adrate 3 dB coupler: S21 = signal attenuation path from port 1 to port 2; S31 = signal attenuation path from port 1 to port 3; S41 = signal attenuation path from port 1 to port 4. Fig. 2.2-19 The 'rat-race' or 'hybrid ring' coupler. narrow band frequencies. The characteristic impedance The reason is that signal balance is not perfect and the of the coupler ring is Z 20 which in the case of Z = 50 resistor helps to absorb unbalanced signals and minimises O is a circular 70.7 O transmission line which is 1.5A, in reflections. circumference. The four Z ports are connected to the ring in such a manner that ports 2 to 3, ports 3 to 1 and 2.2.14.2 The ring coupler ports 1 to 4 are each separated by N/4. Port 4 to port 2 is separated by 0.751. The operation of this device is il- Ring forms of couplers have been known for many years lustrated in Figure 2.2-20. in waveguide, coaxial and stripline configurations. The If a signal is injected at port 1, the voltage appearing at basic design requirements are similar to that of the port 2 is zero, since the path lengths differ by 0.51; thus, quadrature coupler except that curved lines are used port 2 can be treated as a virtual ground. Hence, the instead of straight lines. One such coupler is shown in transmission-line portions of the ring between ports 2 Figure 2.2-18. The principle of operation of ring cou- plers is similar to that of branch-line or quadrature couplers. 70.7 a 2.2.14.3 The 'rat-race' coupler 50 Ca A sketch of a 'rat-race' coupler is shown in Figure 2.2-19. The mean circumference of the ring is 1.52. This coupler is easy to construct and provides good performance for 100 S2 50 S2 100 Q Fig. 2.2-20 (a) Equivalent circuit of ring hybrid with port 1 as input and ports 2 and 4 as outputs (transmission-line model with port 3 Fig. 2.2-18 The 3 dB ring-form branch-line directional coupler. as virtual ground); (b) equivalent circuit at centre frequency. Transmission lines CHAPTER 2.2 and 3, and ports 2 and 4, act as short-circuited stubs microstrip and strip lines, s