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AUGUST 2025 I DESIGN007 MAGAZINE 57 other terminals. This is the most recently deter- mined wiring model and represents the most prac- tical approximation of surface mounting technol- ogy. The equations below present the mathemati- cal model (Figure 2). • Predicted Interconnect Density, δ » Based on the stochastic model of wiring involving all terminals, their probability of length is based on the distance of the sec- ond terminal and the spatial geometry of the other terminals • δ = D * Ni ∕ A ( in. per sq. inch) where: D = ave. interconnection distance (in.) A = routing area (sq. inch) Ni = total number of interconnections E(x) = expectation of occurrence G = pad placement grid (in.) D = E(x)*G E(x) = • Ni= 2*Nt / 3 where: α = empirically derived constant= 0.94 M = board width of grid pts. = (width / G) +1 N = board length of grid pts. = (length / G) +1 Nt = number of terminal leads Adjusting the Wiring Density Model The best way to improve this model is to normalize it to your company's design constraints by deter- mining the standard deviation (sigma) of your most dense boards (this will be predicted) and taking the design and sum of the total wiring lengths on each signal layer (actual). A regression fit will show your wiring density, as seen in Figure 3. Summary Ultra HDI design is new to many designers. Optimize the appropriate design rules and layer stackup by first predicting what the circuit and components require. See the illustrated Coors Statistical Model, and you can use other references to models. This can be an insightful first step in applying UHDI. DESIGN007 References 1. The HDI Handbook, by Happy Holden. 2. "A Statistical Approach to Wiring Requirements," by G. Coors, P. Anderson, and L. Seward. Pro- ceedings of International Electronics Packaging Society (IEPS) 1990, pp. 774–783. 3. Principles of Electronic Packaging, by D.P. Serpahim, R.C. Lasky, and C.Y. Li., pp. 39–52. 4. "New Polymeric Multilayer and Packaging," by H. Ohdaira, K. Yoshida, and K. Sassoka. Proceedings of Printed Circuit World Confer- ence V, Glasgow, Scotland, reprinted in Cir- cuit World, Vol. 17, No. 12, January 1991. ▼ F i g u re 3 : P re d i ct i n g w i r i n g d e m a n d : S t at i st i c a l w i r i n g te c h n i q u e n o r m a l i ze d to yo u r st y l e. 8 , 9 E i g ht Re d e s i g n e d P C B s