easonable isolation between the output ports SO cause the latter to malfunction. With a 1:1 transformer, that one port does not interfere with the other. The the resistor can be physically moved away from the tran- greatest disadvantage of these couplers is their large sistor without upsetting electrical operating conditions. physical size when used in their distributed forms. 18 Purists might argue that an open circuit does not exist at radio frequencies because any unterminated TX line has stray capacitance associated with an open circuit. We will ignore this stray capacitance temporarily because, for our frequencies of operation, its reactance is extremely high. Transmission lines CHAPTER 2.2 Zo/V2 Fig. 2.2-16(c) Effect of port 3 transferred to port 2. Zo/V2 Fig. 2.2-15 A branch-line coupler. 2.2.14.1 The branch-line coupler The basic configuration of the branch-line coupler is Fig. 2.2-16(d) Effect of port 2 transferred to port 1. shown in Figure 2.2-15. It consists of transmission lines, each having a length of 2/4. Two opposite facing-lines have equal impedances, Zo, and the remaining opposite Z(transformed) = Zo/Zo = Z facing-lines have an impedance of Zo/V2. In the case of a 50 S coupler, Zo = 50 O and Zo/V2 = 35.355 D Hence we obtained the transformed Z in parallel with the Z termination of port 2. This situation is shown in Principle of operation Figure 2.2-16(c). We now need to transform the Zo/2 termination at port 2 to port 1. At port 1 All ports are terminated in Zo. Signal is applied to port 1 and it is divided equally between ports 2 and 3. There is no output signal from port 4 because the path from port 1 to 4 is 2/4 while the path from port 1 to 4 via ports 2 and 3 is 32/4. The path difference is 1/2; hence, the signals cancel each other at port 4. The net This condition is shown in Figure 2.2-16(d). result is that the signal at port 4 is zero and it can be We conclude that the hybrid 3 dB coupler provides considered as a virtual earth point. With this virtual a good match to its source impedanc