Properties of On-Chip Inductive Current Loops

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