AWR eBooks

RF Electronics Chapter 3: Transformers and Hybrids Page 58 2022, C. J. Kikkert, James Cook University, ISBN 978-0-6486803-9-0. Wilkinson Transformer Hybrid Figure 3.14 shows the circuit diagram of a Wilkinson Transformer Hybrid. It has two transformers, the left one combines signals A and B into C and the tight one changes to impedance of this signal C to the required output impedance. If the same voltage input is applied to both ports A and B, then there is no voltage drop across the terminating resistor or transformer and port C is at same voltage as ports A and B. If the impedance levels for ports A and B are Z 0 , then for power conservation, the impedance level at port C must be ½ Z 0 . For those situations where the output impedance should be Z 0 then a 3:2 turns ratio transformer will change the impedance level by 2.25, which is close enough to 2:1. Figure 3.14. Wilkinson Transformer Hybrid. If a voltage is applied to port A and 0 Volt is applied to port B, then the voltage at port C is ½ of that at port A. If the input current at port A entering the transformer is I 2 , then through transformer action an equal and opposite current is flowing through the bottom part of the transformer, so that I 2 = I 4 , under all conditions. If the load impedance at port C is ½ Z 0 as before then the input impedance seen at port A at the input of the transformer is 2 Z 0 since the transformer has a 2:1 turns ratio and a 4:1 impedance transformation ratio, since at port C one has half the voltage and twice the current. Consider figure 3.14. For complete isolation between ports A and B, if a signal is applied at port A then the voltage at port B is zero, so that I 3 =0. The current I 4 must thus flow through the resistor. The value of R required for complete isolation between ports A and B can now be calculated. The voltage across the resistor is: � � � � � � � � �� � Eqn. 3.5 Since I 2 = I 4, we must have R = 2Z 0 to achieve isolation between both input ports. Under those conditions the impedance seen at the input port A is Z 0 , being the transformer input impedance of 2Z 0 in parallel with the terminating resistor of 2Z 0 . If this hybrid is used as a power splitter and the loads on ports A and B are matched, then no current will flow through the terminating resistor. Under those conditions that can be removed, at the expense of a poor isolation if unequal loads are present. For a power combiner in an antenna systems, where the output from two identical antenna elements are combined, a hybrid can be used that does not contain any isolating resistor, since the signals arriving at each of the antennae is identical and as a result no power is dissipated in the isolating resistor. The Wilkinson transformer hybrids are commercially available as wideband power- splitters and power-combiners manufactured by companies such as Mini-Circuits. RF Electronics: Design and Simulation 58 www.cadence.com/go/awr

• Cover