Page 382 - Maxwell House

362 Chapter 7

points to the discrete sequence of the reactance as the ratio / rises. The most remarkable fact
that the normalized reactance and value of inductor resorts all possible quantities from 0 to ∞
(point #12 in triangle) while the reactance reaches the infinity as = /2 or = /4.
Therefore, the T-junction with a short-ended and quarter-wave length section in port 3 infuses
into the coaxial line between port 2 and 3 (see Figure 7.1.7a) the resistor of infinite value in
parallel to the line characteristic impedance. If so, there is no shunting and the propagating from
port 2 to port 3 EM wave may pass this discontinuity without reflections! Furthermore, such
stub in T-junction could provide not only an iron-clad support of the center conductor but its
water or other means cooling at high level of power.

This shunt example is a good illustration how useful the method of the equivalent circuit could
be. The CST simulation results are presented in Figure 7.1.10a-c. According to Smith chart in
Figure 7.1.10a, the red curve illustrating the reflection coefficient crosses the Smith chart origin
(zero reflection marked by the number 1 inside a triangle) at the resonance frequency 4.749
GHz or wavelength 63.17 mm. Since all coaxial lines in Figure 7.1.10b-c are air-filled, the
expected stub length is close to quote-wave 15.79 mm. The optimum estimated from numerical
data is =15.40 mm. A pleasant surprise is that the deviation is 0.39 mm or 2.53% only.
Another gift is that the reflections are relatively low || ≤ 0.2 (violet blue circle) over the
frequency band from 3.38 GHz to 6 GHz.

Figure 7.1.10 T-junction stub: a) Smith chart demonstrating matching performance, b) and c)
E-and H-field energy distribution at the resonance frequency, d) Quarter-wave line
transformer, e) Equivalent circuit of the quarter-wave transformer

When > /4 the input reactance of short-ended section becomes capacitive. Therefore, the
same stub may play a role of the inductor or capacitor depending on frequency and ratio /.
We advise the reader to trace the input impedance of a stub loaded on some resistor that
is not equal to its characteristic impedance . Make sure that the quarter-wave series stub in

2
Figure 7.1.10d transforms into ⁄ = , where = / . Therefore, we can

4
match two line with impedances and choosing = � ⁄ = � . As such,
1 2
4

1
2
the equivalent circuit of this stub is the ideal transformer shown in Figure 7.1.10e. For the sake
of simplicity, we omitted all reactive components due to E- and H-field energy accumulation
around the step sharp edges and changes in center conductor diameter.