Design and application of high frequency low profile power transformer

summary

The paper discusses the design issues of high-frequency low-profile power transformers, and gives the design and production method of flat-plate windings. This method can automatically connect the conductors of each layer of the winding in series, thereby solving the connection problem between the conductors of each layer of the winding, avoiding welding, and greatly improving the reliability of the device and the utilization rate of the winding to the core window. The experimental results show that the transformer made by this method has small leakage inductance and high efficiency, and is particularly suitable for use in distributed high-power density switching power supply modules. The paper also gives a computer-aided design method for high-frequency low-profile power transformers, which not only makes the design process more flexible and quick, but also makes the design results more reliable.

Keywords

Computer-aided design of high-frequency low-profile transformer winding production

Abstract:This paper discusses the issues related to high-frequency and low-profile power transformers. A new design and fabrication method for planar winding shas been presented. methodcanresultinlowleakageinductance,highefficiency,andisparticularlyusefulforthedesignofinductorsandtranstformersusedinlow-profileandhigh-power-densityconvertermodules.Finally,acomputer-aideddesignofhigh-frequencyandlow-profilepowertranstormershasbeengiven,whichallowsthetransformerdesigntobefaster,

more flexible and reliable.

Keywords:HighfrequencyLowprofileTransformerwindingFobricationComputer-aideddesign

1 Introduction

With the widespread application of switching power supplies, users have also put forward higher requirements for power modules, such as high efficiency, reliable performance, small size, and often have restrictions on the overall height of the module. Therefore, the research on high-frequency low-profile magnetic components has received increasing attention. The core of this new type of magnetic component is flat and very small (less than 1 cm). The winding is no longer wound with traditional solid round wires or stranded wires, but is realized with flexible or rigid printed circuit boards, and the conductor is flat. This unique structure not only saves the winding fixing frame and improves the utilization rate of the window, but also facilitates heat dissipation, reduces leakage inductance and realizes automated production. In addition, since the current is distributed along the width of the conductor, the loss caused by the skin effect can be reduced. The disadvantage is that when using printed circuit boards to make multi-layer windings, additional welding holes are often required to connect adjacent conductors. When the number of turns is large, the design and production is very complicated. AJYerman et al. in the United States invented a winding production method without welding, but this method requires two layers of conductors to form a turn, so it does not effectively utilize the limited core window height.

The design of the transformer also involves the determination of the geometric structure parameters of the core and windings and the arrangement of the windings. Traditional transformer design generally calculates the product of the core window area and the core cross-sectional area according to the design requirements, and then selects a suitable core to determine the number of winding turns, excitation inductance, etc., but this method is limited to low-frequency applications. When the switching frequency is very high (above 100kHz), the iron loss and copper loss of the transformer will increase significantly, and are closely related to the structure and relative arrangement of the transformer core and windings. Today's users have requirements for the volume of power modules, especially the height, which makes designers tend to use low-profile power transformers. If the traditional method is still used, it will be difficult for the designed transformer to meet the requirements, and even if it meets the requirements, it may not be the best design.

This article will give a novel folding winding design and production method. First, the copper sheet is processed into the required shape, and then folded into a winding. The number of turns formed by each layer of copper conductor is increased to 5/6 turns. In addition, the specific application and test results of low-profile transformers and inductors made of windings in this way in switching power supplies are given. Finally, based on the relationship between the copper loss and iron loss of high-frequency transformers and geometric structure parameters and frequency, computer-aided design is used to find the optimal design solution for the power transformer with the smallest volume and the highest power density according to the user's requirements. This method is not only fast, but also allows designers to easily adjust design parameters until satisfactory design results are obtained.

