V.M. Bogachev – Ph.D.(Eng.), Senior Research Scientist, Professor, Department of Formation and Processing of Radio Signals, «National Research University «MPEI» (Moscow)

E-mail: bogachev_vm@mail.ru

M.V. Balashkov – Ph.D.(Eng.), Associate Professor, Department of Formation and Processing of Radio Signals, «National Research University «MPEI» (Moscow) E-mail: balashkovmv@mail.ru

An integrated system for calculating and investigating the main properties of transients in multistage resonant amplifiers (of RF and microwave ranges) is suggested. The system includes a consistent application of three methods: the new method of accurate calculation of impulse and transient characteristics, the method of abbreviated operator equations and a modified method of matrix beams. Unlike the Yevtianov method, in the method of abbreviated operator equations, a simpler algorithm is used to compose abbreviated equations – the operator circuit function represented as a sum of elementary fractions, divided into two operators. The first operator includes fractions located in the upper, the second – in the lower part of the p-plane. At resonance affect, the first operator is the basic solution component, while the second one gives a small amendment to the main solution (of damping factor order). The calculation of the residuals in poles of any multiplicity (more than a thousand) is performed with precise accuracy on the base of simple recurrent relationships obtained in this paper.

In the previous investigations of authors, some main properties and «paradoxes» of connection between impulse and transfer characteristics have been confirmed. The main «paradox» lies in the fact that the modulus of the impulse response is independent from detuning of the resonance frequency impact, while the transfer characteristic (the time-derivative of the pulse characteristic) in this case has an oscillation. The beat frequency is close to the difference between the resonant and impact frequencies. When resolving the «paradox», it is shown that the modulus of the rise rate of the response coincides with the impulse response modulus under the resonant impact only, and in detuning, it is always less than the latter. In this case, the impulse response modulus is the envelope of the response rate modulus for the non-resonant impact – the curves coincide at the inflection points of the transient characteristics. Similar relationships hold for phase characteristics. It is shown that the maximum absolute error of the main approximation of the method for bands less than 10% … 5% and any order of circuit functions is negligible (<0,01…0,005). With the secondary simplification of the time characteristics by the matrix-beam method, the order of approximation can be reduced by three to five or more times with the given high accuracy. Thus, we can consider that the abbreviated and secondarily simplified operator equations (along with accurate ones) are applicable for the correct solution of the «Amplitude, Frequency, Phase» problem and, consequently, the design of phase information radio systems.

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