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RF Electronics: Design and Simulation

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RF Electronics Chapter 3: Transformers and Hybrids Page 57 2022, C. J. Kikkert, James Cook University, ISBN 978-0-6486803-9-0. Assume that all the windings on the transformers have the same number of turns. For the Audio transformer hybrid in figure 3.12, the voltages at each of the ports are related as: Va = Vc + Vd Vb = Vc – Vd Eqn. 3.3 2Vc = Va + Vb 2Vd = Va –Vb By changing the turns ratio to 0.707, the same equations are obtained for all the ports: Va = 0.707Vc + 0.707Vd Vb = 0.707Vc – 0.707Vd Eqn. 3.4 Vc = 0.707Va + 0.707Vb Vd = 0.707Va – 0.707Vb This ensures that the impedance levels in each port are the same. Note that Va does not couple into Vb and Vc does not couple into Vd and vice versa. A 40 dB isolation is typical under properly matched conditions. Figure 3.13 shows how this audio hybrid can be wired up for use with amplifiers to produce a bi-directional amplifier, to amplify signals travelling in both directions along a wire. If the 2-wire circuit is not terminated properly, then part of the energy travelling out of this amplifier will be reflected and come back as input to the amplifier and be amplified again. If the gain of the amplifier is A dB and the isolation is B dB, then the singing margin is 2×(B-A). The singing margin is the gain around the amplifier/hybrid loop. If the gain around the loop is more than 0 dB, then oscillations will occur. In practice, the singing margin should be better than 6 dB. We should thus have more than 6 dB loss around the loop, even in the worst conditions. Figure 3.13. Bi-directional amplifier. Power Combiner / Splitter In a power combiner or power splitter, the terminating port is not brought out. The power combiner or power splitter is thus a 3-port device. Since linear passive devices are bi- directional, the same device can be used as both a power splitter and a power combiner. Often these devices are still called a hybrid. A common transformer based power splitter is a Wilkinson Hybrid. The two-way power splitters sold by department stores to permit two TVs to be operated from one antenna are Wilkinson Hybrids. RF Electronics: Design and Simulation 57 www.cadence.com/go/awr

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