A Design Method of Magnetic Integrated Resonance Transformer Used in Zero-current military DC DC converter

Abstract: The paper briefly analyzes the working mechanism of resonance circuit in the zero current soft switching DC /DC converter. By utilized of magnetic integration principle, leakage inductance is formed by increasing a magnetic shunt in standartransformer, and power transformer is turned into storage -energy type resonance transformer design method is introduced. The actual product of Model MV48 B5 M200B military DC DC converter is presented for example, specific design parameters of resonance trans-former are provided. Through theoretical analysis and test, the feasibility of the design method is proved

Key Words: soft switching, transformer, resonant inductance, magnetic integration

1 Introduction

High frequency miniaturization is the inevitable trend of the development of switching power supply. Soft-switching military DC DC converter technology is one of the main research directions of modern power electronics. Soft-switching technology makes switching transistor in zero current (ZCS) or zero voltage (ZVS) operation state thus reducing switching loss and improving the working frequency of switching power supply and the efficiency of switching devices.

The basic idea of zero-current soft-switching circuit is starting from the switching conduction, the current in the switching device rises from zero according to the sinusoidal law, when the current drops to zero, turn off the switching tube, thus avoiding the crossing of current and voltage in the process of turning off, reducing the turning off loss, at the same time, because the current rises from zero, the turning on loss also reduces.The resonant unit of the quasi-resonant circuit is generally in the secondary, which is composed of resonant inductance and resonant capacitor. The leakage inductance of the transformer becomes a part of the resonant inductance and participates in the resonance of the circuit.Some researchers believe that the leakage inductance of transformer and resonant capacitor can be used to form a resonant unit, so the resonant inductance can be omitted. But it is difficult to guarantee the leakage inductance of transformer by controlling the consistency of manufacturing process, so this method is not suitable for the serialization design and mass production of military DC DC converter.

This paper introduces a design method of adding a magnetic shunt to a standard transformer to form a leakage inductance and changing the power transformer into a resonant transformer with leakage inductance.

The design method can be applied to different voltage input voltage series, different output voltage, power output military DC DC converter circuit, has a strong engineering applicability.

Principle Analysis of 2 ZCS Quasi-Resonant Circuit

2.1 Basic principles of operation

The soft switching mode can significantly reduce the switching loss and the oscillation caused by the switching process, and can greatly increase the switching frequency, which creates conditions for the miniaturization and modularization of the converter.The basic power architecture of the military DC DC converter is shown in Figure 1. The circuit uses common-collector forward-active clamp ZCS/ZVS topology. The main switch Q1 of VMOS is ZCS switch. The auxiliary switch Q2 of VMOs is ZVS switch.Because the main part of the circuit is ZCS quasi-resonant circuit, and the control and clamp parts have little influence on the design of resonant transformer, so in order to facilitate the analysis, this paper ignores the control and clamp switch Q2 working principle, only study the main switch Q1 and ZCS quasi-resonant circuit.

Fig. 1 Main structure of the circuit

Fig. 1 is a ZCS quasi-resonant circuit compose of a power switch Q1, a transformer T1, a rectifier diode D1, a freewheeling diode D2, and a resonant inductor L2 and a capacitor C1.

Fig. 2 Principle and working waveform of ZCS resonant circuit

In FIG. 2, L2 is a resonant inductance, which is first set as the secondary equivalent leakage inductance of a power transformer, the diode D2 can ensure that the capacitor C1 is not charged in reverse, and since the output filter inductance I3 is much larger than the leakage inductance L2 of the transformer, the load can be equivalent to a current source Io, and the leakage inductance of the secondary side is:

From the equivalent model, the circuit equations can be listed:

To solve the above differential equation, replace the zero state condition I2 (t = 0) = Io, Vc (t = 0) = 0 (the state at the beginning of a switching period is obtained:

Where ω is the resonant angular frequency, Z is the characteristic impedance of the circuit, V is the voltage of the secondary winding of the transformer,

。

To achieve zero current shutdown of the switch tube, I2 must be reduced to 0 before the switch tube is turned off. As can be seen from equation (6), in order to be able to return to zero at any load, iL requires:

Equation (7) is the resonance condition of ZCS quasi-resonant circuit, its physical meaning is that the peak current of resonant unit can not be less than the load current, see Figure 3.

