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On Resistive Ladder Networks for Use in Ultra-Low Frequency Active-RC Filters

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Abstract

It is known that the transfer resistance of a resistive ladder can be many times the sum of the actual resistances used to make it. This fact has recently been utilized in constructing ultra-low frequency active-RC filters for biomedical applications, thus saving a significant amount of silicon area in IC implementation. This paper contains an investigation of four kinds of such ladders, viz., (i) \({L}_{1}\): the \(R-2R\) ladder, as commonly used in data converters, (ii) \({L}_{2}\): the \(R{-}\alpha R\) ladder, which is a generalization of \({L}_{1}\), (iii) \({L}_{3}\): the arithmetic progression ladder, in which the series resistances as well as the shunt conductances increase from input to output in arithmetic progression, and (iv) \({L}_{4}\): the geometric progression ladder, in which the series resistances as well as the shunt conductances increase from input to output in geometric progression. While \({L}_{1}\) is analyzed by inspection, \({L}_{2}\) is shown to obey a linear second-order difference equation with constant coefficients, yielding an explicit and elegant expression for the transfer resistance. \({L}_{3}\) and \({L}_{4}\) also obey such a difference equation but not with constant coefficients, and as such, are not amenable to explicit solution. Theses are analyzed here by using the step-by-step ladder analysis method, starting from the output end, and the results for one-, two-, and three-section ladders are given. The four types of ladders are compared on the basis of a specified transfer resistance. It is shown that \({L}_{3}\) and \({L}_{4}\) have several advantages over \({L}_{1}\) and \({L}_{2}\). However, besides the area saving factor, the choice for a given situation will depend on several factors, viz., the basic resistance, the total resistance used, the number of resistors, the spread of resistors, and the ease of fabricating the resistors, in addition to other possible technological factors.

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Acknowledgments

The work of the author was inspired by Reference [2] and supported by the Indian National Science Academy through the Honorary Scientist scheme. The author thanks Professor Y. V. Joshi for his help in the preparation of the manuscript. The author also thanks the Editor-in-Chief and the reviewers for their constructive comments and suggestions which are believed to have made value addition to the paper.

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  1. S. C. Dutta Roy

    Present address: , 164, Hauz Khas Apartments (SFS), New Delhi, 110016, India

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  1. Department of Electrical Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016, India

    S. C. Dutta Roy

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Dutta Roy, S.C. On Resistive Ladder Networks for Use in Ultra-Low Frequency Active-RC Filters. Circuits Syst Signal Process 34, 3661–3670 (2015). https://doi.org/10.1007/s00034-015-0012-x

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  • DOI: https://doi.org/10.1007/s00034-015-0012-x

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