1. Introduction Transformers have always been a major obstacle to reducing the size, increasing power density, and achieving modularity in power supply equipment and devices. Although the introduction of high-frequency conversion technology can eliminate the bulky power frequency transformer, high-frequency transformers with ferrite cores are still required. While ferrite core high-frequency transformers are smaller than power frequency transformers, they still fall far short of modular requirements. They are not only still relatively large, but also generate significant heat and have considerable leakage inductance. Therefore, in recent years, many experts, scholars, and engineers have been researching solutions to this problem. The successful development of high-frequency planar transformers represents a leap forward in transformer technology. It not only significantly reduces the size of the transformer but also results in very low internal temperature rise, minimal leakage inductance, and an efficiency of up to 99.6%, at half the cost of a typical transformer of the same power. It can be used in single-ended forward, flyback, half-bridge, full-bridge, and push-pull converters as AC/DC and DC/DC converters. It is particularly suitable for low-voltage, high-current converters. Therefore, it is especially suitable for modern computer power supplies. 2. Problems of Conventional Transformer Operation at High Frequency (1) Leakage Inductance (Leakage Inductance for short) In an ideal transformer (fully coupled transformer), the magnetic flux generated by the primary winding should pass entirely through the secondary winding without any loss or leakage. However, in reality, conventional transformers cannot achieve zero loss and leakage. The magnetic flux generated by the primary winding cannot pass entirely through the secondary winding. The uncoupled magnetic flux has its own inductance in the winding or conductor, and the energy stored in this "inductance" is not coupled with the main power transformer circuit. This inductance is called "leakage inductance". The insulation requirements of an ideal transformer and the requirement for tight electromagnetic coupling to reduce leakage inductance in order to obtain very low electromagnetic interference (EMI) are contradictory. When the transformer is not energized (turning off from the power supply or the switch is in the off period), the energy stored in the leakage inductance will be released, forming obvious noise. This noise can be seen as a high-frequency spike pulse waveform on an oscilloscope. The amplitude of the high-frequency spike pulse waveform Uspike and the leakage inductance Lleak are proportional to the product of the current relative to the rate of change over time. That is: |Uspike|=Lleakdi/dt (1) When the operating frequency increases, the rate of change of current relative to time also increases. The effect of leakage inductance will be more serious. The effect of leakage inductance is proportional to the switching speed of the converter. Excessive spike pulses generated by leakage inductance will damage the power devices in the converter and form significant electromagnetic interference (EMI). In order to reduce the amplitude of the spike pulse Uspike generated by leakage inductance, a buffer network must be added to the converter circuit. However, the addition of the buffer network will increase the loss of the converter circuit. As the operating frequency increases, the loss of the converter circuit increases and the efficiency decreases. [align=center] Figure 1 Schematic diagram of conventional transformer and planar transformer (a) Conventional transformer (b) Planar transformer[/align] (2) Inter-winding capacitance When the winding of the transformer is a multi-layer winding, there is a potential difference between the top winding and the bottom winding. There is a potential difference between two conductors, and there is capacitance. This capacitance is called "inter-winding capacitance". When operating at high frequency, this capacitor will charge and discharge at an astonishing rate. Losses will be generated during the charging and discharging process of the capacitor. The more times it is charged and discharged within a given time, the greater the loss. (3) Skin effect (4) Proximity effect (5) Local hot spots When a conventional transformer operates at high frequency, there will be local hot spots in the middle of its core. Therefore, in order to reduce the thermal effect, when the operating frequency of a conventional transformer is increased, its magnetic flux density must be reduced accordingly and its volume increased. This makes it impossible to use it as a high power density power supply. For a low output voltage ideal converter, its step-down ratio is very high. When using a conventional transformer, usually one turn of output winding requires about 32 turns of primary winding. Thus, the primary winding needs to be arranged in multiple layers, so the leakage inductance and inter-winding capacitance are large, and the skin effect and proximity effect are severe. 3 Comparison of conventional transformers and planar transformers Conventional transformers are usually composed of a single core and multiple primary windings, while planar transformers are composed of a single turn (or a few turns) of primary winding and multiple cores. These magnetic cores are all equipped with single-turn secondary windings and packaged into modules, as shown in Figure 1. (1) Conventional transformers have a large number of turns in their primary windings, resulting in a relatively large leakage inductance. In contrast, the single-turn (or several-turn) primary winding and single-turn secondary winding of a planar transformer are tightly coupled, resulting in a very small leakage inductance. The leakage inductance of a 30A planar transformer is only 2.0nH. Therefore, when used in fast switching circuits, it not only has very low losses but also reduces the stress on other components in the circuit. (2) Planar transformers have better frequency characteristics than conventional transformers. Planar transformers can operate between 100 and 500 kHz. (3) Planar transformers can be directly and