# Future-oriented electric vehicle technology: a new transformer design with tolerance

“In order to continuously achieve a good efficiency level in the high-performance segmentation field, we need power switching components with low switching losses. Modern products often use a resonant converter topology, which uses the principle of zero voltage switching (ZVS), which has the advantage of reducing switching losses. They often appear in LLC resonant converters. The resonant Inductor in the circuit can achieve zero voltage switching, making LLC devices very suitable for on-board charger (OBC) applications that require high efficiency and high power.

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In order to continuously achieve a good efficiency level in the high-performance segmentation field, we need power switching components with low switching losses. Modern products often use a resonant converter topology, which uses the principle of zero voltage switching (ZVS), which has the advantage of reducing switching losses. They often appear in LLC resonant converters. The resonant inductor in the circuit can achieve zero voltage switching, making LLC devices very suitable for on-board charger (OBC) applications that require high efficiency and high power.

The term LLC refers to the functions of the three components that the resonant circuit relies on: transformer magnetizing inductance (Lm), transformer leakage inductance (Lr), and resonant capacitor (Cr). If the numerical calculation is correct and the required tolerance is adhered to, this is a known method of using LLC transformer leakage inductance to replace the required resonant inductance. The supplier Pulse Electronics used finite element modeling to design a 3.6 kW LLC transformer with high leakage inductance and tolerance, which can be used as the resonant inductor of the LLC converter.

The system requirements developed for this 3.6 kW LLC transformer include: the turns ratio (N) of the secondary side to the primary side is 2, the magnetizing inductance of the primary side is 36 μH, and the transformer gain (amplification) is 6.

The results show that the magnification is directly related to the leakage inductance of the transformer’s primary winding. Therefore, in order to achieve the magnification, this parasitic parameter needs to have a tolerance. To achieve this goal, an innovative transformer design is used.

Figure 1 shows the LLC circuit block diagram, where the prominent part is the resonant inductor Lr. The resonance circuit and the output/smoothing circuit are inductively coupled.

Fig. 1 LLC converter with ideal transformer model

The magnetic coupling is mainly determined by the geometry of the coil structure and the iron core air gap.

We use the following formula to obtain the amplification factor of the LLC converter:

Magnification = (Lm + Lr) / Lr(1)

The tolerance value of the magnetizing inductance Lm can be controlled by strictly observing the tolerance value of the iron core air gap, but the resonant inductance Lr needs further study.

Figure 2 provides a more complete model. This model includes the leakage inductance of the primary side coil (Lk_prim) and the leakage inductance of the secondary side coil (Lk_sec), as well as the possible external resonance inductance (Lext).

Figure 2 shows the transformer circuit of leakage inductance

Then it becomes clear:

Lr = Lext + Lk_prim (2)

As mentioned earlier, by designing a transformer with a sufficiently large leakage inductance, the external resonant inductor can be omitted. The challenge here is to set an appropriate strict tolerance for this parasitic parameter, and Pusi Electronics has achieved this goal with a novel coil design.

**1 The coil design of the sandwich winding method**

An example is the PQ50/50 platform, whose primary and secondary coil wires are sized just right for 3.6 kW power levels. Taking into account the system requirements of the transformer development goal, the equations (1) and (2) that determine the leakage inductance value explain “the design of separating the primary side coil and the secondary side coil of the sandwich winding method from each other, which is close to the target value” .

Figure 3 shows a cross-sectional view of the coil design used to fine-tune the leakage inductance. The uniqueness of this design is the ability to independently control the distance between the coils and achieve the required leakage inductance value. The width of each coil and the size of the wire harness have been carefully adjusted to fit the coil and fine-tuned to meet the leakage inductance tolerance requirements.

Figure 3 Cross-sectional view of coil design used to fine-tune leakage inductance

**2 Finite element method for optimizing transformer design**

In order to finalize the design and ensure that the leakage inductance is concentrated around the primary side coil, the design of the primary and secondary side coils and the position of the core air gap must be optimized.

The design was developed based on the finite element method, which is a modern method for analyzing technical magnetic problems and developing effective solutions. The generated magnetic flux achieved the expected result. Figure 4 shows the finite element model of each magnetic flux path of the primary side coil and the secondary side coil.

Figure 4 The finite element method analysis model of each magnetic flux path of the primary side coil (left) and the secondary side coil (right)

The prototype design (Figure 5) and electrical testing confirmed the simulation results of the finite element model for the optimized transformer design.

The measurement results of electrical parameters show that the target leakage inductance value and tolerance value have been reached.

In order to calculate the actual primary and secondary winding leakage inductance, we measure the following transformer parameters:

Lso: the primary side inductance when the secondary side is in an open state

Lss: Primary side inductance when the secondary side is in a short-circuit state

Lpo: the inductance of the secondary side when the primary side is in an open state

In addition, three equations are used to calculate the leakage inductance on the primary side (Lk_prim), the leakage inductance on the secondary side (Lk_sec), and the magnetizing inductance (Lm).

Lk_prim = Lso C Lm (3)

Lk_sec = Lpo – Lm×N 2 (4)

Lm = SQRT ((Lso-Lss)×Lpo/N 2) (5)

Table 1 summarizes the measurement and calculation results of the transformer. The excitation and leakage inductance parameter values of the primary winding have reached the target satisfactorily, while the leakage inductance value of the secondary side is relatively low.

Moreover, this result also confirms that the leakage inductance of the secondary winding has been effectively reduced, and the leakage inductance can be concentrated on the primary side through small signal analysis. Theoretically, the induced voltage generated on one winding of the transformer is the turns ratio multiplied by the voltage applied to the other winding, as shown below:

Vout = N×Vin (6)

In fact, the voltage applied to a winding is divided into leakage inductance and magnetizing inductance according to their respective impedances. Therefore, when there is significant leakage inductance in the winding, the voltage across the magnetizing inductance will decrease. Therefore, the voltage induced across the secondary winding will be significantly reduced. When Ns/Np=2, the theoretical induced voltage should be:

Primary side induced voltage (Vp_induced) = secondary side applied voltage

(Vs_applied)×0.5 (7)

Secondary side induced voltage (Vs_induced) = primary side applied voltage

(Vp_applied)×2 (8)

The following is the induced voltage (blue) when a voltage of 2 V (yellow) is applied to the secondary winding and the primary winding of our optimized transformer.

As shown, the induced voltage on the primary side (1.02 V) is close to the theoretical value (ie: half of the applied voltage on the secondary side), while the induced voltage on the secondary side (3.52 V) is significantly lower than twice the applied voltage on the primary side .This shows the concentrated characteristics of the leakage inductance on the primary side

Therefore, the advantages of applying LLC topology circuit to high-power car chargers are confirmed.

The Links: **APT46GA90JD40** **1DI300ZP-120-05** **INFIGBT**