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RF Electronics Chapter4: Transmission Line Transformers and Hybrids Page 73 2022, C. J. Kikkert, James Cook University, ISBN 978-0-6486803-9-0. Unequal Split Wilkinson Hybrid Sometimes an unequal power split is required. If a power ratio of P:1 is required, then the impedances seen at the source end of each of the transmission lines must also have a ratio of P:1. Since the total impedance must be Z 0 = 50 , then the impedances are: 1 1 1 2 1 0 1 1 1 1 1 1 Z P P Z P Z Z Z Z Eqn. 4.12 The line impedances are thus: 0 1 1 Z P P Z Eqn. 4.13 0 2 1 Z P Z Eqn. 4.14 where Z 1 and Z 2 are the transmission line impedances of the hybrid. As a check when an equal split is used, P=1, so that Z 1 = Z 2 = 2Z 0 . Thus for a 10:1 power split in a 50 system, the transmission line impedances are: Z 1 =1.1 Z 0 and Z 2 =11 Z 0 . For a 50 system, Z 2 = 165 . For an RF circuit board substrate, RO4003, which is 0.818 mm thick, at 1 GHz a 50 track is 1.855 mm wide and a 165 track is 0.063 mm wide. As shown in chapter 11, the thinnest recommended track width for PBC manufacture is 0.2 mm. Using laser ablation 0.1 mm tracks are possible. The 165 track is too thin to make accurately, even using laser ablation. In addition, the resistance due to the copper losses of the 165 track is 29 times that of the 50 track. The ability to manufacture and copper losses will thus limit the ratio of the power split. Lowering the impedances of the split lines by reducing the impedance at the junction point just like the compensated Wilkinson hybrid, will reduce the impedances of the transmission lines of the hybrid and may permit it to be constructed. Increasing the substrate thickness will also increase the track width and thus reduce losses as well as easing manufacturing difficulties. Large differences in power ratios are typically required for sampling signals such as transmitter outputs. Edge coupled lines as described in example 4.2 are very suitable for this, so that the limitation on power ratios for Wilkinson hybrids is not a serious limitation. Wideband Wilkinson Hybrid Figure 4.14. Two-stage wideband Wilkinson hybrid. RF Electronics: Design and Simulation 73 www.cadence.com/go/awr