Automatic tuning of digitally-controllable positive-feedback OTAs in continuous-time sigma–delta modulators

This paper proposes a technique suitable for on-chip tuning of digitally-tunable positive-feedback operational transconductor amplifiers in a continuous-time sigma–delta modulator (CT-SDM) with active-RC integrator stages. The work we present relies on phase shift and offset measurement of individual active-RC integrator stages output using comparators to estimate output conductance, DC-gain, and common mode level of the differential output signals. The tuning methodology aims to tune the integrator stages to achieve sufficient DC-gain as required by the SDM. We present experimental results to confirm the correlation of our integrator phase and output offset detection technique with the operational transconductance amplifier (OTA) DC gain. We employ this technique in a tuning process of two digitally-tunable OTA chips implemented in complementary metal-oxide semiconductor 180 nm process configured in a second-order CT-SDM circuit with discrete components. The tuning algorithm results in a measured signal-to-noise and distortion ratio (SNDR) of 46.97 dB, which is close to the maximum SNDR of 47.83 dB achievable across a subset of the digitally-tunable OTA code space. High-speed operation of the CT-SDM and tuning circuitry has been verified through circuit simulations.