V.Ya. Noskov1, E.V. Bogatyrev2, R.G. Galeev3, K.A. Ignatkov4, О.А. Chernykh5

1,4,5 Ural Federal University (Ekaterinburg, Russia)

2 Siberian Federal University (Krasnoyarsk, Russia)

3 JSC «NPP «Radiosvyaz»; Department of Radiophysics and Special Electronic Equipment of the M.F. Reshetnev SibSU (Krasnoyarsk, Russia)

A mathematical model of an autodyne oscillator (autodyne – AD) operating under conditions of synchronous exposure to a signal from a third-party source, as well as its own radiation reflected from the target, has been developed. The model is obtained in the form of a system of linearized differential equations in the vicinity of the stationary mode of the oscillator for small relative changes in the amplitude of the oscillations and the phase difference between the natural oscillations and the oscillations of the synchronizing source. It takes into account the time constants of changes (relaxation) of the amplitude and phase, respectively, the internal parameters of the oscillator (coefficients of autodyne gain, non-isochronicity and non-isodromity), as well as the conditions of external synchronization, the level and phase of its own radiation reflected from the target. The resulting system of linearized equations, taking into account the well-known duality principle, has sufficient generality to analyze the autodyne effect in synchronized AD with any type of active element (tunnel diodes, Gann diodes and avalanche-span diodes, field and bipolar transistors, etc.). These equations are used in the study of quasi-static and dynamic characteristics of synchronized BP.

At the same time, it was found that the synchronization of BP from an external oscillator eliminates the anharmonic distortion of signals characteristic of conventional (unstabilized) BP, which contributes to the expansion of their dynamic range. It is shown that in synchronized BP, by introducing an initial detuning between the frequencies of the external oscillator and the natural frequency of BP within the synchronization band, there is a possibility of a significant increase in the transmission coefficient of the autodyne signal compared to conventional BP. It is also established that the inertia of the phase synchronization process of the oscillator causes the uneven formation of the amplitude-frequency characteristics of the transmission coefficient of the synchronized BP by changing the amplitude of oscillations in the high frequency region. However, this unevenness, with the correct choice of synchronization parameters, is not an obstacle to registering signals in the entire range of the speeds of movement of location objects that exist in practice.

A mathematical model of a system of two mutually synchronized partial oscillators with strong coupling under the influence of its own reflected radiation has also been developed. The model is obtained in the form of a system of linearized differential equations of the fourth order for small relative changes in the oscillation amplitudes of partial oscillators, changes in frequency and phase difference. From this model it can be seen that the reflected radiation, acting on the oscillatory system of the first partial oscillator, causes an autodyne effect in the system of coupled oscillators, which consists in changes in the oscillation amplitudes of each partial oscillator, their phases, frequency and phase difference relative to their values of the stationary mode of the autonomous oscillator.

As a result of calculations and analysis of characteristics with variations in the initial parameters and conditions of mutual synchronization, it was found that autodyne changes in the frequency of generation of a system of coupled oscillators during the movement of a reflecting object cause nonlinearity of the reflected radiation phase and, accordingly, anharmonic distortions of all these changes in the parameters of the self-oscillating system, as with conventional AD. However, the degree and type of these distortions in this system depend on the amplitude and phase ratios of the components of the autodyne response and are determined by the values of the internal parameters of partial oscillators, such as their non-isochronicity, amplitude and frequency detection. In addition, the degree of signal distortion is also determined by the conditions of internal mutual communication between partial oscillators, the value of the relative detuning of the natural frequencies of partial oscillators and the value of the external feedback parameter of the «oscillator –reflecting object» system.

It has been established that a partial oscillator whose own Q-factor of the oscillatory system or output power is greater than that of the second partial oscillator is stabilizing, it causes a decrease in the magnitude of the autodyne deviation of the generation frequency and, thereby, the degree of signal distortion. Compared with conventional autodyne systems based on single oscillators, systems of coupled autodyne oscillators have a number of positive properties. Due to significantly lower frequency deviation, they provide an improvement in the waveform at the same levels of reflected radiation and an expansion of the dynamic range of the autodyne system.

The formation of phase-shifted two signals makes it possible to determine the sign of the radial velocity of reflecting objects and use methods of quadrature signal processing. These capabilities significantly expand the scope of AD in solving problems of radio wave control of motion parameters in the physics of fast-flowing processes, near-range radar and measuring technology.

The results of the experimental studies have confirmed the adequacy of the developed mathematical models of synchronized autodyne systems with respect to the analysis of autodyne parameters and characteristics both at quasi-statistically small and high speeds of movement of location objects. From the results of the studies carried out, it also follows that it is promising to develop integrated autodyne modules with frequency synchronization from an additional low-power oscillator, as well as on the basis of mutually synchronized oscillators. Such technical solutions are of particular relevance in the range of millimeter and shorter waves.

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