Page 366 - Maxwell House

346 Chapter 6

(look back at the discusstion after the expression (6.3) in this chapter) dictates that any EM
wave propagating in line is “obliged” to carry only active energy in that direction. Therefore,
the forward EM wave “has two choices”: stop carrying the active energy totally and transform
itself into an vanscent mode or just “displace” its active E-field energy from the area
where () < 0. The analytical and numerical simulations validate that the wave in WR
′
+
“prefers” the second way. To check E-field displacement phenomenon, we developed the CST
model. Figure 6.8.4a pictures the E-field energy distribution in WR cross section. The peak
magnitude painted in red corresponds to the peak of 0dB. The color range of this image is 40dB.
It means that -40dB of E-field level (duck blue) relates to a deep minimum. Undoubtedly, E-
field intensity drops to the lowest level on the right stub surface and nearby, as expected.
Therefore, we can deposit an R-card on the ferrite surface as Figure 6.8.4a, b illustrates. Then
the forward wave hardly notices the card presence because the conductivity current =

induced by low intensity E-field and extra Ohmic loss are practically zero. The backward wave
has H-field rotating in direction opposite to processing of spins, i.e. (). Therefore, it sees
−
the ferrite stub as ordinary dielectric with positive and close to one relative permeability ()
′
−
(see Figure 2.7.3a in Chapter 2). As we have mention in Chapter 2, microwave ferrites are
ceramics of high-density with dielectric constant ≥ 10. For this reason, the energy of wave

mostly concentrates inside the ferrite stub as Figure 6.8.4b portrays. Clearly, E-field reaches its
peak on the right stub surface and experiences significant attenuation in R-card. Typically, such
isolators can provide the forward loss around 0.1 - 0.2 dB (blue line in Figure 6.8.4c) and the
backward loss exceeding 20 – 25 dB (green line in Figure 6.8.4c).
Note that similar displacement field phenomenon occurs in most types of strip lines as well
many other lines. As an example, we have chosen symmetrical stripline with two ferrite stubs
as Figure 6.8.5a depicts. The external bias is oriented perpendicular to the longitudinal line axis.
Figure 6.8.5b and 6.8.5c illustrate the strong E-field displacement. E-field intensity, as usual, is
normalized to its peak and shown in dB scale. Visibly, the E-field maximum of the forward
wave shifts to the right edge of the trace while the backward wave reaches the same peak at the
left edge. If you need the isolator, just deposit the R-card on the left or right surface of ferrite
stub depending what wave is desired to absorb.

Figure 6.8.5 Stripline with ferrite stubs: a) Schematic, b) E-field of forward wave, c) E-field
of return wave.
6.8.7 Y-Circulator

That is probably the most broadly used gadget from the ferrite device family. There are two
basic designs: coaxial aka stripline (or microstrip) and WR are shown in Figure 6.8.6a and