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Polynomial fitting of nonlinear sources with correlating inputs

Janne P. Aikio (Department of Electrical Engineering, University of Oulu, Oulu, Finland)
Timo Rahkonen (Department of Electrical Engineering, University of Oulu, Oulu, Finland)
Ville Karanko (AWR-APLAC Corp., Espoo, Finland)



The purpose of this paper is to propose methods to improve the least square error polynomial fitting of multi-input nonlinear sources that suffer from strong correlating inputs.


The polynomial fitting is improved by amplitude normalization, reducing the order of the model, utilizing Chebychev polynomials and finally perturbing the correlating controlling voltage spectra. The fitting process is estimated by the reliability figure and the condition number.


It is shown in the paper that perturbing one of the controlling voltages reduces the correlation to a large extend especially in the cross-terms of the multi-input polynomials. Chebychev polynomials reduce the correlation between the higher-order spectra derived from the same input signal, but cannot break the correlation between correlating input and output voltages.

Research limitations/implications

Optimal perturbations are sought in a separate optimization loop, which slows down the fitting process. This is due to the fact that each nonlinear source that suffers from the correlation needs a different perturbation.


The perturbation, harmonic balance run and refitting of an individual nonlinear source inside a device model is new and original way to characterize and fit polynomial models.



This work was supported by the Academy of Finland.


P. Aikio, J., Rahkonen, T. and Karanko, V. (2014), "Polynomial fitting of nonlinear sources with correlating inputs", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 33 No. 4, pp. 1097-1106.



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