时间调制阵列天线的非理想波形调制研究

罗玉川; 向磊; 高彦昌; 倪刚; 陈靖峰; 贺冲; 梁仙灵

doi:10.12265/j.cjors.2021148

时间调制阵列天线的非理想波形调制研究

doi: 10.12265/j.cjors.2021148

上海交通大学电子工程系，上海 200240

基金项目: 国家自然科学基金青年基金(61901263，62001291)

详细信息

作者简介:
罗玉川：（1997—），男，河南人，硕士研究生，主要研究方向为时间调制阵列天线、阵列波束形成

向磊：（1997—），男，江苏人，硕士研究生，主要研究方向为时间调制阵列天线

高彦昌：（1996—），男，山东人，博士研究生，主要研究方向为时间调制阵列、微带电路等

倪刚：（1996—），男，安徽人，博士研究生，主要研究方向为阵列信号处理和无线通信

陈靖峰：（1986—），男，江苏人，上海交通大学电子工程系博士后，工学博士，研究方向为阵列信号处理、无线电测向定位和电子对抗等

贺冲：（1985—），男，湖北人，上海交通大学电子工程系助理教授，工学博士，研究方向为阵列信号处理、相控阵技术和无线电测向与定位等

梁仙灵：（1978—），男，浙江人，上海交通大学教授，博士生导师，高速电子系统设计与电磁兼容研究教育部重点实验室副主任，IEEE高级会员，主要研究方向包括相控阵天线、多波束网络等，发表相关学术论文300多篇，其中IEEE期刊90余篇

通讯作者:
梁仙灵 E-mail：liangxl@sjtu.edu.cn

中图分类号: TN821.1
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出版历程
- 收稿日期: 2021-05-28
- 网络出版日期: 2021-08-25

Research on non-ideal waveform modulation of time modulation array antenna

Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

摘要

摘要: 针对时间调制阵列天线中射频开关的非理想特性，开展了多种波形调制下的谐波特性研究. 首先，推导了非对称梯形波/升余弦波周期调制的傅里叶系数，分析两种调制波的非对称性对各次谐波的幅度、相位和能量占比的影响；在此基础上，通过实验获得了一组实验调制波，并运用三角函数多项式拟合真实调制波形的上升沿与下降沿. 最后，讨论了各种波调制与实测谐波分量的差异性. 结果表明，与已有调制波相比，本文所提出的非对称梯形波、非对称升余弦波和拟合波的调制更接近真实波调制.
- 时间调制阵列(TMA) /
- 开关非理想特性 /
- 周期调制 /
- 傅里叶系数
Abstract: In this paper, aiming at the non-ideal characteristics of the radio frequency switch in the time-modulated array antenna, the harmonic characteristics of various modulation waveforms are studied. First, the Fourier coefficients of the asymmetric trapezoidal/raised cosine waveforms are deduced, and the influence on amplitude, phase and energy proportion of two waveforms are analyzed. On this basis, an experimental modulation waveform are obtained through experiments, and trigonometric polynomials are used to fit the rising and falling edges of the real modulation waveform. Finally, the difference between various waveforms and harmonics is discussed. The results show that compared with existing modulation waveforms, the modulations of the asymmetric trapezoidal waveform, asymmetric raised cosine waveform and the fitted waveform proposed in this paper are closer to real waveform.
- time modulated array (TMA) /
- nonideal characteristics of switches /
- periodic modulation /
- Fourier coefficients

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图 1 N元时间调制阵列

Fig. 1 N-element TMA

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图 2 两种非对称调制波波形

Fig. 2 Two kinds of asymmetric waveforms

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3 两种非对称调制波在t_off,n−t_on,n=T_p条件下谐波对应的傅里叶系数随δ和k的变化情况

3 Changes of corresponding Fourier coefficients with δ and k under t_off,n−t_on,n=T_p modulated by two asymmetric waveforms

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图 4 谐波能量占比随δ和k的变化情况

Fig. 4 Harmonics energy proportions changes with δ and k

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5 射频开关实验测试

5 Experimental test of RF switch

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表 1 上升沿曲线f₁(t)参数

Tab. 1 Parameters of rising curve f₁(t)

项数	a_l	b_l	c_l
l=1	3.329	28.94	−0.257
l=2	2.794	31.90	2.846
l=3	0.055	103.30	3.360

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表 2 下降沿曲线f₂(t)参数

Tab. 2 Parameters of falling curve f₂(t)

项数	a_l	b_l	c_l
l=1	0.602 8	10.59	8.118
l=2	0.525 8	26.97	13.860
l=3	0.094 0	84.72	9.813
l=4	0.020 0	164.90	23.090

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表 3 不同调制波形下的归一化谐波分量比较

Tab. 3 Comparison of normalized harmonic components under different modulation waveforms

调制波形			基波/dB	+1次谐波/dB	+2次谐波/dB	+3次谐波/dB	+4次谐波/dB	+5次谐波/dB
t_{off, n}−t_{on, n}=T_p	矩形^[8]	δ=0, ξ=T_p	0	N/A	N/A	N/A	N/A	N/A
	对称梯形^[8]	δ=0.1T_p k=1, ξ=0.8T_p	0	−19.37	−20.24	−21.74	−23.92	−26.93
	对称升余弦^[8]	δ=0.1T_p k=1, ξ=0.8T_p	0	−19.31	−20.00	−21.15	−22.83	−34.20
	非对称梯形	δ=0.1T_p k=1.2, ξ=0.78T_p	0	−18.51	−19.57	−21.40	−24.11	−27.89
	非对称升余弦	δ=0.1T_p k=1.2, ξ=0.78T_p	0	−18.43	−19.26	−20.68	−22.75	−35.90
t_{off, n}−t_{on, n}=0.5T_p	矩形^[8]	δ=0, ξ=0.5T_p	0	−3.90	−52.07	−17.60	−52.27	−25.32
	对称梯形^[8]	δ=0.1T_p k=1.2, ξ=0.28T_p	0	−4.32	−31.25	−15.00	−32.94	−21.91
	对称升余弦^[8]	δ=0.1T_p k=1.2, ξ=0.28T_p	0	−4.26	−31.02	−14.48	−31.96	−20.29
	非对称梯形	δ=0.1T_p k=1.2 ξ=0.28T_p	0	−3.94	−35.11	−14.94	−35.67	−22.60
	非对称升余弦		0	−3.87	−35.18	−14.23	−35.85	−20.35
	实验波形		0	−3.80	−27.28	−14.28	−27.72	−20.49
	拟合波形		0	−3.72	−30.97	−14.37	−30.19	−21.60

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