# Inductive Power Transmission for Wearable Textile Heater using Series-None Topology

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## Abstract

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## 1. Introduction

_{DD}, which implies the alleviation of voltage stress on the PA. Moreover, the SN structure has inherent advantages in terms of wireless efficiency and safety, because the overall system, including the Tx coil, only resonates when the textile Rx coil is properly coupled to the Tx, unlike in a conventional structure.

## 2. System Modeling

#### 2.1. Circuit Analysis of SS and SN modes

_{T}, C

_{T}, and L

_{T}, where L

_{T}is the inductance of the transmitter (Tx) coil, C

_{T}is a resonant capacitor of Tx, and R

_{T}is the combination of the parasitic resistance of the Tx coil, equivalent series resistance (ESR) of C

_{T}, and the output resistance of PA, represented in V

_{S}. The Rx was composed of R

_{L}, R

_{R}, C

_{R}, and L

_{R}, where L

_{R}is the inductance of the Rx coil, C

_{R}is a resonant capacitor of Rx, R

_{R}is a sum of the parasitic resistance and ESR of C

_{R}, and R

_{L}is load resistance [16].

_{T}and R

_{reflext,SS}, resulting in η

_{T,SS}, given by

_{R}and R

_{L}, resulting in Rx efficiency η

_{R}, given by

_{R}= ωL

_{R}/R

_{R}, which is the Q factor of the Rx coil. Consequently, the total efficiency of the SS mode can be calculated by the multiplication of η

_{T,SS}and η

_{R}:

_{2,pk}and V

_{s,pk}are the peak current of the SS mode and peak source voltage, respectively. The input power of SS mode is obtained by

_{in,SS}and η

_{SS}:

_{reflect}can be compensated by a single capacitor at Tx, C

_{single}, and it is defined as

_{single}when the Rx coil is properly coupled with the Tx coil. This is advantageous in terms of wireless power efficiency and safety compared to the conventional structure. Since L

_{T}does not directly resonate with C

_{single}, Tx power consumption without the Rx coil is automatically reduced.

_{single}in SN mode, there was only reflected resistance R

_{reflect,SN}remaining, as shown in Figure 2d, which can be defined as

_{PTE}and n

_{PDL}, to show the effectiveness of SN mode in a textile coil compared to the conventional SS mode:

_{PTE}or n

_{PDL}is close to 1, SN mode showed high PTE or PDL, the same as that in conventional SS mode, which means that SN mode could replace SS mode without an additional resonant capacitor in Rx. On the other hand, a small n

_{PTE}or n

_{PDL}implied that SN mode showed relatively lower achievable PTE or PDL compared to SS mode in the given wireless power conditions.

#### 2.2. PTE and PDL Properties in SS and SN Modes

_{T}and ${Q}_{R}^{\prime}$. Q

_{T}is the effective Q factor of the Tx, including PA output resistance, 0.45 Ω. When the R

_{L}was much larger than R

_{R}, Rx efficiency η

_{R}was close to 1. In the proposed wearable heater using the textile coil, R

_{R}could be considered as zero because the parasitic resistance of the Rx coil is regarded as the load resistance, resulting in the η

_{R}≈ 1. As shown in Figure 3a, η

_{SS}increased when both Q

_{T}and ${Q}_{R}^{\prime}$ increased. However, η

_{SN}was maximized at the optimal ${Q}_{R}^{\prime}$, which could be found from differentiating Equation (12), while higher Q

_{T}was still desirable for the SN mode in Figure 3b. The achievable PTE ratio between SS and SN modes, n

_{PTE}, is shown in Figure 3c, and it was used to find the design consideration of Tx and Rx coils in SN mode. When n

_{PTE}was close to 1, it was beneficial to use SN mode instead of SS mode in the given inductive link considering the burden of the additional resonant capacitor in the Rx in SS mode.

_{reflect}is not desirable for a large PDL, while it is beneficial for PTE, based on circuit theory. However, SN mode showed a higher PDL in a wide range of ${Q}_{R}^{\prime}$ compared to SS mode, as shown in Figure 4b, due to (1 + ${Q}_{R}^{\prime}{}^{2}$) terms in Equation (15) compared to Equation (7). Therefore, the PDL ratio between SN and SS modes n

_{PDL}could be increased by up to ~60 as ${Q}_{R}^{\prime}$ increased, as shown in Figure 4c. Considering Figure 3c and Figure 4c, we could optimize the textile coil for a wearable heater in SN mode with improved PDL and less PTE loss compared to the conventional SS mode.

