英文文獻科技類（天線的性能）原文及翻譯

1、目 錄 TOC o 1-3 h z u HYPERLINK l _Toc169540757 1 天線的性能 PAGEREF _Toc169540757 h 1 HYPERLINK l _Toc169540758 天線輻射2 HYPERLINK l _Toc169540761 增益3 HYPERLINK l _Toc169540765 有效面積6 HYPERLINK l _Toc169540765 路徑損耗6 HYPERLINK l _Toc169540765 雷達距離方程和截面8 HYPERLINK l _Toc169540765 為什么要使用一個天線？10 HYPERLINK l _Toc1

2、69540766 2 PROPERTIES OF ANTENNAS11 HYPERLINK l _Toc169540767 ANTENNA RADIATION12 HYPERLINK l _Toc169540768 HYPERLINK l _Toc169540769 2.2 GAIN14 HYPERLINK l _Toc169540768 HYPERLINK l _Toc169540769 2.3 EFFECTIVE AREA17 HYPERLINK l _Toc169540768 HYPERLINK l _Toc169540769 2.4 PATH LOSS17 HYPERLINK l _T

3、oc169540768 HYPERLINK l _Toc169540769 2.5 RADAR RANGE EQUATION AND CROSS SECTION19 HYPERLINK l _Toc169540768 HYPERLINK l _Toc169540769 2.6 WHY USE AN ANTENNA?221 天線的性能一個方法是一本有關天線的書是從討論天線如何輻射開始的。從麥克斯韋方程組，我們得出了電磁波。之后，進行冗長的討論，其中包含了很多數(shù)學，我們在討論這些波如何在導體上激發(fā)電流。這個情節(jié)的下半局部，就是電流的輻射和產生的電磁波。你可能已經研究過這個問題，或如果你想增進你的閱

4、歷，參考在電磁學方面的書籍。研究電磁學就有了一些數(shù)學方面的見識來描述天線的輻射，并提供嚴謹，以防止錯誤。我們跳過討論這些方程，直接轉到實際的問題。這是很重要的認識到，天線在電流中產生輻射。設計構成的控制電流產生預期的輻射分布，其所謂的方向圖。在許多情況下，問題是如何防止電流中的輻射，如在集成電路。每當一電流變?yōu)樵诰嚯x上從其返回電流中分隔，它發(fā)熱著。簡單地說，我們的設計就是為了保持兩個電流靠近在一起，以減少輻射。一些討論會忽略電流的分布，而作為代替那么會考慮得出的數(shù)量，如在各個領域的光圈或磁流在一個縫隙或靠近邊緣的一微帶斑紋。你會發(fā)現(xiàn)我們使用任何的概念來提供深入的或簡化的數(shù)學。天線1轉換電路領域

5、，必將成為傳播的電磁波，并通過互惠，從通過電磁波中收集動力。麥克斯韋方程組預測，任何時間變電氣或磁場產生相反的領域和形成一電磁波。波有其兩個領域的面向正交，而且它在正常的方向上傳播給由垂直的電場和磁場所定的飛機。電場、磁場和傳播的方向形成一個右手坐標系統(tǒng)。傳播波場的強度從源端上降低1/R，而靜電磁場下降到1/。任何電路隨時間變化的場在一定程度上有能力輻射。我們只考慮時間諧波領域和使用相符號與時間依賴性。一個外向型傳播的波給出了，其中k是波數(shù)，給出了2/。是波所給予的c/f的波長，其中c是光速在自由空間中為3米/秒和f是頻率。從源頭上減少了波的相位來增大距離?？紤]一個兩線傳輸?shù)木€路與場，必將給它

6、。在一個單一線路上的電流將會輻射，但只要地面返回路徑是很近的，其輻射幾乎會取消其他線的輻射，因為兩者有180的相位差和波程有差不多一樣的遠。除了線路變得越走越遠外，在波長方面，場所產生的兩個電流在所有的方向上將不再取消。在一些方向的相位延遲是不同的輻射從電流在每條線上，和電力從該路線上逃逸。我們保持電路從輻射提供了密切地面的回贈。因此，高速邏輯要求地球平面去減少輻射及其不受歡送的串擾。1.1天線輻射天線輻射球面波在以天線為核心的坐標系統(tǒng)的徑向方向上傳播。在大的距離上，球面波可以近似平面波。平面波是有用的，因為他們把問題簡化了。他們不是自然的，然而，因為它們需要無限的功率。該玻印廷矢量描述兩個方

