UWB 天线的基本限制理论.docx

Fundamental-Limit Perspectives on Ultra-Wideband AntennasAbstract: The fundamental-limit theory for antenna size provides a theoretical limit to assist in the evaluation of antenna performance in terms of antenna size and fractional impedance bandwidth, as well as avoid searching for an antenna with unrealistic performance specifications. Previous research on the limit theory focused on electrically-small, resonant antennas. In this paper, we discuss how the classical fundamental-limit theory can be interpreted for ultra-wideband antennas. The frequency response of Chus equivalent circuit model for spherical TM modes suggests the concept of an ideal antenna. The ideal antenna has ultra-wideband antenna characteristics. The impulse response and cut-off frequency versus antenna size for various spherical TM modes are also presented.INTRODUCTIONSince Wheeler 1 first introduced the concept of fundamental-limit theory in 1947, many people have investigated the theoretical limitation of antenna performance versus size 26. In essence, the fundamental-limit theory for antennas shows that size, efficiency, and bandwidth are trade-offs in the design process. The previous research efforts on the limit theory focused on electrically-small, resonant antennas, even though the theory is not necessarily limited to electrically-small, resonant antennas. In addition, previous research emphasized radiation-Q as the performance evaluation factor. In this paper, we investigate how the classic fundamental-limit theory can be interpreted for ultra-wideband antennas.CONCEPT OF IDEAL ANTENNAThe radial wave impedance of spherical modes (normalized by the intrinsic wave impedance) can be written as the following 2: (1)Where the spherical Hankel function of the second kind and k is is the wave number. Chus equivalent circuit 2 for these spherical modes can be found from the normalized, radial wave impedance. In the same manner, the equivalent circuit model for TE cases can also be obtained. If we consider how much power is delivered to space(radiation), the Chus ladder circuit can be turned into a two-port problem as shown in Fig. 1b. In this case, the port 1 is antenna sphere circumscribing the antenna structure (see Fig. la). The radius of the antenna sphere is denoted by a. Port 2 is a considered to represent free space. Therefore, for the spherical mode can be written as (2)where. This form shows that for the fundamental spherical mode consists of an entire function and two complex poles. This represents what we refer to as an ideal antenna. The entire frequency response of the ideal antenna can be completely described with only two poles. The ideal antenna has a donut-shaped radiation pattern, with an omni-derectional pattern in the azimuth direction.CHARACTERISTICS OF THE RESPONSE AND HIGHER ORDER MODESObserving the basic structure of the ladder circuit representations, we see that they represent high-pass filters. In Fig.2, the pole-residue structures of and the corresponding bode plots are shown for various spherical TM modes. Basically, each mode shows the characteristic of a high-pass filter, as represented by the ladder network form. It is found that each mode has a cut-off frequency that increases with the mode order n. The product of the directivity (given in terms of the ( and performance of mode) and (representing the match process) for each spherical mode corresponds to the gain of the mode. The plot of the Fig. 2b dictates the gain variation versus frequency. Therefore, an antenna exciting a specific spherical mode will have relatively constant gain above the cut-off frequency. This also suggests that the ideal antenna has ultra-wideband characteristics.The poles offer additional insight into the performance of the antenna transmission. The mode is the simplest mode with only two poles and an entire function; is represented by the distance from the poles to the frequency of interest, plus the entire function. As the mode