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Chapter 9

Q. 9.3

FIELD DISPLACEMENT ISOLATOR DESIGN

Design a field displacement isolator in an X-band waveguide to operate at 11 GHz. The ferrite has 4\pi  M_{s} = 3000 G and ϵ_{r} = 13. Ferrite loss can be ignored.

Step-by-Step

Verified Solution

We first determine the internal bias field, H0, such that µ_{e} < 0. This can be found from Figure 9.8, which shows µ_{e}/µ_{o} versus H0 for 4\pi  M_{s} = 3000 G at 11 GHz.
We see that H_{0} = 1200  O_{e} should be sufficient. Also note from this figure that a ferrite with a smaller saturation magnetization would require a much larger bias field.

Next we determine the slab position, c /a, by numerically solving (9.79) for the propagation constants, β_±, as a function of c /a. The slab thickness was set to t = 0.25 cm, which is approximately a/10. Figure 9.14a shows the resulting propagation constants, as well as the locus of points where β_{+} and  c /a satisfy the condition of (9.88). The intersection of β_{+} with this locus will ensure that E_{y} = 0 at x = c + t for the forward wave; this intersection occurs for a slab position of c /a =0.028. The resulting propagation constants are β_{+} = 0.724k_{0} < k_{0}  and β_{−} = 1.607k_{0} > k_{0}.

\left(\frac{k_f}{\mu _e} \right)^2 + \left(\frac{\kappa \beta}{\mu \mu _e} \right)^2 – k_a \cot k_a c\left(\frac{k_f}{\mu _0\mu _e}\cot k_ft +\frac{\kappa \beta }{\mu_0 \mu \mu_e } \right) -\left(\frac{k_a}{\mu _0} \right) \times \cot k_a c \cot k_ad\left(\frac{k_f}{\mu _0\mu _e}\cot k_ft -\frac{\kappa \beta }{\mu_0 \mu \mu_e } \right)=0.            (9.79)

k^+_a=\frac{\pi }{d}                     (9.88)

The electric fields are plotted in Figure 9.14b. Note that the forward wave has a null at the face of the ferrite slab, while the reverse wave has a peak (the relative amplitudes of these fields are arbitrary). A resistive sheet can be placed at this point to attenuate the reverse wave. The actual isolation will depend on the resistivity of this sheet; a value of 75 Ω per square is typical.

FIELD DISPLACEMENT ISOLATOR DESIGN Design a field displacement isolator in an X-band waveguide to operate at 11 GHz. The ferrite has 4π Ms = 3000 G and ϵr = 13. Ferrite loss can be ignored.
FIELD DISPLACEMENT ISOLATOR DESIGN Design a field displacement isolator in an X-band waveguide to operate at 11 GHz. The ferrite has 4π Ms = 3000 G and ϵr = 13. Ferrite loss can be ignored.