Page 380 - Maxwell House

360 Chapter 7

an independent on respective line orientation in space. It is physically and electrically a shunt
junction of three transmission lines. As such, lines 2 and 3 of 50Ω each is connected in parallel
and create the load collectively = 50/2 = 25Ω, i.e. the normalized load is purely resistive,
equal to / = 25/50 = 0.5 and frequency independent. If so, the reflection coefficient in

⁄
arm 1 should be constant | | = |( − ) ( + )| = 1/3 as plotted on Smith charts
1

(blue violet circle) in Figure 7.1.7d. The same supposed to be correct for line 2 or 3 as shown
in Figure 7.1.7e (blue violet circle). The location of phase reference plane in each arm (i.e. the
plane where an incident field phase is zero) is shown in Figure 7.1.7c in red. To check the T-
junction performance we developed the CST model.
Figure 7.1.7b illustrates E- and H-field energy distribution as well the electric current path (solid
green lines) over the coaxial center conductor (shown in gray). The top two pictures correspond
to the port 1 excitation by TEM-mode. The energy delivered to the port 2 and 3 is equal due to
the T-junction is symmetric about the vertical axis. There is some accumulation of H-field
energy around the central conductor branching and clearly > in this area. Therefore, the

equivalent circuit of T-junction should include some series inductor ℒ and ℒ 2 = ℒ and
1
3
small shunt capacitor as shown in Figure 7.1.7f. Smith chart in Figure 7.1.7d demonstrates

that the value of this inductor is quite insignificant because the reflection coefficient in port 1
(red solid curve) practically repeats the circle of constant reflection coefficient of | | = 1/3.
1
The visible deviation is noticeable as the frequencies approach 10 GHz only.
However, the situation looks quite different when the arm 2 (or symmetrically located arm 3)
is excited. It turns out that there is no arm symmetry anymore. According to Smith chart in
Figure 7.1.7e, the equal power division between ports 1 and 3 is observed at very low
frequencies only. As the frequency grows, more energy is reflected back to the port 1 (the
reflection coefficient in Figure 7.1.7e is outside the circle | | = 1/3). The H-field energy
1
concentration is visible again around the center conductor branching. Meanwhile, the peak of
buildup shifts in the direction to the arm 1. The latter means that the energies proceeding to the
arms 1 and 3 are not equal. Clearly, more energy (check the colormap) goes to arm 1. The
equivalent circuit must include again the inductors ℒ 1,2,3 but larger in values since now ≫

.

Note that coaxial T-junction is regularly used as a broadband power divider providing the equal
in magnitude and phase signals in arms 2 and 3 while the port 1 is excited. However, this T-
junction is not matched: 1/9 of income power is reflected (| | = 1/9) and 8/9 goes through
2
1
since 1 − | | = 8/9. If so, 4/9 goes in one of the shunt arms and the same 4/9 in the other
2
1
that corresponds to 0.51 dB (~10%) of mismatch (return) loss. Looking back at Figure 7.1.7,
we see how to match the T-junction in two steps:
1. Impedance matching by increasing the characteristic impedance of the shunt arms 2 and 3
to 100Ω and thereby making = 100/2 = 50Ω, i.e. equal to the arm 1 impedance of
50Ω.
2. Total reactive energy reduction by reducing the imbalance in the components of reactive
energy. To reach this goal, we should boost E-field energy storage around the branching to
get − ≅ 0 by placing, for example, a small coaxial step-up there. As we have shown

earlier in this section it means to enhance a shunt capacitor in equivalent circuit depicted

in Figure 7.1.7f.