Modeling transistor variation using α-power formula and its application to sensitivity analysis on harmonic distortion in differential amplifier

2012 
We propose a statistical MOSFET model using the α-power equation for the I D –V GS curves of a transistor to make it easier to deal with transistor variations using hand calculations. We evaluated the impact of the transistor variation (mismatch) on the harmonic distortion (HD) in a differential amplifier using the statistical α-power model along with a sensitivity simulation using SPICE. We found that the driver transistor variation majorly impacted on the 2nd HD in the differential gain, which was approximately proportional to the transistor current mismatch, whether the mismatch was induced by the threshold voltage variation or by the current factor variation. We further evaluated the HD by directly using the experimental I D –V GS curves to obtain more accurate values. The α-power model, fitted to g m –V GS curves, described the HD more precisely, to make it more agreeable with the results obtained from the experimental data, when we used the differential current equation as a function of the transconductance (g m ), its derivative \( \left(g_{m}^{\prime}\right) \) and their variations (Δg m and Δ\(g_{m}^{\prime}\, \)).
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