RF and Microwave Engineering: Fundamentals of Wireless Communications

6.9 Rat Race Coupler

Just like the branchline coupler, the rat race coupler is a four-port network with equal power-split between the two output ports. Figure 6.40 shows—as an example—a rat race coupler in microstrip technology with corresponding line lengths and characteristic impedances. The annular arrangement of λ/4- and 3λ/4- lines has characteristic impedances of . The power fed into port 1 is equally split between port 2 and port 3. Port 4 is isolated. In contrast to the branchline coupler, the rat race coupler provides output signals with a phase difference of 180°.

Figure 6.40 Microstrip rat race coupler.

The principal behaviour can be derived by investigating the signal paths on the annular arrangement of lines. An incident wave from port 1 separates into two waves each of which travels either in a clockwise or counter-clockwise direction along the ring. At port 4 both waves cancel out due to a λ/2 phase shift. At port 2 and port 3 the waves add up constructively. Like the branchline coupler the rat race coupler can be used as a combiner.

The scattering matrix of an ideal rat race coupler at the centre frequency f₀ is given as

6.58

Rat race couplers can be designed with ...