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本科毕业设计论文 专业名称：机械设计制造及其自动化 学生姓名： 杨 方 元 指导教师： 张 永 红 毕业时间： 2014年6月目录 PROPERTIES OF ANTENNAS21.1 ANTENNA RADIATION31.2 GAIN51.3 EFFECTIVE AREA81.4 PATH LOSS81.5 RADAR RANGE EQUATION AND CROSS SECTION101.6 WHY USE AN ANTENNA?12天线的性能121.1天线辐射131.2 增益151.3有效面积171.4路径损耗181.5雷达距离方程和截面201.6为什么要使用一个天线？21英文原文：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 lot 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 electromagnetics 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 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 currents 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 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 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 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 outward-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 transmission 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 and 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 ground returns. Hence, high-speed logic requires ground planes to reduce radiation and its unwanted crosstalk. 1.1 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 approximated 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 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 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. 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 increases. 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 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 energies 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 proportional 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 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 radiation 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 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 these 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 responses (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 vestigial 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. 1.2 GAINGain is a measure of the ability of the antenna to direct the input power into radiation in a particular direction and is 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 sphere 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 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 efficiency: 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 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 using 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 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 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. First 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 dipole 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 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) 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. 1.3 EFFECTIVE AREAAntennas capture power from passing waves and deliver some of it to the terminals. Given the power density of the incident wave and the 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 mismatch 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. 1.4 PATH LOSSWe combine the gain of the transmitting antenna with the effective area of the receiving antenna to determine delivered power and path loss. The power density at the receiving antenna is given by Eq. (1.3), and the received power is given by Eq. (1.6). By combining the two, we obtain the path loss: Antenna 1 transmits, and antenna 2 receives. If the materials in the antennas are linear and isotropic, the transmitting and receiving patterns are identical (reciprocal) 2, p. 116. When we consider antenna 2 as the transmitting antenna and antenna 1 as the receiving antenna, the path loss is Since the responses are reciprocal, the path losses are equal and we can gather and eliminate terms: = constant Because the antennas were arbitrary, this quotient must equal a constant. This constant was found by considering the radiation between two large apertures 3: (1.7) We substitute this equation into path loss to express it in terms of the gains or effective areas: (1.8) We make quick evaluations of path loss for various units of