Power-electronics design involves a multiplicity of tradeoffs that can be guided by criteria that are useful in assessing how close a design is to optimum. This article surveys some common guiding parameters and introduces a somewhat new optimizing parameter for converter switching efficiency, the form factor product.
Various methods have been advanced to achieve an optimal design. Some involve optimization of magnetic components. For instance, maximum magnetic power density is achieved by the optimal choice of current ripple factor and switching frequency. Maximum power transfer across windings involves an optimal power-loss ratio of winding to core loss of
where Pw and Pc are winding and core losses, Rw is winding resistance, and Rc is the equivalent core resistance, referred to the same winding as Rw. (See the book, Power Magnetics Design Optimization (PMDO) at www.innovatia.com for much more on magnetics design optimization.)
Perhaps the most important converter design parameter is efficiency, which is a measure of the power transfer through the converter:
or for magnetic components, it is the power transfer,
Another can be regarded as structural efficiency or power-component utilization. No part should be oversized more than necessary to provide adequate reliability margins. This can be quantified as the ratio of power handled by the component over the product of its maximum voltage and current ratings, which constitute its design power:
A more detailed coverage of what the power rating of a component needs to be for a given category of converter shows that Pdmax = Vmax x Imax is often a worst-case maximum, and that using it for design power ratings can cause U to be less than its maximum allowed value. The utilization of magnetic components for a range of input voltages can be determined from derived formulas that are seemingly simple. (See PMDO for derivations of the formulas.)
The operating-point of the converter duty-ratio for minimal switching loss depends on the form factors of active and passive switch currents. These parameters are now examined more closely.
Waveshapes are an Important Criterion
A careful study of converter design reveals that waveform shapes are central to the optimization quest. The ideal waveshape for static-voltage power conversion is a constant (static or dc) value. A constant waveform has the same values for peak, average, and rms. These three waveform characteristics are important in design for the following reasons:
Given the significance of these waveform measures, design optimization generally seeks to minimize peak and rms values and maximize average (or in inverters, rms output) values. To quantify these design criteria more directly, optimization parameters which have historically been called figures of merit - or in some cases, figures of demerit - have been defined. The first is the
The form factor of a waveform is its rms value (power lost), normalized to its average value (desired or rated power). We seek to minimize κ. Its minimum value is one and typically it ranges from 1.05 to 5 in converters. As converter power increases, it becomes increasingly important that κ decrease to minimize power loss.
Another waveform figure of demerit is the
This quantity is important in inverter design, where the desired output is the rms value of a bipolar (ac) waveform. It affects the sizing of power parts, normalized to the output rms value. The crest-factor-squared of waveform voltage or current relates to its power. For a sinusoid,
2 = 2 while for a bipolar square wave,
2 = 1/D. For D = 0.5, then χ is the same as for sine-waves. In low-cost inverters, to reduce
2, D is made greater than 1/2 so that typically,
2 ≈ 1.5. The lower value reduces peak voltage and component size while delivering the same average output power, though at a lower voltage.
As important as κ is for converter design, so also is the average ripple factor,
Ripple factor is applied in optimizing the magnetic design of magnetic components (core selection) and for converter circuit waveform optimization, to reduce power loss. Ideally,
= 1 in both magnetic and circuit waveforms, though a constant waveform conflicts with transformer or inductor operation - hence a basic conflict in converter design.