# Magnetics Design for a Dual Active Bridge (DAB)

## 1. INTRODUCTION

## DAB is a DC-DC converter topology composed of an input and output H-bridge connected in series with an inductor and an isolated transformer. The power is transferred between the input and output bridge through the transformer. The leakage inductor (L_{lk}) determines the maximum power that the system is able to provide while the phase angle (β) between the two bridges controls the power transfer. This parameter can be selected between 0 (no power transfer) and 90º (maximum power transfer).

_{lk}

*Figure 1. DAB converter diagram*

## When only the β angle is changed to adjust the power, it is said that the converter works with Simple Phase Shift (SPS) Modulation. In this case, the power transfer can be linearly controlled, achieving Zero-Voltage-Switching (ZVS) in the semiconductors in most of the power range due to the energy stored in the leakage inductor, although with difficulties when working with light-loads. To extend ZVS boundary, a new parameter is introduced in the equation, the α angle phase-shift of each bridge.

## Keeping the same angle for both bridges, α_{1} = α_{2}, and therefore the power transfer is given by changing only two parameters, α and β, is known as Dual Phase Shift (DPS) Modulation. There is one more control called Triple Phase Shift (TPS) Modulation, in which the two α angles are controlled separately (α_{1 }≠ α_{2}). TPS modulation provides a small improvement in performance and optimization compared to DPS modulation, but at a cost of adding complexity to the control.

_{1}

_{2}

_{1 }

_{2}

*Figure 2. DAB waveforms*

## In SPS modulation, the leakage inductance is selected according to the following equation [1]:

As observed, the leakage inductance doesn’t only affect the power transfer. The switching frequency (**f _{sw}**) is selected by the trade-off between inductor and transformer size (the higher the frequency, the lower the size) and the increase in AC losses in transformer and semiconductors. Regarding the turns ratio (

**n=n1/n2**) it should be chosen to ensure that maximum power transfer can be done in the worst-case condition of the converter, which is when the difference between

**V**and

_{in}**V**is the highest. For converters with a wide input or output voltage range (e.g., battery charge system), it is typical to select the turn ratio in the nominal voltage condition and adjust the leakage inductance to reach maximum power in the worst-case point. This allows the circulating current in the inductor to be balanced in the whole converter operation and not be too high in

_{out}**extreme**cases.

## In DPS modulation, the equation [1] changes according to the relation between α and β angles, so that equation [2.a, 2.b] is given by four-states:

## For TPS modulation, equation [2.a, 2.b] becomes more complex, and it is not included in the scope of this paper, since DPS modulation has been selected for hardware validation due to the sake of simplicity.

When the converter is designed and the leakage inductance value is selected, the maximum **β** angle value is commonly limited to 65-70º as a safe-margin, because of parasitic effects, dead-band duty cycle loss and other concerns that are introduced by the hardware.

## 2. TRANSFORMER DESIGN EXAMPLE

## The following section is aimed to design an optimum transformer for a DAB converter using the Frenetic Online tool. The DAB converter specifications are provided in *Figure 3*:

*Figure 3. Transformer specifications with DAB simulation waveforms*

## The project has been created as a custom transformer. The waveforms have been uploaded with a CSV file from a simulation software with the following conditions:

## · Vin = 400V

## · Vout = 20 to 28 V (24 Vnom)

## · Pout = 600W

## · Lmag = 3000 uH

## · Llk = 130 uH

## The turn ratio has been fixed to 10, close to the nominal point focusing on a good balance between core losses and winding losses in the transformer.

## As commented in the previous sections, the critical points in the transformer are given in the limit points of the output voltage range. First, to select the core, the operation point at maximum voltage is chosen due to the highest Vμs in the primary winding, which produces the maximum **B**_{ACpk-pk} in the core. The Frenetic Online algorithm suggests designs based on the product area formula. *Figure 4* shows the results given in the design list window.

_{ACpk-pk}

*Figure 4. List of designs suggested by Frenetic Online for the DAB converter*

## PQ40/40 has been selected from the list. The next step is select the number of turns.

For this design, the goal is to have the minimum number of turns possible in the secondary side. Due to the high RMS current present in the winding, minimizing the turns allows the transformer to increase wire gauge and decrease winding losses.

## On the other hand, to keep the desired turn ratio, it is also necessary to adjust the primary turns, and very low values can produce an increase in core losses. The primary/secondary turns are fixed to 20/2.

