EP4641595A1

EP4641595A1 - Transformer

Info

Publication number: EP4641595A1
Application number: EP24172422.8A
Authority: EP
Inventors: Ozan Güngörmez
Original assignee: Vestel Elektronik Sanayi ve Ticaret AS
Current assignee: Vestel Elektronik Sanayi ve Ticaret AS
Priority date: 2024-04-25
Filing date: 2024-04-25
Publication date: 2025-10-29

Abstract

According to the invention, there is provided a transformer comprising a primary winding, a secondary winding, a core, and an air gap positioned within the core. In some embodiments, a minimum number of windings of the primary and/or secondary windings are passed through a point in the core where the air gap is located.

Description

The invention relates to a transformer, and in particular to a transformer design avoiding fringing effect.

Background

Transformers are fundamental components in electrical systems, serving the critical function of transferring electrical energy between circuits with minimal losses. They operate based on the principles of electromagnetic induction, wherein alternating current in the primary winding induces a magnetic field in the core, subsequently inducing a voltage in the secondary winding. However, traditional transformer designs often encounter challenges that compromise their efficiency and performance.
One significant challenge is core saturation, which occurs when the magnetic flux within the core reaches its maximum limit, resulting in a reduction of transformer efficiency and potential overheating. Additionally, eddy currents induced in the core material contribute to energy losses and further decrease efficiency. These issues are particularly pronounced in transformers used in high-power applications, where minimizing losses is essential for optimal performance and reliability.
Conventional approaches to address core saturation and eddy current losses include using high-quality ferromagnetic materials and optimizing core geometry. While these methods offer some improvement, they may not fully mitigate the challenges associated with core saturation and losses, especially in demanding operating conditions.
Moreover, the fringing effect, a consequence of magnetic flux lines extending beyond the core, exacerbates these challenges. Fringing occurs due to the reluctance of the air surrounding the core, leading to magnetic flux leakage and inefficiencies in energy transfer. Traditional transformer designs may overlook the fringing effect, resulting in suboptimal performance and increased losses.
Historically, air gaps were primarily incorporated into transformer designs to enhance mechanical stability or accommodate thermal expansion. However, recent advancements in transformer technology recognize the potential of strategically positioned air gaps to mitigate core saturation effects, reduce eddy current losses, and address the fringing effect.
Given the importance of transformers in various industries, there is a growing demand for innovative solutions that address the challenges of core saturation and losses while optimizing efficiency and reliability. A transformer design that optimally positions the air gap within the core structure represents a promising approach to achieve these objectives. By precisely controlling the magnetic flux density, such transformers offer the potential for significant performance enhancements and operational benefits across a wide range of applications.
In light of these considerations, there exists a need for a transformer design that incorporates an optimally utilized air gap to effectively mitigate a transformer fringing effect, core saturation effects, reduce eddy current losses, and optimize overall efficiency and performance. Such a design would represent a significant advancement in transformer technology, addressing the limitations of conventional designs and meeting the evolving requirements of modern electrical systems.

SUMMARY OF INVENTION

In view of the above problems the present invention provides a transformer and a method for manufacturing the transformer according to the independent claims.
According to the invention, the temperatures have been significantly reduced. This may be achieved by passing the windings of the transformer through the air gap that causes this fringing effect to a minimum, that is, to leave the part corresponding to the air gap essentially empty while the windings are being wound. In this way, these fringed magnetic flux lines will have minimal effect on the transformer wires.
The transformer according to the invention may be configured such that a fraction of a winding of the primary winding is covering the point where the air gap is located.
The transformer according to the invention may be configured such that half a winding of the primary winding is covering the point where the air gap is located.
The transformer according to the invention may be configured such that the air gap is placed in the middle of the core.
The transformer according to the invention may be configured such that a space twice as large as the air gap is left in the center of the core.
The transformer according to the invention may be configured such that an edge transformer insulation material under the primary winding is covering the air gap.
The transformer according to the invention may be configured such that a second number of windings of the secondary winding is covering the air gap.
The transformer according to the invention may be configured such that the second number is a fraction of a winding of the secondary winding.
The transformer according to the invention may be configured such that the second number is half a winding of the secondary winding.
The transformer according to the invention may be configured such that the second number is greater than the first number.
The transformer according to the invention may be configured such that an edge transformer insulation material is placed between the primary and secondary winding.
The transformer according to the invention may be configured such that an edge transformer insulation material is placed between the primary and secondary windings.
The transformer according to the invention may be configured such that the secondary winding is wound without margins to the edges.
The transformer according to the invention may be configured such that at least two core parts complement each other such that there is no air gap on the sides of the transformer.
The transformer according to the invention may be configured such that an insulation tape is placed over the primary and/or secondary winding according to a turn ration of the transformer.
The transformer according to the invention may be configured such that an insulation tape is placed over the primary and/or secondary winding according to an insulation distance between the primary and secondary winding.
According to the invention, there is provided a transformer comprising: a primary winding, a secondary winding, a core and an air gap positioned within the core. In some embodiments, a minimum number of windings of the primary and/or secondary windings are passed through a point in the core where the air gap is located.
According to the invention there is further provided a method of manufacturing a transformer according to the invention.

