Page 414 - Maxwell House

394 Chapter 8

dielectric substrate, i.e. it is shorter than in free space. Note that PD = 3 dB (thicker magenta
solid curve) corresponds to the couplers in which the input power from port1 is divided
equally between port3 and port4. They belong to a special class of couplers named hybrids.
8. It may seem surprising, but this coupler provides the frequency independent phase shift of
90° between signals coming to port2 and port3. This feature combined with 3 dB power
division makes them the universal element of coherent power combiners and splitters,
diplexers, balance amplifiers, phase shifters, mixers, phased array beam-forming networks,
and many other applications.
9. The described theory of couplers is based on the assumption that the even- and odd-mode
have the same or very closed propagation constant. Generally, it is not quite right because
both modes are quasi-TEM only. As we have mentioned before, any deviation from TEM
makes the mode propagation constants frequency dependable. The most troubling is that
± ++ ± ++ . If so,
they become not equal, i.e. ≠ , i.e. possess different wavelengths ≠
how to meet the requirement that the coupler length should be quarter-wavelength? Which
of them? That is not the issue for narrow banded couplers but the serious limitation for
wideband design due to fast deterioration of directivity and isolation. Therefore, we need
some technique to equalize the even- and odd-mode propagation constant. Typically, it
requires slowing the odd-mode while leaving the even-mode propagation constant
practically unchanged. Figure 8.2.4c and Figure 8.2.4d illustrate two approaches. Both as
many others are based on the differences in EM field structures of modes. In so-called
wiggly coupler in Figure 8.2.4c, the odd-mode should follow the saw tooth path and
thereby slows down (green line) due to the most part of its energy concentrated into and
nearby the gap. Meanwhile, the energy of even-mode is accumulated in dielectric substrate.
If so, this mode barely notices the presence of a gap and practically does not slow down
(red line). The analogous effect occurs in forward (blue line) coupler with shunt periodic
stubs depicted in Figure 8.2.4d. According to [1] such coupler has good performance
covering from 2 GHz to 4 GHz.

We shall not pursue this subject here anymore asking the reader to turn to the appropriate
literature [3, 8] for more information. Note that such kind of directional coupler can be realized
using almost any type open and closed transmission line including the optical lines.
8.2.4 WR Hybrids

As we have mentioned before, hybrids as well as 3-dB couplers, belong to the broad family of
four-port power dividers/splitters with an equal power split, i.e. 3-dB split, between two ports
keeping one of the ports isolated. The effect of isolation may be accomplished by means of
particular geometrical structure (like WR magic-T) or wave interference at the isolated port
(like ring or branch hybrid).
4
Let us start from so-called WR magic-T shown in Figure 8.2.5a . It incorporates two WR tees:
H-plane tee formed by WR of ports 1, 2, 3 and E-plane tee shaped by WR of ports 2, 3, 4.
Remind that the term H-plane means that the WR branches are located in the plane containing
H-field vector while E-field vector belongs to E-plane.

4 Public Domain Image, source: http://www.slideshare.net/KaziMdRahaman/seminar-on-magic-tee