RadarEquationforpointTarget雷达气象学讲义-台大周仲岛教授.ppt

3-dB beam width 當脈衝離開天線以天線直徑大小平行電磁波束行進。由於繞射緣故，此一平行電磁波束在到達第一個繞射零點 (距離為 r = Da2/? )後開始發散成圓錐狀。雷達波束的束寬( beam width )定義為能流密度不小於最大值的一半之波束寬，或稱之為3-dB束寬。 由於雷達天線發射出之雷達束的能流密度可以 S(r, ?, ?)表示。天線無法將能量完全集中在一個窄束中，因此脈衝能流密度分佈呈現主瓣 (main lobe) 和幾個副瓣 (side lobe) 現象。現有一般雷達設計，副瓣的能流密度沒有大於主瓣百分之一的。事實上，所有副瓣能流密度的總和僅佔主瓣的百分之幾而已。 天線-反射器經常成拋物圓形, 能流密度(輻射強度)與離束軸(beam axis)距離 (?) 成 [1-4(?/Da)2] 2的關係。在此情形下, 常態化能流密度形狀(或稱為輻射形狀函數radiation pattern)與偏角的關係可寫成： ?2(?) = S(?)/S(?0) = {8J2[(?Dasin?)/?] / [(?Dasin?)/?]2}2 其中?為離束軸之偏角大小, ?為雷達發射電磁波波長, Da為天線直徑, J2 是Bessel function of second order。 雷達發射之微波脈衝可視為厚度為c? (脈衝寬) 的球形殼以光速往外傳播並擴張。因此, 在一封閉球體內所發射之脈衝能量（Pt’)為常數, 但是散射物所接收到的能流密度大小與距離平方成反比。此外由於天線本身,傳輸線,天線罩等造成的電磁波能量減損, 進入天線之脈衝能量 Pt 要大於實際發射出的 Pt’ 。 Antenna beam pattern Beam pattern 束形 天線(雷達發射之微波脈衝)束形, 脈衝之主瓣以及多個副瓣清楚可見。 Beam pattern With a parabolic reflector and Gaussian illumination(氣象常用) Width of the beam at 3 dB, ?1/2 = 70 ?/ Da Width of the main lobe (between nulls) ?null = 170 ?/ Da Level of first side lobe: -23dB below the value on the axis 天線增益 Antenna Gain The maximum directional gain of the antenna gt’ ? Sp / [ Pt’/4?r2 ] Pt’ is difficult to measure, so usually Pt (the power delivered to the antenna’s input port)is measured. Sp is the peak power and measured at distance far ( r 2Da2/?) from the antenna. Thus, the computed gain gt accounts for losses of energy associated with the antenna system (radome and waveguide). The incident radiation power density at range r without considering attenuation is given by Si(?, ?) = Pt gt ?2(?, ?) / 4?r2 ?2(?, ?) is the normalized [i. e., ?(?, ?) = 1 at ?0, ?0] power gain pattern and gt is the antenna power gain along the beam axis. Signal processor (receiver) Separating clutter signal and weather signal: an example The (back) -scattering cross section (反) 散射截面 The cross section ? of a scatterer (hydrometeor) is an apparent area that intercepts a power ? Si which, if radiated isotropically, produces at the receiver a power density Sr = Si ?