BRIEF DESCRIPTION OF DRAWINGS

Figure 1 describes the effect of leakage flux and fringing effect on a transformer;
Figure 2 describes the magnetic flux and temperature effects in transformers with a normal and distributed air gap;
Figures 3a and 3b describe the distribution of magnetic flux in transformers with a central (left) and distributed (right) air gap;
Figure 4 describes transformer temperatures at 90VAC input voltage according to a conventional transformer design;
Figure 5. describes a transformer design according to the invention showing transformer temperatures at 90VAC input voltage;
Figure 6. describes that when leaving air gaps in transformers the air gap is generally left over only one of the two core parts;
Figure 7. describes an edge band being placed at the midpoint of the transformer according to the invention;
Figure 8. describes the primary winding being wound and when winding the primary winding only a fraction of a winding is passed through the line where the air gap is located.
Figure 9. describes insulation tape laid according to the turn ratio specified in a transformer data sheet;
Figure 10. describes the secondary winding having a fraction of a secondary winding passed through the center of the transformer where this air gap is located;
Figure 11. describes insulation tape laid according to the turn ratio specified in the transformer data sheet;
Figure 12. describes the auxiliary winding of the primary winding wrapped and the core being fully seated on a plastic section;
Figure 13. describes that when placing a plastic structure of both core parts, both core parts are fully complementing each other and no air gap is left on the sides of the transformer;
Figure 14. describes the transformer design according to the invention.

