This paper exploits the inherent analytical relationship between the dc, small-signal, and harmonic balance circuit equations. This provides the basis for unified dc, small-signal, and large-signal analyses using a single nonlinear circuit description. Our approach ensures consistent circuit simulation results and permits simultaneous optimization of dc, small-signal, and large-signal responses with multidimensional specifications. Applying this concept to FET parameter extraction leads to nonlinear device models suitable for both small-signal and large-signal analyses. We also demonstrate simultaneous small-signal and large-signal minimax optimization of an FET broad-band amplifier to extend the dynamic operating range.