Ground Plane Partitioning for Current Recycling of Superconducting Circuits

Superconducting single flux quantum (SFQ) technology using Josephson junctions (JJs) is an excellent choice for the computing fabrics of the future. Current recycling is a necessary technique for the implementation of large SFQ circuits with energy-efficiency, where circuit partitions with similar bias current requirements are biased serially. Though this technique has been verified for small scale circuits, it has not been implemented for large circuits as there is no trivial way to partition the circuit into circuit blocks with separate ground planes. The major constraints for partitioning are (1) equal bias current and (2) equal area for all the partitions; (3) minimize the connections between adjacent ground planes with high-cost for non-adjacent planes. For the first time, all these constraints are formulated into a cost function and it is minimized with the gradient descent method. The algorithm takes a circuit netlist and the intended number of partitions as inputs and gives the output as groups of cells belonging to separate ground planes. It minimizes the connections among different ground planes and gives a solution on which the current recycling technique can be implemented. The parameters of cost function have been initialized randomly along with minimizing the dimensions to find the solution quickly. On average, 30% of connections are between non-adjacent ground planes for the given benchmark circuits.