PRACTICAL HYBRIDS
Practical Hybrids and their Theoretical Parameters
To give perfect isolation between appropriate ports every hybrid network has to have a form of symmetry. Quadrature hybrids have symmetry about two axes and 0-180° hybrids have symmetry about a single axis. Each hybrid must also include a network to match a single input port to a pair of output ports if input and output impedances are to remain equal. The form of circuit determines the extent to which its parameters depart from the ideal as the input frequency is varied. The following diagrams in this Section show parameters for various types of hybrid. They are mostly derived from an analysis by digital computer.
For convenience of presentation of results, component values are shown relative to the characteristic input or output impedance Z0 at the centre or design frequency f0 . The hybrids which have been analysed are in the form of transmission lines, lumped components, transformers, or a mixture of these components. A whole family of variations exist where, for instance, quarter-wave lines may be replaced by T or π sections of lumped components. Circuits which use lumped components are generally useful at frequencies up to about 200 MHz, transmission lines are convenient from 30 MHz to 3 GHz and waveguides may be used at higher microwave frequencies. Transmission lines may be either unbalanced or balanced.
In the following analyses the hybrids are first treated as power splitters then as power combiners. In each case the analysis is considered, in turn, from the point of view of input ports A and C and then input ports B and D. (it is important to consider both points of view if a 0-180° hybrid is used as a splitter and if either type is used as a combiner).
The analysis shows the variation of input voltage reflection coefficient with frequency, the equality of power split, the difference in phase between outputs, and the cross-losses. A few remarks are made concerning the practical realisation of the hybrid. It is often possible to use wideband matching techniques to slightly improve certain aspects of performance but this is not dealt with in this Report. Details of parameters are omitted in some cases because they depend to a large extent on the physical or mechanical construction of the hybrid.
If a hybrid with a finite cross-loss is used as a power combiner and one generator fails to produce the correct input voltage, the input admittance seen by the other generator will change. This change will depend on the state of the output voltage and output impedance of the faulty generator. The analysis of this condition may easily be performed by the methods used in the Report but for the sake of brevity it has been omitted.
The transmission line "3dB coupler" hybrid is now so widely used in broadcasting that although its main features are summarised in this Section, it is dealt with in more detail in Appendix I. It should be noted that, in order to show the superior bandwidth of the 3 dB coupler, the width of its frequency scale is doubled relative to that of other hybrids.
List of Practical Hybrids
All of these hybrids are considered in the following pages. The electrical performances of most of them are given in detail.
QUADRATURE HYBRIDS; all ports capable of being coaxial (unbalanced).
6.1 3dB Coupler 6.2 Branch-Line 6.3 Lumped Branch-Line 6.4 Capacity-Coupled Branch-Line 6.5 Lumped Capacity-Coupled Branch-Line 6.6 Higgins
QUADRATURE HYBRIDS; one or more ports cannot be coaxial (unbalanced).
6.7 Maxwell Bridge
0°-180° HYBRIDS; all ports capable of being coaxial (unbalanced).
6.8 Rat Race 6.9 "Z0" Rat Race 6.10 Cross-over Rat Race 6.11 Dual-load Rat Race 6.12 Split Drum 6.13 Transformer
0°-180° HYBRIDS; one or more ports cannot be coaxial (unbalanced).
6.14 Waveguide Magic T 6.15 Wilkinson 6.16 Lumped Wilkinson 6.17 Bridged T
