Characterizing Complementary Bipolar Junction Transistors by Early Modelling, Image Analysis, and Pattern Recognition

This work reports an approach to study complementary pairs of bipolar junction transistors, often used in push-pull circuits typically found at the output stages of operational amplifiers. After the data is acquired and pre-processed, an Early modeling approach is applied to estimate the two respective parameters (the Early voltage $V_a$ and the proportionality parameter $s$). A voting procedure, inspired on the Hough transform image analysis method, is adopted to improve the identification of $V_a$. Analytical relationships are derived between the traditional parameters current gain ($\beta$) and output resistance ($R_o$) and the two Early parameters. It is shown that $\beta$ tends to increase with $s$ for fixed $V_a$, while $R_o$ depends only on $V_a$, varying linearly with this parameter. Several interesting results are obtained with respect to 7 pairs of complementary BJTs, each represented by 10 samples. First, we have that the considered BJTs occupy a restricted band along the Early parameter space, and also that the NPN and PNP groups are mostly segregated into two respective regions in this space. In addition, PNP devices tended to present an intrinsically larger parameter variation. The NPN group tended to have higher $V_a$ magnitude and smaller $s$ than PNP devices. NPN transistors yielded comparable $\beta$ and larger $R_o$ than PNP transistors. A pattern recognition method was employed to obtain a linear separatrix between the NPN and PNP groups in the Early space and the respective average parameters were used to estimate respective prototype devices. Two complementary pairs of the real-world BJTs with large and small parameters differences were used in three configurations of push pull circuits, and the respective total harmonic distortions were measured and discussed, indicating a definite influence of parameter matching on the results.