A. Massarini

Self-capacitance of inductors

A new method for predicting the stray capacitance of inductors is presented. The method is based on an analytical approach and the physical structure of inductors. The inductor winding is partitioned into basic cells-many of which are identical. An expression for the equivalent capacitance of the basic cell is derived. Using this expression, the stray capacitance is found for both single- and multiple-layer coils, including the presence of the core. The method was tested with experimental measurements. The accuracy of the results is good. The derived expressions are useful for designing inductors and can be used for simulation purposes.

Stray capacitances of single-layer solenoid air-core inductors

This paper presents a method for predicting parasitic capacitances of solenoid HF inductors made of one layer of turns with circular cross sections, uniformly wound around a cylindrical nonconductive core. The method is based on an analytical approach to obtain the turn-to-turn and turn-to-shield capacitances of coils. The influence of the wire insulation is taken into account. An equivalent lumped parallel capacitance is derived. The method was tested by experimental measurements. The calculated and measured values were in good agreement in the considered cases. The derived expressions are useful for designing HF inductors and can also be adopted for modeling and simulation purposes.

Lumped parameter models for single- and multiple-layer inductors

A method for modeling inductors under high-frequency operation is presented. The method is based on analytical approaches which can predict turn inductances, turn-to-turn and turn-to-core capacitances using physical structure of windings. Turn inductances, turn-to-turn and turn-to-core capacitances of coils are then introduced into suitable lumped parameter equivalent circuits of inductors. The overall inductance and stray capacitance can be obtained through the use of the equivalent circuits. Both single- and multiple-layer inductors are considered. The method was tested with experimental measurements. The accuracy of the results was good in most cases. The derived expressions can be useful for the design of HF inductors and can also be used for simulation purposes.

High-frequency small-signal model of ferrite core inductors

A circuit model of ferrite core inductors is presented. The behavior of the model parameters versus frequency is considered. The total power loss in inductors consisting of the winding resistance loss and the core loss, is modeled by a frequency-dependent equivalent series resistance. The total inductance given by the sum of the main inductance and the leakage inductance is obtained as a function of frequency. In order to study the core equivalent resistance and main inductance versus frequency, the magnetic field distribution in the core is derived from Maxwells equations for a long solenoid. The complex permeability and permittivity of the ferrite core are introduced in the electromagnetic field equations. Experimental results are also given.

Model of laminated iron-core inductors for high frequencies

We propose a model with frequency-dependent lumped parameters to represent the behavior of laminated iron-core inductors that are used in switching converters, i.e., for excitation frequencies above several kilohertz. The model applies to laminated iron cores with air gaps. We show that the core parameters can be calculated by using the same analytical expressions as those valid for gapless cores if a properly defined equivalent magnetic permeability is introduced instead of the iron sheet permeability. We compare the inductor model parameters calculated as functions of frequency with those obtained by measurements for two test inductors. The behavior of the inductors showed that the effects due to the eddy currents in the laminated iron core and the turn-to-turn and turn-to-core stray capacitances become significant in different frequency ranges.

Feedforward control of DC-DC PWM boost converter

A new feedforward control circuit suitable for applications in the dc-dc pulsewidth modulated (PWM) boost converter operated in the continuous conduction mode (CCM) is proposed. Its principle of operation is described, analyzed for steady state, and experimentally verified. The peak value of the sawtooth voltage at the noninverting input of a PWM modulator is held constant and the voltage at the inverting input of the PWM modulator varies in proportion to the converter dc input voltage. As a result, the complement of the on-duty cycle (1-D) is proportional to the dc converter input voltage, yielding the converter output voltage theoretically independent of the converter input voltage. The circuit is very simple and significantly improves line regulation of the output voltage. The measured open-loop line regulation at fixed loads was less than 5% for the converter dc input voltage change by 400%. The load regulation was also good even without a negative feedback loop.

Analysis of networks with ideal switches by state equations

A new computer-oriented method for a large-signal time-domain analysis of networks containing ideal switches is presented. The method is based on a state variable approach that exploits an efficient novel algorithm developed for the systematic formulation of state equations and output equations for linear active networks. Switched networks consisting of linear elements and both externally and internally controlled switches can be investigated. Diracs delta impulses are permitted in the analysis in order to find out the correct topology after switching. A new simple and convenient method for representing Diracs delta impulses is also introduced. An example is both discussed in detail and analyzed with a computer code.

Stray capacitances of single-layer air-core inductors for high-frequency applications

A method for predicting stray capacitances of HF inductors dependent on their geometry is presented. The analysis is performed for inductors made of one layer of turns with circular and rectangular cross-sections. The wire is uniformly wound around a cylindrical nonferromagnetic core. The method is based on an analytical approach to obtain the turn-to-turn and turn-to-shield capacitances of coils. The influence of insulating coatings of the wire is also taken into account. An overall equivalent stray capacitance is derived according to the typical HF equivalent lumped parameter circuit of inductors. The method was tested with experimental measurements and the accuracy of the results was good in most cases. The derived expressions are useful for designing of HF inductors and can be also used for simulation purposes.

Transform method for calculating low-frequency shielding effectiveness of planar linear multilayered shields

A two-dimensional analytical solution for quasistatic magnetic field shielding with planar infinite multilayered shields is presented. The magnetic field source is a system of long straight wires parallel to the shield, carrying sinusoidal currents. The analysis assumes that material media can be considered linear under the applied source fields. The spatial Fourier cosine and sine transforms are applied to the analytical expressions of the magnetic field intensity and flux density is obtained by solving the diffusion equation in each layer. Using transfer relations for every layer in terms of transformed variables allows one to obtain the shielded field, and thus the shielding effectiveness, with no need to determine the integration functions explicitly. The results obtained with both this approach and a finite-element computer code are in good agreement. The method seems to be also suited for the analysis of problems with more complex geometries and source distributions.

High-frequency behavior of laminated iron-core inductors for filtering applications

Laminated iron-core inductors are largely used in power electronics applications. In particular, coupling reactors and filtering devices employ such a type of inductor in the medium-high power range. In this paper, a model is proposed to represent the behavior of these inductors that are used in switching converters, i.e., for excitation frequencies above several kHz.