电磁场与电磁波复习及考试

1、1Field and Wave Electromagnetic电磁场与电磁波电磁场与电磁波2010. 6.112Ch. 2 Vector analysis Ch. 3 Static electric fieldsCh. 4 Solution of electrostatic fields Ch. 5 Steady electric currentCh. 6 Static magnetic fields Ch. 7 Time-varying fields and Maxwells equationsCh. 8 Plane electromagnetic wavesCh. 10 Waveguide

2、s and Cavity resonatorsCh. 11 Antennas and Radiation SystemsContents 31. Vector addition and Subtraction2. Products of Vectors 3. Orthogonal coordinate systems4. Gradient of a scalar field5. Divergence of a vector field 6. Divergence Theorem7. Curl of a vector field8. Stokess theorem9. Two null iden

3、tities10. Helmholtzs theoremChapter 2Vector AnalysisPreface4Chapter 7 Time-varying fields and Maxwells equations1. Maxwells Equations2. Electromagnetic Boundary Conditions 3. Potential Functions4. Wave Equations and Their Solutions5. Time-Harmonic Fields 5Review1. Maxwells Equations ()CSDH dlJdSt CS

4、BdE dldStdt 0SB dS SD dSQThe integral formDHJtBEt 0BDThe differential form SignificanceFaradays lawAmperes circuital lawGausss lawNo isolated magnetic charge2. Electromagnetic Boundary Conditions 212()0naEE212()0naBB212()nSaDD212()nSaHHJ63. Potential Functions4. Wave Equations and Their Solutions222

5、1EJEtt 222HHJt BAAEVt VAt 222AAJt222VVt1( , )d4VtuVtVRRR,RRR,( , )d4VtutVRRJ RA RRR75. Time-Harmonic Fields ( , , , )Re ( , , )j tE x y z tE x y z e/ 0EjHHJjEEH 22 AAJ 22VV 相量的模相量的模正弦量的幅值正弦量的幅值初位相初位相复角复角频率是已知频率是已知？频率频率( )cos()( )cos()mumiu tUti tIt相量乘以相量乘以 e ej j t t，再取实部，再取实部 ( )cos()( )cos() uijmu

6、mmjmimmu tUtUU ei tItII e三角表达式相量表达式（复数表示正弦量）()()cHjEjEjEj221EEjJ 22HHJ 8Chapter 8 Plane Electromagnetic Waves4. Plane Waves in Lossy Media3. Polarization of Plane Waves5. Group Velocity6. Flow of Electromagnetic Power and the Poynting Vector1. Plane Waves in Lossless Media2. Transverse Electromagnet

7、ic Waves11. Oblique Incidence at a Plane Dielectric Boundary7. Normal Incidence at a Plane Conducting Boundary8. Oblique Incidence at a Plane Conducting Boundary9. Normal Incidence at a Plane Dielectric Boundary10. Normal Incidence at Multiple Dielectric Interfaces922020 xxd Ek Edz0000( )( )( )jk zj

8、k zxxxEzEzEzE eE e0000( , )Recos() (V/m)jk zj txEz tE eeEtk z000pdzucdtk 00222 (rad/m)fkccTc002 (m)k000 (rad/m)kc 1. Plane Waves in Lossless Media0EjH 00000000120377 ( )k 1000( )= (V/m)njkaRjk RE RE eE e 1( )( ) or (A/m1( )( ) ),nH RaH RRjREE 1( )( ) or ( ) ( ) (V/m)nE RH REHjRaR 22222xyzkkkk xxyyzz

9、nka ka ka kkaxyzRa xa ya z2.Transverse Electromagnetic WavesEHan11( , )cos() ( , )cos() xxxmyyymEz ta EtkzEz ta Etkz xylinear polarizationcircular polarizationxyExyEelliptically polarizedxyExyExy ( ) ( ) jkzxxxmjkzjyyymEza E eEza E ee3. Polarization of Plane Waves124. Plane Waves in Lossy Media220cE

10、kE cccjjkj -1 (m ) ccjkj 1/2=()(1)cjjjjjj 00zzj zxEE eE eeFor a good conductor f(1)(1) ( )cjjf2 (m/s)puf22 (m)puff111= (m); for good conductors: = (m)2f135. Group Velocity1 (m/s)./gudd211=()1pgppppgppduddudduuuduuduud22 2 d 1 d2SVV(EH ) ds(E) vtEvH 2 (W/m ).SEH ddemSVV(ww ) vtvspS d21Re (W/m )2avSEH