2. Development and application of high frequency low profile power transformer

2.1 Multilayer printed circuit board type and "z" folded winding

D. V. D. Linde et al. reported in 1991 the use of printed circuit board technology to make multilayer windings and their applications. Figure 1 shows the winding conductor series connection method used. Ends 1 and 2 in the figure are the lead-out ends of the winding. The figure shows a winding with "6 turns" (of course it can be larger), which is actually composed of three double-sided PCBs. The upper and lower conductors of each double-sided PCB are connected by "local solder holes". Each layer of conductor has a "connecting copper sheet" extending outward, and adjacent double-sided PCBs are connected by the solder holes on these "connecting copper sheets". If the required number of winding turns is large, there will be many connection points and connection lines. For example, when the number of winding turns is only 10, there must be 20 connection points and 11 connection lines. When the number of winding turns is large, it may not be possible to realize the production of the winding, because the number of "connecting copper sheets" is limited by the size of the magnetic core. The increase in connection points not only brings difficulty to production, but also affects reliability. In order to solve the connection and welding problems, AJYerman and others invented the "z" folded winding. First, a copper sheet of a certain shape is corroded by a flexible PCB, as shown in Figure 2, and then folded into a winding. The winding in the figure is made of a flexible PCB folded in a "z" shape with 4 half turns, with a total of 2 turns. It is actually folded by a conductor 7 represented by a solid line on the top layer and a conductor 8 represented by a dotted line on the bottom layer, and one turn of the winding is actually formed by half a turn on the top layer and half a turn on the bottom layer. Ends 5 and 6 are lead ends, dotted lines 1, 2 and 3 are folding lines, 9 is insulating material, and 4 is a through hole left for the core column of the magnetic core. The advantage of this method is that it avoids welding and improves the reliability of the entire component, but since two layers of copper foil are required to form a full turn, when the number of turns is required to be large and the height of the magnetic core is required, the height of the winding cannot meet the requirements.

Figure 1 Connection of multi-layer PCB winding Figure 2 A winding with 2 turns made by folding 4 half turns of a flexible PCB in a "Z" shape

2.2 A new design of folded winding

Figure 3 shows a new folding winding design pattern, with the dotted line being the folding line. It can be seen that due to the certain angle α between the center lines of adjacent annular conductors, the number of turns formed by each annular conductor is actually only (1-α/360), with the maximum value being 5/6 (α=60o). Compared with the folding winding design introduced earlier, this new scheme enables designers to obtain more coil turns when the height of the core window is limited, or to connect windings in parallel to reduce losses and increase current capacity. In order to distinguish it from the "z"-shaped winding folding method, the new design method is called the "5/6 turns" winding folding method. In addition to eliminating the welding process and reducing the connection resistance, the new design also improves the utilization rate of the core window height. The disadvantage is that the adjacent folding lines are not parallel, and it is not very convenient to stagger the primary and secondary windings to reduce leakage inductance and high-frequency losses.

Of course, for E-type cores, similar methods can also be used to design their windings. Figure 4 is a square winding expansion diagram suitable for E-type cores. End 1 and end 2 are the current inflow and outflow ends. The pattern is folded to form a winding with 5 turns.

Figure 3 New design of folded winding

Figure 4: Square winding sheet suitable for E-type core

2.3 Development and test results of low profile transformer

In order to verify the feasibility and reliability of the new winding design method, the author designed and manufactured a low-profile transformer and filter inductor, and used them in an active clamping synchronous rectification forward DC/DC converter, as shown in Figure 7. Its rated power is 50W, the input and output voltages are 48V and 5V respectively, and the switching frequency is 200kHz. C2 in the figure is a clamping capacitor, which clamps the voltage Uds across the main switch at a certain value level during the main switch off period, thereby avoiding excessive voltage stress on the switch tube V2. In addition, the use of active clamping technology can not only realize the automatic reset of the transformer core without additional reset measures, but also make the excitation current flow in the positive and negative directions, so that the core runs in the first and third quadrants of the magnetization curve, thereby improving the utilization of the core.

The structural parameters of the magnetic core used in the transformer are shown in Figure 5. Its material is MnZn ferrite with a magnetic permeability of 1000. The thickness of the primary and secondary winding conductors are 0.1mm and 0.15mm respectively (the skin depth of the copper conductor is about 0.2mm at a frequency of 200kHz), the number of layers are 12 and 4 respectively, and the actual turns ratio is 10:4. First, use CAD software to design and draw the unfolded pattern of the winding, and then use a CNC cutting machine to process the copper sheet to obtain the required winding pattern. Of course, in mass production, it is necessary to consider using equipment such as punching machines to process the copper sheet winding. Figures 3 and 6 are the unfolded patterns of the primary winding and the secondary winding respectively. Folding along the folding line in sequence forms the winding. If the influence of the lead and folding is ignored, the DC resistance of the winding is the sum of the DC resistance of each layer of the circular conductor. The DC resistance of the winding can be calculated as follows:

Rdc=2πρNl/twln(r0/r1)(1)

Where: Rdc——DC resistance of winding;

Nl——number of copper conductor layers;

ρ – resistivity of copper conductor;

tw——copper conductor thickness;

r0——outer radius of winding;

r1 – inner radius of the winding.

