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44 PCB007 MAGAZINE I NOVEMBER 2024 ere is no standard for the Complexity Index; it is whatever fits your data the best. You need to experiment to find the definition of the CI equation that gives the highest r 2 value (goodness of fit). FPY is affected primarily by the physical attributes of the board; these can be quantified by Parametric Panels (PCQR 2 ). But random effects also affect FPY, like handling, operator training, equipment maintenance, production shis, and unexpected events. ese show up in the high variability of the yield predictions. First Pass Yield Calculations e first pass yield equation is derived from the Weibel probability failure equations and the Gompertz function. is equation is a more general form of the equation typically used to predict ASIC yields by defect density (Equation 2). 100 FPY Percentage (%) = ______________ exp[(log CI/A)^B] Where: FPY = first-pass yield CI = Complexity index A, B = Fabrication capability coefficients constants To determine the constants A and B in Equa- tion 2, a fabricator must characterize his man- ufacturing process by selecting a number of printed circuits currently being produced and having various complexity indexes—hopefully some low, medium, and high. e first pass yield (at electrical test without repair) of these printed circuits for several production runs is recorded. Any statistical soware program like Excel, that has a model-based regression analysis, can now determine A and B from this model: FPY estimate = f [x] = 100¸EXP{LOG10 (complexity index¸PARM[1])^PARM[2] } Where x = Complexity Index, PARM[1] = A and PARM[2] = B Fabrication Yields e FPY is computed from a board's design characteristic. is is the yield of production before any repair or rework. PCB yield data is a gamma distribution. is is only common sense, as you can have a typically high-yielding board having some bad production runs. e resulting mean and standard deviation would reflect the lower yield data, but on the plus side, you cannot have greater than 100% yield. us, the normal mean and standard deviation do introduce some errors that we will ignore. If you can calculate and insert a gamma distribu- tion average, do it. Defining a PCB's Complexity e basic truth about printed circuit boards, substrates, and hybrid circuits is that design factors have a cumulative effect on manufac- turing yield. ese factors all affect producibil- ity. Specifications may be selected that individ- ually do not adversely affect yields but cumula- tively can dramatically reduce yield and prof- itability. A simple algorithm is available that collects these factors into a single metric called the Complexity Index (CI) (Equation 1): (Area) (Holes/unit area)^2 (no. Layers)^3 Complexity Index = _________________ (Minimum trace width) (Minimum annular ring) (Minimum hole diameter) Where: Area = Top area of the substrate to be designed Holes = Total number of drilled holes, blind, buried, and through Holes/unit area = Holes divided by board area Trace width = The minimum trace width on the substrate Layers = The total number of layers in the substrate Annular ring = Half the difference between the via land and the hole diameter Hole diameter = Finished hole size Equation 2 Equation 1