Frequency Characteristics of Multilayer Planar High-Frequency Transformers

To meet the modern demands of electronic devices for miniaturization, lightweight design, and portability, as well as the requirements of advanced assembly processes such as SMT, many conventional magnetic components are being replaced by a variety of compact, planar magnetic components. Both theoretical analysis and experimental results demonstrate that planar magnetic components offer numerous advantages, including small size, excellent thermal conductivity, reduced power losses at high power densities, and compatibility with SMT processes.

To precisely design high‑frequency magnetic components with excellent performance in a single step, it is necessary to calculate their parasitic parameters, including leakage inductance, winding distributed capacitance, skin effect, and proximity effect. At present, relatively mature computational methods have been developed for specific magnetic components such as laminated transformers, matrix transformers, and thin‑film transformers with circular spiral windings. This paper discusses the design of two types of planar multilayer transformers with air gaps. First, the circuit‑model design is based on frequency‑response relationships; it assumes that the magnetic material exhibits linear frequency characteristics and no hysteresis, thereby eliminating the need to distinguish between the nature of the input voltage. Second, the distribution of magnetic flux within the windings must be taken into account to determine how to optimize the amount of core material used and to achieve a uniform flux distribution. Knowledge of eddy‑current distribution further facilitates the calculation of copper losses in the windings and eddy‑current losses within the core material.

The devices discussed in this paper are fabricated using TDK’s MnZn ferrite material. They are employed in high-frequency planar magnetic components to investigate the frequency-dependent relationships between inductance and voltage ratio. Additionally, the study examines the flux distribution and eddy current distribution for two distinct winding configurations, and a boundary element method is implemented to develop CAD and CAE software, which is then used to perform relevant numerical calculations.

2 Planar Multilayer High-Frequency Transformer Structure and Calculation Model
High‑frequency DC converters operating at frequencies close to 1 MHz require inductance values on the order of a few microhenries. For high‑frequency applications, the most common inductor structures are multilayer magnetic circuits featuring open‑circuit, closed‑circuit, or helical geometries. In this study, the primary and secondary windings of the experimental samples have the same number of turns: three turns for Type I and one turn for Type II. The magnetic core material is ferrite, with dimensions of 17.6 × 17.6 × 20 mm³. Figure 1 illustrates a helical winding configuration, whose core geometry corresponds to a basic open‑circuit design. For computational convenience, these structures are assumed to be two‑dimensional, axisymmetric, and unbounded, as shown in Figure 2. During design calculations, it is essential to account for the properties and parameters of the ferrite, insulating, and winding materials—such as permeability, dielectric constant, electrical conductivity, and others—and then employ the boundary element method (BEM) in conjunction with PC‑based CAD/CAE software to determine the desired values.

3. Relationship Between Inductance and Frequency Characteristics
Figure 3 shows the experimental results of the inductance–frequency characteristics for a planar magnetic device with a helical winding structure. The characteristic curves presented in Figure 3 were obtained using an HP4285A precision LCR meter over a frequency range of 100 kHz to 1 MHz. Because the permeability of the core material decreases with increasing frequency, the inductance L likewise decreases as the frequency rises.

4 Relationship Between Voltage Ratio and Frequency Characteristics
The following discussion examines the relationship between the input–output voltage ratio and frequency under no-load conditions. Figure 4 shows the voltage ratios of an open‑circuit planar magnetic core structure, demonstrating that they exhibit a frequency‑dependent behavior. This behavior is similar to that observed in thin‑film microtransformers employing closed magnetic core structures. Tests also reveal that the voltage ratio of Type I transformers remains relatively stable, whereas Type II transformers display a peak at 5 MHz. At low frequencies, the magnetic coupling strength is quite weak; consequently, the voltage ratio does not equal the turns ratio, i.e., Nout/Nin ≠ Vout/Vin.

5 Magnetic Flux Distribution in the Transformer at a Frequency of 1 MHz
When designing the transformer, the author calculated the harmonic magnetic field distribution within the magnetic core and windings, revealing that substantial boundary‑layer components exist inside the transformer structure, particularly around the windings. Figure 5 shows the computed magnetic flux under the condition of excitation of the primary winding with the secondary winding open‑circuited. Numerical results from this structural analysis indicate that the flux distribution within the planar open‑circuit core differs from that in conventional core structures; this flux is generated by eddy currents induced in the secondary winding. Figure 5(a) depicts the flux distribution leaking out of the ferrite core; such leakage fields give rise to electromagnetic interference (EMI), which can pose numerous challenges in electronic device design. Figure 5(b) illustrates the situation where no leakage flux is present.

6 Eddy current distribution in the transformer at a frequency of 1 MHz
When transformers operate at high frequencies, eddy‑current losses represent a serious issue that affects both the windings and the magnetic core. Experimental results indicate that, in planar‑type core structures, the proximity effect often has a more pronounced impact than the skin effect; Figure 6 presents the outcomes of numerical simulations. In design calculations, the magnetizing current is applied to the primary winding, while the secondary winding is left open‑circuited. As shown in Figure 6, the winding configuration exerts a highly sensitive influence on the eddy‑current distribution.

7 Experimental Results and Problem Analysis
The paper presents experimental and computational results on the frequency characteristics, magnetic flux distribution, and eddy current distribution of two planar high-frequency transformers with air gaps. The primary winding is connected to a sinusoidal current source spanning 100 kHz to 1 MHz, while the secondary winding is left open-circuited. The disparity between the secondary-to-primary voltage ratio and the turns ratio indicates that magnetic coupling is quite weak. The computational findings demonstrate that, in the planar open‑circuit core configuration, the distributions of magnetic flux and eddy currents differ from those observed in conventional transformer magnetic circuits. These results were obtained using a CAD/CAE program based on the boundary element method.