11、6. Flow of Electromagnetic Power and the Poynting Vector147. Normal Incidence at a Plane Conducting Boundary xzyanraniErEiHrHiReflected waveIncident wavePerfect conductorMedium 2 ( 2= )Medium 1 ( 1= 0)z=021Re (W/m )2avSEH1 ( )( )nH RaE R( ) ( ) nE RaH R 158. Oblique Incidence at a Plane Conducting B

12、oundary i rPerfect conductorE iE rH iH rzxMedium 1 ( 1= 0)z=0anianrReflected waveIncident wavey i rPerfect conductorE iE rH iH rzxMedium 1 ( 1= 0)z=0anianrReflected waveIncident wavey169. Normal Incidence at a Plane Dielectric Boundary xzyanraniErEiHrHiReflected waveIncident waveMedium 1( 1, 1)z=0 E

13、tHtantTransmittedwaveMedium 2( 2, 2)002120210212; rtiiEEEE maxmin1 (Dimensionless).1ESE maxmin1 (Dimensionless).1ESSE 1710. Normal Incidence at Multiple Dielectric Interfaces xzyanraniErEiHrHiReflected waveIncident waveMedium 1( 1, 1)z=0 E3H3an3TransmittedwaveMedium 2( 2, 2)Medium 3( 3, 3) ani+E2+H2

14、+ an2-E2-H2-z=d ( )( ) ( ). ( )xyTotal E zZ zTotal Hz2111111121cossin(),cossinljlZlljl3222222232cossin(0).cossindjdZdjd1811. Oblique Incidence at a Plane Dielectric Boundarytotal reflection1221112121 /2sin/sin/sin/tctiiwhennnxzc02102021021coscos2cos; coscoscoscosrittiiitiitEEEE 02102021021coscos2cos

15、; coscoscoscosrtitiitiitiEEEE 221122121/sin.1 (/)B 19()2 (V/m)jxyizEe eirE iE rH iH rxyOA uniform plane wave is obliquely incident upon an infinite perfectly conducting plane placed at x=0 from the air. If the electric field intensity of the incident wave is Find:(1) The propagation vector (or wave

16、number vector) of the wave(2) The angle of incidence (3) The reflected angle (4) The complex magnetic field intensity of the incident wave (5) The complex electric field intensity of the reflected wave 20773sin 103sin 10 (V/m)2xzEetkyetkyFind:(1) The frequency of the wave (2) The phase constant of t

17、he wave k (3) The phase velocity of the wave (4) The intrinsic impedance of the wave (5) The wavelength of the wave (6) The polarization of the wave A wave propagates in a lossless medium characterized by r = 1, r = 4. The electric field intensity in the region is given by210.05(43 )( )(35) V/mjxzxy

18、Ejeeer( , )Etr( )H r,tH r,tS r avSr已知真空中正弦电场的复矢量为已知真空中正弦电场的复矢量为磁场强度的复矢量磁场强度的复矢量 磁场强度的瞬时值表达式磁场强度的瞬时值表达式 能流密度矢量能流密度矢量能流密度矢量的平均值能流密度矢量的平均值电场强度的瞬时值表达式电场强度的瞬时值表达式22(34 )( , )5 (V/m)jxyizx ye eEk( , )ix yH( , )x yrE当均匀平面波由空气向位于当均匀平面波由空气向位于x=0的平面的理想导体表面斜投射的平面的理想导体表面斜投射时，如图时，如图1所示。已知入射波电场强度为所示。已知入射波电场强度为试求：

19、试求：入射波的传播矢量入射波的传播矢量平面波的频率平面波的频率f 入射角入射角 入射波的磁场强度入射波的磁场强度反射波的电场强度反射波的电场强度23Example. The electric field intensity of a uniform plane wave in free space is given by ,Determine:377cos(6 )V/mxEty a(1) The phase velocity of propagation : 8001 3 10(/ )pyyvaam s (2) The phase constant 006k (rad/m) (3) The w

20、ave frequency 91.8 10222pkvfHz(4) The intrinsic impedance 000120Z(5) The wavelength 2263mk24A uniform plane wave propagating in a dielectric medium strikes normally upon a perfect conductor (z=0). If the incidence electric field is rE The polarization of the incidence wave? Obtain the expression of

21、the reflected electric field intensity rH(3) Obtain the expression of the reflected magnetic field intensity totalH(4) Obtain the expression of the total magnetic field intensity in the dielectric medium Example. 0.2100 100 jzixyjaaeE111222zxy25rE1R the incidence wave represents a right-handed circu