7、向的傳播和功率密度的電磁波。這是從矢量穿過產生的電場和磁場中發(fā)現(xiàn)的，并標注為S： S = E H* W/均方根RMS值是用來表達場的重要性。H*是復雜的共軛的磁場相。磁場在遠區(qū)場上是與電場成正比的。比例常數(shù)是，自由空間中的阻抗)： W/ ()因為玻印廷矢量是兩個場的矢量的產物，這是正交的兩個場以及三重定義了一個右手坐標系統(tǒng)：(E, H, S)。考慮一對以天線為核心的同心球形。靠近天線的場減少為1/R, 1/, 1/等等。恒指定的條件將要求功率輻射與輻距離和將不會被保存的功率一起增長。場方面的比例1/, 1/，和更高，功率密度隨距離減少，比面積增加的速度快。在球形里面的能源大于在球形外部的能量。

8、這些能量不輻射，但是代替集中在天線周圍，它們是近區(qū)場的條件。只有1/條件的玻印廷矢量1/R場的條件所代表的輻射功率，因為該球形的面積的增長為，并給出了一個常數(shù)的積。所有輻射功率流經內部球體將傳播到球形的外部。符號的輸入抗依賴于近區(qū)場的場類型的優(yōu)勢：電氣電容式或磁場電感。在共振零抗上儲存的能量是平等的，因為是近區(qū)場。存儲場的增多增加了電路的Q和縮小阻抗帶寬。從天線到目前為止，我們只考慮輻射的場和功率密度。功率流是相同的通過同心的球形： 平均功率密度是成正比于1/的?？紤]在同一坐標的角度上的兩個球形的面積的差異。天線的輻射，只有在徑向方向;因此，沒有功率可能在或方向上游走的。功率在面積中的通量管上

9、游走，并如下，不僅平均坡印亭矢量，而且功率密度的每個局部都是與1/成正比的： 自從在一個輻射波S是成正比于1/的之后，E是成正比于1/R。界定輻射強度以此來消除1/的依賴是很方便的：U(, ) = S(R, , ) W/solid angle輻射強度，只取決于輻射的方向和在所有的距離上保持不變。一探針天線測量相對輻射強度方向圖是通過在天線的周圍移動軌跡在一個圓圈常數(shù) R上。當然很多時候天線在旋轉而且探頭是固定的。一些方向圖已經建立了名稱。方向圖隨著球面坐標系的常數(shù)角度就叫做錐形常數(shù)或大圈常數(shù)。大圈削減當=0或= 90是主要的平面方向圖。其他命名削減也使用，但他們的名字取決于特定的測量定位，而且

10、它是必要的注釋，這些方向圖小心地在人們對不同定位器的測量方式之間去防止造成混亂。方向圖通過采用3個規(guī)模來衡量的：1線性功率，2平方根磁場強度，及3分貝dB。該分貝的規(guī)模是最常用的，因為它揭示了更多的低層次的反響旁瓣。圖1 .1顯示出了方向圖許多特點的。半功率波束有時也只是被稱為波束。第十功率和零的波束也被使用在一些應用中。這方向圖是來自一個拋物反射面，該反射面的裝置是移下來的軸。剩余的瓣當?shù)谝桓卑曜優(yōu)閰⒓拥街鞑ㄊ鴷r發(fā)生，并形成了一個肩膀。為了讓一個裝置坐落于拋物線的軸上，第一旁瓣都是平等的。1.2 增益增益是天線在一個特定的方向上的指導輸入功率到輻射能力的一個衡量，也是衡量頂峰的輻射強度。通過

11、各向同性天線的輸入功率Po在距離R來考慮功率密度輻射：S = Po/4。一各向同性天線在所有的方向上的輻射是相同的，其輻射功率密度S是由輻射功率除以一個球形的面積4得到的。各向同性散熱器被認為是100的效率。一個實際天線的增益增加了在頂峰輻射方向上的功率密度： or ()增益是通過指導輻射遠離其他局部的輻射范圍來取得的。在一般情況下，增益定義為天線的增益偏頗的規(guī)模： 功率密度 輻射強度 () 圖1.1 天線方向圖的特點在輻射面積上的輻射強度的外表積分除以輸入功率Po，這是天線或天線效率的相對功率輻射的一個衡量： 效率這里的Pr是輻射功率。在天線上的物質損失或者由于弱阻抗匹配的反射功率減少輻射功

