Page 390 - Maxwell House

370 Chapter 7

continuation of electric current along the post. Meanwhile, this resonance circuit itself should
be connected in parallel to the equivalent transmission line shown in Figure 6.1.2a of Chapter
6. It means at least theoretically that this post may serve as the equivalent to a short circuit.
Smith chart in Figure 7.2.5d proves it and demonstrates the full reflection (|| = 1) of incident
wave at resonance frequency. As expected for the series resonance circuit, the impedance is
capacitive (i.e. > ) at frequencies below resonance and inductive (i.e. > ) above.

The current peak on the post bottom (Figure 7.2.5b) and almost zero on its top mean that the
electrical length of the post at the resonance frequency should be around /4 or ( ) 4 =
⁄
⁄
(300/9.6957)/4 = 7.735 mm that is very close to the post physical length h = 8.16 mm. It means
that the quarter-wave estimation could be used as a starting point of computer simulation. It
may seem surprising that so small post is capable of stopping EM wave propagation in WR
beyond the post. The possibility of this phenomenon can be explained assuming that the current
on the post excites at resonance frequency two TE10-modes running in opposite direction from
the post: the first is the reflected one and the second passes simultaneously with the incident
wave. If both waves have the same magnitude and opposite phase at resonance frequency, they
cancel each other.
We especially paid such close attention to the resonance post to illustrate how unusual can be
the microwave realization of conventional circuit elements. Looking back at Table 7.2, we see
that the same circuit element could be developed many different ways. In spite the fact that the
modern microwave technology achieves the high level of maturity and perfection it always
keeps open for new discoveries, ideas, engineering intuition, and creativity. At this point, we
stop the discussion of discontinuities. There are myriad of them in a different type of feed lines.
We hope that now our reader may classify them and build the appropriate equivalent circuits
applying the fundamental principle of energy conservation.

7.3 SCATTERING MATRIX AND RF MULTI-PORTS CIRCUIT
EVALUATION

7.3.1 Introduction
Any regular feed line performs better or worse only one but critical task. It transfers EM energy
“safely” from some area A to area B. However, in practice, that is far from enough. Many
networks including multiple feed sections may be quite complicated and provide the filtering
of signals, preliminary linear signal processing, splitting between or combining from multiple
sources of EM energy, and some additional functions depending on system mission. It will not
be big news that any linear RF device or network of such devices is the combination of few or
commonly much more than few discontinuities of different types. Bearing it in mind, we can
conclude that the development procedure of single device or network of devices is the synthesis,
more or less complicated. If so, a design engineer must know how to build the whole from
multiple subsets while meeting the system specifications. As we have mentioned before this
task is very complicated, does not have the unique solution and, unfortunately, in some cases
does not have a suitable or physically achievable solution at all. Meanwhile, the practical way
around is the straightforward analysis of multiple combinations of discontinues through some
computer optimization procedure or “try and fall” process. The latter can be done