DESCRIPTION OF EMBODIMENTS

The fringing effect significantly impacts transformer performance, particularly in applications where efficiency is crucial. Magnetic flux lines extend beyond the core into the surrounding air due to the reluctance of the air medium. This extension leads to energy leakage and inefficiencies in energy transfer, resulting in increased losses and reduced efficiency.
Conventional transformer designs exacerbate the fringing effect due to factors such as core geometry, winding arrangement, and operating conditions. However, by strategically integrating air gaps within the transformer core, the adverse effects of the fringing effect can be mitigated. These air gaps redirect magnetic flux lines, confining them within the core, thus improving energy transfer efficiency and reducing losses.
The invention relates to improvements that result from the elimination of various effects on the transformers used in various power electronic converter structures and in particular in flyback converter topologies. A new transformer design has been made to eliminate various effects such as the fringing effect that occurs in transformer structures where an air gap must be left between the cores.
Before designing a transformer, concepts such as magnetic field strength, magnetic flux density, and magnetic permeability of the material used must be well understood. These concepts are basically important in terms of the structure of the transformer, the effects it can cause, and the points that need to be paid attention to in the design. Accordingly, H represents the magnetic field strength or intensity. H is considered as the external source of the magnetic field and refers to the magnetizing force it pumps into the environment. B is the magnetic flux density. B is a parameter that shows the magnetizing strength of the environment or how effectively the amount of magnetic field is used. In addition, the magnetic flux density (B) tells the amount of magnetic force induced on a certain object due to the magnetizing force H. There is the following relationship between B and H: $B = μ \cdot H$
Here µ refers to the magnetic permeability of the material, which is a measure of the ability of the material to support the formation of a magnetic field within itself. And it is the degree of magnetization achieved in response to a magnetic field applied to a material.
An important thing to consider when changing the magnetic material or structure of the transformer core to be selected is the µ value, which defines the magnetic permeability of that material. In systems with the same number of turns but different core materials, the inductance values will vary depending on this magnetic permeability value. A core with a low magnetic permeability can also cause the inductance value to decrease for the same turns ratio; this means that the transformer will heat up more by generating higher current peaks, especially in topologies such as flyback converters.
Another important consideration in transformers is the air gap. The air gap allows the transformer to be driven to a current and inductance value that is not saturated. By creating an air gap in the transformer, more power can actually be extracted from the transformer. In addition, increasing the air gap in the core also increases the overall reluctance value of the system. In short, reluctance is like a kind of resistance that the flux encounters as it travels through the core. Just as there is resistance to electric current, there is reluctance to magnetic flux. Therefore, as the reluctance increases, the inversely proportional permeability decreases accordingly. Since this reduces the magnetic permeability and magnetic flux of the core, a more inefficient system is obtained. Creating an air gap also increases the leakage inductance values and reduces the efficiency of the system.
Transformers are designed for minimum inductance in many applications, taking into account the topology used in the design. One of the most important design considerations is the saturation current value at which the transformer becomes saturated. At the point where the maximum saturation current that can be passed through the transformer is exceeded, the transformer will overheat and there will be significant deviations in the inductance value, which tells that the transformer is saturated. When making designs, an inductance value should be defined according to the appropriate saturation current value, taking into account various temperature conditions. This is because there is an inverse relationship between the inductance value and the saturation current of the transformer. At the point where the saturation current value of the transformer is to be increased, the air gap in the transformer is to be increased so that the saturation or bias current of the transformer increases, but at that time the inductance value of the transformer decreases. The decrease in the inductance of the transformer causes the switching frequency value to increase, especially for systems operating in QR (Quasi Resonant Mode) structure, and this indicates that a QR Metal-Oxide-Semiconductor Field-Effect Transistor, MOSFET, will increase the switching losses. In addition, since the decrease in this inductance ratio actually means that the transformer will want to transfer more energy in a shorter time, even if our saturation current value increases, it will also cause an increase in our peak current values on the MOSFET.
Since the magnetic flux permeability µ of the cores used is very high compared to the magnetic flux permeability (u0) of the air, most of the magnetic energy is stored in the air gap. As can be seen from the formula (2), the magnetic energy varies in direct proportion to the magnetic flux density and the air gap left in the core. $E \approx \frac{B^{2} \cdot V}{2 \cdot μ_{0}}$
While the magnetic flux lines move in a straight path inside the core, when they reach the air gap, these magnetic field lines begin to spill out, as shown in Figure 1. This situation is called the "fringing effect" and is one of the most important parameters to consider in transformer design. Figure 1 shows the "leakage flux" effect caused by the windings of the transformer, this effect is the leakage flux escaping from the transformer due to the magnetic flux windings. Although these leakage fluxes cause irregularities in the magnetic flux of the transformer, they are negligible compared to the fringing effect. When copper or aluminum is used in the magnetic element windings, these lines spreading outward from the air gap create short-circuit currents called "eddy currents" on the wires at the points where they intersect with the corresponding wires. This causes the windings to heat up.
Figure 1 shows the effect of leakage flux and fringing on a transformer.
In addition, the magnetic flux lines scattered outward from the air gap created by the fringing effect cause eddy currents to occur at the point where the transformer windings intersect and cause that winding of the transformer to heat up more. These magnetic flux lines created by the fringing effect will cause voltage to be induced in the wire at the points where they intersect the wire. And since the wire is short-circuited within itself, this induced voltage will cause small short-circuit currents. In addition, this situation shows that the parts of the windings that are close to the air gap actually get hotter. Figure 2 shows the temperature distribution in a structure with and without an air gap.
2 shows the magnetic flux (below) and temperature effects (top) in transformers with normal (e.g. distinct) and distributed air gap.