12、率。在這本書，在設計的過程中上述方程中的積分和那些后續(xù)表達的概念多于我們執(zhí)行的操作。只有現(xiàn)實世界中的理論簡化，我們才能找到封閉形式的解決方案，該方案將要求實際一體化。我們通過用數(shù)值方法來解決大局部積分，該方法涉及把積分分成小片段和做一加權和。不過，使用實測值的積分減少平均隨機誤差，提高了結果，這是有幫助的。在一個系統(tǒng)中發(fā)送器的輸出阻抗或接收器的輸入阻抗可能與天線的輸入阻抗不匹配。最大增益出現(xiàn)上一個接收器的阻抗共軛匹配天線，這意味著電阻局部是相同的和無功局部是相同的幅度，但有相反的跡象。增益測量的精度要求在天線和接收機之間的調諧器使得它倆共軛匹配。此外，錯配的損失必須通過計算后的測量來消除。無論

13、錯配的影響對于一個給定系統(tǒng)來說是分開考慮，或天線測量到系統(tǒng)阻抗和錯配的損失被認為是效率的局部。例子 計算峰值功率密度在10公里長的輸入功率為3瓦特的和增益為15分貝的天線。先把dB增益轉換成一個比例：G = = 。功率分布在 半徑為10公里或面積為4平方米的球面上。功率密度是：我們使用方程式1-2來計算電場強度：雖然增益通常是與各向同性天線有關的，一些天線的增益涉及到一個/2的各向同性增益為分貝的偶極子。如果我們把天線近似作為一個點源，我們通過使用方程式來計算電場輻射： ()這僅要求天線相比徑向距離R要小.方程式忽略了電場的方向，這我們界定為兩極分化。電場的單位是伏特/米。我們通過用R乘以方程

14、式及消除相位來確定遠區(qū)場的方向圖，只有當提到在遠區(qū)場中的另一點時，相位才是有意義的。遠區(qū)場電場的單位是伏特： 或 ()在分析的過程中，我們往往把輸入功率看成為1瓦特，就很容易地從電場中乘以一個常數(shù)= 來可以計算增益。1.3有效面積 天線通過波來獲得功率并傳遞一些到終端。給出入射波的功率密度和天線的有效面積，功率傳送到終端是成果。 ()為了一口徑天線，如1角，拋物反射面，或平板陣列，有效面積是物理面積乘以口徑效率。在一般的情況下，損耗歸因于材料，分布和錯配減少了有效面積到物理面積的比例。為拋物反射面估計的典型口徑效率是55。甚至有極小的物理面積的天線，如偶極子，有有效面積，因為他們通過的波消除了

15、功率。1.4路徑損耗我們把發(fā)射天線的增益與接收天線的有效面積結合起來，以確定傳遞的權力和路徑損耗。在接收天線的功率密度是在方程式1.3中給出，以及接收功率是在方程式1.6中給出。把兩者結合，我們就得出路徑損耗： 天線1發(fā)射和天線2接收。如果天線中的材料是線性和各向同性的，發(fā)射和接收方向圖是相同的交互2，第116頁。當我們考慮到天線2作為發(fā)射天線和天線1作為接收天線，路徑損耗是 由于反響是交互的，路徑的損失都是平等的，我們可以收集和消除條款：=常數(shù)由于天線是任意的，這系數(shù)必須等于一個常數(shù)。這個常數(shù)是通過考慮在兩個大光圈3之間的輻射來得出的： ()我們把這個方程代入到路徑損耗，以表達它在增益或有效

16、面積中的條件： ()我們對路徑損耗作出快速評價，以距離R的各種單位和在公式中使用百兆的頻率f。路徑損耗(dB)= ()其中Ku取決于長度單位： 例子 計算直徑為3米，頻率為4 GHz，假設口徑效率為55的拋物反射面的增益。增益是在方程式1.7中與有效面積有關： 我們通過來計算一圓孔的面積。結合這些方程，我們有： ()其中D是直徑和是口徑效率。把值代入上式，我們得到的增益為： ()例子 計算一頻率為2.2 GHz，發(fā)射天線增益為25dB，接收天線增益為20dB的50公里的通訊線路的路徑損耗。路徑損耗在兩個小孔之間當頻率在增加時傳輸會發(fā)生什么變化？如果我們假定有效面積依然保持為常數(shù)不變，作為在一個

