The Pole-Zero Locations of Some Trimmed Distributed RC Networks and the Application to Low Pass Active Filters

The voltage transfer functions of abraded uniform distributed resistance-capacitance (RC) networks are discussed. A straight trim cut and an L-shaped trim cut either near the input port or near the output port of a uniform RC network are considered, and the pole-zero locations for these four cases are evaluated. It is shown that the trim cuts near the output port of an unloaded RC network have no effect on the pole positions of the transmission function. A straight cut near the input port is modeled by linearly tapered RC networks, and a loaded RC network is used to analyze the L cut near the input port. Measured results of trimmed thick film RC networks show good agreement with these models. From this analysis it is shown that the open circuit transfer function of a trimmed RC network with a straight cut near the input may be further approximated by two dominant poles and a delay term. This cut is shown to be the most useful in functionally adjusting the magnitude response of a distributed low pass active filter, and the dominant pole-pair locus of the trimmed distributed lumped active filter is plotted.