A 25.8% 3σ/μ-Accuracy, 0.12%/°C Temperature Drift Sigma-Delta Modulation Calibrated Pseudo-Resistor With GΩ to TΩ Tuning Range

This article presents an on-chip self-calibrated pseudo-resistor (PR) based on a sigma-delta modulation (SDM) loop. The proposed real-time calibration mechanism facilitates the implementation of an accurate low-drift ultra-high-value (UHV) PR with a wide tuning range at minimum hardware expenditure. Experimental results demonstrate that the resistance can be precisely tuned from 1.5 G<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Omega $</tex-math> </inline-formula> to 2.5 T<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Omega $</tex-math> </inline-formula>. The average temperature drift is 0.12%/°C within the temperature range from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$- 40~^{\circ } $</tex-math> </inline-formula>C to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$80~^{\circ } $</tex-math> </inline-formula>C, which is comparable to the on-chip high-resistance poly resistor. The relative accuracy (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3\sigma $</tex-math> </inline-formula>/<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $</tex-math> </inline-formula>) is 25.8% under room temperature, representing an improvement of over one order of magnitude compared to an uncalibrated PR. To validate the proposed calibration loop, a capacitively-coupled instrumentation amplifier (CCIA) embedding the calibrated PR has been fabricated in a standard 180-nm CMOS process, occupying a core area of 0.187 mm<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>. The CCIA achieves an accurately tunable high-pass corner frequency (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f_{\text {HP}}$</tex-math> </inline-formula>) from 0.13 to 217 Hz, a total harmonic distortion (THD) as low as 0.0093%, and a linear output swing up to 3.9 V<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PP</sub>. The input-referred noise (IRN) is measured at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.40~\mu $</tex-math> </inline-formula>V<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rms</sub> within a 0.5–200-Hz bandwidth. In conclusion, this work paves the way for implementing accurate tunable on-chip UHV resistors in mass production.