Mutual inductance between intentional inductors: closed form expressions

We present closed form analytical expressions for the mutual inductance between intentional inductors. The formalism is applicable for border to border separations that are longer than 0(1/10) of the inductor radius. The results are exact in leading order multi-pole expansion for the magnetic field generated by a superposition of current loops, acting on an external device. The derived expressions are simple analytical formulae. We present examples for the closed form expressions for a number of configurations used by RF designers including non Manhattan devices. The computational complexity of the result is linear with the number of segments. Detailed comparisons against standard methods are included, the CPU gains are two orders of magnitude. The formulae are useful for quick estimation of magnetic noise parameters during RF circuit layout synthesis