caa a22 4500 606206671 CHVBK 20210128101012.0 cr unu---uuuuu 210128e20151101xx s 000 0 eng 10.1007/s00034-015-0012-x doi (NATIONALLICENCE)springer-10.1007/s00034-015-0012-x DuttaRoy S. Department of Electrical Engineering, Indian Institute of Technology Delhi, 110016, Hauz Khas, New Delhi, India aut On Resistive Ladder Networks for Use in Ultra-Low Frequency Active-RC Filters [Elektronische Daten] [S. DuttaRoy] 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) $${L}_{1}$$ L 1 : the $$R-2R$$ R - 2 R ladder, as commonly used in data converters, (ii) $${L}_{2}$$ L 2 : the $$R{-}\alpha R$$ R - α R ladder, which is a generalization of $${L}_{1}$$ L 1 , (iii) $${L}_{3}$$ 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) $${L}_{4}$$ 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 $${L}_{1}$$ L 1 is analyzed by inspection, $${L}_{2}$$ 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. $${L}_{3}$$ L 3 and $${L}_{4}$$ 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 $${L}_{3}$$ L 3 and $${L}_{4}$$ L 4 have several advantages over $${L}_{1}$$ L 1 and $${L}_{2}$$ 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. Springer Science+Business Media New York, 2015 Resistive ladder networks nationallicence Transfer resistance nationallicence Ultra-low frequency filters nationallicence Difference equation nationallicence Bio-medical signal processing nationallicence Circuit theory nationallicence Circuits, Systems, and Signal Processing Springer US; http://www.springer-ny.com 34/11(2015-11-01), 3661-3670 0278-081X 34:11<3661 2015 34 34 https://doi.org/10.1007/s00034-015-0012-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00034-015-0012-x text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- DuttaRoy S. Department of Electrical Engineering, Indian Institute of Technology Delhi, 110016, Hauz Khas, New Delhi, India aut NATIONALLICENCE 773 0- Circuits, Systems, and Signal Processing Springer US; http://www.springer-ny.com 34/11(2015-11-01), 3661-3670 0278-081X 34:11<3661 2015 34 34