The calculation of a transformer's parasitics, such as its self capacitance, is fundamental for predicting the frequency behavior of the device, reducing this capacitance value and moreover for more advanced aims of capacitance integration and cancellation. This paper presents a comprehensive procedure for calculating all contributions to the self-capacitance of high-voltage transformers and provides a detailed analysis of the problem, based on a physical approach. The advantages of the analytical formulation of the problem rather than a finite element method analysis are discussed. The approach and formulas presented in this paper can also be used for other wound components rather than just step-up transformers. Finally, analytical and experimental results are presented for three different high-voltage transformer architectures.

Self-Capacitance of High-Voltage Transformers

This paper presents practical techniques for determining stray capacitances in a two-winding high frequency transformer for circuit simulation and computer-aided design purposes. These techniques fall into two categories: The two-port network approach; and the step-response approach. The first approach can be employed for high frequency transformer circuit models with the effect of stray capacitances modeled as a /spl pi/-shape network of three lumped stray capacitances. The second approach is useful for the transformer circuit model with the overall effects of stray capacitances modeled as lumped stray-capacitance connected cross the primary side. These techniques have been verified in the modeling and numerical simulation of a 500 W 25 kHz two winding E-core transformer. The merits and limitations of these techniques are also discussed.

/pdf/experimental-determination-of-stray-capacitances-in-high-15e07udeb4.pdf

Experimental determination of stray capacitances in high frequency transformers

Parasitic capacitances of conventional transformers can be used as resonant elements in resonant DC-DC converters in order to reduce the overall system size. For predicting the values of the parasitic capacitors without building the transformer different approaches for calculating these capacitances are compared. A systematic summary of the known approaches is given and missing links between the different theories and missing equations are added. Furthermore, a new simple procedure for modelling parasitic capacitances which is based on the known approaches is proposed. The resulting equations are verified by measurements on four different high voltage transformers.

https://www.hpe.ee.ethz.ch/uploads/tx_ethpublications/01518701.pdf

Using transformer parasitics for resonant converters - a review of the calculation of the stray capacitance of transformers

As long as it works linearly, a two winding transformer is, from an electrostatic point of view, a three port system. Its capacitance matrix includes six independent values. Consequently, whatever its shape, introducing six capacitances in the right places of the equivalent circuit allows the user to account for the whole electrostatic behaviour of this component. With such an equivalent circuit, resonance frequencies can be computed and, reversely, the six capacitances are all deducible from measured resonance frequencies. Thus, using this circuit by hand or by software, interwinding currents of real electronic circuits can be forecasted together with parasitic resonances related to the transformer. After this global approach, a microscopic approach is adopted. A closer look at the winding layer shape and then, at the wire shape itself leads to two simple models which allow the six capacitances of the equivalent circuit to be computed by hand. Values found are approximate but, thanks to analytical expressions, two design rules leading to lower capacitance values are inferred. Measurements are presented to establish the reliability of the equivalent circuit and to evaluate the interest of the proposed designing rules. >

Stray capacitances of two winding transformers: equivalent circuit, measurements, calculation and lowering

A high-density transformer using nanocrystalline core is developed for a 30 kW, 200 kHz resonant converter. Loss models are established for nanocrystalline cores through experimental characterization. The important parasitic models are also developed considering litz wire effects. Following a minimum size design procedure, several transformers with both nanocrystalline and ferrite cores are designed and prototyped. While all transformers meet the converter performance requirement during testing, using nanocrystalline core can achieve a significantly higher power density even at 200 kHz.

High-Density Nanocrystalline Core Transformer for High-Power High-Frequency Resonant Converter

The electrostatic properties of inductors and transformers are investigated. Two devices have been built on the same magnetic core. Both are cylindrical coaxial winding transformers and all the windings are almost identical. These one-layer windings are rolled in the same direction for one transformer and in opposite direction for the other. All the possible connections of the two windings are tested. Based on a simple electrostatic model, these devices are analytically studied and an equivalent circuit is proposed to take electrostatic phenomena into account. Then, an electromagnetic simulation software is used to compute the electrostatic field with the real shapes of wires and coil layers. Capacitances are deduced from stored electrostatic energy in the whole space. Finally, many impedance measurements from 100 Hz to 40 MHz allow the equivalent circuit to be validated.

Electrostatic of wound components: analytical results, simulation and experimental validation of the parasitic capacitance

The aim of this paper is to represent the electrical behaviour of any number of magnetically coupled windings with couplers and inductors. Two methods, mathematicaly justified, are proposed. The second one introduces only positive inductances. As an exemple, it is applied to the representation of a three column three phase transformer. The obtained circuits supply the requisite guide to design more complete circuits which allow the high frequency behaviour of wound components to be taken into account, especialy in electronics simulation softwares

Des schémas équivalents pour les circuits couplés multi-enroulements

The aim of this paper is to represent the electrical behaviour of any number of magnetically coupled windings with couplers and inductors. Two methods, mathematicaly justified, are proposed. The second one introduces only positive inductances. As an exemple, it is applied to the representation of a three column three phase transformer. The obtained circuits supply the requisite guide to design more complete circuits which allow the high frequency behaviour of wound components to be taken into account, especialy in electronics simulation softwares.

M. Bensoam

Papers

Electrostatic of wound components: analytical results, simulation and experimental validation of the parasitic capacitance

Des schémas équivalents pour les circuits couplés multi-enroulements

Des schkmas kquivalents pour (es circuits couplks multi- enroulements