22、larly polarized wave. theof the reflected wave 0.20.2100 100 100 100 jzrxyjzxyRjaaejaae E1rzraZHE0.20.21100 100 1100 100 jzzxyjzyxajaaeZjaaeZ rHZ(3) the of the reflected wave Solution：261iziaZHE0.21100 100 jzzxyajaaeZ0.21100 100 jzyxjaaeZ0.20.2total11100 100 100 100 jzjziryxyxjaaejaaeZZHHH2100 100 c

23、os 0.2yxjaazZtotal0szzJaH 2100 100 zyxajaaZ 200 xyjaaZiH（4）theof the reflected wave the total magnetic field in the dielectric medium is sJ（5）the surface current on the perfect conductor 27irt1 12 2E tH iH txyO28irt1 12 2E tH iH txyOirt1 12 2E tE iH txyO E r29irt1 12 2E tE iH txyO E r30313233Chapter

24、 10 waveguides and cavity resonators2. Rectangular Waveguides 1. General Wave Behaviors along Uniform Guiding Structures341. General Wave Behaviors along Uniform Guiding Structures()()zj tj tzzjtzeeeee2222220 0 xyxyE(k )EandH(k )H00021jzzxEHEhxy00021jzzyEHEhyx00021zzxHEHjhxy00021jzzyHEHhyx0()( , , ;

25、 )Re( , )j tzE x y z tEx y e3521 (rad/m).cfkfg222211ccffkff211cggfuuu.d/ df21pcuuuff2gpu uu .21 ( )cTMfZf2 ( )1TEcZff222kh2222220 0 xyxyE(k )EandH(k )H22 or 2cchhf 362. Rectangular Waveguides the method of separation of variablesazyxb ,the method of longitudinal fields2220220z(h )E ( x,y)xy0zE ( x y

26、)X( x)Y( y),2XYhXY 0000000000E00000yzxyzx axzytxzy bEEEEEEEE00000000000000000000E00000yxyx axzzxzzx azzyzzyxybbyEHExHExHEyHyEEEE37 1 2 3ynk,nb, , , 1,2,3,xmkma, 0,1,2,ynknb, 0,1,2,xmkmaTM waveTE wave0ezzmnEE sinxsinyab02ezxmmnEE cosx sinyhaab 02ezynmnEE sinx cosyhbab 02ezxjnmnHE sinx cosyhbab02ezyjm

27、mnHE cosx sinyhaab 0ezzmnHH cosx cosyab02ezxmmnHH sinx cosyhaab02ezynmnHH cosx sinyhbab02ezxjnmnEH cosx sinyhbab02ezyjmmnEH sinx cosyhaab 38221 (Hz)2cmnmnfab222 (m)cmnmnab21 (rad/m).cfkf21 ( )cTMfZf2 ( )1TEcZffg222211ccffkff211cggfuuu.d/ df2= 11pcuuuu/ff2gpu uu .39 Example. A rectangular wave-guide

28、is filled with dielectric (perfect) medium ( r = 1, r =9),.and operates at a frequency 3GHz. If the dimensions of the wave-guide is a=2cm and b=1cmSolution：Show that the 10TE can propagate at this frequency811 10prrcu 899101 102.5 103 1022 0.02pcufHzHza m/s 10TESo the can propagate at this frequency

29、 in the waveguide. 221 (Hz)2cmnmnfab222 (m)cmnmnab402101116cff210101czpfkuf2998923 102.5 10110 111 103 10 (2)Determine phase constant: rad/m 21TEmncmnZff002101120240 113111116rrcff (3)Determine wave impedance21 (rad/m).cfkf2 ( )1TEcZff41102101ppcuuff86 11 10/11m s(4) Determine the phase velocity21cm

30、ngmnpfuuf81110/6m s(5) Determine the group velocity21pcuuuff211cggfuuu.d/ df42zayxb ,图 2若矩形波导形状如图若矩形波导形状如图2所示，宽壁的内尺寸为所示，宽壁的内尺寸为a=2cm，窄窄壁的内尺寸为壁的内尺寸为 b=1cm，其内充满理想介质其内充满理想介质( r=1， r=9)，工作频率为工作频率为3GHz。试求：试求：(1) TE10和和TM11模式的截至频率模式的截至频率fc10和和fc11 ;(2) 判断判断TE10和和TM11中哪个模式可以在上述波导中传播中哪个模式可以在上述波导中传播;(3) 该传输模式的波导波长该传输模式的波导波长 g ;(4) 接接(2)结果，该传输模式的相速度结果，