﻿ 磁耦合谐振式无线电能传输天线仿真设计
 舰船科学技术  2019, Vol. 41 Issue (1): 129-132 PDF

Simulation and design of antenna based on magnetic coupling resonant radio energy transmission
XIA Jun, LI Yuan-jiang, TIAN Yu-bo
School of Electronics and Information, Jiangsu University of Science and Technology, Zhenjiang 212003, China
Abstract: Magnetic coupling resonant radio energy transmission system has many advantages, such as high transmission efficiency, long transmission distance and high transmission power, which attract researchers at home and abroad. As the core part of the system, the antenna has a direct impact on the transmission efficiency. Using HFSS software to simulate and design 6 sets of antenna model, the helix radius of the antenna is between 50 mm and 100 mm. The frequency splitting phenomenon of transmitting and receiving antennas in the process of energy transmission is analyzed. The matching between transmitting and receiving antennas is achieved by adjusting the capacitor’s value. Thus, the transmission efficiency of the original resonant frequency point is improved. The relationship between the transmission efficiency and the radius of the antenna is analyzed.
Key words: radio energy transmission     antenna     transmission efficiency
0 引　言

1 耦合模型理论

1.1 耦合模基本理论

 $\frac{{{\rm d}{a_m}(t)}}{{{\rm d}t}} = (j{\omega _m} - {\Gamma _m}){a_m}(t) + \sum j{k_{mn}}{a_n}(t) + {S_m}(t)\text{。}$ (1)

1.2 磁耦合谐振式无线电能传输耦合模理论分析

 图 1 磁耦合谐振式无线电能传输原理框图 Fig. 1 Flow chart of magnetic coupling resonant radio energy transmission

 图 2 磁耦合谐振式无线电能传输系统等效电路图 Fig. 2 Flow chart of magnetic coupling resonant radio energy transmission system equivalent circuit
 \left\{ \begin{aligned} & \frac{{{\rm d}{a_1}}}{{{\rm d}t}} = - (j{\omega _1} + {\Gamma _1}){a_1} + j{k_{12}}{a_1} + s \text{，} \\ & \frac{{{\rm d}{a_2}}}{{{\rm d}t}} = - (j{\omega _2} + {\Gamma _2} + {\Gamma _L}){a_2} + j{k_{21}}{a_2} \text{。} \end{aligned} \right. (2)

 $\frac{{{\rm d}{W_1}}}{{{\rm d}t}} + \frac{{{\rm d}{W_2}}}{{{\rm d}t}} = 0\text{。}$ (3)

 $\begin{split} & \frac{{{\rm d}{W_1}}}{{{\rm d}t}} = \frac{{{\rm d}{{\left| {{a_{1 \pm }}} \right|}^2}}}{{{\rm d}t}} = j{k_{12}}({a_{2 + }}{a_{1 - }} - {a_{1 + }}{a_{2 - }})-\\ & 2{\Gamma _1}{\left| {{a_{1 \pm }}} \right|^2} + s({a_ + } + {a_ - }) \text{，} \end{split}$ (4)

 $\begin{split} & \frac{{{\rm d}{W_2}}}{{{\rm d}t}} = \frac{{{\rm d}{{\left| {{a_{2 \pm }}} \right|}^2}}}{{{\rm d}t}}=\\ & j{k_{21}}({a_{1 + }}{a_{2 - }} - {a_{1 - }}{a_{2 + }}) - 2({\Gamma _2} + {\Gamma _L}){\left| {{a_{2 \pm }}} \right|^2}\text{。} \end{split}$ (5)

${\omega _1} = {\omega _2}$ 时， $j{k_{12}}({a_{2 + }}{a_{1 - }} - {a_{1 + }}{a_{2 - }})$ = 0， $s({a_ + } + {a_ - })$ 为激励源注入发射天线中的功率， $2{\Gamma _1}{\left| {{a_1}} \right|^2},2{\Gamma _2}{\left| {{a_2}} \right|^2}$ $2{\Gamma _L}{\left| {{a_2}} \right|^2}$ 分别表示发射天线、接收天线和负载RL的损耗功率。设定S对系统的输入功率为P，结合式（3）～式（5）可以得出下式：

 \begin{aligned}{l} P = s({a_{1 + }} + {a_{1 - }}) = 2{\Gamma _1}{\left| {{a_{1 \pm }}} \right|^2} + 2({\Gamma _2} + {\Gamma _L}){\left| {{a_{2 \pm }}} \right|^2} = \\ 2{\Gamma _1}{W_1} + 2({\Gamma _2} + {\Gamma _L}){W_2}\text{，}\;\;\;\quad\quad\quad\quad\quad\quad\quad\quad\quad \end{aligned} (6)

 ${P_L} = 2{\Gamma _L}{W_2}\text{，}$ (7)

 $\eta = \frac{{{P_L}}}{P} = \frac{{{\Gamma _L}{W_2}}}{{{\Gamma _1}{W_1} + ({\Gamma _2} + {\Gamma _L}){W_2}}}\text{，}$ (8)

 $\eta = \frac{{{R_L}{L_1}{W_2}}}{{{R_1}{L_2}{W_1} + ({R_1} + {R_L}){L_1}{W_2}}}\text{。}$ (9)

2 天线仿真设计

 图 3 HFSS仿真模型图 Fig. 3 Flow chart of simulation model based on HFSS
2.1 频率分裂现象

 图 4 电容85 pF时天线的S21参数 Fig. 4 The S21 parameters of the antenna when the capacitor’s value is 85 pF

2.2 调节电容值

 图 5 电容90 pF时天线的S21参数 Fig. 5 The S21 parameters of the antenna when the capacitor′s value is 90 pF
2.3 天线传输效率与螺旋半径关系

3 结　语

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