# Technologies for the mobility of the future: New transformer design with minimal tolerance

01/20/2021 Knowledge

Electric vehicles and the future promise of autonomous driving require progress in many key technologies—among them the charging of high-performance batteries. On-board chargers (OBC) may benefit from a novel design for power transformers.

In order to continue achieving good efficiency levels in the high-performance segment, power switches with low switching losses are required. Modern products frequently use resonant converter topologies that offer the advantage of reducing switching losses using the "ZVS" principle (zero-voltage switching). These are most notably used in LLC resonant converters where the resonant inductance enables zero-voltage switching, making them ideal for high-efficiency multi-kW OBC applications.

The term LLC refers to the fact that the resonant circuit relies on the function of the three components: the transformer's magnetizing inductor (Lm), the transformer's leakage inductance (Lr), and the resonant capacitor (Cr). This is a known method of replacing the required resonant inductor with the leakage inductance of the LLC transformer if the value is calculated correctly and the required tight tolerance is adhered to. The supplier Pulse has used finite element modeling to design a 3.6kW LLC transformer where the high-precision, tight-tolerance leakage inductance of the transformer serves as the resonant inductor of an LLC converter.

Figure 1 shows the LLC block diagram with the highlighted resonant inductor Lr. The resonant circuit is inductively coupled with the output/smoothing circuit. The magnetic coupling is primarily determined by the geometry of the coils and the core air gap.

The amplification of the LLC converter is determined using the following formula:

Amplification = (Lm + Lr) / Lr (Equation 1)

While the tolerance of the magnetizing inductor Lm can be controlled by complying with the strict tolerance value for the core air gap, the resonant inductor Lr needs further study.

A more complete model that reflects the leakage inductance of the primary (Lk_prim) and secondary (Lk_sec) coils as well as possibly an external resonant inductor (Lext) is provided in Figure 2.

The following is now apparent: Lr = Lext + Lk_prim (Equation 2)

As mentioned, the need for the discrete resonant inductor can be eliminated by designing the transformer with a sufficiently high leakage inductance. The challenge here is to properly define a tight tolerance for such a parasitic parameter, which Pulse has achieved with this novel coil design.

Sandwich coil design

One example would be the PQ50/50 platform with primary and secondary coil wires with dimensions that are suitable for the 3.6kW power level. Taking into account the system requirements that the transformer was developed for, the equations 1 and 2 that were used to determine leakage inductance revealed that a split primary coil with a sandwich-type secondary coil came closest to achieving the target value.

Figure 3 shows the coil cross-section surface of a patented coil design for fine-tuning leakage inductance. What's unique about this design is the ability to control the distance between the coil segments independently of one another and to achieve the required leakage inductance. The width of each coil sector and the wire bundle size are carefully adapted to the coil precision to fine-tune them to the leakage inductance tolerance requirement.

Finite element method for optimized transformer design

As a finishing touch to the design and to ensure that the leakage inductance is concentrated around the primary coil, it is essential to optimize the design of the primary and secondary coils and the position of the core air gap.

This design was developed using finite element modeling, a modern method for analyzing technical magnetic problems and developing effective solutions. It results in a magnetic flux that achieves the desired result. Figure 4 shows the finite element model of the individual flux paths of the primary and secondary coils.

A prototype design (Figure 5) and an electrical test confirmed the simulation of the finite element model for the optimized transformer design. The measurement of the electrical parameters shows that the target leakage inductance and tolerance values were met. This shows how this novel design allows the leakage inductance of the LLC transformer to be replaced by a discrete resonant inductor.

Finite element method

The finite element method (FEM) is used to calculate components on a computer. It is commonly used to simulate mechanical deformations of solid bodies resulting from the effects of factors such as pressure and temperature. This allows design errors to be identified and avoided in advance, thus saving costs. It involves dividing a unit virtually into tiny, finite elements. In this case, FEM is used to simulate how a ferrite core transformer would react to magnetic flux.

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