One of the possible solutions is to distribute the air gap homogeneously throughout the transformer, which is one of the most ideal solutions. As shown on the right side of Figure 2, the temperature effects are more evenly spread when a distributed air gap is used than when a normal/distinct air gap is used as shown on the left side of Figure 2. However, using such a transformer is both costly and very difficult to manufacture. Another solution is to use a dispersed air gap core structure instead of a central air gap. Features such as the dispersed air gap, which carries the saturation current to higher levels and reduces the fringing effect, are advantageous for transformer design. However, the main disadvantage of dispersed air gap transformers is that although it does not make a big difference in tests, it makes it difficult to use dispersed air gap cores in systems where electromagnetic interference, EMI, emissions may be very high, as it collectively raises the curve in tests.
Figures 3a and 3b shows the distribution of magnetic flux in transformers with central and distributed air gaps.
As mentioned above, some methods can be developed to eliminate the fringing effect, which is one of the most important effects in transformer design. In order to minimize this fringing effect and the eddy currents generated by this effect, it is necessary to move the transformer wires away from the air gap of the transformer. In this way, these conductive lines are removed from these residual magnetic flux lines that occur in the air gap of the transformer. Or, as another method, passing a minimum level of conductive line through the point where the air gap of the transformer occurs is also one of the important solutions.
The study conducted by the inventors here, which gives better results and better performance than other methods, is as follows; It is the minimum passage of primary and secondary windings from the point where the air gap of the transformer occurs. And a transformer design was made based on this.
Figure 4 shows the transformer temperatures at 90VAC input voltage in a conventional transformer design. As shown in Figure 4, in the temperature tests performed with a 17IPS62R10 90V card on the product in a 40°C hot room; a higher temperature value was read in the region near the center where the air gap is located compared to other regions. And the core and windings of the transformer appear to be colder than this region. The fact that the hot zone occurs in the very center of the transformer and is hotter than other parts of the transformer actually tells; it shows that effects such as fringing, Eddy current, skin effect, proximity effect may be more dominant in the transformer than core or conductor wire losses. However, the fact there is no homogeneous heating directly on the conductor wires eliminates effects such as the Skin Effect and the Proximity Effect. Accordingly, the magnetic flux lines that appear in the air gap cause short-circuit currents at the points where they intersect with the primary and secondary windings of the transformer, and most of the energy accumulates in this air gap. And it shows that the temperature difference occurs very intensely in this air gap due to this accumulation.
After this basic problem was identified, two different designs were made; to remove the primary and secondary windings of the transformer from this air gap and to pass the primary and secondary windings of the transformer through the line where this air gap passes in a minimal way. As a result of these designs, temperatures have been significantly reduced, as shown in Figure 5. But this is the main difference between the two designs; it is considered the best solution to pass the windings of the transformer through the air gap that causes this fringing effect to a minimum, that is, to leave the part corresponding to the air gap empty when the windings are wound. Thus, these fringed magnetic flux lines will have minimal effect on the transformer wires. And looking at the temperature results obtained, it is possible to see that the heat is distributed evenly over the entire core and a general heating map not only in the center but also on all the windings. In addition, these methods have significantly improved the temperature in a 40°C environment.
Figure 5 shows the transformer temperatures at 90VAC input voltage according to the invention.
Specifically, while the maximum temperatures in the transformer having the conventional design (Figure 4) are shown to be 121 and 116 degrees, these are reduced in the transformer designed according to the invention (Figure 5) to 103 and 104 degrees, respectively.
The transformers used in these results obtained as a result of the tests, the transformer design stages and some issues that need to be considered are given below.
As shown in Figure 6, when air gaps 10 are left in transformers, the air gap is generally left over only one of the two core parts 20. This can be seen in Figure 7. This situation both facilitates the work of transformer manufacturers and reduces production costs.
First, although the air gap 10 is not left exactly in the center, the short sides of the transformer cores can be attached to the plastic structure in both directions. Therefore, it should be assumed that there will be an air gap 10 right in the middle. A space twice the size of the air gap 10 is left in the exact center of the core.
This is to minimize effects such as fringing caused by the transformer air gap 10 on the windings of the transformer and to prevent primary or secondary winding wires from passing through this air gap line.
The transformer winding steps are as follows.
First, as shown in Figure 7, an edge tape 30 with a minimum width of 2 mm and a height of 0.4 mm, which is the edge tape transformer insulation material used in transformers, is placed in the center of this calculated transformer.
Then the primary winding 40 is wound as shown in Figure 8. When winding the primary winding 40, almost no winding is passed through the line where the air gap is located. In other words, a minimum amount of a primary line 41 is passed through the center of the transformer where the air gap of the transformer coincides.
Then, as shown in Figure 9, insulation tape 50 is placed according to the winding ratio specified in the transformer data sheet. And on top of this, 2 rounds of edge band transformer insulation material were placed to protect the secondary winding from the effect of this air gap 10. Minimum width 4.5mm, height 0.75mm.
As shown in Figure 10, the secondary winding 60 has a minimum secondary lead 61 through the center of the transformer where this air gap is located. In addition, there is no need to add edges to save space.
Then, as shown in Figure 11, insulation tape 70 was applied according to the winding ratio specified in the transformer data sheet.
Then, as shown in Figure 12, an auxiliary primary winding 80 was wrapped and the core was fully seated on the insulation tape 70, i.e. a plastic part.
Here, as shown in Figure 13, when placing the plastic structure 90 of both core parts 20, care should be taken to ensure that both core parts 20 fully complement each other and that no air gap is left on the sides of the transformer. Otherwise, both in the measurements made on the transformer after winding and in the temperature results, if an air gap is left on the sides rather than in the center, the temperature results will be better in a dispersed air gap.
As a result, the design is made to minimize effects such as the fringing effect caused by the air gap of the transformer on the windings of the transformer and to avoid passing primary or secondary winding wires through this air gap line. With this transformer design, these effects occurring in the transformer are reduced to a minimum level when the product is loaded with full load at 90VAC input voltage in a 40°C environment; the transformer temperature value measured at 120° and above was reduced to a maximum of 103° - 104° level bands as a result of this process. In addition, in this design, as opposed to central or dispersed air gap structures; A successful study was achieved in minimizing the above mentioned temperature and other effects occurring in both the transformer and the designed power card in transformer structures where an air gap is required. In addition, the internal structure of the designed transformer is as shown in Figure 14.
