Abstract
Introduction. In many physical processes, the spectrum of the modulated signal is transferred to the low-frequency region, which also manifests itself in active dielectrics in radio sound. In the general case, the analysis of the spectrum transformation process is a very difficult task related with solving a system of nonlinear differential equations. And in the accepted form, the principle of superposition is not applicable here, since the parameters of the output signal cannot be determined by algebraic summation of the signals received separately from each source. The spectrum of an input amplitude-modulated signal is nonlinearly related to the spectrum at the output. Aim. The conversion of the current spectrum under supplying an amplitude-modulated voltage to an active non-linear element with a non-linear current-voltage characteristic is considered. Materials and methods. In the analysis of the spectral transformation, a power approximation of the current-voltage characteristic in the form of a polynomial of the third degree with trigonometric functions is used. In the examples, spectrum transformations for a mono signal, amplitude-modulated signal, and beats are considered. Application of amplitude modulation methods is essential for transferring the spectrum of the signal to the low frequency region. Results. A graphical representation of the dependence of the current function on time for an AM signal and beats, as well as their spectral representation, is given. Conclusion. The paper analyzes the transformation of the signal spectrum for the current when applying any, but amplitude-modulated voltage on the ohmic nonlinear element. The carrier signal is represented as a harmonic trigonometric function of the cosine of the current time. However, signal spectrum conversion has not related with detection.
Highlights
In many physical processes, the spectrum of the modulated signal is transferred to the low-frequency region, which manifests itself in active dielectrics in radio sound
In many physical processes, the spectrum of the modulated signal is transferred to the lowfrequency region, for example, in the occurrence of radio sound in active dielectrics [1] or the appearance of an acoustic signal at the beats frequency during the interaction of signals from two ultrasonic sources [2]
The analysis of the spectrum transformation process is a very difficult task related to solving a system of nonlinear differential equations
Summary
The spectrum of the modulated signal is transferred to the lowfrequency region, for example, in the occurrence of radio sound in active dielectrics [1] or the appearance of an acoustic signal at the beats frequency during the interaction of signals from two ultrasonic sources [2]. Research and analysis can be carried out using relatively simple methods if the form of the current-voltage characteristic (CVC) for a nonlinear element (NE) in the dynamic mode is the same as for a constant voltage (or in static mode). In the analysis of the spectral transformation under the influence of harmonic voltage, for example, a power approximation in the form of a polynomial with trigonometric functions is used: cos ω + ⋯ +. 3. Spectrum transformation for amplitude-modulated signal Under AM, the spectrum of the modulating signal is transmitted to the region of the carrier frequency, forming the upper and lower side components of the spectrum.
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