[091] Core Loss Modeling - Part III Sinewave Versus Triangle Wave Losses

Calculating the difference between sinewave and triangle wave excitation shows that sinewave measurements are sufficient for loss calculations.

Introduction

The first two parts of this article showed how the core losses for real waveforms could be modeled better. In the first part, a continuous expression was used to model a wide range of excitations. In the second part, the effect of duty cycle on the loss of the core material was included in a single equation. In this third and final part, we return to the discussion of the sinewave versus the triangle wave excitation to analyze the difference between the two for a given material. 

Adaptive Steinmetz Equation

Part I of this article [6] showed how a single adaptive equation could be used for predicting the core losses of a ferrite material. Figure 1 shows the specific equation for the Magnetics “R” material. The equation adapts itself to the changing slope of the curves with frequency, providing a continuous equation for all frequencies. 

Equation 1: Core Loss Equation for R Material and All Frequencies

Having a single equation is very important for extending core-loss analysis into duty-cycle effects, and for making the incorporation of core loss into design programs manageable. 

Sinusoidal Core Excitation

All core loss curves are measured using sinusoidal excitation. However, in squarewave converters, the excitation of the core is not sinusoidal at all. A 50% square wave voltage drive results in a triangular current waveform in the inductor, and a triangular waveform for the core excitation. Figure 1 compares a sinusoidal excitation with a triangle wave excitation. Notice that both waveforms of Figure 2 have the same peak value, or the same peak flux excitation. 

As mentioned in part II of this series, Mr. Rudy Severns demonstrated many years ago that the difference in loss is small between a sinusoidal excitation and a 50% triangle wave. The waveforms of Figure 1 give an indication of why this happens. For part of the waveform, the sinusoidal curve has a lesser slope than the triangular, and for other parts, the slope is greater. 

In this article, we will go ahead and confirm numerically the difference for the Magnetics R material.  

Figure 1: Sinusoidal and 50% Duty Cycle Triangular Waveforms