The rotating transformer is a part of a DC-DC power conver-sion system. On the primary side of the rotating transformer, a DC-voltage is converted to a high frequency voltage by a half bridge converter. This reduces the size of the transformer and maximizes the power transfer, as shown in (2). On the secondary side of the transformer, the high frequency voltage is rectified and supplied to the load.
Two different winding topologies can be placed in the rotating pot core transformer. The first topology is the adjacent winding topology, which is shown in Fig. 4a, where each winding is placed in a separate core half. Therefore, one side of the transformer can be completely isolated from the other side, and for example placed in vacuum. The second topology is the coaxial winding topology, which is shown in Fig. 4b, where the windings are placed around each other. This topology requires the use of an extra winding bobbin, which reduces the effective winding area. Because both windings rotate around each other with a small gap in between, vibration due to rotating can easily damage the windings. In this paper, both winding topologies are compared and the differences from a magnetic and electrical point of view are identified. III. ANALYSIS
The design of a rotating transformer requires modeling in the electromagnetic and thermal disciplines. A. Magnetic model
An axissymmetric magnetic reluctance model has been derived to calculate the inductances of the transformer. The magnetic flux paths, shown in Fig. 5, have been identified by a 2D FEM model and based on the physical layout a reluctance model has been created. The model is shown Fig. 6a, for the adjacent winding topology. Rrepresents the reluctance and the subscripts c, ag and lk indicate the flux paths through the core, airgap and leakage paths, respectively.
Combining the reluctances of each half of the core and the airgaps, results in the reluctance network as shown in Fig. 6b, which can be rewritten as an equivalent electric circuit, shown n Fig. 6c. Where, Lmpresents the magnetizing inductance,Llkp
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and Llks presents the leakage inductance on the primary and secondary side, respectively.
1) Magnetizing inductance: The magnetizing inductance has been calculated by
（3）
where the path of the mutual flux lines has been assumed through the both
half cores and the airgaps. The reluctances for the pot core are determined by
RCa?RCe??z?o?r?(ro2?ri2) （4） r l n () o r i R cb ?
2 ???or
? z
（5）
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Where ro and ri are the outer and inner core radius of the part, respectively and ?zis the height of the core part. Due to the fringing flux around the airgap, an extra fringing flux factor,Ff, has been added to calculate the airgap reluctance [8]
（6）
（7）
2) Leakage inductance: In the rotating transformer there are various leakage flux lines, that do not link both windings. Because those flux lines do not have an a priori known path, it is inaccurate to model them with a reluctance network as well. A different approach is to calculate the leakage inductance by the stored energy in the winding volume. The magnetic energy of the leakage flux can be expressed by
11LlkI2??B?Hdv22v （8）
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which is equal to the energy of the magnetic field in the winding volume [8]. An expression for the magnetic field strenght can be found by Ampere’s circuital law. In the case of the adjacent winding topology, the magnetic field strength can be expressed for the primary winding as function of the axial length
（9）
In the airgap, the magnetic field strength can be defined by assuming a uniform mmf
（10）
Along the secondary winding, the magnetic field strength can be expressed similarly as (9). As the secondary winding space is traversed, the mmf linearly falls to zero, since Np?i p =?Ns?is. Solving the integral, (8), yields
（11）
whereLlk is the total leakage inductance seen from the primary side. A similar expression for the leakage inductance can be derived for the coaxial winding topology, where the magnetic field strength should be expressed as function of the radius.
3) Verification: The inductances of the prototype trans-formers have been calculated and obtained from 2D FEM simulations and measurements on the prototype transformers (section IV). The inductances for the adjacent and coaxial winding topology are shown in Fig. 7 and 8, respectively. The figures show that by increasing the airgap, the magnetizing inductance and, thereby, also the magnetic coupling decreases.The leakage inductance is almost constant for an increasing airgap and depending on the winding topology. A lower leakage inductance is found in the coaxial winding topology,because both windings share an almost identical flux path.
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