An Early Modeling Approach to Digital Electronics

An Early modeling approach of transistors characterized by simplicity and accuracy in representing intrinsic non-linearities is applied to the characterization of propagation delay and level transition switching properties of NPN and PNP small signal transistors. Eight types of devices were considered, each represented by 5 samples taken from the same lot, totaling 20 NPN and 20 PNP transistors. Four switching time measurements were experimentally obtained, and the transistors also had their Early parameters $V_a$ (the Early voltage) and $s$ (a proportionality constant such that $R_o = 1/tan(s I_B)$ accurately estimated by using an experimental-numeric procedure that involves Hough transform accumulation in order to identify the crossing of the base current ($I_B$) indexed characteristic isolines, yielding the respective $V_a$. The timing measurements exhibited strong positive Pearson correlations when taken pairwise. When these measurements were compared individually to the respective Early parameters, no significant Pearson correlation was obtained. However, a strong relationship was observed between the product of the two Early parameters and the ratio between the fall and rise time. A Pearson correlation coefficient of 0.78 was observed between these variables in the case of NPN devices. This suggests that transistors with larger average current gain tend to have more similar rise and fall times. The different relationship observed for PNP devices (Pearson 0.41) suggests some intrinsic difference in the way the Early parameters influence the rise and fall times of small signal transistors.