distance R and for frequency f in megahertz using the formula. path loss(dB)= (1.9) where Ku depends on the length units: Example Compute the gain of a 3-m-diameter parabolic reflector at 4 GHz assuming 55% aperture efficiency. Gain is related to effective area by Eq. (1.7): We calculate the area of a circular aperture by. By combining these equations, we have (1.10) where D is the diameter and is the aperture efficiency. On substituting the values above, we obtain the gain: (39.4dB)Example Calculate the path loss of a 50-km communication link at 2.2 GHz using a transmitter antenna with a gain of 25 dB and a receiver antenna with a gain of 20 dB. Path loss = 32.45 + 20 log2200(50) - 25 - 20 = 88.3 dB What happens to transmission between two apertures as the frequency is increased? If we assume that the effective area remains constant, as in a parabolic reflector, the transmission increases as the square of frequency: where B is a constant for a fixed range. The receiving aperture captures the same power regardless of frequency, but the gain of the transmitting antenna increases as the square of frequency. Hence, the received power also increases as frequency squared. Only for antennas, whose gain is a fixed value when frequency changes, does the path loss increase as the square of frequency. 1.5 RADAR RANGE EQUATION AND CROSS SECTIONRadar operates using a double path loss. The radar transmitting antenna radiates a field that illuminates a target. These incident fields excite surface currents that also radiate to produce a second field. These fields propagate to the receiving antenna, where they are collected. Most radars use the same antenna both to transmit the field and to collect the signal returned, called a monostatic system, whereas we use separate antennas for bistatic radar. The receiving system cannot be detected in a bistatic system because it does not transmit and has greater survivability in a military application. We determine the power density illuminating the target at a range by using Eq. (1.2): (1.11) The targets radar cross section (RCS), the scattering area of the object, is expressed in square meters or dB: 10 log(square meters). The RCS depends on both the incident and reflected wave directions. We multiply the power collected by the target with its receiving pattern by the gain of the effective antenna due to the currents induced: (1.12) In a communication system we call Ps the equivalent isotropic radiated power (EIRP), which equals the product of the input power and the antenna gain. The target becomes the transmitting source and we apply Eq. (1.2) to find the power density at the receiving antenna at a range from the target. Finally, the receiving antenna collects the power density with an effective area. We combine these ideas to obtain the power delivered to the receiver: We apply Eq. (1.7) to eliminate the effective area of the receiving antenna and gather terms to determine the bistatic radar range equation: (1.13) We reduce Eq. (1.13) and collect terms for monostatic radar, where the same antenna is used for both transmitting and receiving: Radar received power is proportional to 1/ and to . We find the approximate RCS of a flat plate by considering the plate as an antenna with an effective area. Equation (1.11) gives the power density incident on the plate that collects this power over an area: The power scattered by the plate is the power collected, times the gain of the plate as an antenna,: This scattered power is the effective radiated power in a particular direction, which in an antenna is the product of the input power and the gain in a particular direction. We calculate the plate gain by using the effective area and find the scattered power in terms of area: We determine the RCS by Eq. (1.12), the scattered power divided by the incident power density: (1.14) The right expression of Eq. (1.14) divides the gain into two pieces for bistatic scattering, where the scattered direction is different from the incident direction. Monostatic scattering uses the same incident and reflected directions. We can substitute any object for the flat