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The Influence of Multitone Disturbances on Nonlinear Systems
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Autors: J.Nitsch, Y.Bychkov, N.Korovkin, S.Sherbakov, S.Demkin, A.Himeen. In this paper we numerically and analytically analyze nonlinear systems which are excited by a two-tone disturbance. The nonlinear system is perturbed by an input signal of the form:  .
It is well known, that the impact of the demodulation on the nonlinear part of a system leads to the occurrence of currents and voltages with frequencies  .
Amplitudes of these oscillations can reach up to  ,
and thereby may interfere with working quantities of the system [1].
For this reason two-tone disturbances represent a more substantial
hazard for complex electronic objects than single-tone interferences.The design of a protection measure against two-tone interferences needs the use of a reliable software. In [2] it is shown, that the PSPICE standard package yields essentially incorrect results when it is used for beat. This is due to the solvers of the differential or finite-difference equations used in standard packages. The highly reliable new method of integration offered in [3] and used in this paper gives accurate and effective solutions for beat problems. We solve our problem using an analytical-numerical method of variable order. This method is intended for the analysis and synthesis of nonlinear non-stationary, nonautonomous systems with arbitrary sources described by ordinary integro-differential equations. It is based on the description of solutions by means of generalized functions with regular components applying Taylor's series and the generalized Laplace transformation. It consists of analytical and numerical parts. In the analytical part the nonlinear integro-differential equations are identically transformed to algebraic equations which are linear with regard to Laplace images. In the numerical part the maximum possible step of calculation and minimal possible order of the method are specified at their optimum combination to ensure numerical stability of the solution. The basic advantages of this approach are reduced to the determination of areas containing unknown values of exact solutions, with the opportunity of the investigation of the singular components in these solutions. For disturbing frequencies equal to  the calculation step was at a level of  .
The used procedure of setting and controlling the length of the integration
step provides the opportunity to the following analyses: the existence
and uniqueness of the solution, coordination of step length and speed
of change of the solution, as well as the control of limiting levels
of local and global errors. In correspondence with the specified conditions
the procedure of step setting is fully adaptive. At the level
of the absolute local error of calculation  ,
the order (the order of Taylor's polynomial) is equal to 18. This
order is a function of e and of the dynamic properties of
the system considered. The level of the global error of calculation
of one period of the process is  ,
and after ten periods -  .
Detailed research has shown, that the required solution has a stable
character.1. J.Nitsch, N.Korovkin, E.Solovyeva “Examination of the Demodulation Effect of Two-Tone Disturbances on Nonlinear Elements”, Review of Radio Science, 2004 2. K.Y.Huang, Y.Li, C.-P.Lee “A Time-Domain Approach to Simulation and Characterization of RF HBT Two-Tone Intermodulation Distortion”, IEEE Trans. Microware Theory Tech., vol. 51, pp.2055-2062, Oct. 2003. 3. J.A.Bychkov., S.V.Scherbakov: “Analytical-numerical calculation method of dynamic systems”, St.-Petersburg, Energoatomizdat, 2001. |
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