UWB 天線的基本限制理論.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 天線的基本限制摘要：天線尺寸的基本限制理論為根據(jù)天線尺寸和分?jǐn)?shù)阻抗帶寬來評估天線性能，以及避免尋找不可實現(xiàn)性能參數(shù)的天線提供了一個理論限制。先前的限制理論研究集中于電小耦合天線。在這篇文章中，我們討論了典型的基本限制理論如何應(yīng)用于天線。的球形模式等效電路模型提出了理想天線的概念。這個理想天線擁有UWB天線的特性。文章也展示了各種球形TM模式的沖擊響應(yīng)和截止頻率與天線尺寸的對比。 介紹自從Wheeler 1947年首次提出基本限制理論的概念后，很多人研究了基于天線性能與尺寸26的理論限制。本質(zhì)上，天線的基本限制理論表明天線的尺寸，效率，帶寬在設(shè)計中相互制約。先前的限制理論研究集中于電小耦合天線，盡管這個理論并不局限于電小耦合天線。另外，先前的研究認(rèn)為品質(zhì)因數(shù)Q 為性能評估的重要因素。本文中，我們研究了典型的基本限制理論如何應(yīng)用于天線。理想天線的概念球形模式的徑向波阻抗（通常用內(nèi)部波阻抗表示）可以寫成如下形式： （1） 式中， 是球形的第二類Hankel 函數(shù)，k 是波數(shù)。的球形模式的等效電路【2】可以從歸一化徑向波阻抗得出。同理，TE波的等效電路也可得到。如果我們考慮有多少功率輻射出去，Chu 的梯形電路可以轉(zhuǎn)化為二階問題，見表Fig. 1b。圖中，Port 1 是包圍天線結(jié)構(gòu)的天線球（見Fig.1a.）。天線球的半徑用a表示。Port 2 認(rèn)為是代表自由空間。 Fig.1. (a)天線球體的定義 (b)Chu的二端口散射參數(shù)表示法的電路模型。梯形持續(xù)到元件標(biāo)記改變?yōu)橹?。TE模存在雙重階梯。因此，表示從天線球輸入輻射到空間的轉(zhuǎn)移功率。例如，球形模式的可寫為如下形式： (2)式中，。這種形式表明基本球形模式的存在一個整體函數(shù)和兩個復(fù)極點。這就是我們所說的理想天線。理想天線的整個頻率響應(yīng)可以完全用兩個極點來描述。理想天線有個環(huán)形的輻射方向圖，方位角方向是全向方向圖。響應(yīng)特性和高次模從梯形電路的基本結(jié)構(gòu)我們看到它們代表高通濾波器。在Fig.2中，繪出了各種球形TM模式的極點冗余結(jié)構(gòu)和響應(yīng)波特圖?；旧?，每種模式表示一種高通濾波器特性，如梯形網(wǎng)絡(luò)結(jié)構(gòu)所展示的那樣。我們發(fā)現(xiàn)每種模式的截止頻率隨著階數(shù)n 的增加而升高。每種球形模式的方向性（用該模式的和表示）和（代表匹配程度）與它的增益相符合。Fig.2b的曲線表明增益隨頻率的變化規(guī)律。因此，特定球形模式激勵下的天線在截止頻率以上增益相對恒定。這也表明理想天線的超寬頻特性。極點提供了對天線傳播性能的另外見解。模只有兩個極點和一個整體函數(shù)，是最簡單的模式；代表從極點到感興趣的頻率的距離，加上整個函數(shù)。隨著階數(shù)（n）的增加，極點數(shù)隨著增加。對每種模式，實頻率最大的極點主導(dǎo)響應(yīng)特性。UWB天線的尺寸限制對于各種球形TM模的Chu式等效電路的沖擊響應(yīng)見Fig.3a。此響應(yīng)和時域超寬頻天線的后期性能相符合。隨著模數(shù)n的增加，峰值幅度增加，脈沖寬度變窄。天線球（a）尺寸的增加將引起沖擊寬度變寬。因為高階球形模式的品質(zhì)因數(shù)Q更高，引起后期響應(yīng)出現(xiàn)震蕩。然而，震蕩很快凋落。各種球形TM模的天線球尺寸和3dB截止頻率的關(guān)系見Fig.3b。隨著天線尺寸的減小或者激勵模數(shù)的增加，我們發(fā)現(xiàn)截止頻率增加。低于截止頻率時，TM模天線的輸入阻抗呈容性，我們需要考慮寬帶阻抗匹配。實際上，寬帶阻抗匹配不易獲得，典型結(jié)果是窄的阻抗帶寬。在此頻率范圍內(nèi)，設(shè)計天線的時也需考慮損耗，。另一方面，頻率高于截止頻率時，將天線設(shè)計為簡單的超寬帶天線更合適。為了獲得實際天線的寬帶響應(yīng)，一般需要在饋源到天線球加上一種尖端。結(jié)論天線尺寸的經(jīng)典基礎(chǔ)限制理論應(yīng)用于超寬帶天線方面。各種球形TM模的Chu式等效電路的頻率響應(yīng)提出了理想天線的概念，它的整個頻率響應(yīng)僅用兩個復(fù)極點就可描述。以上表明理想天線有超寬帶特性。根據(jù)沖擊寬度和3dB截止頻率，討論了超寬帶天線的尺寸限制。3dB截止頻率標(biāo)準(zhǔn)也可應(yīng)用于決定那種天