Figure 3 Resonant Current and Output Current

In theory, the higher the peak current of the resonant unit circuit is, the easier it is to satisfy the resonant condition under various conditions, but the peak current flowing through VMOS switching devices, rectifier diodes and resonant capacitors will increase the current stress and loss of these devices. It is a relatively ideal state that the peak resonance current is equal to the load current, which can ensure that Q1 can be turned off at zero current under any load condition, and the DC consumption is minimized. In engineering design, taking into account temperature, discreteness of components and other conditions, the ratio of Ito IPK is 0.75.

2.2 Calculation of Resonant Inductance

The resonant unit shown in FIG. 2, the characteristic frequency of its resonance:

Because the input voltage, output resistance and other parameters are included in the equation Z, the equation can calculate the resonant inductance value of the resonant circuit of ZCS quasi-resonant military DC DC converter with different transmission voltage and power.

The design principle of the transformer with 3 magnetic flux density

3.1 Brief Introduction of Magnetic Integration Technology

The magnetic integration technology is a new technology which integrates the magnetic elements in a core structure by using the relationship between the magnetic flux and the winding current of each magnetic element in the power converter, so as to reduce the volume of the magnetic element, reduce the loss of the core and the winding, and improve the power density of the power converter.The aim of changing the branch structure of the magnetic core is how to obtain more branch magnetic circuits, which can be achieved by three methods: adding additional magnets in the magnetic core to obtain the multi-branch magnetic circuit structure; combining the existing general magnetic core to obtain the multi-branch magnetic circuit; selecting the special designed core shape to obtain the multi-branch magnetic circuit directly.

3.2 Shape and Magnetic Circuit Design of Magnetic Collection Transformer

In this paper, the resonant circuit parameters should be designed reasonably, the resonant inductance and resonant capacitor design should not only meet the zero current condition, but also consider the current stress of other devices and the loss of the whole circuit. In order to accurately control the size of the resonant inductance, the resonant inductance and power transformer are magnetically integrated into a specially designed core to make it become the transformer leakage inductance.Considering that the distributed capacitance between the primary and secondary of transformer in ZCS soft switching circuit is equivalent to the capacitance between the DS poles of VMOS switch tube, which leads to longer shutdown time of VMOs and is not conducive to the realization of high-frequency circuit, the distance between the primary and secondary windings of U core is relatively far, the distributed capacitance is small, and it is easy to achieve high-voltage isolation, and the window area of U core is large, so it is easy to increase magnetic shunt.Based on the above analysis, the magnetic core structure of the integrated magnetic transformer designed in this paper is shown in Figure 4. The design idea is to add a rectangular central column with a very small cross-sectional area in the middle of the U-shaped transformer core, so that a branch magnetic circuit is added to the U-shaped transformer, and copper is coated on the surface of the magnetic core, so as to reduce the distributed capacitance between the primary and secondary transformer and the leakage inductance caused by other leakage magnetic flux besides the branch magnetic circuit, although this leakage inductance always exists and its proportion is small.In order to facilitate the analysis, this paper will be identified as a relatively small fixed value, its role through the circuit test results, adjust the center column magnetic shunt leakage inductance to correct.

