# Near-Field Coupling Effect Analysis of SMD Inductor Using 3D-EM Model

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## Abstract

**:**

## 1. Introduction

## 2. Equivalent Circuit Model of SMD Inductor from Impedance Measurement

#### 2.1. Impedance Measurement of Wire-Wound Inductor

#### 2.2. Equivalent Circuit Analysis

## 3. 3D-EM Model of SMD Inductor

#### 3.1. Inner Structure Acquisition to Produce 3D-EM Model

#### 3.2. Permeability Estimation in the Low Frequency Region

#### 3.3. The Damped Harmonic Oscillator

- The complex permeability formula from damped harmonic oscillator model is set as in (11), and the three unknown variables need to be determined.
- Another loss tangent from the impedance of circuit model in (13) should be calculated, and the two loss tangents are compared to be equal, for finding the three unknowns using optimization algorithm.

#### 3.4. Optimization Process

- (1)
- In Figure 6, where the impedance of the inductor was the parameter to be compared, ${\mu}_{r}^{\prime}=20,{\mu}_{r}^{\u2033}=0,{\epsilon}_{r}=12$ and $\sigma =0.01$ in the magnetic material seems valid in EM model up to 100 MHz. However, since ${\mu}_{r}^{\u2033}$ starts rising from ~1 MHz as in Figure 7, the parameters of ${\mu}_{r}^{\prime}=20\mathrm{and}{\mu}_{r}^{\u2033}=0$ could be valid only up to 1 MHz.
- (2)
- Loss tangent, $\mathrm{tan}{\delta}_{circuit}$, came from experiment, which means that $\mathrm{tan}{\delta}_{circuit}$ includes the loss in the air as well as the loss in the magnetic material. However, noting that loss tangent in the air is null, it is reasonable to say that $\mathrm{tan}{\delta}_{circuit}$ mainly represents the loss tangent of magnetic material in the SMD inductor. Then, we compared the two loss tangents in (12) and (13) for the estimation of ${\mu}_{r}^{\prime}\mathrm{and}{\mu}_{r}^{\u2033}$. So, the increase of ${\mu}_{r}^{\u2033}$ could be mainly due to the core loss in the magnetic material above 1 MHz in Figure 7b.
- (3)
- Since ${\mu}_{r}^{\prime}\mathrm{and}{\mu}_{r}^{\u2033}$ were derived by the comparison of two loss tangents, not by comparison of the ${\mu}_{r}^{\prime}\mathrm{and}{\mu}_{r}^{\u2033}$ data, it would be instructive to check the magnetic field distribution around the SMD inductor. Figure 8 shows cross sectional view of the magnetic field distribution around SMD inductor at 100, 200 and 300 MHz, respectively, using 3D-EM model. One can see that most of the magnetic fields is restricted inside the core material of the inductor for the three cases.

## 4. Tuning of Other Electrical Properties

#### 4.1. Permittivity Tuning

#### 4.2. Conductivity Tuning

## 5. Near Field Coupling Analysis

#### 5.1. Validation of SMD Inductor 3D-EM Model

#### 5.2. Coupling Path Visualization

## 6. Conclusions

- (1)
- The inductance formula of SMD inductor is not available in an analytic form, so we measured experimental impedance, which was used to develop a circuit model. So the loss tangent of the magnetic material of SMD inductor was effectively defined using the circuit parameters in the developed circuit model.
- (2)
- The damped harmonic oscillator model, a well-known model that satisfies the Kramers-Kronig relationship, was introduced for comparison with the circuit parameters in terms of loss tangent.
- (3)
- The two loss tangents, one from the circuit model and the other from damped harmonic oscillator model were compared to extract the complex permeability of SMD magnetic material.
- (4)
- The P2SO optimization method, which was developed based on the PSO algorithm, to avoid a local minimum and the complex permeability was efficiently applied to find the optimized permeability values, which turned out to be valid.

_{21}) and impedance were calculated, and compared with the measured ones.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**(

**a**) A picture and (

**b**) an equivalent circuit model of 2-port shunt measurement for SMD inductor.

**Figure 7.**(

**a**) Comparison of the two loss tangents, and (

**b**) Extracted inductive and resistive permeabilities.

**Figure 12.**Illustration of (

**a**) forward situation and (

**b**) reverse situation of coupling path visualization techniques.

**Figure 13.**CC vector plot (

**a**) bird’s-eye view (

**b**) front view at 100 MHz and (

**c**) bird’s-eye view (

**d**) front view at 300 MHz.

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**MDPI and ACS Style**

Choi, G.R.; Kim, H.; Hong, Y.; Hwang, J.; Kim, E.; Nah, W.
Near-Field Coupling Effect Analysis of SMD Inductor Using 3D-EM Model. *Electronics* **2023**, *12*, 2845.
https://doi.org/10.3390/electronics12132845

**AMA Style**

Choi GR, Kim H, Hong Y, Hwang J, Kim E, Nah W.
Near-Field Coupling Effect Analysis of SMD Inductor Using 3D-EM Model. *Electronics*. 2023; 12(13):2845.
https://doi.org/10.3390/electronics12132845

**Chicago/Turabian Style**

Choi, Gyeong Ryun, HyongJoo Kim, Yonggi Hong, Joosung Hwang, Euihyuk Kim, and Wansoo Nah.
2023. "Near-Field Coupling Effect Analysis of SMD Inductor Using 3D-EM Model" *Electronics* 12, no. 13: 2845.
https://doi.org/10.3390/electronics12132845