Figure 5 Q-type core structure dimensions

Figure 6: Expanded view of the secondary winding of the power transformer

Adjacent conductors are electrically isolated by insulating tape with low dielectric constant and good withstand voltage performance. The secondary winding is sandwiched between the primary winding, so the leakage inductance is very small, 0.464μH, accounting for only 1.5% of the excitation inductance. The AC resistance (see Table 1) can be calculated according to the Dowell model: (2)

Where: Rac——AC resistance of winding;

M=△(sinh2△＋sin2△)/(cosh2△－cos2△)

D=2△(sinh△－sin△)/(cosh△＋cos△) △=tw/δ;δ（skin depth）=

f——switching frequency;

μo——vacuum magnetic permeability, μo=4π×10－7.

The filter inductor also uses the same magnetic core, but leaves an air gap of about 1mm to prevent core saturation and reduce losses caused by DC bias. The winding of the inductor is made up of two windings with the same number of turns connected in parallel to reduce copper losses. The height of the entire magnetic core of the transformer and inductor is only 8mm.

The input and output power measurement method of the transformer is as follows: first multiply the measured voltage at both ends of the winding and the instantaneous value of the current flowing through, and then calculate the average value of the product in one or more cycles, which is the input or output power of the transformer. This process is completed by the TektronixA6302 digital oscilloscope. In order to avoid the influence of high frequency on the measurement, the two ends of the winding are connected to the two input channels of the oscilloscope respectively, and the voltage difference between them is the voltage at both ends of the winding. The third channel of the oscilloscope inputs the current waveform measured by the current probe (TektronixA6302).

Table 1 Parameters of low profile power transformer and inductor

Figure 8 shows the relationship between the transformer efficiency and input power. It can be seen that the transformer has a very high conversion efficiency. When the output power of the converter is 50W, even under natural ventilation cooling, the transformer has no obvious temperature rise (<50℃), which is mainly due to its small power consumption and good heat dissipation performance. The relationship between the efficiency and output power of the entire converter is shown in Figure 9. Due to the use of synchronous rectification technology, the converter has a higher conversion frequency and

The efficiency at 50W is close to 90%.

In summary, the "5/6 turns" low-profile transformer winding folding manufacturing method has the following advantages:

(1) Avoiding welding between adjacent conductors;

Figure 7 Active clamp synchronous rectification forward DC/DC converter

Figure 8 Transformer efficiency and input power relationship

Figure 9 Relationship between converter efficiency and output power

(2) The core window height can be utilized to the maximum extent, thus improving the window filling factor;

(3) Minimize the loss of copper material during processing;

(4) The production method is simple, quick, clean and environmentally friendly;

(5) Allow designers to select copper sheet materials of different thicknesses according to specific applications;

(6) It is particularly suitable for use in high-frequency and high-power density switching power supply modules.

3. Optimization design of high frequency low profile power transformer

3.1 High-frequency transformer loss model

(1) Core loss model

The iron loss of the transformer is mainly caused by hysteresis and eddy current effects. Hysteresis loss is generally believed to be caused by the movement and friction of magnetic domains of magnetic materials. Hysteresis loss is proportional to the frequency, while eddy current loss is proportional to the square of the frequency. The most commonly used magnetic loss power density (unit volume) calculation formula will be used here:

Pc=kBmfn(3)

Where k is the loss coefficient, B is the peak-to-peak value of the magnetic flux density, f is the alternating frequency of the magnetic field, k, m, and n are related to the characteristics of the magnetic material and can be obtained from the loss curve provided by the magnetic material supplier. At high frequencies, due to the influence of the eddy current effect, the magnetic lines of force in the core are unevenly distributed. However, when a ferrite soft magnetic material with high resistivity is used as the core material, the eddy current is very small and the influence on the distribution of the magnetic lines of force can be ignored. Therefore, it can be considered that the distribution of the magnetic lines of force on the cross section of the core is uniform. For the E-E type core shown in Figure 10, its loss is:

Pc=kfnΦm(2W2L)1－m(2Hw＋W)(4)

(2) Winding loss model

Although PL Dowell established a simple transformer copper loss and leakage inductance calculation model under a one-dimensional approximation of the electromagnetic field, the model is very convenient to use. It can be used to predict the copper loss and leakage inductance of high-frequency transformers and achieve the optimal design of high-frequency transformers.

