Filters with Decreased Passband Error

Most analog low-pass filters consist of poles. Stable causal all-pole filters give a 20-dB/dec asymptotic error |1 - H(s)| in the passband. Pole-zero filters are typically used to improve performance around crossover, and shift error between phase and gain, but common causal filter types still give a 20-dB/dec asymptotic error in the passband. This brief describes the theory and practice of a class of filters which can have arbitrarily good asymptotic behavior in the passband. It presents graphical and numerical tools for designing such filters, as well as a number of realizable circuit topologies for robustly implementing this class of filters. Aside from direct applications to the design of filters with asymptotically lower passband error, understanding such filters helps shed light on several unusual phenomena, such as how overshoot can occur in pure RC transmission lines (with driven shielding, but no inductive elements). This brief is presented in the context of low-pass filters but is equally applicable to bandpass and high-pass filters through standard transformations.