it has low VSWR at all ports and high isolation between output ports. The input and output impedances at each port are designed to be equal to the characteristic impedance of the microwave system. This is achieved by making the line impedance of the system impedance – for a system the Wilkinson lines are approximately Hybrid coupler Coupled-line directional couplers are described above. When the coupling is designed to be it is called a hybrid coupler. The S-matrix for an ideal, symmetric hybrid coupler reduces to; The two output ports have a 90° phase difference (-i to −1) and so this is a 90° hybrid. Hybrid ring coupler The hybrid ring coupler, also called the rat-race coupler, is a four-port directional coupler consisting of a 3λ/2 ring of transmission line with four lines at the intervals shown in figure 12. Power input at port 1 splits and travels both ways round the ring. At ports 2 and 3 the signal arrives in phase and adds whereas at port 4 it is out of phase and cancels. Ports 2 and 3 are in phase with each other, hence this is an example of a 0° hybrid. Figure 12 shows a planar implementation but this design can also be implemented in coax or waveguide. It is possible to produce a coupler with a coupling factor different from by making each λ/4 section of the ring alternately low and high impedance but for a coupler the entire ring is made of the port impedances – for a design the ring would be approximately . The S-matrix for this hybrid is given by; The hybrid ring is not symmetric on its ports; choosing a different port as the input does not necessarily produce the same results. With port 1 or port 3 as the input the hybrid ring is a 0° hybrid as stated. However using port 2 or port 4 as the input results in a 180° hybrid. This fact leads to another useful application of the hybrid ring: it can be used to produce sum (Σ) and difference (Δ) signals from two input signals as shown in figure 12. With inputs to ports 2 and 3, the Σ signal appears at port 1 and the Δ signal appears at port 4. Multiple output dividers A typical power divider is shown in figure 13. Ideally, input power would be divided equally between the