of the wave is v = 2p f = 18.85 × 109 1/s. From (6.32) and (6.33) we

and the tilt angle rotates counterclockwise as the wave propagates. By setting u = −p/2 in (6.38) we solve l = p ( b + − b − ) = 12 mm. Also, lengths producing a rotation of u = −p/2 −np (n is a positive integer) give a tilt angle of −90° for the output wave. If the wave would propagate to the direction opposite to the field, the tilt angle would rotate clockwise, as seen to the direction of propagation, but in the same direction with respect to the coordinate system as before.

6.2.3 Isolators

An ideal isolator passes signals in the forward direction without loss but totally absorbs signals propagating in the reverse direction. In practice, the insertion loss may be below 0.5 dB in the forward direction and more than 20 dB in the reverse direction for a good isolator. Isolators are used for matching and for stabilizing oscillators against frequency changes due to varying load impedance.

The operation of an isolator may be based on a ferromagnetic resonance, on shifting of field pattern, or on the Faraday rotation. Figure 6.16 shows a waveguide isolator. There is a ferrite rod in a circular waveguide in a static magnetic field. Because of the Faraday rotation, the polarization of a wave propagating in the forward direction turns 45° clockwise in the ferrite. This wave does not attenuate significantly in the resistive cards at the input and output, because the electric field is now perpendicular to both cards. The polarization of a reverse wave turns 45° counterclockwise, as seen, to the

Figure 6.16 Waveguide isolator based on the Faraday rotation.