Analytical evaluation of inductance of spiral inductors using partial element equivalent circuit (PEEC) technique

In planar circuits, inductors are in spiral form. Due to geometrical complexity of planar or quasiplanar inductors, accurate computation of the inductance is usually difficult and time consuming. The partial element equivalent circuit (PEEC) technique is found suitable for this purpose. In this paper, the thickness of conductor is ignored since it has only a very small effect on the value of inductance. The six-fold integrals are thus reduced to four-fold integrals. It is found that these integrals can be analytically evaluated. The analytical expressions not only overcome the singularity of the Green´s function in the integral when the source and field points coincide, but also take the effect of ground plane into account. As closed-form results are used, very fast and accurate computation can be achieved. The PEEC technique is briefly reviewed and the analytical integration results for the integrals are listed. The inductances of RF-MEMS inductors and spiral inductors placed above the ground plane are evaluated. Numerical results are presented and compared with those in existing literature.