Large signal analysis of low-voltage bipolar analog functional elements using Fourier-series approximations

This paper discusses the large signal performance of low-voltage analog functional elements built around bipolar-junction transistors. Fourier-series approximations are obtained for the transfer characteristics of the basic building blocks; such as the balanced emitter-coupled pair, the unbalanced emitter-coupled pair with different transistor sizes, the emitter-coupled pair with bias offset and the triple-tail cell. Using the Fourier-series approximations of these basic building blocks, closed-form expressions are obtained for the amplitudes of the harmonics and inter-modulation products at the output of analog functional elements; such as the basic differential pairs, squaring circuits, operational transconductance amplifiers, multipliers, mixers and triplers, excited by a multisinusoidal input signal. Using these expressions comparison between the large signal performance of analog functional elements can be performed and the parameters required for a predetermined performance can be determined.