大学物理大学-射频电路第05讲圆波导与同轴线

1、第5讲内容波导同轴线A6oouu0al 40 A七 seun Ewt/O wnosResearch Institute of Antennas & RF Techniques5.1 圆波导场方程（纵向场表示法）South China University of Technology只要求出纵向场，其它场分量可由上式求出。South China University of TechnologyE z 和 H z 满足波动方程2 Ez + kC Ez = 0V,2 Hz + kC Hz = 0柱坐标中表示为：V,2a2 i a i a2+ +ar2r ar r2 a1A边界条件为EzaHz理想导体

2、表面 切向电场为零TM波 H = 0South China University of Technology应用分离变量法，令Ez = R(r)0()e-pz 代入方程，得r2 d2 R r dR 2 2 _1 d2 +rIT + c =一0 乔A上式等号左边只含与r有关的项，右边只含与屮有关的项。欲使此式对一切的r、屮值均成立，等式两边应分别等于同一常数m2,即d 2d1d2 R、dr21 dR+ +r dr根据圆周自然边界条件，得m为整数.上面第一式的通解为cos m(p0 = A cos m(p + A2 sin m(p = Am - 0,1,2,Lsin m(pSouth China

3、University of Technology第二式为贝塞尔方程，其通解为R(r ) = B Jm (kcr ) + B2 Nm (kcr )South China University of Technology根据自然边界条件： Ez(r = 0)丰 g得B2 = 0根据理想导体表面边界条件Jm ZzkcaZ = 0 , 得截止波数kc =如n = 1,2,Lc a截止波长2兀a 几c =pmn肯pmn为m阶Besse 1函数的第n个零点。South China University of Technology于是，TMmn模的电场纵向分量为/如八cos丁邛zm = 0，l，2,Ln =

4、 1,2,3,Lp cos卫仗=Eo Jm （如 r） . -j,a sm m显然，TMmo模不存在。相位常数与波阻抗分别为P=4k 2 - kC =Er =E,= P=P HHr眈 kSouth China University of TechnologyP mncaTE 波 = 0同理，可得圆柱形波导中TE波的H为cos me a m = 0,1,2,L Hz = H Jm 心.S，Jsin men = 1,2,3,Lc2兀 a, / ,、& =J (p ) = 0cm mnmn肯pmn为m阶Besse 1函数导数的第n个零点。Er _Ee _仲 _ k “ H H 卩卩 TE波的相位常数

5、与波阻抗分别为2(P爲 JLlb _1 a丿0 = (k 2 - kC =2South China University of TechnologySouth China University of Technology波导模式分布South China University of Technology波导有两种简并现象，一种是TEn和TMin当m不为零时，波导因为存在极化简并，使波导的模式简并现象J 模式简并是指两种模式的m,n值不同，场结构不同，但截止波长相同，传输特性相同 的简并。因为P0n = P1n，故&|叫=STM另一种是极化简并，模式的m，n相同，场分量相同，只是极化面旋转了90

6、度 得信号传输中可能产生极化面偏转，故很少用于长距离传输South China University of Technology极化简并South China University of Technology波导常用的三个模式圆波导常应用TEii、TEoi和TM01模 TEii模A主模A与矩形波导TE10模相近，可用作矩形一圆 波导转换A存在极化简并A可用作极化衰减器、波形转换器或铁氧体 环形器等South China University of Technology纵截面上场分布=3.41qSouth China University of Technology波导TE11模的电场动态图E

7、FieldV/m3. 19906+003I 2.99916+003I 2.79916+0032.5992e+0032.3993e+0032.19936+0031.99946+0031.79946+0031.59956+0031.3996e+003199 Ee+00 三;9.9969e+0027.9975e+002 5.9982e+002I 3.9988e+002I 1.99946+002 0,00006+000South China University of Technology波导TE11模的电场动态图E FieldV/m3. 1990e+S032.99916+003I 2.79916+0

8、032.5992e+S032.3993+0032.igg3e+031.99946+0031.7995e+0031.5gg.5e+0031.3996e+0031.1996e+0039.99716+0027.99776+002 j 5.99836+0023.99896+002i. ggdee+sezI 1.94856-002E FieldV/mSouth China University of Technology波导TE11模的电场动态图:久 1990 已+00WE.99916+003E.79926+003.59926+0032.39936+0032.ig94e+S031.gg95e+S03:1

9、 79956+003:1 59966+003:1 39976+003:1 19976+0039. 99816+0027.9988e+0025.9995e+0024.0003e+S02E.00106+0021.69316-001South China University of Technology波导TE11模的磁场动态图H F1e1dA/m9. 2527e+000 I X.67446+000 I 氏09626+000 I 7.5179e+000E.9397e+00SE.3614e+S005. 7E；M2e：+0005.20496+000斗 6266s+000U.04846+0003.4701

10、6+0002.8919e+0002.313Ee+000 1.7354e+000I 1.15716+000I 5.7884e-001I 5.8384e-004South China University of Technology波导TE11模的磁场动态图South China University of Technology波导TE11模的磁场动态图H F1e1dA/m0247e+000I 2.8357e+000I 2.6467e+0002145776+0002.2687e+0002.0797e+0SS1.89S7e+0SS1.70176+0005127e+0001.3236e+000134F

