Behavioral dimensional SPICE models of thick-film resistors at cryogenic temperatures

摘要

This work presents novel two-dimensional behavioral temperature models of thick-film resistors working in low-temperature conditions, which is based on measurements of a large set of thick-film resistors in the temperature range between -180°C and +20°C. The test resistors were made of 5 various resistive inks (three from Inst. of Electronic Materials Technology, Warsaw (R323, R324, R325) and two from Du Pont (DP1931, DP1939)). Ten resistor coupons, each consisting of 36 resistors with various dimensions, were made of every ink. Resistor planar dimensions (length and width) were from the range between 0.59 and 5.91 mm. A large set of R(T, l, w) characteristics was analyzed. Every resistor from the test coupon was allocated into one of four subgroups - Power, Long, Wide or Normal resistors. The mathematical model as multiplication of two polynomials was elaborated based on above mentioned measurements. First polynomial approximates temperature behavior of normalized resistance, while the second one describes resistance dependence on planar resistor dimensions. Special computational procedures for multidimensional approximation purpose were elaborated. Next, based on these mathematical models, the behavioral temperature SPICE models were created for each resistors' subgroup.