Equivalent circuit model of resistive IC sensors derived with the box integration method

We present an automatic method to produce compact equivalent circuit models of spatially inhomogeneous resistors. Local variations in space of the resistivity due to physical interactions such as magnetic fields or mechanical stress are automatically included. The equivalent circuit model is computed using symbolic algebra, such that the functional relation between the resistivity and the fields interacting with it is included in the circuit design model. Modeling is based on the discretization of the sensor geometry with a mesh of elements and vertex nodes together with the current continuity equation using the box integration method. The resistivity is described by the tensor field of electrical conductivity and depends on the physical interactions to be modeled. The element internode conductivity is mapped to a set of lumped conductances and transconductances (voltage controlled current sources) between the nodes of the discretization mesh. These conductances and transconductances are translated into an equivalent circuit net list. Optionally, the electrical network representing the sensor is simplified before translation by symbolic linear algebra. Thus, equivalent circuit models consisting of many simple elements can be generated as well as models with only a few, algebraically complicated elements. The method is demonstrated using the public domain circuit simulator SPICE3 for the example of a magnetic Hall sensor, with and without the piezoresistive effect.