Estimation of threshold voltage from frequency of ring oscillator

This paper proposes the estimation method of the threshold voltage (Vth) of the transistor from the frequency of the ring oscillator (RO) without analog measurement. Two distributions of delays, in which the contour lines are nearly orthogonal with each other, are derived from the measured frequencies of three kinds of ROs. The Vth can easily be calculated from the two distributions by fitting to the quadratic function and using the `goal-seek' function of Excel. The accuracy of the calculated Vth is evaluated for various conditions. By optimizing the condition and dividing the fitting range, the error decreases down to 5mv which is sufficient for an accurate estimation.