Analysis of the DC/DC Zeta topology converter ripples by applying its limiting continuous mathematical model

Objectives. A DC/DC Zeta topology converter represents a unipolar electronic device for converting an input positive voltage into a stabilized output voltage of the same polarity, which can be set at voltages both below and above the input voltage. The aim of this work is to analyze Zeta converter circuitry, which requires the following tasks to be solved: using Kirchhoff’s Circuit Laws, obtain systems of equations describing converter operation in the phase of energy accumulation and in the phase of energy transfer; using a method proposed by A.I. Korshunov, combine the resulting systems of equations into a marginal continuous mathematical model; using expressions describing constant components of currents and voltages in Zeta converter, analyze their ripples and obtain equations for their calculation; compare the current and voltage values obtained from the continuous limiting mathematical model with the Zeta simulation results.

Methods. The tasks are solved using Kirchhoff’s rules and the method for obtaining the limiting continuous mathematical model proposed by A.I. Korshunov. The results are analyzed using a circuit modelling in NI Multisim.

Results. It is shown that the phase coordinates of the mathematical model tend to real values of converter currents and voltages at a switching frequency of the power switch of more than 200 kHz. A strong correspondence was established between the calculated ripple values and their values obtained in the simulation (when changing the duty factor).

Conclusions. Mathematical models comprise the basis of unified calculation methods for any radio electronic circuit. The developed limiting continuous mathematical model allows a range of changes in current flowing through the choke windings and voltages on capacitor plates to be evaluated, including their maximum and minimum values for various converter parameters, such as power switch switching frequency, duty factor, element ratings, etc. Obtaining this information in turn enables the rational selection of the electronic component base of the converter.

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