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 应用科技  2018, Vol. 45 Issue (5): 26-32  DOI: 10.11991/yykj.201803016 0

### 引用本文

ZHAO Yingsheng, LIU Changjun. REV-based fast phase optimization in a microwave power transmission system[J]. Applied Science and Technology, 2018, 45(5), 26-32. DOI: 10.11991/yykj.201803016.

### 文章历史

REV-based fast phase optimization in a microwave power transmission system
ZHAO Yingsheng, LIU Changjun
School of Electronics and Information Engineering, Sichuan University, Chengdu 610064, China
Abstract: A fast phase optimization method based on rotating element electric field vector (REV) for antenna array is presented to increase the transmission efficiency and the receiving power in a microwave power transmission (MPT) system. The proposed method is analyzed by electromagnetic simulation and verified through experiments on the basis of phased-array and MPT theory. It shows that in both Fresnel region and far field region, the proposed method can enhance receiving power of MPT effectively, and the maximum power improvement ratio reaches 179% at most. Additionally, the proposed method can greatly shorten the optimization time down to 3% of that by traditional methods. Therefore, the proposed method is feasible in MPT applications.
Keywords: microwave power transmission    REV    phase shift    fast optimization    transmission efficiency    receiving power    antenna calibration    LabWindows/CVI

REV法作为一种基于功率分析的天线阵列校准方法，非常适用于MPT领域的发射天线阵相位优化。本文研究了一种基于REV的相位优化方法，在保证传输效率有效提高的条件下，将优化时间降低至(2×N2+1)T。与传统方法相比，大幅度地缩短了发射天线阵元相位优化时间，且优化时间稳定。

1 旋转矢量法原理

 $\begin{array}{c}P = {E_0}^{\rm{2}} = {E_{\overline m }}^2 + {E_m}^{\rm{2}} + \\ 2{E_{\overline m }}{E_m}{\rm{cos}}\left( {{\varphi _{\overline m }} - {\varphi _m}{\rm{ + }}\Delta {\varphi _m}} \right)\end{array}$ (1)

 $\frac{{{E_m}}}{{{E_0}}}{{\rm{e}}^{{\rm{j}}({\varphi _m} - {\varphi _0})}} = \frac{{{E_m}{{\rm{e}}^{j{\varphi _m}}}}}{{{E_m}{{\rm{e}}^{j{\varphi _m}}} + {E_{\overline m }}{{\rm{e}}^{j{\varphi _{\overline m }}}}}} = \frac{{{E_m}}}{{{E_m} + {E_{\overline m }}{{\rm{e}}^{j\left( {{\varphi _{\overline m }} - {\varphi _m}} \right)}}}}\;\;\;\;\;$ (2)