plate and use the idea of an effective area and its associated antenna gain. An antenna is an object with a unique RCS characteristic because part of the power received will be delivered to the antenna terminals. If we provide a good impedance match to this signal, it will not reradiate and the RCS is reduced. When we illuminate an antenna from an arbitrary direction, some of the incident power density will be scattered by the structure and not delivered to the antenna terminals. This leads to the division of antenna RCS into the antenna mode of reradiated signals caused by terminal mismatch and the structural mode, the fields reflected off the structure for incident power density not delivered to the terminals. 1.6 WHY USE AN ANTENNA? We use antennas to transfer signals when no other way is possible, such ascommunication with a missile or over rugged mountain terrain. Cables are expensive and take a long time to install. Are there times when we would use antennas over level ground? The large path losses of antenna systems lead us to believe that cable runs are better. 中文译文：天线的性能天线的方法一书是从天线辐射的讨论开始。从麦克斯韦方程,推导出电磁波。之后漫长的讨论,其中包含大量的数学,我们将讨论如何将这些波激发电流在导体上。第二个故事是讲电流辐射并产生电磁波。你可能已经研究了这个问题,或者如果你想进一步的它的背景,咨询关于电磁学的书。电磁学的研究为数学描述天线辐射和防止错误提供了一些见解。我们跳过这些方程的讨论,直接转移到实际的方面。重要的是要意识到天线辐射电流。设计由控制电流来产生所需的辐射分布,称为模式。在许多情况下,问题是如何防止辐射电流,电路等。每当当前分开的距离成为返回电流,它就是辐射。简单的说,我们设计两个电流接近,减少辐射。一些讨论将忽略电流分布,而是考虑派生的数量,比如字段在一个孔或槽磁电流或微带贴片的边缘。你会发现我们使用任何提供洞察力或简化了数学的概念。天线将绑定电路领域转化为传播电磁波,通过互惠,收集功率从路过的电磁波。麦克斯韦方程预测, 任何随时间变化的电场或磁场产生的反向场，并且形成的电磁波。正交面向波有两个频段,它传播的方向正常定义是平面垂直的电场和磁场。电场、磁场和传播的方向形成一个右手坐标系。传播波场的强度从源端上降低1/R，而静电磁场下降到1/。随时间变化的磁场会引起任何电路具有辐射在一定程度上的能力。我们只考虑时间谐波领域和使用相符号与时间依赖性。一个外向型传播的波给出了，其中k是波数，给出了2/。是波所给予的c/f的波长，其中c是光速（在自由空间中为3米/秒）和f是频率。从源头上减少了波的相位来增大距离。考虑一个两线传输的线路与场，必将受它影响。在一个单一线路上的电流将会辐射，但只要地面返回路径是很近的，其辐射几乎会取消其他线的辐射，因为两者有180的相位差和波程有差不多一样的远。除了线路变得越走越远外，在波长而言，由两个电流产生的场将不再取消在所有方向上。在某些方向上的相位延迟是不同的用于从每一行的当前的辐射，并且从电源线逸出。我们不断从电路提供近地面辐射的回报。因此，高速逻辑要求的接地平面，以减少辐射和不必要的串扰。1.1天线辐射天线辐射球面波传播的径向坐标系统集中在天线上。大的距离,可以近似球面波为平面波。球面波是非常有用的,因为他们简化问题。他们虽然不是物理学的,然而,由于他们需要无限的力量。该玻印廷矢量描述两个方向的传播和功率密度的电磁波。这是从矢量穿过产生的电场和磁场中发现的，并标注为S： S = E H* W/均方根（RMS）值是用来表达场的重要性。H*是复杂的共轭的磁场相。磁场在远区场上是与电场成正比的。比例常数是，自由空间中的阻抗( = 376.73)： W/ (1.1)因为玻印廷矢量是两个场的矢量的产物，这是正交的两个场以及三重定义了一个右手坐标系统：(E, H, S)。考虑一对以天线为核心的同心球形。靠近天线的场减少为1/R, 1/, 1/等等。恒指定的条件将要求功率辐射与辐距离和将不会被保存的功率一起增长。场方面的比例1/, 1/，和更高，功率密度随距离减少，比面积增加的速度快。在球形里面的能源大于在球形外部的能量。这些能量不辐射，但是代替集中在天线周围，它们是近区场的条件。只有1/条件的玻印廷矢量（1/R场的条件）所代表的辐射功率，因为该球形的面积的增长为，并给出了一个常数的积。所有辐射功率流经内部球体将传播到球形的外部。符号的输入抗依赖于近区场的场类型的优势：电气（电容式）或磁场（电感）。在共振（零抗）上储存的能量是平等的，因为是近区场。存储场的增多增加了电路的Q和缩小阻抗带宽。从天线到目前为止，我们只考虑辐射的场和功率密度。功率流是相同的通过同心的球形： 平均功率密度是成正比于1/的。考虑在同一坐标的角度上的两个球形的面积的差异。天线的辐射，只有在径向方向;因此，没有功率可能在或方向上游走的。功率在面积中的通量管上游走，并如下，不仅平均坡印亭矢量，而且功率密度的每个部分都是与1/成正比的： 自从在一个辐射波S是成正比于1/的之后，E是成正比于1/R。界定辐射强度以此来消除1/的依赖是很方便的：U(, ) = S(R, , ) W/solid angle辐射强度，只取决于辐射的方向和在所有的距离上保持不变。一探针天线测量相对辐射强度（方向图）是通过在天线的周围移动轨迹在一个圆圈（常数 R）上。当然很多时候天线在旋转而且探头是固定的。一些方向图已经建立了名称。方向图随着球面坐标系的常数角度就叫做锥形（常数）或大圈（常数）。大圈削减当=0或= 90是主要的平面方向图。其他命名削减也使用，但他们的名字取决于特定的测量定位，而且它是必要的注释，这些方向图小心地在人们对不同定位器的测量方式之间去避免造成混乱。方向图通过采用3个规模来衡量的：（1）线性（功率），（2）平方根（磁场强度），及（3）分贝（dB）。该分贝的规模是最常用的，因为它揭示了更多的低层次的反应（旁瓣）。图1 .1显示出了方向图许多特点的。半功率波束有时也只是被称为波束。第十功率和零的波束也被使用在一些应用中。这方向图是来自一个抛物反射面，该反射面的装置是移下来的轴。残余的瓣当第一副瓣变为加入到主波束时发生，并形成了一个肩膀。为了让一个装置坐落于抛物线的轴上，第一旁瓣都是平等的。1.2 增益增益是天线在一个特定的方向上的指导输入功率到辐射能力的一个衡量，也是衡量顶峰的辐射强度。通过各向同性天线的输入功率Po在距离R来考虑功率密度辐射：S = Po/4。一各向同性天线在所有的方向上的辐射是相同的，其辐射功率密度S是由辐射功率除以一个球形的面积4得到的。各向同性散热器被认为是100的效率。一个实际天线的增益增加了在顶峰辐射方向上的功率密度： or (1.2)增益是通过指导辐射远离其他部分的辐射范围来取得的。在一般情况下，增益定义为天线的增益偏颇的规模： 功率密度 辐射强度 (1.3) 图1.1 天线方向图的特点在辐射面积上的辐射强度的表面积分除以输入功率Po，这是天线或天线效率的相对功率辐射的一个衡量： 效率这里的Pr是辐射功率。在天线上的物质损失或者由于弱阻抗匹配的反射功率减少辐射功率。在这本书，在设计的过程中上述方程中的积分和那些后续表达的概念多于我们执行的操作。只有现实世界中的理论简化，我们才能找到封闭形式的解决方案，该方案将要求实际一体化。我们通过用数值方法来解决大部分积分，该方法涉及把积分分成小片段和做一加权和。不过，使用实测值的积分减少平均随机误差，提高了结果，这是有帮助的。在一个系统中发送器的输出阻抗或接收器的输入阻抗可能与天线的输入阻抗不匹配。最大增益出现上一个接收器的阻抗共轭匹配天线，这意味着电阻部分是相同的和无功部分是相同的幅度，但有相反的迹象。增益测量的精度要求在天线和接收机之间的调谐器使得它俩共轭匹配。此外，错配的损失必须通过计算后的测量来消除。无论错配的影响对于一个给定系统来说是分开考虑，或天线测量到系统阻抗和错配的损失被认为是效率的部分。例子 计算峰值功率密度在10公里长的输入功率为3瓦特的和增益为15分贝的天线。先把dB增益转换成一个比例：G = = 31.62。功率分布在 半径为10公里或面积为4平方米的球面上。功率密度是：我们使用方程式（1-2）来计算电场强度：虽然增益通常是与各向同性天线有关的，一些天线的增益涉及到一个/2的各向同性增益为2.14分贝的偶极子。 如果我们把天线近似作为一个点源，我们通过使用方程式（1.2）来计