Fig. 4 Core Structure Diagram

Fig. 5 Design of leakage magnetic circuit

Fig. 5 is a schematic diagram showing the change of the magnetic circuit of the U-shaped magnetic core. When there is no intermediate shunt circuit in the magnetic core, the magnetic flux generated by the primary coil access current I1 will be fully coupled to the secondary coil, and the leakage inductance LK1 of the transformer is approximately zero. The magnetic circuit diagram is shown in FIG. 5 (a). When there is an intermediate shunt circuit in the magnetic core, FIG. 5 (B)According to the definition of leakage inductance, the magnetic flux produced by the current I of the primary winding is divided into two parts, Φ 12 and Φ 13. Φ 13 passes through the central column magnetic circuit, but does not pass through the secondary winding. According to the definition of leakage inductance, the magnetic flux produced by Φ 13 through the central column is the leakage magnetic flux of the transformer. The inductance produced in this part of the magnetic flux winding is the leakage inductance of the transformer, which is equivalent to the resonant inductance in the secondary circuit.

Leakage inductance design of 3.3 magnetic integrated transformer

As can be seen from the previous section, the leakage inductance of transformer can be changed by changing the cross section of the central column to meet the resonance conditions of the resonant circuit, but because the magnetic core is sintered and shaped once, the theoretical inductance is always different from the actual value, on the other hand, the resonant inductance of military DC DC converter with the same output power and different output voltage is also different, so it is obviously not economical to design a transformer core for each output voltage.In order to solve this problem, air gap 8 is designed in the central magnetic branch, so that the air gap δ can be adjusted to meet the requirements of different resonant inductors in engineering applications.When there is an air gap in the central magnetic shunt, as shown in FIG. 6, since the permeability of the air is far less than the permeability of the magnetic core, the effective permeability in the central magnetic shunt will decrease, and the middle 13 will decrease, and thus the corresponding inductance will also decrease; furthermore, the larger the air gap length 8, the smaller the magnetic flux passing through the central magnetic shunt, and the smaller the equivalent leakage inductance relative to the transformer, so that the leakage inductance of the transformer, that is, the resonant inductance in the resonant circuit, can be accurately controlled by controlling the air gap length δ.

Fig. 6 Schematic diagram of magnetic circuit

In order to simplify the analysis, the integrated circuit resonant transformer can be regarded as a C-type core with the same cross-sectional area as the central magnetic column embedded in the secondary side magnet (Fig. 7), and the inductance generated by the core in the secondary winding is the leakage inductance of the transformer.

Fig. 7 Schematic diagram of equivalent inductance

Where: RC — Magnetoresistance of the core circuit, R § Magnetoresistance of the air gap circuit

In general, RC = R, the formula of inductance calculation can be approximately as follows:

3.4 Design of Magnetically Integrated Resonant Transformer Winding

ZCS circuit adopts PFM control, the conduction time of VMOs switch Q1 is fixed, the frequency is variable, its winding design method is different from PWM circuit, for fixed input voltage and load conditions, there is a specific working frequency, according to the law of electromagnetic induction, the voltage of primary winding:

Integrate both sides of formula (17) to get:

If the ratio of the first turn to the second turn is N, then:

Where K1 is the ratio of the maximum switching frequency to the resonant frequency:

Secondary winding turns:

The Power VMOS conduction time of forward ZCS circuit is a function of input voltage and load, and its resonance frequency f is low at the low end of input voltage, and the low end resonance frequency is 0.75 of the design frequency.

The above formula does not consider the influence of the parameters such as the coil resistance of transformer, the on resistance of VMOS device and the voltage junction of rectifier diode on the calculation of Max, and the calculated coil turns should be corrected experimentally.

4 design example of Resonant Transformer

Taking the military DC DC converter with 48V input voltage, 5V output voltage and 200W output power as an example, the design method of the transformer mentioned above is described in detail.

Input voltage: 36V ~ 75V

Output Voltage: 5V

Output current: 40A

Maximum operating frequency: 800K

On time: 500ns

4.1 Power, size and design of transformer

The converter is packaged in a standard half-brick structure. Based on the above analysis and combined with the characteristics of this project, the design dimensions of the magnetic core shown in Figure 4 are shown in Table 1.

The transformer power volume design method is the most commonly used transformer design method, which calculates the core volume parameter A × A (the product of the core window area A and the effective core area A) according to the volt-ampere value of the transformer.