17、拋物反射面上，傳輸?shù)脑黾邮穷l率的平方：其中B在一個固定的范圍內是一個常數(shù)。無論頻率是多少，接收孔徑捕獲同樣的功率，但發(fā)射天線增益的增加是頻率的平方。因此，接收功率的增加也是頻率的平方。只有當頻率變化時其增益是一個固定值的天線，它的路徑損耗的增加是頻率的平方。1.5雷達距離方程和截面雷達使用雙路徑損耗來運作。雷達發(fā)射天線輻射一個照亮一目標的場。這些事件場激發(fā)外表電流，也輻射產生出第二個場。這些場傳播到接收天線，他們在那里收集。大局部雷達使用相同的天線來傳遞場并收集返回的信號，稱為單系統(tǒng)，而我們在雙基地雷達中使用單獨的天線。在一個雙系統(tǒng)中無法偵測到接收系統(tǒng)，因為它不傳輸和在軍事上的應用具有更大的生

18、存能力。我們在一個范圍內通過使用方程式來確定有啟發(fā)性目標的功率密度： ()目標的雷達散射截面RCS，對象的散射面積是表示在平方米或dB：10 log平方米。RCS取決于事件和反射波的方向。我們乘以通過目標與它的由于電流誘導的有效天線的增益接的收方向來收集的功率：發(fā)射功率/功率密度事件 ()在一個通信系統(tǒng)，我們叫Ps為等效各向同性輻射功率EIRP，這相當于輸入功率和天線增益的積。目標成為傳遞的來源和我們應用方程式1.2來找到在接收天線上在一個從目標的范圍內的功率密度。最后，接收天線收集功率密度與有效面積。我們把這些想法結合起來，以獲取傳遞給接收器的功率： 我們應用方程式來消除接收天線的有效面積和

19、收集的條件來確定雙基地雷達距離方程： ()我們減少方程式，并為單雷達收集條件，這里的同一天線是用于發(fā)射和接收的： 雷達的接收功率是成正比與的1/和的。我們通過考慮板作為一有有效面積的天線來找到一平板的近似RCS。方程式1.11在板上給出了功率密度事件，該板在一面積上收集這種功率：功率由板分散是收集的功率，乘以作為天線的板的增益： 這個分散的功率是在一個特定的方向的有效輻射功率，這在天線是輸入功率和在某一特定方向上增益的積。我們通過使用有效面積來計算板的增益，并找到就面積而言的分散的功率： 我們由方程式來確定RCS ，分散的權力除以事件的功率密度： ()為了雙站散射，方程式的正確數(shù)式把增益劃分為

20、兩件，在這分散的方向是不同于這次事件的方向的。單散射使用相同的事件和反射的方向。我們可以把任何對象代替為平板和使用一個有效的面積的觀點及其相關的天線增益。 天線是一個有著獨特RCS特征的對象，因為局部的接收到的功率將傳遞給天線終端。如果我們提供了一個良好的阻抗匹配到這個信號，它不會重新輻射和RCS是減少的。當我們從一個任意方向照亮天線，一些事件的功率密度將由結構分散和不會傳遞給天線終端。這導致天線RCS在重新輻射信號的天線模式上分工所造成的終端錯配和結構模式，為了事件的功率密度不傳遞給終端場反映了結構。1.6為什么要使用一個天線？當沒有其他方法是可行的時候，我們使用天線來傳輸信號，如與導彈或在

21、崎嶇的山區(qū)地形上的通信。電纜昂貴，而且需要很長的時間來安裝。當我們在水平地面上會使用天線的時候就這些？天線系統(tǒng)的大的路徑損失會令我們相信，電纜運行更好。2 PROPERTIES OF ANTENNASOne approach to an antenna book starts with a discussion of how antennas radiate. Beginning with Maxwells equations, we derive electromagnetic waves. After that lengthy discussion, which contains a lo

22、t of mathematics, we discuss how these waves excite currents on conductors. The second half of the story is that currents radiate and produce electromagnetic waves. You may already have studied that subject, or if you wish to further your background, consult books on electromagnetics.The study of el

23、ectromagnetics gives insight into the mathematics describing antenna radiation and provides the rigor to prevent mistakes. We skip the discussion of those equations and move directly to practical aspects. It is important to realize that antennas radiate from currents. Design consists of controlling

24、currents to produce the desired radiation distribution, called its pattern .In many situations the problem is how to prevent radiation from currents, such as in circuits. Whenever a current becomes separated in distance from its return current, it radiates. Simply stated, we design to keep the two c

