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Transistors are the cornerstone of modern electronics. Yet, their relativelycomplex characteristics, allied with often observed great parameter variation,remain a challenge for discrete and integrated electronics. Much of transistorresearch and applications have relied on transistor models, as well asrespective equivalent circuits, to be employed for circuit analysis andsimulations. Here, a simple and yet accurate transistor equivalent circuit isderived, based on the Early effect, which involves only the voltage $V_a$ and acompanion parameter $s$. Equations are obtained for currents and voltages in acommon-emitter circuit, allowing the derivation of respective gain functions.These functions are found to exhibit interesting mathematical structure, withgain values varying almost linearly with the base current, allowing the gainsto be well characterized in terms of their average and variation values. Theseresults are applied to deriving a prototypic Early space summarizing thecharacteristics of transistors, enriched with recently experimentally obtainedprototypes of NPN and PNP silicon BJTs and alloy germanium transistors. Thougha trade-off between gain and linearity is revealed, a band characterized bysmall values of $V_a$ stands out when aiming at both high gain and lowdistortion. The Early equivalent model was used also for studying the stabilityof circuits under voltage supply oscillations, as well as parallel combinationsof transistors. In the former case, it was verified that more traditionalapproaches assuming constant current gain can yield stability factors thatdeviate substantially from those derived for the more accurate Early approach.The equivalent circuit obtained for parallel combinations of transistors wasshown also to closely follow the Early formulation.

Towards a Simple, and Yet Accurate, Transistor Equivalent Circuit and  Its Application to the Analysis and Design of Discrete and Integrated  Electronic Circuits