Improved Broadband Matching Bound

In radio frequency systems where a load is driven by a source through a passive impedance matching circuit, the bandwidth over which match can be attained is limited. The Bode–Fano upper bound is often invoked to find this limit. We show that the bound is loose for some loads and, hence, cannot be attained by any network. We present a simple method to improve the bound and give conditions under which the improved bound is tight. The improved bound requires no additional assumptions or conditions beyond what is used for the Bode–Fano bound. Applications to analytical and numerical load models are demonstrated.

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