number (n) increases, the number of poles increases. For each mode, the poles with the largest real frequency dominate the response.SIZE LIMITATION OF UWB ANTENNASThe impulse responses of Chus equivalent circuits are shown in Fig. 3a for various spherical TM modes. The responses correspond to late-time performance of ultra-wideband antennas in the time domain. As the mode number increases, the peak amplitude increases and the pulse width becomes narrower. An increase in the size of antenna sphere (a) results in a wider pulse width. Since higher spherical modes have higher radiation-Q, the resulting late-time responses have some ringing. However, the ringing decays fast.The size of antenna sphere versus 3dB cut-off frequency for the various spherical TM modes is plotted in Fig. 3b. As the antenna size decreases or the excited mode number increases, it is found that the cut-off frequency increases. Below the cut-off frequency, the input impedance of the TM-mode antenna becomes capacitive and we need to consider wideband impedance matching. In practice, the wideband impedance match is not easily obtained and a narrow impedance bandwidth is the typical result. Loss may also be added to the antenna to obtain an acceptable in this frequency range, while compromising and the related energy transmission. On the other hand, above the cut-off frequency, it is more suitable to design an antenna as a simple ultra-wideband antenna. To obtain a wideband response from a practical antenna, a form of tapering from the feed terminals to antenna sphere is generally required.CONCLUSIONThe classical fundamental-limit theory on antenna size is interpreted in an ultra-wideband antenna perspective. The frequency response of Chus equivalent model for spherical TM modes suggests the concept of an ideal antenna, with the entire frequency response described by only two complex poles. It was shown that the ideal antenna has ultra-wideband characteristics. The size limitations of ultra-wideband antennas in terms of pulse width and 3dB cut-off frequency were developed. The 3dB cut-off frequency criterion can also be used to determine which antenna is more suitable in a frequency range of interest, either resonant or ultra-wideband antennas. The demonstrated concepts and approaches in this paper are not limited to spherical modes and can be generalized for and cases.UWB 天线的基本限制摘要：天线尺寸的基本限制理论为根据天线尺寸和分数阻抗带宽来评估天线性能，以及避免寻找不可实现性能参数的天线提供了一个理论限制。先前的限制理论研究集中于电小耦合天线。在这篇文章中，我们讨论了典型的基本限制理论如何应用于天线。的球形模式等效电路模型提出了理想天线的概念。这个理想天线拥有UWB天线的特性。文章也展示了各种球形TM模式的冲击响应和截止频率与天线尺寸的对比。 介绍自从Wheeler 1947年首次提出基本限制理论的概念后，很多人研究了基于天线性能与尺寸26的理论限制。本质上，天线的基本限制理论表明天线的尺寸，效率，带宽在设计中相互制约。先前的限制理论研究集中于电小耦合天线，尽管这个理论并不局限于电小耦合天线。另外，先前的研究认为品质因数Q 为性能评估的重要因素。本文中，我们研究了典型的基本限制理论如何应用于天线。理想天线的概念球形模式的径向波阻抗（通常用内部波阻抗表示）可以写成如下形式： （1） 式中， 是球形的第二类Hankel 函数，k 是波数。的球形模式的等效电路【2】可以从归一化径向波阻抗得出。同理，TE波的等效电路也可得到。如果我们考虑有多少功率辐射出去，Chu 的梯形电路可以转化为二阶问题，见表Fig. 1b。图中，Port 1 是包围天线结构的天线球（见Fig.1a.）。天线球的半径用a表示。Port 2 认为是代表自由空间。 Fig.1. (a)天线球体的定义 (b)Chu的二端口散射参数表示法的电路模型。梯形持续到元件标记改变为止。TE模存在双重阶梯。因此，表示从天线球输入辐射到空间的转移功率。例如，球形模式的可写为如下形式： (2)式中，。这种形式表明基本球形模式的存在一个整体函数和两个复极点。这就是我们所说的理想天线。理想天线的整个频率响应可以完全用两个极点来描述。理想天线有个环形的辐射方向图，方位角方向是全向方向图。响应特性和高次模从梯形电路的基本结构我们看到它们代表高通滤波器。在Fig.2中，绘出了各种球形TM模式的极点冗余结构和响应波特图。基本上，每种模式表示一种高通滤波器特性，如梯形网络结构所展示的那样。我们发现每种模式的截止频率随着阶数n 的增加而升高。每种球形模式的方向性（用该模式的和表示）和（代表匹配程度）与它的增益相符合。Fig.2b的曲线表明增益随频率的变化规律。因此，特定球形模式激励下的天线在截止频率以上增益相对恒定。这也表明理想天线的超宽频特性。极点提供了对天线传播性能的另外见解。模只有两个极点和一个整体函数，是最简单的模式；代表从极点到感兴趣的频率的距离，加上整个函数。随着阶数（n）的增加，极点数随着增加。对每种模式，实频率最大的极点主导响应特性。UWB天线的尺寸限制对于各种球形TM模的Chu式等效电路的冲击响应见Fig.3a。此响应和时域超宽频天线的后期性能相符合。随着模数n的增加，峰值幅度增加，脉冲宽度变窄。天线球（a）尺寸的增加将引起冲击宽度变宽。因为高阶球形模式的品质因数Q更高，引起后期响应出现震荡。然而，震荡很快凋落。各种球形TM模的天线球尺寸和3dB截止频率的关系见Fig.3b。随着天线尺寸的减小或者激励模数的增加，我们发现截止频率增加。低于截止频率时，TM模天线的输入阻抗呈容性，我们需要考虑宽带阻抗匹配。实际上，宽带阻抗匹配不易获得，典型结果是窄的阻抗带宽。在此频率范围内，设计天线的时也需考虑损耗，。另一方面，频率高于截止频率时，将天线设计为简单的超宽带天线更合适。为了获得实际天线的宽带响应，一般需要在馈源到天线球加上一种尖端。结论天线尺寸的经典基础限制理论应用于超宽带天线方面。各种球形TM模的Chu式等效电路的频率响应提出了理想天线的概念，它的整个频率响应仅用两个复极点就可描述。以上表明理想天线有超宽带特性。根据冲击宽度和3dB截止频率，讨论了超宽带天线的尺寸限制。3dB截止频率标准也可应用于决定那种天