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 $\Omega $ to 2.5 T $\Omega $ . The average temperature drift is 0.12%/°C within the temperature range from $- 40~^{\circ } $ C to $80~^{\circ } $ C, which is comparable to the on-chip high-resistance poly resistor. The relative accuracy ( $3\sigma $ / $\mu $ ) 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 mm². The CCIA achieves an accurately tunable high-pass corner frequency ( $f_{\text {HP}}$ ) 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_PP. The input-referred noise (IRN) is measured at $2.40~\mu $ V_rms 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.