**Subject :**Microwave Engineering

## Hybrid Rings (Rat-Race Circuits)

A hybrid ring consists of an annular line of proper electrical length to sustain standing waves, to which four arms are connected at proper intervals by means of series or parallel junctions. Figure shows a hybrid ring with series junctions.

**Figure : Hybrid ring**

The hybrid ring has characteristics similar to those of the hybrid tee. When a wave is fed into port 1, it will not appear at port 3 because the difference of phase

shifts for the waves traveling in the clockwise and counterclockwise directions is 180°. Thus the waves are canceled at port 3. For the same reason, the waves fed into port 2 will not emerge at port 4 and so on.

The S matrix for an ideal hybrid ring can be expressed as :

It should be noted that the phase cancellation ocurs only at a designated frequency for an ideal hybrid ring. In actual hybrid rings there are small leakage couplings, and therefore the zero elements in the matrix of above equation are not quite equal to zero.