Method for determining the responses from a non-linear system using the Volterra series

• Main Authors: Mohammed Kassim Ahmed, Samah Fakhri Aziz, Naors Y. Anad Alsaleem, Konstantyn Sielivanov, Mykola Moskalets
• Format: Article
• Language: English
• Published: PC Technology Center 2020-08-01
• Series: Eastern-European Journal of Enterprise Technologies
• Subjects: nonlinear system; volterra series; transfer function; nonlinear non-inertia circuit
• Online Access: http://journals.uran.ua/eejet/article/view/210754
• ISSN: 1729-3774; 1729-4061

A methodology has been proposed for estimating the nonlinear effects in radio tracts of receiving and transmitting devices in radio-electronic means of mobile communication systems, based on using the nonlinear transfer functions of the higher-order Volterra series. A procedure has been devised for obtaining the output responses from a nonlinear non-inertia circuit under the harmonious input action using a method for determining the transfer functions of higher orders obtained on the basis of the transfer functions of lower orders. We have derived the analytical expressions for the output responses from a nonlinear system of different orders for three inputs for the case of representing a nonlinear system in the form of a nonlinear non-inertia circuit. The values of the transfer functions of higher orders for a nonlinear non-inertia circuit were determined by using a state variable method. This paper demonstrates the derivation of analytical expressions to calculate a harmonic coefficient based on the second and third harmonics using the nonlinear higher-orders transfer functions of a nonlinear non-inertia circuit. It has been shown that the use of the nonlinear transfer functions to the fifth order inclusive allows a more accurate assessment of nonlinear effects in the form of the harmonious and intermodulation distortions in the radio tracts of radio-electronic means of mobile systems. The outlined technique for determining the nonlinear transfer functions is invariant to the topology of a nonlinear electrical circuit, as well as to the quantity and type of nonlinear elements. Existing estimation procedures of electromagnetic compatibility related to the problems of calculating intermodulation interference can be improved by the introduction of the determined magnitudes of influence products. The proposed methodology makes it possible to evaluate the set of nonlinear effects in the problems related to electromagnetic compatibility in the groups of radio-electronic means with the accuracy required by users