Matching Networks for Broadband Multiport Radio-Frequency Systems: Theory, Analysis and Design

In wireless radio-frequency transceivers, the impedance matching network between the source amplifiers and load antennas is a critical stage that determines the bandwidth. If well designed, the network is capable of matching the impedances of the sources and loads over a broad bandwidth. However, perfect matching between sources and loads across all frequency is generally impossible if the matching network is passive. For a single load driven by a source through a two-port network, the maximum achievable bandwidth is governed by the Bode-Fano upper bounds, introduced by Bode and Fano in 1940s, on the integral over all frequency of the logarithm of the reflection coefficient of cascaded matching network and load. Since then, extensions of the Bode-Fano bounds to multiport systems where multiple sources drive multiple loads through multiport networks have only been partially examined for specific loads. In this dissertation, we derive multiport broadband matching bounds that generalize the classical results of Bode and Fano. We also present a step-by-step recipe to compute the bounds from the characteristics of the loads, which applies to any number of coupled loads. The bounds determine the maximum achievable bandwidth for any given loads that are matched by an arbitrary passive multiport network.

Various matching networks can be designed for multiport systems. A class of narrowband networks that maximize the power transfer from sources to loads at a design frequency are called ``decoupling networks'', since they eliminate the mutual coupling of the loads. Existing design techniques for decoupling networks work for a small number of loads with specific structures. Another class of networks are broadband matching networks, which approximately match sources and loads over a broad bandwidth. Design methods for two-port broadband matching networks are well known, but there is a lack of understanding in the network structures that achieve broadband matching bounds for multiport systems.

In this dissertation, we present a systematic design method for decoupling networks that is applicable for any number of coupled loads. This method synthesizes networks with minimum complexity in that it achieves the lower bound on the number of circuit components required in any decoupling network. With the assistance of multiport broadband matching bounds derived in the dissertation, we also present examples of broadband matching networks that maximize the bandwidth and approach these bounds. We find that the achievable bandwidth of multiport systems generally scales with the ratio of the number of loads to the number of sources, and introduce a class of networks called ``determinant networks'' that achieve the scaling bandwidth. In multiport systems where there are more loads than sources, we show that non-reciprocal components are essential to the design of matching networks that achieve the broadband bounds. Finally, when evaluating the effect of antenna coupling on a pair of dipoles that are approximately a quarter wavelength apart, we find that the coupled dipoles exhibit significantly more bandwidth than isolated ones. This implies that antenna coupling may have a positive effect on the bandwidth if the antennas are properly spaced and matched.