Bandwidth Analysis of Multiport Radio Frequency Systems—Part I

When multiple radio frequency sources are connected to multiple loads through a passive multiport matching network, perfect power transfer to the loads across all frequencies is generally impossible. In this two-part paper, we provide analyses of bandwidth over which power transfer is possible. Our principal tools include broadband multiport matching upper bounds, presented herein, on the integral over all frequency of the logarithm of a suitably defined power loss ratio. In general, the larger the integral, the larger the bandwidth over which power transfer can be accomplished. We apply these bounds in several ways. We show how the number of sources and loads, and the coupling between loads, affect achievable bandwidth. We analyze the bandwidth of networks constrained to have certain architectures. We characterize systems whose bandwidths scale as the ratio between the numbers of loads and sources. The first part of this paper presents the bounds and uses them to analyze loads whose frequency responses can be represented by analytical circuit models. The second part analyzes the bandwidth of realistic loads whose frequency responses are available numerically. We provide applications to wireless transmitters where the loads are antennas being driven by amplifiers. The derivations of the bounds are also included.