Figure 14 shows the transformer design according to the invention.
In addition, there are various methods to eliminate effects such as fringing that occur in these transformers. If these methods are to be compared with the methods used above.
When considering methods such as creating a gradual air gap in transformers to eliminate the fringing effect and creating a low-voltage side winding to create an anti-fringing area; these methods are solutions that require changes in the transformer core, changes in the transformer windings, and additional windings. According to the invention, there are no design differences in the transformer core and transformer windings, transformer turns and similar areas that affect the external physical appearance of the transformer. In addition, these methods are not positive methods in transformer structures, which require extra cost, are more difficult to implement, require extra labor, and especially require a large air gap. It is a more effective and simpler solution to solve the problem without making significant changes to the transformer core and windings. In addition, creating a gradual air gap results in different reluctance values between opposing transformer core surfaces. My design eliminates the transformer fringing effect, leakage flux effect, eddy current effect, and similar effects in transformer structures used in power electronics topologies such as flyback, where an air gap must be left, and provides a significant improvement, especially in terms of temperature.
In addition, in order to eliminate factors such as fringing and eddy current effects in transformers that require an air gap, besides the design I have made, there are techniques such as using a dispersed air gap, using a segmented air gap structure, distributing the air gap homogeneously within the core, and moving the winding wires of the transformer further away from the air gap. However, in systems where an air gap is mandatory and these effects are strongly observed, creating a dispersed air gap cannot completely eliminate these effects and has negative effects, especially in EMC CE tests, due to the increase in the distribution area of the magnetic flux. Using a transformer with a partial air gap is both more expensive and very difficult to manufacture. And such a structure requires a significant modification of the transformer core. In structures where the air gap is distributed within the core, which is another method, the cost increases significantly and the manufacturing process becomes much more difficult. In addition, another method is to move the windings further away from this air gap region to avoid these effects in the transformer; this is both less effective than my design in terms of temperature and has disadvantages such as increasing the maximum height of the transformer, distorting the shape of the transformer, and obtaining a chubbier and heavier transformer.
According to the invention, since the magnetic flux permeability of the core used is very high compared to air, most of the energy is collected in this air gap of the transformer structure, thus it is important to minimize the effects such as fringing and eddy current that occur in structures that require an air gap. These effects have various consequences on the transformer, especially temperature, inefficiency and the transformer not operating at the desired inductance values. Unlike all other techniques, in transformer structures where an air gap must be left with the design according to the invention; while the transformer windings are being wound, these effects are reduced to a minimum level by almost never passing the primary and secondary windings of the transformer through the area where the air gap of the transformer is located, and it produced positive results on the transformer for temperature and similar tests. All of the above solutions actually cause changes in a new transformer core or differences in the transformer image. In addition, these designs also have negative aspects such as extra cost, space and so on.
One feature of the invention is to prevent the primary and secondary winding wires from passing through this air gap line by minimizing the effects such as fringing effect on the transformer windings due to the air gap of the transformer and short circuit currents (eddy currents) on the windings. In this way, the effects such as eddy current and leakage flux caused by the magnetic flux emitted from this air gap of the transformer windings are almost eliminated and reduced to a minimum. Since the transformer windings contacted by the magnetic fluxes emitted from the air gap of this transformer are at a minimum rate, these effects will not occur or will be at a tolerable level. Thus, important problems such as temperature have been solved in the most cost-effective and rapid way, without modifying the transformer core or thickening the transformer windings, without adding any extra size or deformation to the transformer.
The invention provides at least the following further advantageous technical effects:
By mitigating the fringing effect, transformers achieve higher efficiency and improved performance across various operational conditions. With reduced energy leakage and better confinement of magnetic flux lines within the core, the transformer can transfer energy more effectively, resulting in lower losses and improved overall efficiency.
One of the primary benefits of addressing the fringing effect is the reduction in losses associated with energy leakage. When magnetic flux lines extend beyond the core into the surrounding air, significant energy is lost. By strategically integrating air gaps 10 within the core to redirect these flux lines, losses are minimized, leading to more efficient energy transfer and reduced wastage.
Addressing the fringing effect enhances the reliability and longevity of transformers. With reduced losses and optimized energy transfer efficiency, the transformer operates more consistently and reliably over time. This increased reliability ensures that the transformer can maintain its performance even under varying load conditions, minimizing downtime and maintenance requirements.
By mitigating the fringing effect, transformers can deliver more consistent performance across different operating conditions. With better control over magnetic flux distribution and reduced energy losses, the transformer maintains stable voltage regulation and power transfer capabilities, ensuring reliable operation in diverse applications.
Optimizing transformer efficiency by addressing the fringing effect can lead to significant cost savings over the operational lifespan of the equipment. Reduced energy losses translate to lower electricity consumption, resulting in decreased operational costs for end-users. Additionally, the enhanced reliability and longevity of the transformer contribute to lower maintenance and replacement expenses, further enhancing cost-effectiveness.
Improving transformer efficiency through the mitigation of the fringing effect also brings environmental benefits by reducing energy consumption. With lower energy losses, less electricity is wasted during power transmission and distribution, contributing to overall energy conservation efforts and environmental sustainability.
This application is not limited to the embodiments described herein. The scope of the invention as defined in the claims encompasses other variations and modifications apparent to those skilled in the art.

