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RF Electronics Chapter 3: Transformers and Hybrids Page 59 2022, C. J. Kikkert, James Cook University, ISBN 978-0-6486803-9-0. The conventional TV splitter is a cut down version of the Wilkinson hybrid. Since the cable losses will mask any unequal loads, the terminating resistor is not normally present and since impedance variations can be tolerated, no output transformer is used. The omission of those components reduces the cost for this consumer-oriented circuit. If a Wilkinson Transformer hybrid is used to combine the output from two transmitters, any unbalance will be dissipated in the resistor R. For two 100 Watt transmitters, 50 Watt will be dissipated in the resistor and 50 Watt will be radiated if one of the amplifiers fails. The resistor must thus be selected with this power requirement in mind. Example 3.2: Wilkinson Transformer Hybrid Design The transformer on the left of figure 3.14 combines signals A and B. If an input is applied to port A but no input is applied to port B, then for a 50 Ω impedance at port A, the transformer must provide a 100 Ω impedance, since it is in parallel with the 100 Ω resistor. The impedance at port C is thus 25 Ω, since both windings on that transformer are the same. The transformer on the right provides an impedance transformation from 25 Ω to 50 Ω. If we use the same toroidal core as was used in example 3.1, then the required number of turns can easily be calculated. That transformer at 1 MHz, had N1 = 3.093. and a 1000:1 bandwidth. For a 25 Ω winding, N25 = N1(25) turns = 15.46 turns are required. Since this has to be an integer number, 16 turns are used. The left transformer will thus have a bifilar winding with 16 turns on it. The leakage inductance will then be 125.8 nH and the magnetising inductance will be 125.8 µH. The 25 Ω to 50 Ω impedance transformation transformer will have a 2:3 turns ratio auto-transformer, with a total number of 21.87 turns. This can be obtained with a 7 turn trifilar winding, so that the 25 Ω winding will consist of two 7 turn windings in series and the 50 Ω winding will have the three 7 turn windings in series. The resulting leakage inductance is 251.6 nH and the magnetising inductance is 251.6 µH. To simulate the Wilkinson hybrid in Cadence AWR DE, ideal transformer elements XFMR are used. To make this into a practical model, the transformer representation in figure 3.3 meeds to be used. The transformer on the left of figure 3.15 has two 25 Ω windings in series. The corresponding leakage and magnetising inductances are calculated in figure 3.15 as Ls25 and Lm25. The transformer on the right of figure 3.15 provides a 25 Ω to 50 Ω impedance transformation. Its leakage and magnetising inductances are calculated in figure 3.15 as Ls50 and Lm50. Figure 3.15. Wilkinson Hybrid model for computer simulation. RF Electronics: Design and Simulation 59 www.cadence.com/go/awr

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