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RF Electronics Chapter4: Transmission Line Transformers and Hybrids Page 80 2022, C. J. Kikkert, James Cook University, ISBN 978-0-6486803-9-0. For the 1.5 Rat-Race hybrid, a three-quarter wavelength and three one-quarter wavelength transmission lines are required. At microwave frequencies, it is very convenient to arrange these transmission lines in the shape of a circle, as shown in figure 4.24, with the three quarter wavelength line on top and the three quarter wavelength lines at the bottom. One-quarter wavelength will thus occupy a 60-degree arc. The layout can then be made conveniently using six 60-degree arcs, 4 T-junctions and 2 short transmission lines with the same length as the T-junctions are wide, as spacers. Figure 4.25. 1.5 Rat-Race hybrid circuit for PCB layout. Figure 4.25 shows the circuit schematic, which results in the PCB layout of figure 4.24. The radii of the arcs can be tuned, to obtain the correct centre frequency, without causing any track connection errors. In figure 4.25, MCURVE2 tracks are used to include EM mode matching in the simulation. Intelligent EM based T-junctions, MTEEX$, are used to ensure that the simulation is as accurate as possible, without doing a full EM simulation using AXIEM. The simulation of the PCB circuit of figures 4.24 and 4.25 shows a near identical performance to the one shown in figure 4.22. The main difference is a 0.07 dB increase in insertion loss of the coupled ports due to the resistive losses in the Microstrip tracks. Lower line impedances can be obtained with a compensated 1.5 Rat-race hybrid, by having 44.5 , quarter wavelength transmission lines at the 4 inputs to the hybrid, for a 50 system. The line impedances of the hybrid then become 56.119 instead of 70.71 . Computer simulation shows that this does not increase the bandwidth of the isolation and it does not reduce the losses for a typical PCB layout, so that compensated 1.5 Rat-race hybrids are not used in practice. Branchline Coupler The Branchline coupler consists of 4 transmission lines in a ring, as shown in figures 4.26 and 4.27. If an input is applied at the top left port 1, then part of the output appears at the RF Electronics: Design and Simulation 80 www.cadence.com/go/awr