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Journal of Radio Electronics Online scientific journal · eISSN 1684-1719
2026, № 6 · NONLINEAR WAVE DYNAMICS IN RADIO ELECTRONICS

A mathematical model of the Colpitts oscillator for the analysis of electromagnetic susceptibility and phase stability of self-oscillating circuits

P.S. Glazunov1, A.I. Grinko2, L.S. Bolotnikov2, V.A. Vdovin1, V.A. Cherepenin1

1 Kotelnikov IRE RAS, Moscow, Russia
2 Bauman Moscow State Technical University, Moscow, Russia
Full text DOI: 10.30898/1684-1719.2026.6.6 UDC 621.373.5 EDN DQQHGH

Abstract

A mathematical model of the Colpitts oscillator is proposed based on a system of differential equations describing the dynamics of a self-oscillating circuit with allowance for parasitic electromotive forces induced by an external electromagnetic field in various loops of the circuit. The relevance of the study is determined by the increasing complexity of the modern electromagnetic environment and the miniaturization of electronic components, which leads to a reduction in their interference immunity. It is shown that short-term pulsed interference can cause a phase shift in the oscillator’s oscillations. It is established that the magnitude of this phase shift depends on the amplitude of the interference, the time of its application, and the loop into which it is introduced. Numerical experiments are used to identify the most vulnerable parts of the circuit, which can be applied in the design of interference-resistant self-oscillating circuits and in the optimization of their topology.

  • electromagnetic compatibility
  • Colpitts oscillator
  • self-oscillating circuit
  • phase shift
  • electromagnetic susceptibility
  • Pulsed interference
  • numerical simulation
Аннотация (на русском)

Математическая модель осциллятора Колпитца для анализа электромагнитной восприимчивости и фазовой устойчивости автогенераторных схем

Предложена математическая модель осциллятора Колпитца на основе системы дифференциальных уравнений, описывающих динамику автогенератора с учетом паразитных электродвижущих сил, наводимых внешним электромагнитным полем в различных контурах схемы. Актуальность исследования обусловлена усложнением современной электромагнитной обстановки и миниатюризацией электронных компонентов, приводящей к снижению их помехоустойчивости. Показано, что кратковременное импульсное воздействие способно вызывать фазовый сдвиг колебаний осциллятора. Установлено, что величина этого фазового сдвига зависит от амплитуды помехи, момента ее приложения и контура, в который она вводится. С помощью численных экспериментов выявлены наиболее уязвимые участки схемы, что может быть использовано при проектировании помехоустойчивых автогенераторных схем и оптимизации их топологии.

For citation

Glazunov P.S., Grinko A.I., Bolotnikov L.S., Vdovin V.A., Cherepenin V.A. A mathematical model of the Colpitts oscillator for the analysis of electromagnetic susceptibility and phase stability of self-oscillating circuits // Journal of Radio Electronics. – 2026. – No. 6. https://doi.org/10.30898/1684-1719.2026.6.6

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