#### 2.3. Coil Design for Wearable Textile Heater

_{T}is always desirable to achieve better PDL and PTE for fixed PA output resistance. Therefore, the Tx coil was designed to have maximal quality (Q) factor in the experiment conditions considering practical limitations. The Tx coil was designed using 22 American Wire Gauge (AWG) with a 0.3 mm pitch, with a sweep of frequencies and number of turns performed with an electromagnetic (EM) simulator (FEKO, Altair) and measurement, while the lumped-model circuit simulation was performed with LTSpice (Analog Devices). A Tx coil quality factor of 238 without PA output resistance (Q

_{T}= 153.4 including PA) was achieved at N

_{T}= 8 at 2 MHz carrier frequency, as shown in Figure 5a. From the calculated result from Figure 3c and Figure 4c, ${Q}_{R}^{\prime}$ = 1 was selected considering optimal PTE loss (large nPTE) and improved PDL (large nPDL) in the textile coil. When ${Q}_{R}^{\prime}$ = 1, the PTE loss from the conventional SS structure was only 10%, while PDL was improved by 176%, as shown in Figure 5b. Although the figure of merit (FoM) between PDL and PTE could be one of clear standards as described in [17], the design balance between PDL and PTE is still flexible for the design purpose and applications. The Rx coil was designed using conductive thread with a 0.25 mm pitch at 2 MHz carrier frequency. The washable conductive thread (ELITEX

^{®}, Art. 110/f34_PA/Ag) had basic 110 dtex/34 filaments yarn counts with a silver coating of 1 μm thickness that showed 70 ± 20 Ω/m at DC and had a 259 °C melting point based on the datasheet. The number of turns of Rx coil N

_{R}was swept to find the optimal condition of ${Q}_{R}^{\prime}$ = 1. As shown in Figure 5c, N

_{R}= 7 showed the nearest value to 1. The coil parameters for Tx and Rx are summarized on Table 1. The coil parameters in Table 1 show one of the exemplar designs for the wireless wearable heater for t-shirts. While the outer diameters or thickness of coils could differ by geometrical limitations in practical applications such as gloves, socks, or t-shirts, the optimization procedure is the same as that of the SN topology.

## 3. Experiment Results

_{DD}for the temperature controls in the wearable textile heater. The coupling coefficient of the proposed inductive link was 0.24 at 4 cm distance with Q

_{T}= 153.4, including PA output resistance and ${Q}_{R}^{\prime}$ = 1.1 as shown in Table 2. All parameters and variables were acquired by the network analyzer (ZND, Rohde and Schwarz) in the experiment.

_{DD}. Temperature was measured by thermal imaging camera, and was controlled by the input PA power and increased up to 42.5 °C from room temperature when the PA provided the output power of 5 W. For individual PA powers, temperature in the wearable textile heater reached the target temperature within 1 min.

_{reflect}and L

_{T}resonated with C

_{single}at 2 MHz carrier frequency from the PA, as shown in Figure 2d. Therefore, the entire inductive link from the Tx to the Rx resonated in-phase between input voltage and current because the real parts of the inductive link remained, and the temperature in the wearable textile heater increased up to 42.5 °C from room temperature, as shown in Figure 8a. The PA did not automatically deliver the inductive power to the wearable textile heater when the Rx coil moved farther from the Tx coil. In this case, the imaginary parts of Z

_{reflect}were reduced compared to the nominal condition, and the resonant frequency of the Tx moved farther from the 2 MHz carrier frequency, resulting in an almost 90° phase shift between input voltage and current waveforms, shown in Figure 8b. Therefore, the temperature of the wearable textile heater stayed at room temperature, and the energy was rarely dissipated in this condition.

