Electron-density and electron energy distribution functions (EEDFs) are measured in a 20-cm-diam by 14-cm-long cylindrical, inductively coupled plasma source driven by fields from a planar, spiral coil at 13.6 MHz. Radio-frequency (r-f) -filtered Langmuir probes are used to obtain spatial profiles of electron population characteristics in argon at powers and pressures of interest for etching and plasma-assisted deposition (l-100 mT). Electron densities range from lOlo to 10" cm3 with lOO-500 W of rf power and peak on axis in the center of the cylindrical volume. The EEDFs show that the observed average electron energy varies by 1-2 eV spatially, with the highest values of average energy occurring at those regions of strongest rf electric field. The EEDF measurements also reveal a significant population of cold electrons trapped in a potential well at the location of peak electron density. From these spatial measurements, spatial estimates of conductivity and ionization rate are deduced.

In the last quarter of a century, high-frequency (HF) transformer design has been one of the major concerns to power electronics designers in order to increase converter power densities and efficiencies. Conventional design methodologies are based on iterative processes and rules of thumb founded more on expertise than on theoretical developments. This paper presents an analytical design methodology for litz-wired HF power transformers that provides a deep insight into the transformer design problem making it a powerful tool for converter designers. The most suitable models for the calculation of core and winding losses and the transformer thermal resistance are first selected and then validated with a 5-kW 50-kHz commercial transformer for a photovoltaic application. Based on these models, the design methodology is finally proposed, reducing the design issue to directly solve a five-variable nonlinear optimization problem. The methodology is illustrated with a detailed design in terms of magnetic material, core geometry, and primary and secondary litz-wire sizing. The optimal design achieves a 46.5% power density increase and a higher efficiency of 99.70% when compared with the commercial one.Index Terms-Analytical design methodology, highfrequency (HF) transformers, litz wire, photovoltaic (PV) power electronic converters.

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A key factor in the design of power electronic converters is the development of control systems and, in particular, the determination of their stability. Due to ease of application, the Bode criteria are currently the most commonly used stability criteria, both with regard to its classic version and to the subsequent revisions proposed in the literature. However, as these criteria have a limited range of applicability, on occasions it is necessary to resort to other universally applicable criteria such as the Nyquist criterion. Unlike Bode, the Nyquist criterion can always be applied, although its use considerably complicates the tuning of the controller. This paper proposes a new stability criterion, called Generalized Bode Criterion, which is, on the one hand, based on the Nyquist criterion, and therefore always applicable, and, on the other hand, calculated from both the Bode diagram and the 0 Hz phase of the open-loop transfer function, thus making the criterion easy to be applied. This way, the proposed criterion combines the advantages of Nyquist and Bode criteria and provides an interesting and useful tool to be applied to the controller design process. The criterion is validated by means of simulation and experimental tests made on a voltage control loop for a stand-alone PV system including a battery, a boost converter, an inverter and an ac load. The tests are also used to show the limitations of the classic Bode criterion and its revisions to correctly determine the stability of complex systems.

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Foil conductors and primary and secondary interleaving are normally used to minimize winding losses in high-frequency transformers used for high-current power applications. However, winding interleaving complicates the transformer assembly, since taps are required to connect the winding sections, and also complicates the transformer design, since it introduces a new tradeoff between minimizing losses and reducing the construction difficulty. This paper presents a novel interleaving technique, named maximum interleaving, that makes it possible to minimize the winding losses as well as the construction difficulty. An analytical design methodology is also proposed in order to obtain free-cooled transformers with a high efficiency, low volume and, therefore, a high power density. For the purpose of evaluating the advantages of the proposed maximum interleaving technique, the methodology is applied to design a transformer positioned in the 5 kW-50 kHz intermediate high-frequency resonant stage of a commercial PV inverter. The proposed design achieves a transformer power density of 28 W/cm 3 with an efficiency of 99.8%. Finally, a prototype of the maximum-interleaved transformer is assembled and validated satisfactorily through experimental tests.

Toroidal inductors are present in many different industrial applications, thus, still receive researchers' attention. AC winding loss in these inductors have become a major issue in the design process, since switching frequency is being continuously increased in power electronic converters. Finite element analysis software or analytical models such as Dowell's are the main existing alternatives for their calculation. However, the first one employs too much time if different designs are to be evaluated and the second one lacks accuracy when applied to toroidal inductor windings. Looking for an alternative that overcomes these drawbacks, this paper proposes an accurate, easy-to-use analytical model, specifically formulated for calculating high-frequency winding loss in round-wire toroidal inductors.

Three-phase dynamic systems and multiphase generators are frequently modeled and controlled in the synchronous reference frame. To properly model the cross-coupling terms in this reference frame, complex vector theory and transfer function matrices are commonly applied, obtaining multipleinput multiple output (MIMO) dynamic models. The stability of MIMO systems can be assessed through the Nyquist Generalized Stability Criterion. However, the use of the Nyquist diagram complicates the controller design. The Bode diagram is a more intuitive tool for the controller design, however, the Bode Stability Criterion is not applicable to MIMO systems. In this paper, the MIMO Generalized Bode Criterion is proposed. Since this stability criterion is based on the Nyquist Generalized Stability Criterion it can be applied to any system. Furthermore, it is simple to use, as it only requires information contained in the open-loop transfer matrix and the Bode diagram. The proposed stability criterion thus offers an interesting tool for the controller design procedure in MIMO systems, as it is shown in in this paper for two common applications: the current control loop of a power converter, a 2×2 system, and the current control loop of two independent power converters in parallel, a 4×4 system.