Inductive Characteristics of Power Distribution Grids in High Speed Integrated Circuits
ISQED '02 Proceedings of the 3rd International Symposium on Quality Electronic Design
Frequency Characteristics of High Speed Power Distribution Grids
Analog Integrated Circuits and Signal Processing
Scaling trends of on-chip power distribution noise
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
GLSVLSI '05 Proceedings of the 15th ACM Great Lakes symposium on VLSI
ISQED '06 Proceedings of the 7th International Symposium on Quality Electronic Design
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
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The variation of inductance with circuit length is investigated in this paper. The nonlinear variation of inductance with length is shown to be a result of inductive coupling among circuit segments. If the distance between the forward and return current paths of a current loop is much smaller than the loop length, the inductive coupling to the forward current is similar to the coupling to the return current, resulting in negligible coupling. The inductance of these circuits therefore varies approximately linearly with length. Similarly, the effective inductive coupling between two parallel current loops is reduced through cancellation and has a negligible effect on the net inductance of a circuit. As a general rule, the inductance of circuits where the distance between the forward and return current is much smaller than the characteristic dimensions of the circuit scales linearly with circuit dimensions. This linear behavior can be used to simplify the inductance extraction and circuit analysis process.