## Modeling

Non-linear measurement data has been exploited in various ways to create behavioral models for high frequency transistors. These include frequency-domain descriptive behavioral models, including Poly Harmonic Distortion (PHD) Models, S-function and X-parameter*. Formulations of these models have been developed in the travelling wave domain with a desire to represent nonlinear behavior of high frequency transistors. Work demonstrated using the Cardiff Model, based on PHD models, has shown that by considering higher order mixing terms in the PHD formulation, a model can be developed that does not require the simulator to interpolate between datasets for different fundamental and harmonic source and load pull impedance measurements.

By carrying out fundamental-interpolation and harmonic-extrapolation on measurement data, the system can take advantage of the intelligence of behavioral modeling. Interpolation carried out on measurement data can reduce the density of impedance grids hence reducing utilization time. Measurement systems that cannot achieve a high enough impedance termination at higher harmonics can take advantage of harmonic extrapolation to achieve these values.

Behavioral Model formulations for Cardiff Model

The frequency-domain model formulations described above all operate in the traveling-wave domain. The measured behavior in this case can be described as a function of various inputs such as DC bias (V1,0 and V2,0) and input drive (A1,1) as shown in (1), where the subscript h denotes the harmonic index and n denotes the port index.

(1)

<!--[if !vml]--><!--[endif]-->    (2)

Previous work [9] has derived an equivalent Fourier series description of the behavior (3), where the coefficients Kn,h,m and the necessary mixing order, ω can be determined via a least-squares fit of measured data. Theoretically, the minimum number of measurements required for the least-squares algorithm to extract x coefficients is x measurements. In order allow for inaccuracies in the practical measurement scenario and allow for redundancies, 2*x measurements can be considered as a recommended minimum set.

<!--[if !vml]--><!--[endif]-->     (3)

Where             <!--[if !vml]-->           m: phase index

* X-parameter is a registered trademark of Agilent Technologies