Page 376 - Maxwell House

356 Chapter 7

Looking back at the field distribution in Figure 7.1.2 we can see that the impedance equalizing
creates some small but visible areas of reactive energy concentration: electric energy around
the sharp edges and magnetic energy around the center conductor of reduced diameter.
According to Smith chart in Figure 7.1.2c, > at all frequencies. If so, some extra tiny

series inductor may improve further the match performance. To get it we proceed in two steps.
First off all, let us check the model without bead simply putting 2 = 1 thereby keeping
untouchable so-called the coaxial step down discontinuity in CST model. The simulation data
are depicted in Figure 7.1.3 and demonstrate that the energy storage reverses, i.e. > . If

so, the step-down discontinuity can be associated with a lumped inductor as seen in Figure
7.1.3c. Therefore, we can expect that the optimum of matching performance rests somewhere
between > 1 and < 2.1 giving us ≅ and close to zero reflections. Following
2 2
this path we found the best, broadband matching while 2 = 1.65. The scaled up central area
of Smith chart in Figure 7.1.3d demonstrates that the reflection coefficient drops almost 5 times.
Regrettably, although such matching method looks attractive it is not very practical. The
material with required dielectric constant may not exist or not available for this application
because of cost issue, production difficulties, etc. Check the alternative option like adjusting
the spacing between beads such way that the reflection between adjacent beads or group of
beads is canceled. The phasor diagrams is a useful guide.

We paid so much attention to this relatively simple case to exhibit only the highly fruitful
symbiosis between two powerful scientific branches: Maxwell’s EM wave concept and
classical circuit theory. The most of the following discontinuity analysis is based on this
productive and descriptive partnership.

Figure 7.1.3 Step-down discontinuity: a) E-field energy distribution, b) H-field energy
distribution, c) Smith chart revealing the inductive impedance, d) Smith chart showing
matching performance between 0 and 10GHz for adjusted bead of dielectric constant 2 =
1.65

7.1.2 Step Up in Coaxial line
We have seen above that the step down in coaxial line (see Figure 7.1.3) is equivalent to the
serially connected inductor. Now, let us consider the metal step-up (tagged in bright blue)
demonstrated in Figure 7.1.4a assuming as usual that this discontinuity longitudinal length (w
= 2 mm in CST model) is much less than the operational wavelength.