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Decoupling capacitors are fundamental keys for the reduction of transient noise in power delivery networks; their arrangement and values are crucial for reaching this goal. This work deals with the optimization of the decoupling capacitors of a power delivery network by using a nature-inspired algorithm. In particular, the capacitance value and the location of three decoupling capacitors are optimized in order to obtain an input impedance below a specific mask, by using a nature-inspired algorithm, the genetic one, in combination with two electromagnetic solvers used to compute the objective function. An experimental board is designed and manufactured; measurements are performed to validate the numerical results.

The high level of integration in digital electronic chips based on threedimensional (3D) technology requires accurate modelling of the vertical interconnects (the through silicon vias -TSVs). An accurate prediction of the signal propagation and crosstalk of the TSVs cannot be based on the single via since the interaction among adjacent TSVs in a high density array cannot be neglected. An algorithm is proposed that extends the approach for modelling a TSV array with a complete analytical evaluation of the final multiport scattering parameter matrix, thus making the electromagnetic modelling of such structures more efficient without relying on commercial circuit solvers. The proposed method requires much less processing time with respect to commercial solvers with a comparable accuracy.Introduction: In the recently developed integrated circuits (ICs), through silicon vias (TSVs) are used to vertically interconnect the stacked chips when using 3D technology. Moreover, the increasing bandwidth of digital signals forces the IC passive interconnects as well as the TSVs to ensure a good quality of the propagating signals.To achieve such integrated devices to work properly, an exhaustive analysis is necessary for the TSV characterisation and design; this analysis can be based on efficient equivalent circuits or on time consuming full wave solvers. The high density of vertical interconnects in a TSV array [1, 2], as well as nonlinear effects such as depletion capacitance [2, 3], makes the equivalent circuit the most feasible method able to combine a large circuit model with limited computational time. The use of full wave solvers is necessary for investigating the physic phenomena of the TSV electromagnetic field propagation, as well as for identifying the topology of the equivalent circuit; however, they become impracticable for the analysis of a large problem such as a TSV array. Closed-form expressions are developed [1, 4] to obtain accurate values for the self and coupling R, L, G, C parameters of the TSV array. In [1], a method for developing an equivalent circuit for a large TSV array is presented, where the model complexity is reduced by combining the effect of the return ('ground') TSVs. Thus, the final S-parameter matrix consists of just the signal TSVs. However, the reduced RLGC matrices are combined within a commercial circuit simulator for achieving the final S-parameters. This work is based on [1] up to the analytical definition of the reduced impedance (for resistance R and inductance L) and admittance (for conductance G and capacitance C) matrices; then it extends that work to analytically evaluate the final multi-port S-parameter matrix of the coupled signal TSVs of the array, similar to [5], thus without relying on any simulator throughout the modelling procedure.

To reduce the noise created by a power delivery network, the number, the value of decoupling capacitors and their arrangement on the board are critical to reaching this goal. This work deals with specific improvements, implemented on a genetic algorithm, which used for the optimization of the decoupling capacitors in order to obtain the frequency spectrum of the input impedance in different positions on the network, below previously defined values. Measurements are performed on a specifically manufactured board in order to validate the effectiveness of the proposed algorithm and the optimization results obtained for a specific example board.

An iterative optimization for decoupling capacitor placement on a power delivery network (PDN) is presented based on Genetic Algorithm (GA) and Artificial Neural Network (ANN). The ANN is first trained by an appropriate set of results obtained by a commercial simulator. Once the ANN is ready, it is used within an iterative GA process to place a minimum number of decoupling capacitors for minimizing the differences between the input impedance at one or more location, and the required target impedance. The combined GA–ANN process is shown to effectively provide results consistent with those obtained by a longer optimization based on commercial simulators. With the new approach the accuracy of the results remains at the same level, but the computational time is reduced by at least 30 times. Two test cases have been considered for validating the proposed approach, with the second one also being compared by experimental measurements.