Unformatted text preview: 13.13. PROBLEMS 13.37 Problem 13.5: Use trig identities to prove the ﬁnal steps leading to ng tan led in
(13.18) and jZo cot kd in (13.19). Problem 13.6: Recalling that the reflection coefﬁcient is given by l" = (Z; —
Zo)/(ZL + Z0) and that the normalized load for using a Smith Chart is given by
zL = ZL/ZD, show that l/zL corresponds to —F, or a 180° rotation on the Smith Chart. Problem 13.7: Pr0ve that the magnitude of the reﬂection coefﬁcient is less than or
equal to one. Problem 13.8: Consider a 50—9 transmission line circuit feeding a 250 load. Since
the load is not matched to the transmission line impedance of 50 9, if the load were
to be directly connected to the input transmission line, then some input power will be
reﬂected back. So we use the circuit shown below. On the left is a transmission line
carrying an input signal speciﬁed by the amplitude V+ of the forward—going voltage
wave on that transmission line. On the right is a load impedance of 25 Q. The. goal
is to transfer all of the input power to the 25—9 load impedance. .IIIIIII/lllllllillllllllll
V+ ——>
z, = so a I’ll/[IIIIIIIIIIII’Il’ll’l Figure 13.39: Openstub matching of a transmission line to a load. An opencircuit stub tuner is used to match the total impedance of the structure on
the right (of the dashed line) to the 509 impedance of the transmission line on the
left carrying the input signal. You have at your disposal two design parameters: you
can choose the lengths 21 along the transmission line and 62, the length of the stub.
Assuming that the wavelength of the waves at the frequency of operation is A in all
of the transmission lines, you need to specify the lengths £1 and 62 in terms of the
wavelength such that the impedance of the structure to the right of the dashed line
is exactly 50 Q. You need to design using Smith Charts. Matlab© work: Go to the course website and download the matlab ﬁle for the function
“smith303.m”. The function “smith303” is called as follows: ...
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 Fall '06
 RANA
 Electromagnet

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