## Data Acquisition and Model Construction
### Inductor Series Resistance Characterization and Modelling
#### 2.2.2 Large Signal Loss Characterization and Modelling  
In order to account for the impact of large signals on inductor losses, another type of characterization is necessary. The objective is to apply a large current ripple to the inductors to be characterized, with variable magnitude and frequency. Measuring the induced losses will help derive a more representative model for the total losses taking place in the device under high ripple current magnitude and variable frequency. For this purpose, the inductor is now connected to a full-bridge inverter as depicted in Figure 7. This test bench configuration is offering the opportunity to apply a voltage square wave to the Device Under Test (DUT) that will in turns produce of triangular current waveform, very similar to the one taking place in real conditions. If the applied voltage square wave is a pure AC signal, the resulting triangular waveform will also be an AC signal with no DC part. In fact, this test bench is producing an energy flow from the DC capacitor to the AC inductor and vice versa. No power is dissipated by a load, except for the losses produced by the circulation of power in the components. In this test bench, the total DC power required to supply the full bridge inverter is measured, considering that most losses are dissipated in the inductor. For this, the full-bridge inverter is always operating in Zero Voltage Switching (ZVS) to minimize switching losses while active devices are oversized to minimize conduction losses. Also, they are driven by gate drivers and a control board that is supplied externally. In such a way, the measured losses are mainly the ones taking place in the DUT. Figure 6: Evolution of the series resistance of the MSS1210-473 47 \(\upmu\)H inductor with respect to frequency. Practical characterization in blue and equivalent model in dashed red. Figure 7: Bench topology for the inductor AC losses measurement under high ripple current and variable frequency. (**Left**) the schematic, (**Right**) the low voltage “high” current full-bridge inverter (30 V up to 5 A). In Figure 8a below, the blue curve with cross presents on the left the evolution of the measured losses inside the inductor for a 1A ripple current over a frequency range from 50 kHz to 150 kHz. In the same plot, the red curve with dots represents the losses estimated with the equivalent series resistance obtained from the previous characterization method. As it can be seen in Figure 8a, taking into account the measured equivalent series resistance from Figure 5, it is not possible to derive the same amount of losses dissipated in the inductor while performing the characterization test depicted in Figure 7. Indeed, in the left of Figure 8 it appears that the inductor losses are significantly underestimated with the model derived from the impedance analyser characterization. To take into account the extra AC losses produced by the high ripple current with respect to the frequency, there is a need to add an additional resistance to the model. For this purpose, the loss curve is fitted by action on the two additional parameters \(k_{hr}\) and \(P_{hr}\) in the Equation (6). The resulting equivalent resistance is set to produce the same amount of losses with respect to the frequency as is it shown in Figure 7, right. The total inductor resistance is now fully described in Equation (7), also illustrated in Figure 8b. \[R_{hr}(f)=L\times k_{hr}\times f^{p_{hr}} \tag{6}\]  
\[R_{total}=R_{0}+L\times k_{lr}f^{p_{hr}}+L\times k_{hr}f^{p_{hr}} \tag{7}\]  
Figure 8: **(a)** Evolution of the power losses in the inductor under test for a frequency range from 50 kHz to 150 kHz. Left, comparison of the losses between the AC losses measure and the model described with Equation (5). Right comparison of the losses between the measure and the model described in Equation (7). **(b)** Equivalent impedance model of the inductor under test.