 $\begin{split} {P_0} = & ({E_{\overline m }}{{\rm{e}}^{{\rm{j}}{\varphi _{\overline m }}}} + {E_m}{{\rm{e}}^{{\rm{j}}({\varphi _m} + 0)}}){({E_{\overline m }}{{\rm{e}}^{{\rm{j}}{\varphi _{\overline m }}}} + {E_m}{{\rm{e}}^{{\rm{j}}({\varphi _m} + 0)}})^*} = \\ & ({E_{\overline m }}^2 + {E_m}^2) + {E_{\overline m }}{E_m}{{\rm{e}}^{{\rm{j}}({\varphi _{\overline m }} - {\varphi _m})}} + {E_{\overline m }}{E_m}{{\rm{e}}^{{\rm{j}}({\varphi _m} - {\varphi _{\overline m }})}}\;\;\;\;\;\;\; \\ \end{split}$ (3)
 $\begin{split} {P_{{\rm{\pi }}/2}} = & ({E_{\overline {\rm{m}} }}{{\rm{e}}^{{\rm{j}}{\varphi _{\overline m }}}} + {E_m}{{\rm{e}}^{{\rm{j}}({\varphi _m} + {\rm{\pi }}/2)}}){({E_{\overline m }}{{\rm{e}}^{{\rm{j}}{\varphi _{\overline m }}}} + {E_m}{{\rm{e}}^{{\rm{j}}({\varphi _m} + {\rm{\pi }}/2)}})^*} = \\ & ({E_{\overline m }}^2 + E_m^2) + {E_{\overline m }}{E_m}{{\rm{e}}^{{\rm{j}}({\varphi _{\overline m }} - {\varphi _m})}}{{\rm{e}}^{ - {\rm{j\pi }}/2}} + {E_{\overline m }}{E_m}{{\rm{e}}^{{\rm{j}}({\varphi _m} - {\varphi _{\overline m }})}}{{\rm{e}}^{{\rm{j\pi }}/2}} \end{split}$ (4)
 $\begin{split} {P_{\rm{\pi }}} = & ({E_{\overline m }}{{\rm{e}}^{{\rm{j}}{\varphi _{\overline m }}}} + {E_m}{{\rm{e}}^{{\rm{j}}({\varphi _m} + {\rm{\pi }})}}){({E_{\overline m }}{{\rm{e}}^{{\rm{j}}{\varphi _{\overline m }}}} + {E_m}{{\rm{e}}^{{\rm{j}}({\varphi _m} + {\rm{\pi }})}})^*} = \\ & ({E_{\overline m }}^2 + {E_m}^2) + {E_{\overline m }}{E_m}{{\rm{e}}^{{\rm{j}}({\varphi _{\overline m }} - {\varphi _m})}}{{\rm{e}}^{ - {\rm{j\pi }}}} + {E_{\overline m }}{E_m}{{\rm{e}}^{{\rm{j}}({\varphi _m} - {\varphi _{\overline m }})}}{{\rm{e}}^{j{\rm{\pi }}}} \end{split}$ (5)
 ${{P}} = {\left( {\begin{array}{*{20}{c}} {{P_0}}&{{P_{{\rm{\pi }}/2}}}&{{P_{\rm{\pi }}}} \end{array}} \right)^{\rm{T}}}$ (6)
 ${{A}} = \left( {\begin{array}{*{20}{l}} 1& \;\;\; 1& \;\,\,\, 1 \\ 1& \;\! { - {\rm{j}}}& \;\;\; {\rm{j}} \\ 1&{ - 1}&{ - 1} \end{array}} \right)$ (7)
 $\begin{split} {{Z}} = & {\left[ {{z_1}\;{z_2}\;{z_3}} \right]^{\rm{T}}} = \\ & [\left( {{E_{\overline m }}^2 + {E_m}^2} \right)\;{E_{\overline m }}{E_m}{{\rm{e}}^{{\rm j}({\varphi _{\overline m }} - {\varphi _m})}}\;{E_{\overline m }}{E_m}{{\rm{e}}^{{\rm j}({\varphi _m} - {\varphi _{\overline m }})}}]\end{split}$ (8)
 ${{Z}} = {{{A}}^{{\rm{ - }}1}}{{P}}$ (9)

REV方法简便，但会引入求解的二义性，即存在2个解。文献[10]对目前国内外已提出的消除旋转矢量法解的二义性的方法进行了总结，并提出了一种新的解决方法。该消除方法在无线能量传输系统中并不适用。在实际的无线传输系统应用中，优化阵元相位时，可以实时测试得到接收端输出的功率值。本文提出消除二义性的方法为：将2个不同的解引入测试系统，通过测试实际的输出功率，优选输出功率高的解为正解。该方法结合了实验测量，在无线能量传输领域中，比常规的方法更快捷。

2 微波无线能量传输系统中的REV

 $\cot \theta = \frac{R}{L}$ (10)
 $G = \frac{{41 \; 253}}{{{\theta _{EP}}{\theta _{HP}}w}}$ (11)
 $\gamma = \frac{R}{L}{\rm{ = }} = \cot \left( {\sqrt {\frac{{41 \; 253}}{{Gw}}} /10} \right)$ (12)

