Abstract
The theory and design of lumped element quadrature hybrids is presented. The principal area of interest is in passive circuits, exhibiting exact quadrature performance, for use in radio frequency circuits. The state of the art prior to the present research is reviewed, considering the available theory in the literature, and also the general specifications of commercially available products. The fundamental limitations of exact quadrature hybrids are considered, and governing equations are derived for realisable circuits. The theory of approximation as it applies to quadrature hybrids is considered, and useful classes of function are solved. Particular attention is paid to a rational Chebychev class of function, which offers the prospect of exceptionally wide bandwidth. The approximation functions in the real frequency domain are then transformed into the equivalent functions using the complex frequency variable, so as to be suitable for synthesis. Passive circuits, which implement the approximation functions already considered, are synthesized. Both low-pass and band-pass circuits are found to exhibit suitable properties. Practical realisations of the synthesized circuits are described, together with their measured performance. Good agreement is seen between theory and practice. Other aspects of quadrature hybrid design are considered, including a comparison with approximate phase hybrids, active circuits, power handling, weak couplers, graphical techniques and a figure of merit method of assessing the performance of quadrature hybrids. The direction for future research is considered and an assessment of the achievements of the research is made.