11、ie+0009.4563e-0017.5662e-001 5.6761B-0S1I 3.7860B-0S1I 1.89596-001I 5.8384e-004South China University of Technology矩形波导TEio模与圆波导TEii模转换器 TE01模一圆波导中损耗最低的模式South China University of Technology高次模场强轴对称，无极化简并电流无纵向分量损耗最低，频率升高，损耗下降可用于长距离传输线作高Q谐振腔South China University of Technology横截面上场分布纵截面上场分布壁面电流分布TE01

12、模场与壁面电流分布South China University of TechnologyE FieldV/m3. 00 65 e+00 3I 2.8186e+003I 2.6307e+00328e+0032. 2549e+0S32.0670S+0031.8791S+0031.69126+0031.50336+0031.31546+0031.12746+0039.3954e+0027.51 E 旅：+驱| 5.6372e+002I 3.7582e+A02I 1.87916+002波导TE01模的电场动态图I 1.8098e-004South China University of Techno

13、logyH F1e1dA/m1.25966+0011.18096+001I 1.10226+0011.02356+0019.4479e+00S8.6608e+0S07.8737e+A007.0866e+A006.sgge+eee5.5123e+0004.7252e+0003.93806+0003.1509e+000j 2.3638e+0S0I 1.57E6e：+000I 7.89506-001波导TE01模的磁场动态图I 2.37006-003South China University of TechnologyH F1eldA/m1.26006 + 0011.1812e+S01I 1.10

14、25e+S011.02376+0019.45016+0008.6626e+S007.8752e+S007.0878e+0006.3004e+000551306+0004.7256e+0003.9381e+000150 7e：+00Sj 2.38336+0001.57596+0007.88476-001波导TE01模的磁力线动态图I 1.05796-003JsurfA/nSouth China University of Technology波导TE01模的电流动态图I 5.1480e+000I 4.8263e+000 扌 4.50466+0004.1829e+0003.8612e+0003.5

15、395e+0003.2178e+0002.8961e+000 2.57446+0002.2527e+0001.9309e+0001. F；092e+0001.2875e+000 j 9.6583e-001I 6.44138-001 I 3.2242e-001 I 7.sssse-ee1+TEo i模高Q谐振腔South China University of Technology TMoi 模J A高次模场强轴对称，无简并轴线上纵向电场最强壁面上只有纵向电流可作雷达旋转关节South China University of Technology图中 虚线 为电 力线壁面上电流分布纵截面上场分布

16、TM01模场与壁面电流分布South China University of Technology波导TM01模的电场动态图E FieldV/mSouth China University of Technology3.33806+0033.1294e+0032.g2S8e+0032.71226+0032.50356+0032.29496+0032.0863e+0031.8777e+0031.6691e+0031.46056+0031.2519e+0031.0336+0038.3706+0026.2609e+0024.1748e+0022.0888e+0022.7234e-001波导TM01模

17、的电场动态图E FieldEV/mSouth China University of Technology3.3380e+0033.1294e+0032.9208e+0032.7122e+0032.5035e+SS32.2949e+0032.0863e+0031.8777e+0031.6691e+0031.46056+0031.2519e+0031.0433e+0038.34706+0026.26096+0024.1748e+0022.0888e+0022.7234e-001波导TM01模的电场动态图South China University of Technology波导TM01模的磁场动

18、态图South China University of Technology波导TM01模的磁场动态图South China University of Technology波导TM01模的磁场动态图South China University of Technology波导TM01模的电流动态图5.2 同轴线South China University of Technology同轴线是由两根共轴的圆柱导体所组成，内 外导体间均匀填充时，主模为TEM波，也可传 输TE、TM波（高次模）。TEM 波戈=Hz = oSouth China University of Technology根据Ma

19、xwel 1方程组，同轴线TEM波满足jPEr =咖比冋=血江丫1Q (H r drEr =HqE = E = 0 qzH = H = 0 rzTEM模场分布South China University of Technology横截面场纵截面场South China University of Technology同轴线横截面TEM模电场动态图South China University of Technology同轴线横截面TEM模磁场动态图H F1e1dA/m1. 10008+0011.05466+001I 1.0093e+0019.63946+0009.1859e+S008.7323e

20、+0008.2788e+0007.8253e+0007.3717e+0006.9182e+0006.46478+0006.0111e+0005.557Ee+BBB| 5.10418+0004.65068+0004.19708+000I 3.74358+000South China University of Technology电流、电压与特性阻抗I =(S Hdi =经乞-烬U = fb Edr = Ea ln-e -烬 a r0 aZ 二 U 旦 ln -c I 2 兀 aA电介质填充时儿二160 bZc -ln ()匕a:传输功率J P = Mu =1 咗二注 ln b 22 Z “ ac功率容量South China University of TechnologyPc =匚 ln导体衰减常数介质衰减常数Ec 介质击穿电场强度(1+1) 竺a b 2a 2ln ba高次模同轴线也存在高次模，采用与South China University of Technology分析方法，考虑到同轴线存在内导体边界条件，可以得到求截止波数的特征方程对于TM波E = R(r )0 (g 於cos m(p0 = A cos m(p + A2 sin m(p = Am = 0,1,2,