters can also be
used by replacing y, g, and b with z, r, and x, respectively, in these equations.
9.6.1. Invulnerable Bridged-T Network. Consider the network in Figure' 9.42
and the following general definitions:
I
""1=--'
,ffE
(9.93)
- W
W=-.
WI
(9.94)
d=RwlC. (9.95)