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# High-Frequency Model of a Transformer for Conducted EMI Analysis

Year: 2013
Fig. 1. 2-winding transformer.
The switching frequency of power electronic systems is continuously increasing to meet the higher power density requirements. It is getting increasing more difficult to simultaneously meet the stringent EMC standards and converter performance. Accordingly, virtual prototyping is gaining popularity as it offers the designer a comprehensive insight into the electromagnetic behavior of the system before the final hardware design.

An accurate simulation model is needed for each component of the power converter to analyze the complete system. With this goal in mind, a high-frequency model of the transformer (Fig. 1) used in a commercial battery charger system is proposed. The simulation results are verified against the measured data.

The existing high frequency models are not able to accurately predict the impedance, either common- or differential-mode, over a wide frequency range (10 kHz- 110 MHz). The existing methods for modeling a choke ignore the inter-winding capacitance for simplicity. This is not the case for a transformer, and hence a new lumped circuit model is proposed in Fig. 2. The coupling factors kC and kD are adjusted so that the common-mode current does not have any effect on the differential-mode elements and vice-versa.

A series or parallel R-L-C combination is used to predict the predominant capacitive or inductive behavior of the common- or differential-mode impedance, respectively. The no. of resonance peaks determines the number of stages of R-L-C used.

The simulation model is obtained by numerically fitting a lumped circuit of R-L-C in MATLAB to the measurement results. Finally, all the passives are combined to obtain the complete high-frequency model of the transformer, and the impedance measured in different configurations is compared against the Saber simulation model. The results of the common-mode impedance are shown in Fig. 3; it is within 3 dB of the measured result.

Fig. 2. Proposed high frequency model of 1:1 transformer to predict the first resonance peak.
Fig. 3. Comparison of common-mode impedance by measure-ment and the simulation model.