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384 Other Direct Filter Design Methods
9.5. In the permuted circuit below, L" = lj, K 2 , = i, and M 2 , and K 2
, are
resonant at (.oJ = -t radians. Find L 2l M 2l and K 2
in the figure in Problem
9.4.
L" L,
)M,
s
j>
9.6. Use Equations (9.67)-(9.69) to find e h in Equation (9.68).
9.7. A variable-length transmission line having Zo= R, has input SWR S
with respect to (wrt) R,. The line is terminated by an impedance that
produces an SWR So wrt Ro' as pictured below. Set Igi equal to
(S-I)/(S+ I) and use Equations (9.70)-(9.71) to show that the maximum
S is S = S, X So, where S, is the SWR of R, wrt Ro, i.e., (R, - Ro)
/(R, + Ro)=(S,- I)/(S, + I). Also, find the minimum S, including any
special conditions.
s_ 7
J
() 7', R, )
I
S,+R,
9.8. Work Example 7.1 in Chapter Seven using formulas from Chapter
Nine.
9.9. Derive K = 2GJt + I from Equation (9.82) and '1m" = JGJt + I -.fGi from
Equation (9.83) using Equations (7.57), (7.64), and (9.81).
9.10. At a stopband frequency, an invulnerable filter has short-circuit parameters
YIl=y,,=(l3.68+j5.883)XIO- 3 and Y21=Y12=(-0.02+j3.333)
X 10- 3 mhos. .
(a)
(b)
(c)
What is the relative size of the load-plane image in the input
plane?
What is the value of L min , the minimum possible loss?
How many different load admittances can produce this L min
value?