Scaling of X-parameters for device modeling

The relationships between X-parameters of a given transistor and a second transistor geometrically scaled with respect to the first are derived and presented for the first time. The different types of X-parameters scale differently. These relationships enable X-parameters measured on a fixed size of transistor, diode, or other similar test structure to be scaled to other sizes and produce X-parameter functions as continuous function of size (e.g. total gate width or area). This capability endows X-parameters with a key property of conventional scalable “compact models”, enabling an improved MMIC design capability where size/geometry is a key design degree of freedom. The scalable X-parameters for device modeling are implemented in a commercial nonlinear simulator. The theoretical predictions are validated with numerical results from simulation-based extractions and experimental nonlinear measurements taken with an NVNA on active devices of different sizes.