**Subject :**Microwave Engineering

## Phase shifter

Let us describe the behavior of ferrites in the nonreciprocal phase shifter .

A nonreciprocal phase shifter consists of a thin slab of ferrite placed in a rectangular waveguide at a point where the de magnetic field of the incident wave mode is circularly polarized. Ferrite is a family of MeO . Fe_{2}O_{3} , where Me is a divalent iron metal. When a piece of ferrite is affected by a dc magnetic field, the ferrite exhibits Faraday rotation. It does so because the ferrite is nonlinear material and its permeability is an asymmetric tensor, as expressed by

Where

which is the tensor magnetic susceptibility. Here X is the diagonal susceptibility and K is the off-diagonal susceptibility.

When a dc magnetic field is applied to a ferrite, the unpaired electrons in the ferrite material tend to line up with the de field because of their magnetic dipole moment. However, the nonreciprocal precession of unpaired electrons in the ferrite causes their relative permeabilities (μ_{r}^{ },μ_{r}^{-}) to be unequal and the wave in the ferrite is then circularly polarized. The propagation constant for a linearly polarized wave inside the ferrite can be expressed as :

where

The relative permeability μ_{r }rchanges with the applied de magnetic field as given by :

It can be seen from above equation , that if

then μ_{r}^{ }is infinite. This phenomenon is called the gyromagnetic resonance of the ferrite. A graph of μ_{r} is plotted as a function of Hdc for longitudinal propagation in Figure