February_EDFA_Digital

edfas.org 1 7 ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 21 NO. 1 from two six-input and six-output FUB functions. For each design example, Table 2 first provides the number of standard cells, the number of standard cell types, and the number of logic functions for the five industrial designs. Also provided in Table 2 are the standard cell incor- poration errors (Err.), the number of different FUB imple- mentations in each FUB template (FT), and the runtimes (RT) for the two solvers in seconds. The standard cell incorporation error captures the mismatch between the target cell usage exhibited by the industrial design and the FUB template, and is calculated as , where | ∆ i | is the absolute difference between the targeted number of cells of logic function i and the number in the FUB template, and T is the total number of cells of all logic functions in the targeted design. Minimum values for standard cell incorporation error, FUB template size, and solver runtimes are shaded for each design example. It is evident from the table that some circuits are easier to mimic with the CM-LCV design methodology than others (e.g., 0.1% minimum standard-cell incorporation error for the “Block U” design to 6.7% for the “Block I” design). Additionally, the templates created by the BARON solver exhibit smaller error comparedwith the templates created by the convex solver. However, run times for the convex solver are at least 1,000 times faster than theBARON. Thus, the performance of a given solver is not always better than another. Overall, results from the table indicate that the optimization problem is highly complex. Figure 4 shows five histograms of the measured stan- dard cell usage from the industrial designs and the FUB templates producedby the two solvers. In considerationof space constraints, only 15 logic functions, which have the maximumstandard cell incorporation error, are shown in Fig. 4. These histograms highlight two of the difficulties of the FUB template selectionproblem. First, larger standard cells with six inputs are more difficult to incorporate into FUBs, which lead to the solvers having fewer options for design reflectionwhen constructing the FUB template that matches the usage measured in the industrial designs. Second, some standard cells are actually overused in Fig. 4 Standard cell histogram comparison for five industrial designs, namely, (a) Block C, (b) Block U, (c) Block D, (d) Block G, (e) Block I against CM-LCV FUB arrays created using the flow of Fig. 3. The first bar of each histogram is the standard cell measurement from the corresponding design, and the remaining bars are the standard cell measurements from the CM-LCV FUB arrays created by the two solvers. (a) (b) (c) (d) (e)