work theory ——RF & microwave basics Prof. Wu Qun -1- 硕士学位课系列讲座 March 2003 Power Transfer Basics - + I Low frequencies z wavelengths >> wire length z current (I) travels down wires easily for efficient power transmission z measured voltage and current not dependent on position along wire High frequencies z wavelength ≈ or << length of transmission medium z need transmission lines for efficient power transmission z matching to characteristic impedance (Z0) is very important for low reflection and maximum power transfer z measured envelope voltage dependent on position along line -2- 硕士学位课系列讲座 March 2003 Transmission Line Basics z Zo determines relationship between voltage and current waves z Zo is a function of physical dimensions and ε r z Zo is usually a real impedance (. 50 or 75 ohms) Coaxial Waveguide a b w Twisted-pair h h εr w1 w w2 Characteristic impedance for Coplanar microstrip transmission lines Microstrip (assumes ic dielectric) -3- 硕士学位课系列讲座 March 2003 认识平面传输线 微带线和带状线结构 非对称带状线结构和 嵌入式微带结构 -4- 硕士学位课系列讲座 March 2003 微带线和带状线的演变 -5- 硕士学位课系列讲座 March 2003 带状线的结构及其主模场结构 •带状线的主要参数有特性阻抗、相速度、波导波长、衰减和功率容量等 •边缘电容效应 -6- 硕士学位课系列讲座 March 2003 带状线的分析 •带状线传输的主模是TEM模 •用静态场的分析方法来求特性阻抗 或 1 L Z = Z 0 = 0 C v pC •求电容C的方法有多种,其中较常用的是利用复变函数中的保角变换法求 电容C -7- 硕士学位课系列讲座 March 2003 (一)导体带为零厚度时的特性阻抗 •导体带的厚度的情况下,利用保角变换法可求得特性阻抗 •式中,K(*)为第一类完全椭圆积分,k为模数; 30π K(k') Z 0 = ε r K(k) = •其中k与带状线的尺寸W和b有关,W是中心导体带的宽度;b是上下接地 板的间距。当t → 0 时 1 1 1 π/ 2 1 K(k) = dq = dϕ ∫ 2 2 ∫ 2 ϕ 0 1− q 1− kq 0 1− k sin πW k = th 2b -8- 硕士学位课系列讲座 March 2003 (一)导体带为零厚度时的特性阻抗 • k’为为补模数(余模数) π k'= 1− k 2 = 1− th 2 ( W / 2b) = sech (πW / 2b) K(k') •有关的文献资料中给出了与k值相对应的的值,于是可根据k求出特 性阻抗。 K(k) -9- 硕士学位课系列讲座 March 2003 (二)导体带厚度不为零时的特性阻抗 •(1)宽导体带情况 W /(b − t) ≥ ε r 2 1 C f = ln+1 π t t Z 0 = 1−1− W / b C f b b r
