AWR eBooks

RF Electronics: Design and Simulation

Issue link: https://resources.system-analysis.cadence.com/i/1325428

Contents of this Issue

Navigation

Page 75 of 406

RF Electronics Chapter 3: Transformers and Hybrids Page 62 2022, C. J. Kikkert, James Cook University, ISBN 978-0-6486803-9-0. The equations for this hybrid are: V a -V d =V 1 V c -V e =V 1 Eqn. 3.6 V c -V d =V 2 V b -V e =V 2 Subtracting the first two equations and the last two equations and adding the resulting equations gives: 2 b a c V V V Eqn. 3.7 Now consider the conditions required for isolation. If V b =0. For isolation between ports A and B, the current through the bottom transformer is zero, since with a load connected to B the voltage must be zero. That means V 2 =0 and thus V e =0 and V d =½V a . For the input impedance at A to be Z 0 then the load resistor must be ½Z 0 . Under those conditions, the current into A goes through the load and out of C. The voltages are thus: At input A V a = Z 0 I Eqn. 3.8 Across the Load ½V a = ½Z 0 I Eqn. 3.9 At the output C ½V a = ½Z 0 I Eqn. 3.10 The equations are thus consistent and the assumption that V b =0 is justified and we have full isolation when R=½Z 0 . The circuit works thus as a proper hybrid. Note: Like the Wilkinson transformer, the impedance at the summing port C has an impedance of ½Z 0 and a transformer needs to be used to change that to Z 0 if required, similar to that for the Wilkinson transformer of figure 3.14. Many Way Hybrids Figure 3.21. A four-way combiner. RF Electronics: Design and Simulation 62 www.cadence.com/go/awr

Articles in this issue

Links on this page

view archives of AWR eBooks - RF Electronics: Design and Simulation