Robust design of high gain amplifiers using dynamical systems and bifurcation theory

An infinite DC gain CMOS positive feedback amplifier with 90° phase margin was designed and its nonlinear dynamics was studied using level 1 MOS models. Analytical derivations were utilized to investigate its equilibrium point, turning point, stability and branching properties. Analysis suggested this amplifier would show parameter-dependent supercritical pitchfork bifurcation. Bifurcation signals the instability of this amplifier when positive feedback factor is large. By decreasing the parameter until the bifurcation was eliminated, an amplifier with an infinite DC gain at operating-point was theoretically designed. Branching diagram was presented with numerical simulation. Gain nonlinearity was explained and methods to decrease this nonlinearity were proposed. Circuit simulation results verified out derivations.