tightly fixed to the base plate, resulting in excellent heat dissipation. This type of special transformer is a small component with a large surface area. Therefore, it does not have the problem of local overheating. (4) Because planar transformers can improve heat dissipation, they can achieve high magnetic flux density and high power density through tight packaging. Conventional transformers cannot compare with them. A 150W planar transformer module has a volume of 5.38 (length) × 1.60 (width) × 1.17 (height) cubic centimeters. (5) Planar transformer technology can significantly reduce the production cost and sales price of transformers. It can reduce production cost and sales price by 50%. Because it can reduce the stress on other components in the circuit, other components in the converter circuit can use low-power devices. Because the heat dissipation conditions of the planar transformer are very good, it can use a very small heat sink. In addition, after the mass production of transformer modules, its price will be reduced even more. (6) The reliability of the planar transformer is higher than that of the conventional transformer. In the planar transformer, even if one core is damaged, the remaining cores and parallel wires in the planar transformer can still work normally, while if a conventional transformer is damaged in one place, the entire transformer cannot work normally. Currently, the power of planar transformer module products is 150W, 300W, 450W, 750W, 900W and 1500W. 4. Internal Structure of Planar Transformer and Measurement and Calculation Method of its Inductance The planar transformer used as a transformer, as described above, is made of several ferrite cores. Two cores are used as transformers, and one core is used as an inductor. Three cores constitute one transformer/inductor module. Many modules can be connected together to form a planar array transformer. This structure of the planar transformer can solve the problem of local overheating in the middle of the core when the transformer operates at high frequencies. One transformer module contains two ferrite cores. The transformer module is assembled from one set of square ferrite cores, which are bonded together with epoxy resin, as shown in Figure 2(b). One winding is inserted into the interior of each core and bonded to the inner surface of the core and the corner of the output end, as shown in Figure 2(a). After the winding passes through the core, it rotates 180° and winds back. Therefore, the "start" and "end" of each winding are at opposite corners of the core. An inductor of similar size is added to the center tap of the transformer section inside the module. Its prominent solder joint connects to the filter capacitor. Details regarding this transformer and its core can be found in the references. The terminals of the transformer's secondary winding are directly connected to the common-cathode Schottky rectifier TO-228. This saves the user the amount of assembly work such as tapping on the transformer's secondary winding. Furthermore, the Schottky rectifier has a very low forward voltage drop when turned on, so the overall circuit efficiency can be very high. The primary winding passing through the transformer is added later. The transformer's equivalent transformation rate is determined by the ratio of the product of the number of modules Ne and the number of turns in the primary winding Np to 1, i.e., the transformation rate is: (Ne × Np): 1. High conversion rates can be achieved by increasing the number of turns in the primary winding or by increasing the number of modules. Planar transformers can modularize power supplies and are used in distributed power supplies. Their characteristics are unmatched by other transformers. In the market, it is recognized as the smallest transformer with the highest current density. The schematic diagram of the internal circuit of the module is shown in Figure 3. In the figure, the inductor is connected between the center tap of the secondary winding of the transformer and the output terminal. This arrangement is to save the amount of assembly work. The maximum leakage inductance of each module is only 4nH. The leakage inductance is measured using 5 modules with the output terminal of the rectifier shorted by copper strips and the primary winding having 3 turns. The leakage inductance measured at this time is 0.18μH. Because the primary inductance of the transformer is equal to the product of the leakage inductance of one module and the number of modules and the square of the number of primary turns. Its mathematical expression is: Lp=Lmod×Ne×Np2 (3) Where Lp——the primary inductance of the transformer; Lmod——the leakage inductance of 1 turn passing through 1 module; Ne——the number of modules; Np——the number of primary turns. The primary inductance given by formula (3) is the inductance measured when the secondary side is open-circuited; while the leakage inductance given is the inductance measured when the secondary side is short-circuited. Five half-bridge flat transformers with three turns of primary winding have a transformation ratio of 9:1. Substituting the data above, we can get: 0.18μH=Lmod×5×9. Therefore, the leakage inductance of one module (two square magnetic cores) is: Lmod=0.18μH/(5×9)=180nH/45=4nH. For five modules with two turns of primary winding, their leakage inductance can be calculated by formula (3): Lleak=Lmod×Ne×Np2 (the output end should be short-circuited) =4×5×22=80 (nH). Because it has very few turns of primary winding, its proximity effect is minimal. The transformer core (dual-core assembly) dimensions of interest to magnetic circuit designers are as follows: —Core area: 0.68 cm²; —Magnetic circuit length: 2.8 cm; —Core volume: 2.0 cm³. The technical specifications for the transformer unit inductor in the module (dual-core assembly) are: minimum inductance of 10.0 μH per square turn per module; maximum leakage inductance of 4 nH. The filter inductor unit is similar in size to the transformer unit, also with 3 turns. The allowable current is typically determined by the rated current of the external rectifier. At 30A, the filter inductor's technical specifications specify a minimum inductance of 2 μH.