 $\begin{split} \Delta {\phi _{kg\_ij\_ab}} = & \frac{{2{\rm{\pi }}}}{\lambda }\sqrt {{{\left[ {(k - i)d} \right]}^2} + {{\left[ {(g - j)d} \right]}^2} + {R^2}} - \\ & \frac{{2{\rm{\pi }}}}{\lambda }\sqrt {{{\left[ {(k - a)d} \right]}^2} + {{\left[ {(g - b)d} \right]}^2} + {R^2}}\end{split}$ (13)
 $\Delta {\phi _{kg\_ij\_ab}}{^\prime _a} = \frac{{2{\rm{\pi }}d(k - a)}}{{\lambda \sqrt {{{[(k - a)d]}^2} + {{[(g - b)d]}^2} + {R^2}} )}}\;\;\;\;\;$ (14)
 $\begin{split} {P_{{\rm{total}}}} = & \sum\limits_{i = - N}^N {\sum\limits_{j = - N}^N {{{\left| {{E_{ij\_{\rm{total}}}}{{\rm{e}}^{{\rm{j}}{\theta _{ij\_t{\rm{total}}}}}}} \right|}^2}} } = \\ & {\sum\limits_{i = - N}^N {\sum\limits_{j = - N}^N {\left| {\sum\limits_{k = - N}^N {\sum\limits_{g = - N}^N {{E_{kg\_ij}}} {{\rm{e}}^{{\rm{j}}{\theta _{kg\_ij}}}}} } \right|} } ^{\rm{2}}}\end{split}$ (15)
 $\begin{split}G(a) = & {P_{{\rm{total}}}}{\__{{\rm{REV}}}} = \\& \sum\limits_{i = - N}^N {\sum\limits_{j = - N}^N {\left\{ {{{\left| {\sum\limits_{k = - N}^N {\sum\limits_{g = - N}^N {{E_{kg\_ij}}} } {{\rm{e}}^{{\rm{j}}({\theta _{kg\_ij}} + ({\theta _{ab}} - {\theta _{kg\_ab}}))}}} \right|}^2}} \right\}} } {\rm{ = }}\\& \sum\limits_{i = - N}^N {\sum\limits_{j = - N}^N {\left\{ {{{\left| {\sum\limits_{k = - N}^N {\sum\limits_{g = - N}^N {{E_{kg\_ij}}} } {{\rm{e}}^{j(\Delta {\varphi _{kg\_ij\_ab}} + {\theta _{ab}})}}} \right|}^2}} \right\}} } {\rm{ = }}\\& \sum\limits_{i = - N}^N {\sum\limits_{j = - N}^N {\left\{ {{{\left| {\sum\limits_{k = - N}^N {\sum\limits_{g = - N}^N {{E_{kg\_ij}}} } {{\rm{e}}^{{\rm{j}}\Delta {\varphi _{kg\_ij\_ab}}}}} \right|}^2}} \right\}} } n\end{split}$ (16)
 $\begin{split} F(a) = & \frac{{\partial {\kern 1pt} G(a)}}{{\partial a}} = \\ & 2\sum\limits_{i = {\rm{ - }}N}^N {\sum\limits_{j = {\rm{ - }}N}^N {\{ \sum\limits_{k = - N}^N {\sum\limits_{g = - N}^N {[{E_{kg\_ij}}\Delta {\phi _{kg\_ij\_ab}}{{^\prime }_a}H(a)} } )} } ]\} \end{split}$ (17)
 $H(a) = \sum\limits_{k' = - N}^N {\sum\limits_{g' = - N}^N {{E_{k'g'\_ij}}\sin (\Delta {\phi _{k'g'\_ij\_ab}} - \Delta {\phi _{kg\_ij\_ab}})} } \;\;\;\;$ (18)
 $\eta = \frac{{{P_{{\rm{max}}}} - {P_{{\rm{min}}}}}}{{{P_{{\rm{min}}}}}} \times 100{\rm{\% }}$ (19)

3 仿真结果分析

3.1 REV在MPT中的有效性

3.2 不同校准位置对无线能量传输效率的影响

4 实验