An exact expression for the thermal variation of the emitter base voltage of bi-polar transistors

Statistical Circuit Design: Characterization and Modeling for Statistical Design

“…23. This completes the information necessary for the current gain form of equation (24) where the terms are as defined for equation (24) and Xm and Xn are selected from the distribution corresponding to Fig. 23, normalized such that the median is zero.…”

“…Two comments about equation (24) are in order. First, in the absence of better information, the numbers Xm and X" are selected from the global distribution, normalized so that the median is zero.…”

“…The second comment relates to the form of the expression. To obtain the relationship between two parameters, a visual technique was used in that a two-dimensional scatter plot of the measured values was compared with the scatter plot indicated by equation (24). Typical results are shown in Fig.…”

“…The only realistic solution is to gain some understanding of the transistor parameter combinations and interdependencies and charac terize these in the format of equation (24). For a first attempt, it seemed reasonable to assume that the sheet resistance of the active base region would be a fairly basic entity afí'ecting a number of the model parameters.…”

“…The intercept currents are found to be highly correlated for tran sistors on an integrated circuit and the form of equation (24) for this situation is only will processing techniques change but it is hoped that, as appro priate measured data become available, interdependencies will be observed which were expected but could not be detected with existing data.…”