Analysis of a Digitizer Circuit With T-Network for Low-Resistance Measurement

An efficient interfacing circuit designed for measuring low resistance (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_X</i>, less than 1 Ω) and generating a digital output is presented. The digitizer (resistance to digital converter, RDC) circuit utilizes a dual-slope integrator with a T-network in feedback, three single pole single throw (SPDT) switches, and a comparator. Conventional dual-slope integrators face challenges when measuring low <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_X</i> connected to the inverting terminal, as the high input current causes the op-amp to saturate. Reducing the input voltage to even 0.01 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> doesn’t resolve this issue. Alternatively, connecting <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_X</i> in feedback produces a low output voltage that is susceptible to inherent circuit noise, leading to significant measurement errors. Consequently, no digitizers have been developed to accurately measure <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_X</i> below 10 Ω so far. The circuit overcomes these limitations by using a T-network which enables the incoming current (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I_X</i>, 98.09 - 71.75 μA) through <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_X</i> to amplify the feedback current (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I_C</i>), hence significantly improving sensitivity which is a novel feature. During charging, lead resistance (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_L</i>) with fixed resistance <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> (or <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_X</i>) is measured, while during discharging, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_X</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_L</i> are measured together. Subtracting <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_L</i> ensures accurate <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_X</i> measurement, independent of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_L</i>, in a two-wire configuration. The circuit is experimentally tested for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_X</i> in the range of 0.1 - 0.9 Ω (full span) in which the power dissipation ranges from 0.96 - 4.63 nW, while the measurement time varies from 1.29 - 1.51 s. The circuit yields accurate results with an average error of ± 0.68% across the full span of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_X</i>.