_{T}. While the measured PTE of the proposed SN mode was reduced by 11%, it showed a 1.6 times higher PDL on average compared to the SS mode without the compensated capacitor in the Rx coil, which showed similar trends in the calculated results. The derived equations proved reliability by showing that the error rate was within 10% between calculated and measured results. The error rates of η

_{SS}, η

_{SN}, and n

_{PDL}were 2.97%, 6.23%, and 10%, respectively. The measured PDLs and the temperatures of the wearable textile heater for SS and SN modes are shown in Figure 9 with respect to controllable PA supply voltage V

_{DD}.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Simplified conceptual representation of proposed wearable heater using inductive power transmission with textile coil.

**Figure 2.**(

**a**) Circuit model of series-series (SS) topology, (

**b**) simplified equivalent SS circuit model, (

**c**) circuit model of proposed series-none (SN) topology, and (

**d**) equivalent SN circuit model using textile coil.

**Figure 3.**Calculated PTEs of (

**a**) SS mode, η

_{SS}, (

**b**) SN mode, η

_{SN}, and (

**c**) PTE ratio of SS and SN modes, n

_{PTE}, as function of Q

_{T}and ${Q}_{R}^{\prime}$ for k = 0.24 and R

_{R}= 0 Ω.

**Figure 4.**Calculated PDLs of (

**a**) SS mode, P

_{out,SS}, (

**b**) SN mode, P

_{out,SN}and (

**c**) PDL ratio of SS and SN modes, n

_{PDL}, as a function of function of Q

_{T}and ${Q}_{R}^{\prime}$ for k = 0.24, R

_{R}= 0 Ω, and V

_{s,pk}= 5 V.

**Figure 5.**(

**a**) Measured Q factor of wire-wound Tx coil for 200 kHz, 2 MHz, and 6.78 MHz carrier frequencies without power-amplifier (PA) output resistance; (

**b**) ${Q}_{R}^{\prime}$ optimization for designated Q

_{T}considering n

_{PDL}and n

_{PTE}; and (

**c**) resulting Q factor of conductive-thread textile Rx coil vs. number of turns at 2 MHz carrier frequency.

**Figure 6.**Experiment setup of optimized wire-wound Tx coil and conductive-thread textile Rx coil with power amplifier.

**Figure 8.**Transient waveforms of input voltage and current with temperature in wearable textile heater for (

**a**) aligned and (

**b**) misaligned Tx and Rx coils.

**Figure 9.**Measured (

**a**) power delivered to load (PDL) and (

**b**) temperature of wearable textile heater for SS and SN modes with respect to controllable PA supply voltage V

_{DD}.

Tx/Rx Coil | Parameters | |||||||
---|---|---|---|---|---|---|---|---|

Material | Outer Diameter | Thickness | Pitch (mm) | Turn | Parasitic Res. | Ind. (μH) | Q | |

Tx coil | Copper | 16 cm | 22 AWG | 0.3 | 8 | 0.82 Ω | 15.5 | 238 |

Rx coil | Coated Textile | 16 cm | 1 μm ^{1} | 0.25 | 7 | 214.3 Ω | 18.3 | 1.1 |

^{1}Thickness of silver layer, 70 ± 20 Ω/m at DC.

Fixed Parameters | Topology | |||
---|---|---|---|---|

k | ${Q}_{T}$ | ${Q}_{R}^{\prime}$ | Series-Series (SS) | Series-None (SN) |

0.24 | 153.37 | 1.07 | ||

Calculated PTE | 90.7% | 81.8% | ||

Measured PTE | 88% | 77% | ||

Calculated ${n}_{PDL}$ | 1.76 | |||

Measured ${n}_{PDL}$ | 1.6 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Kwon, H.; Lee, K.-H.; Lee, B. Inductive Power Transmission for Wearable Textile Heater using Series-None Topology. *Electronics* **2020**, *9*, 431.
https://doi.org/10.3390/electronics9030431

**AMA Style**

Kwon H, Lee K-H, Lee B. Inductive Power Transmission for Wearable Textile Heater using Series-None Topology. *Electronics*. 2020; 9(3):431.
https://doi.org/10.3390/electronics9030431

**Chicago/Turabian Style**

Kwon, Hyeokjin, Kang-Ho Lee, and Byunghun Lee. 2020. "Inductive Power Transmission for Wearable Textile Heater using Series-None Topology" *Electronics* 9, no. 3: 431.
https://doi.org/10.3390/electronics9030431