e Z. Assuming earth point Figure 2.2-15 becomes Figure 2.2-16(a). lossless lines, it divides its signal equally at ports 2 and 3. We know from transmission line theory (Equation Since signal travels over 2/4 to port 2, there is a phase 2.2.57) that for a 2/4 length, Zin = Z6/Z1. In other delay of 90° at port 2 and another 90° phase delay from words, a short circuit at port 4 appears as open port 2 to port 3. Thus the signal arriving at port 3 suffers circuits at port 1 and 3. This result is shown in a delay of 180° from the signal at port 1. Figure 2.2-16(b). If we now transform the impedance The response of such a coupler designed for 5 GHz is at port 3 to port 2, we get shown in Figure 2.2-17. As you can see for yourself, the signal path from port 1 to port 2 (S21) is 3 dB down at 5 Zo/V2 GHz. This is also true of the signal response to port 3 (S31). The signal attenuation to port 4 is theoretically infinite but this value is outside the range of the graph. A similar analysis will show that power entering at port 2 will be distributed between ports 1 and 4 and not at port 3. A similar analysis for port 3 will show power dividing between ports 1 and 4 but not at port 2. The net Zo/V2 result of this analysis shows that signals into port 2 and 3 are isolated from each other. This is a very useful feature Fig. 2.2-16(a) Virtual short circuit at port 4. in mixer and amplifier designs. Zo/V2 The advantage of the quadrature coupler is easy construction but the disadvantage of this coupler is its narrow operational bandwidth because perfect match is only obtained at the design frequency where each line is exactly N/4 long. At other frequencies, each line length is no longer 2/4 and signal attenuation increases while signal isolation decreases between the relevant ports. Finally, you may well ask 'if port 4 is at virtual earth, Fig. 2.2-16(b) Effect of virtual short circuit at port 4. why is it necessary to have a matched resistor at port 4?' CHAPTER 2.2 Transmission lines f GHz Fig. 2.2-17 Unadjusted response of the qu