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336 Chapter 6

phase shift again. All in all, the total phase shift = 2 + and must be equal to 2 to be
in phase with the red wave moving in positive direction of the z-axis. Therefore, 2 + = 2
or = Λ/4, i.e. the quarter of the wavelength Λ in WR (check (6.25)). That is only a rough
estimate. The actual position of shorting wall may vary depending on the dipole diameter and
its height mostly due to the interaction of reflected wave with a metal dipole. So the best way
to optimize the transition is numerical simulation to avoid the labor- and time-consuming
experimental design. Figure 6.7.5 illustrates the results of such numerically optimization using
CST model.

Figure 6.7.5 Coax-to-WG adapter: a) E- and H-field energy distribution, b) E- and H-field
pattern, c) Smith chart, d) Equivalent circuit.

As expected, the maximum concentration of electrical energy takes place around the dipole end
and in the gap between the dipole and bottom WR wall (see Figure 6.7.5b). Meanwhile, the
magnetic field supported by the dipole current accumulates along the dipole length, and
according to Figure 6.7.5b, its force lines embrace the dipole. If so, the equivalent circuit shown
in Figure 6.7.5d must include the capacitance and inductance . The additional
1
capacitance 1 ≪ takes into consideration the electrical energy growth around the sharp
2
vertexes of coax-to-WR connection. From electrical science [10] we know that Pi-network
(really, L-network since 1 ≪ ) shown in red plays the role of impedance transformer
2
matching the WR high impedance of hundred Ohms to the low coaxial line impedance like 50
or 75 Ohms. In spite of simplicity, such transformer optimized by proper choice of the dipole
height, its diameter, and length of shorter WR section provides quite good performance with
low reflection coefficient. Smith chart in Figure 6.7.5c demonstrates its frequency behavior
between 8 GHz and 12 GHz. Note that it takes about a minute to run this project on an ordinary
laptop, but the process of interactive or automatic optimization takes certainly more time.

Evidently, the electric dipole is not the only radiator that can excite EM wave in WR. In Chapter
4 we considered the alternative radiator, specifically a magnetic dipole in the form of the loop
with electric current. Looking back at Figure 4.3.5c, we see that the loop H-field vector is
perpendicular to loop plane while the E-files vector lies in its plane. As such, the required match
between loop EM fields and TE10-mode in WG can be achieved if we put the loop in the position
depicted in Figures 6.7.6a and 6.7.6b developing a so-called end-launched or loop-type
21

21 Public Domain Image, source:
http://central.oak.go.kr/journallist/journaldetail.do?article_seq=11043&tabname=abst&resource_seq=-
1&keywords=null