In high-frequency applications, in order to reduce copper loss and increase current capacity, the winding conductor is usually made of flat copper sheets, and each layer has only one turn of conductor, as shown in Figures 10 and 12. This allows the current to be distributed along the width of the conductor, reducing the loss caused by the skin effect, and also helps to reduce the overall height of the transformer. If the influence of the connection points of each layer of conductors is ignored, for a winding with N turns, its DC resistance is:

Rdc=2Nρ(L+Wc+2Ww)/(Ww－2dw)tw(5)

Where tw and dw are the conductor thickness and the gap between the winding and the core respectively. Due to the high frequency effect, the resistance of the winding will increase significantly. The AC resistance of the winding can be expressed as:

Rac=FrRdc(6)

Where Fr is the ratio of AC to DC resistance, which is related to the geometric size and layout of the core and winding. Based on the PL Dowell model, when the primary and secondary windings are arranged separately, the Fr value is:

Fr=M＋[D(N2－1)]/3(7)

Where: N is the number of winding layers starting from the zero leakage magnetic field;

M=△(sinh2△＋sin2△)/(cosh2△－cos2△)

D=2△(sinh△－sin△)/(cosh△＋cos△)

△=tw/δ, δ is the skin depth at frequency f.

The calculation of Fr is more complicated when the primary and secondary windings are arranged alternately. Here is an example to illustrate. When one winding is sandwiched between the other winding and the number of turns is an even number, and the zero leakage magnetic field line just divides the winding into two halves (that is, the number of conductor layers on both sides is an integer), Fr can be calculated according to formula (7), but N should be half of the actual number of winding turns; when the number of winding conductor layers is an odd number, see Figure 11, the corresponding AC and DC resistance proportionality coefficient Fr

In practical applications, the shape of the magnetic core is not necessarily limited to the E-type. If other shapes are selected, the copper loss and iron loss can be calculated according to the corresponding calculation formula.

When the transformer is used in a switching power supply, the current waveform flowing through the winding is not a sine wave, but contains high-order harmonics. Therefore, it is not enough to only consider the influence of the fundamental wave. The appropriate approach should be to first obtain the harmonic components of the current waveform, and then obtain the winding loss for each current harmonic component. In order to calculate the winding loss for the current harmonic component, it is necessary to calculate the AC/DC resistance proportionality coefficient Fr at each harmonic frequency, which can be obtained using formula (7) or (8).

3.2 Algorithm Design

Based on the transformer loss model introduced above, a program can be written to find the minimum effective volume core. The process is shown in Figure 14. After inputting the converter topology, transformer efficiency, core height, material, input and output voltage, power and other parameters, this program will automatically change the geometric structure size of the transformer, and then calculate the corresponding loss and efficiency, and find the smallest volume core that meets the given maximum magnetic flux density, minimum excitation inductance and core height requirements, and give the corresponding core geometric structure size and copper loss, iron loss, etc. In the figure, ηo, Bsat, Ve, Ae, Le and Hco represent the target efficiency of the transformer, the saturation magnetic flux density of the magnetic material, the effective volume of the core, the effective cross-sectional area, the magnetic path length and the allowable height of the core. The specific design steps are as follows:

(1) Select a switching power supply topology, such as forward or flyback.

(2) Determine the primary-to-secondary winding turns ratio based on the input-output voltage and the switch control square wave pulse duty cycle. For a forward switching power supply:

nps=Np/Ns=DUi/Uo(11)

Where: nps is the primary-to-secondary winding turns ratio, Np is the primary winding turns

Ns is the number of turns of the secondary winding, D is the duty cycle of the switch control square wave pulse, Ui is the primary input voltage, and Uo is the power supply output voltage.

(3) By setting the number of primary winding turns Np to a certain value, the number of secondary winding turns Ns can be obtained at the same time.

(4) Select the layout of the primary and secondary windings: separate and independent layout or staggered layout of the primary and secondary windings. After the winding layout is determined, the AC and DC resistance ratio coefficient Fr of the primary and secondary windings at different harmonic frequencies can be calculated.

(5) Calculate the current IP (t), IS (s) of the primary and secondary windings and the amplitude of each harmonic respectively, so as to calculate the loss of the winding, including high-frequency loss.

(6) Within the set range, the geometric structure parameters of the core and winding are changed in turn, such as the core height hc, width W, window depth L, window width Ww and conductor thickness tw, and then the core loss Pc and winding loss Pw under a certain geometric structure are calculated respectively.

(7) Calculate the transformer efficiency η and magnetic flux density Bmax

The efficiency of the transformer is:

η=P0/(P0＋Pc＋Pw)(12)

For a forward active clamp switching power supply:

Bmax=UiDT/4NpAe(13)

Where T is the control square wave pulse period.

(8) Find the core and winding geometric structure parameters with the smallest volume and meeting the efficiency requirements (> target efficiency ηo) and magnetic flux density requirements (<0.5Bsat). If the efficiency requirements are not met, repeat the process from (3) to (8). If the efficiency requirements are met, the search process ends and the transformer structural parameters are output.