25、urrents close together, to reduce radiation. Some discussions will ignore the current distribution and instead, consider derived quantities, such as fields in an aperture or magnetic currents in a slot or around the edges of a microstrip patch. You will discover that we use any concept that provides

26、 insight or simplifies the mathematics. An antenna converts bound circuit fields into propagating electromagnetic waves and, by reciprocity, collects power from passing electromagnetic waves. Maxwells equations predict that any time-varying electric or magnetic field produces the opposite field and

27、forms an electromagnetic wave. The wave has its two fields oriented orthogonally, and it propagates in the direction normal to the plane defined by the perpendicular electric and magnetic fields. The electric field, the magnetic field, and the direction of propagation form a right-handed coordinate

28、system. The propagating wave field intensity decreases by 1/R away from the source, whereas a static field drops off by 1/. Any circuit with time-varying fields has the capability of radiating to some extent. We consider only time-harmonic fields and use phasor notation with time dependence . An out

29、ward-propagating wave is given by , where k, the wave number, is given by 2/. is the wavelength of the wave given by c/f , where c is the velocity of light (3 m/s in free space) and f is the frequency. Increasing the distance from the source decreases the phase of the wave. Consider a two-wire trans

30、mission line with fields bound to it. The currents on a single wire will radiate, but as long as the ground return path is near, its radiation will nearly cancel the other lines radiation because the two are 180out of phase and the waves travel about the same distance. As the lines become farther an

31、d farther apart, in terms of wavelengths, the fields produced by the two currents will no longer cancel in all directions. In some directions the phase delay is different for radiation from the current on each line, and power escapes from the line. We keep circuits from radiating by providing close

32、ground returns. Hence, high-speed logic requires ground planes to reduce radiation and its unwanted crosstalk. 2.1 ANTENNA RADIATIONAntennas radiate spherical waves that propagate in the radial direction for a coordinate system centered on the antenna. At large distances, spherical waves can be appr

33、oximated by plane waves. Plane waves are useful because they simplify the problem. They are not physical, however, because they require infinite power. The Poynting vector describes both the direction of propagation and the power density of the electromagnetic wave. It is found from the vector cross

34、 product of the electric and magnetic fields and is denoted S: S = E H* W/ Root mean square (RMS) values are used to express the magnitude of the fields. H* is the complex conjugate of the magnetic field phasor. The magnetic field is proportional to the electric field in the far field. The constant

35、of proportion is , the impedance of free space ( = 376.73): W/ (1.1) Because the Poynting vector is the vector product of the two fields, it is orthogonal to both fields and the triplet defines a right-handed coordinate system: (E, H, S). Consider a pair of concentric spheres centered on the antenna

36、. The fields around the antenna decrease as 1/R, 1/, 1/, and so on. Constant-order terms would require that the power radiated grow with distance and power would not be conserved. For field terms proportional to 1/, 1/, and higher, the power density decreases with distance faster than the area incre

37、ases. The energy on the inner sphere is larger than that on the outer sphere. The energies are not radiated but are instead concentrated around the antenna; they are near-field terms. Only the 1/ term of the Poynting vector (1/R field terms) represents radiated power because the sphere area grows as

38、 and gives a constant product. All the radiated power flowing through the inner sphere will propagate to the outer sphere. The sign of the input reactance depends on the near-field predominance of field type: electric (capacitive) or magnetic (inductive). At resonance (zero reactance) the stored ene

39、rgies due to the near fields are equal. Increasing the stored fields increases the circuit Q and narrows the impedance bandwidth. Far from the antenna we consider only the radiated fields and power density. The power flow is the same through concentric spheres: The average power density is proportio

40、nal to 1/. Consider differential areas on the two spheres at the same coordinate angles. The antenna radiates only in the radial direction; therefore, no power may travel in the or direction. Power travels in flux tubes between areas, and it follows that not only the average Poynting vector but also

41、 every part of the power density is proportional to 1/: Since in a radiated wave S is proportional to 1/, E is proportional to 1/R. It is convenient to define radiation intensity to remove the 1/ dependence: U(, ) = S(R, , ) W/solid angle Radiation intensity depends only on the direction of radiatio

42、n and remains the same at all distances. A probe antenna measures the relative radiation intensity (pattern) by moving in a circle (constant R) around the antenna. Often, of course, the antenna rotates and the probe is stationary. Some patterns have established names. Patterns along constant angles