As can be seen from FIG. 4 and Table 1:

(Area occupied by a × d leakage flux)

The area product method is usually used to confirm whether the core meets the output power requirements, and the approximate formula is:

Where: P0-Output Power

△ B — — Flux density variation

F-TRANSFORMER FREQUENCY

K — Waveform coefficient (forward converter, K = 0.014)

The main characteristics of the material are shown in Figure 8 and Figure 9. From Figure 8, we can see that the B value of DM51W is 430 mT at 100 ℃, the resonant frequency of the converter is 1 MHz, corresponding to the flux density-power loss curve of 1 MHz, the B value is 80 mT, the power consumption of the core is 800 mW/cm3, this power consumption is acceptable, so BM = 80 mT, because the actual circuit power level adopts active clamp circuit, the core works in 1-3 quadrants.

Fig. 8 DM51W magnetic flux density-magnetic field intensity curve

Fig. 9 DM51W Flux Density-Power Loss Curve

According to equation (23), taking into account the 120% overload condition,

Comparing formula (22) with formula (25), A · A > AP, it can be seen that the magnetic core size meets the requirements.

4.2 Winding design

According to formula (18), calculate the primary winding,

Calculate the secondary winding according to the formula (22),

The output current of the transformer is large and the working frequency is high, skin effect and proximity effect of the conductor need to be taken into account, 0.2mmx13 whole copper sheet is used in the secondary, so that the skin effect is reduced and the proximity effect is eliminated, and the loss can be reduced.

4.2 Calculation of Transformer Leakage Inductance and Air Gap Length of Central Column

From equation (8), the characteristic impedance of the resonant circuit

As can be seen from formula (11) and formula (12), that resonant inductance and resonant capacitance value are:

Known by expression (16)

The leakage inductance L2 obtained by equation (29) is the total leakage inductance of the resonant transformer, and the inherent leakage inductance of the transformer can not be ignored because the value of L2 is relatively small, although measures such as enhancing coupling are taken to control the leakage inductance caused by discrete magnetic flux, so the air gap size determined by equation (31) needs to be corrected by testing.

In summary, the design parameters of the transformer are

Primary: d 0.05mm X 96 Leeds wire double winding 4 turns

Secondary: 0.2mm × 13 copper sheet winding 1 turn

Magnetic column gap: 0.55mm

Core structure size: shown in Table 1.

The physical photos of the transformer are shown in Figure 10:

Fig. 10 Photographs of internal physical objects of products

6 Test Verification

6.1 Test of transformer

The integrated magnetic circuit resonant transformer with output voltage of 5V and output power of 200W is designed according to the above method. The circuit test is carried out in the access circuit. The measured waveforms of the key points are shown in Fig. 11.

Fig. 11 Measured waveform of circuit

11 (a) and 11 (B), the smaller the load current is, the smaller the resonance current zero-crossing time is, and the easier it is to satisfy the resonance condition. The larger the load current is, the larger the resonance current zero-crossing time is, and the less easy it is to satisfy the resonance condition; when the load current is constant, the higher the input voltage is, and the smaller the resonance current zero-crossing time is, as compared with figs. 11 (C) and 11 (d).It can be seen from the above waveforms that under various load conditions, the main switch is in the zero-current mode, which verifies that the leakage inductance design idea of integrated magnetic transformer is correct and the parameter design method is reasonable.

Fig. 12 Photographs of physical products

6.2 Application of transformers

According to the above magnetic integration principle, the designed resonant transformer can be applied to a series of products, in which the measured waveform of the MV48B5M200Bmilitary DC DC converter is shown in Figure 12, and the technical indicators are shown in Table 2:

7 Conclusion

According to the principle of magnetic integration, this paper presents a design method of integrating the resonant inductance of ZCS quasi-resonant military DC DC converter into the power transformer. The theoretical analysis and experimental verification results show that the resonant inductance of the resonant transformer designed by this method can be controlled accurately by adjusting the magnetic shunt air gap, which is suitable for mass production.