Claims

A transformer comprising:
a primary winding;

a secondary winding;

a core;

an air gap positioned within the core;

wherein a minimal number of windings of the primary winding is covering a point where the air gap is located.
The transformer according to claim 1 wherein a fraction of a winding of the primary winding is covering the point where the air gap is located.
The transformer according to claim 2 wherein half a winding of the primary winding is covering the point where the air gap is located.
The transformer according to any one of claims 1 to 3 wherein the air gap is placed in the middle of the core.
The transformer according to any one of claims 1 to 4 wherein a space twice as large as the air gap is left in the center of the core.
The transformer according to any one of claims 1 to 5 wherein an edge transformer insulation material under the primary winding is covering the air gap.
The transformer according to any one of claims 1 to 6 wherein a second number of windings of the secondary winding is covering the air gap.
Transformer according to any one of claims 1 to 7, wherein the second number is a fraction of a winding of the secondary winding, and
optionally, the second number is half a winding of the secondary winding.
Transformer according to any one of claims 1 to 8, wherein the second number is greater than the first number.
The transformer according to any one of claims 1 to 9 wherein an edge transformer insulation material is placed between the primary and secondary winding.
The transformer according to any one of claims 1 to 10 wherein an edge transformer insulation material is placed between the primary and secondary windings.
The transformer according to any one of claims 1 to 11 wherein the secondary winding is wound without margins to the edges.
The transformer according to any one of claims 1 to 12 wherein at least two core parts complement each other such that there is no air gap on the sides of the transformer.
The transformer according to any one of claims 1 to 13 wherein an insulation tape is placed over the primary and/or secondary winding according to the insulation distance between the primary and secondary winding.
Method of manufacturing a transformer according to any one of claims 1-14.