According to the above conditions and requirements, the mathematical model for solving the minimum magnetic core volume can be written:

minVe=2AeLe

subHc≤Hco, Bmax≤0.5Bsat, η≥ηo

Table 2 lists the transformer design results for active clamp forward converters obtained using the design program. The input voltage of the converter is 48V and 5V, the rated power is 200W, the operating frequency is 200kHz, the transformer winding turns ratio Np:Ns=6:2, each layer has only one conductor, and the core material is MnZn ferrite. In order to reduce high-frequency loss and leakage inductance, the primary and secondary windings are arranged in an interlaced manner, and the two secondary windings are first connected in parallel and then the primary is sandwiched in the middle. Of course, in order to fully ensure the reliability of the transformer operation, the allowable temperature rise limit of the transformer and the maximum allowable current density of the conductor should also be added to the constraints of the optimization program. The calculation of the transformer temperature rise involves the establishment of the transformer thermodynamic model, and the traditional transformer thermodynamic empirical model is not necessarily suitable for high-frequency low-profile transformers. This will be studied in depth in subsequent work.

Table 2 High frequency low profile transformer design results

3.3 Further discussion on factors affecting core volume

In order to obtain a more satisfactory high-frequency low-profile transformer design, it is necessary to have a deep understanding of the factors that affect the transformer performance and the extent of their influence. In view of this, the author used the above design procedure to further study the relationship between the core volume, core height, frequency, efficiency, etc. The converter topology used is the same as that introduced in Section 2.3, and the transformer winding turns ratio is 6:2. When the primary winding is sandwiched between two parallel secondary windings, the relationship between the minimum volume of the transformer core and the frequency is shown in Figure 15. The core volume initially decreases significantly with the increase of frequency, and after reaching the minimum value, it increases with the increase of frequency. The greater the output power, the faster the increase. There are two reasons why the volume of the magnetic core increases with the increase of frequency. First, as the frequency increases, the skin effect becomes more severe. Therefore, in order to achieve the same efficiency, the width of the conductor must be increased to reduce high-frequency losses, which increases the lateral size of the magnetic core and its volume. On the other hand, the core loss is related to the frequency and the size of the core. The higher the frequency and the smaller the size, the greater the loss. Therefore, in order to keep the loss unchanged as the frequency increases, the size of the magnetic core must be increased, and the volume naturally increases.

Figure 15 Relationship between minimum transformer core volume and frequency

Figure 16 is the minimum volume and efficiency curve of the transformer. Obviously, the transformer with high efficiency is also large in volume, but the two are not linearly related. As can be seen from the figure, the efficiency of the transformer is not the greater the better, because when the efficiency is very high, the volume increases rapidly, and the most suitable efficiency should be taken at the knee point of the curve. For a transformer with an output power of 100W, the efficiency is more suitable to be 98.5%. When there are many conductor layers, the thickness of the conductor is not a skin depth or a larger value to improve the efficiency and reduce the volume of the core. In fact, when a skin depth is taken as the thickness of the conductor, not only is the volume of the core larger than when the conductor thickness is taken as the optimized value (the optimized thickness of the conductor is determined by the optimization program), but the core height is also larger, see Figure 17 and Figure 18. Because when there are more conductor layers, the loss of the winding will be more severe due to the leakage magnetic effect. Only by reducing the thickness of the conductor and increasing its lateral size can the copper loss be guaranteed not to be too high, so the volume of the core also increases.

4 Conclusion

This paper introduces the design and production method of low-profile high-frequency magnetic component windings, and gives a new winding design and production scheme. The specific design and test results show that the use of magnetic components with this new type of winding in switching power supplies not only has low power consumption and temperature rise (<50°C), but also reduces the volume and height of the entire power module. The new winding design and production method can also greatly save copper materials, so it is very practical. This paper also gives the optimization design of the transformer used in high-frequency switching power supplies. Unlike traditional design methods, this design algorithm takes into account the influence of high frequency on copper loss and iron loss, and can easily adjust the design parameters of the transformer, such as height, bottom area, etc., as needed, and finally gives the structure of the magnetic core with the minimum effective volume and the parameters such as the thickness of the winding conductor, which can be used in specific designs. In addition, the design program is also used to further study the relationship between the core volume, core height, frequency and efficiency.

Figure 16 Relationship between minimum transformer core volume and efficiency

Figure 17: Changes when conductor thickness is fixed to a skin depth and replaced by an optimized value

Comparison of minimum core volume and frequency curves of transformers

Figure 18 When the conductor thickness is fixed to a skin depth and replaced by the optimized value

Comparison of transformer core height and frequency curves