*Figure 5. Example of core losses for a PQ40 with 3C95 material with 20, 30 and 10 turns.*

## Typically, magnetizing inductance in DAB is not included as a design parameter. In other topologies like the Phase-Shift Full Bridge (PSFB), low magnetizing inductance value can help the system to achieve ZVS during light-load operation, when the energy stored in the leakage inductor is not enough to discharge the capacitances for the semiconductors. This also applies to the DAB, although in most cases leakage inductance is much higher compared to the PSFB, and the possibility of having DPS and TPS modulation can help to achieve ZVS without decreasing magnetizing inductance. For this example, magnetizing inductance is kept as the value given by the number of turns with no gap in the core. Adding a gap and increasing it causes the magnetizing inductance to drop, if desired.

Once the number of turns has been selected, the wire in primary and secondary sides need to be selected. For a proper design, it is recommended to upload a CSV with the worst-case condition in terms of winding losses, which are given at minimum output voltage of 20V and maximum power for this converter.

## The winding structure has a huge impact on the transformer design. Different strategies allow us to enhance transformer overall efficiency or increase leakage between primary and secondary to reduce or replace the external inductor in soft-switching topologies, among other things.

The interleaving arrangement exhibits the lowest leakage inductance and therefore the maximum efficiency in terms of total losses. An intermediate approach can be done with partial-interleaving or not-interleaving strategies. For very high leakage inductance values, the transformer windings shall be separated into two-chambers, controlling the leakage with the distance between the windings.

*Figure 6. Transformer design with interleaving arrangement (Low-Leakage)*

*Figure 7. Transformer design with two-chamber arrangement (High-Leakage)*

Table 1 summarizes the two designs with the different winding arrangement.

*Table 1. Transformer design summary*

In the DAB topology, as the leakage inductance is fundamental in the power transfer between input and output and higher values need~~s~~ to be achieved, the two-chamber option becomes very interesting to reduce/remove the external inductor as a cost of increase transformer losses, due to the proximity effect in the windings.

## 1. HARDWARE TEST

In order to validate the results obtained in Frenetic Online, two samples have been assembled in the Frenetic facilities. The leakage inductance has been measured with Bode100, previously calibrated. The results are provided in Table 2.

*Table 2. Transformer inductance measurement*

*Figure 8. Transformer Sample for Case 1 and Case 2*

The operating point to validate the two designs has been selected on the nominal voltage and maximum power. To achieve the desired inductance value, an external inductor has been manufactured for each case. It should be noted that the two-chamber case requires inductance is lower than the interleaving case, allowing the inductor to reduce the total size. It could be observed that there is a ringing in the voltage waveform produced by the different parasitic elements present in the setup, especially the interwinding capacitance of the transformer. The ringing looks more attenuated in the two-chamber case, because interwinding capacitance is five times less than the interleaving sample.

*Figure 9. Converter Specifications and oscilloscope waveforms for Case 1 (Interleaving) and Case 2 (Two-chamber).*

The test was carried out until the transformer temperature stabilized. The temperature has been recorded with a thermal camera. The results are shown in Figure 10.

*Figure 10. Max, Hotspot temperature for Case 1 (Interleaving) and Case 2 (Two-chamber).*

In Case 1 (interleaving), the maximum temperature achieved is **58ºC**, while for Case 2 (Two-chamber) it is **71.1 ºC**. The difference between Frenetic Online and the real measurement can be explained because the measured leakage inductance is higher than the predicted by the tool, as well as the waveform are ideal from a simulation. If the measured waveform is introduced in Frenetic Online, then the losses can be recalculated. The new results are shown in Table 3.

*Figure 11. Transformer real waveforms and FFT uploaded in Frenetic Online.*

*Table 3. Transformer design summary with real waveforms*

As shown, the design with two-chamber exhibits more losses, but on the other hand, it allows for the reduction of the size of the external inductor (from a PQ40 to a PQ32 in this example) and a slight improvement in the efficiency of the system by having less interwinding capacitance and therefore less voltage ringing.

As a complementary analysis, a planar transformer sample has been assembled and tested in the same conditions as the previous cases. *Figure 13 *shows that the planar solution exhibits the highest temperature (thus, the highest losses), but its compact size makes it the best choice for low profile converter designs, in which the total height is quite critical. Also, the voltage ringing is more pronounced, due to the high interwinding capacitance, and it must be considered for the extra losses that it could introduce in the converter.

*Figure 12. Converter Specifications and oscilloscope waveforms for Case 3 (Planar)*

*Figure 13. Planar Transformer measurements and size.*

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