43、of the spherical coordinates are called either conical (constant ) or great circle (constant ). The great circle cuts when = 0 or = 90are the principal plane patterns. Other named cuts are also used, but their names depend on the particular measurement positioner, and it is necessary to annotate the

44、se patterns carefully to avoid confusion between people measuring patterns on different positioners. Patterns are measured by using three scales: (1) linear (power), (2) square root (field intensity), and (3) decibels (dB). The dB scale is used the most because it reveals more of the low-level respo

45、nses (sidelobes). Figure 1.1 demonstrates many characteristics of patterns. The half-power beamwidth is sometimes called just the beamwidth. The tenth-power and null beamwidths are used in some applications. This pattern comes from a parabolic reflector whose feed is moved off the axis. The vestigia

46、l lobe occurs when the first sidelobe becomes joined to the main beam and forms a shoulder. For a feed located on the axis of the parabola, the first sidelobes are equal. 2.2 GAINGain is a measure of the ability of the antenna to direct the input power into radiation in a particular direction and is

47、 measured at the peak radiation intensity. Consider the power density radiated by an isotropic antenna with input power Po at a distance R: S = Po/4. An isotropic antenna radiates equally in all directions, and its radiated power density S is found by dividing the radiated power by the area of the s

48、phere 4. The isotropic radiator is considered to be 100% efficient. The gain of an actual antenna increases the power density in the direction of the peak radiation: or (1.2)Gain is achieved by directing the radiation away from other parts of the radiation sphere. In general, gain is defined as the

49、gain-biased pattern of the antenna: power density radiation intensity (1.3) FIGURE 1.1 Antenna pattern characteristics. The surface integral of the radiation intensity over the radiation sphere divided by the input power Po is a measure of the relative power radiated by the antenna, or the antenna e

50、fficiency: efficiency where Pr is the radiated power. Material losses in the antenna or reflected power due to poor impedance match reduce the radiated power. In this book, integrals in the equation above and those that follow express concepts more than operations we perform during design. Only for

51、theoretical simplifications of the real world can we find closed-form solutions that would call for actual integration. We solve most integrals by using numerical methods that involve breaking the integrand into small segments and performing a weighted sum. However, it is helpful that integrals usin

52、g measured values reduce the random errors by averaging, which improves the result. In a system the transmitter output impedance or the receiver input impedance may not match the antenna input impedance. Peak gain occurs for a receiver impedance conjugate matched to the antenna, which means that the

53、 resistive parts are the same and the reactive parts are the same magnitude but have opposite signs. Precision gain measurements require a tuner between the antenna and receiver to conjugate-match the two. Alternatively, the mismatch loss must be removed by calculation after the measurement. Either

54、the effect of mismatches is considered separately for a given system, or the antennas are measured into the system impedance and mismatch loss is considered to be part of the efficiency. Example Compute the peak power density at 10 km of an antenna with an input power of 3 W and a gain of 15 dB. Fir

55、st convert dB gain to a ratio: G = = 31.62. The power spreads over the sphere area with radius 10 km or an area of 4 . The power density is We calculate the electric field intensity using Eq. (1-2): Although gain is usually relative to an isotropic antenna, some antenna gains are referred to a /2 di

56、pole with an isotropic gain of 2.14 dB. If we approximate the antenna as a point source, we compute the electric field radiated by using Eq. (1.2): (1.4) This requires only that the antenna be small compared to the radial distance R. Equation (1.4) ignores the direction of the electric field, which

57、we define as polarization. The units of the electric field are volts/meter. We determine the far-field pattern by multiplying Eq. (1.4) by R and removing the phase term since phase has meaning only when referred to another point in the far field. The far-field electric field unit is volts: or (1.5)

58、During analysis, we often normalize input power to 1 W and can compute gain easily from the electric field by multiplying by a constant = 0.1826374. 2.3 EFFECTIVE AREAAntennas capture power from passing waves and deliver some of it to the terminals. Given the power density of the incident wave and t

59、he effective area of the antenna, the power delivered to the terminals is the product. (1.6) For an aperture antenna such as a horn, parabolic reflector, or flat-plate array, effective area is physical area multiplied by aperture efficiency. In general, losses due to material, distribution, and mism

60、atch reduce the ratio of the effective area to the physical area. Typical estimated aperture efficiency for a parabolic reflector is 55%. Even antennas with infinitesimal physical areas, such as dipoles, have effective areas because they remove power from passing waves. 2.4 PATH LOSSWe combine the g