1. ElectromagneticWave Microwave Engineering CHO, Yong Heui

2. Microwave Engineering1. Wave equationE and H wave equation 2 2 2 E = 0 : E wave equation t 2 2: H wave equation 2 H = 0 t ( E ) = ( B ) Proof: Faradays law+ curl operatortSourceless system 2 EM Wave Lab 3. Microwave Engineering1. Wave equationWave propagation Propagation direction: z-direction 22 2 2 E = 0 : simplified wave equation z t Cartesian coordinate system 3EM Wave Lab 4. Microwave Engineering1. Wave equationWave propagation Assumption: E = x cos(vt z ) Propagation: constant wavefrontvt = z 4 EM Wave Lab 5. Microwave Engineering1. Wave equationWave velocity Substitution: () 1 v 2 cos(vt z ) x = 0 1 Wave velocity: v = = f Uniqueness theorem5 EM Wave Lab 6. Microwave Engineering1. Wave equationWhys EM wave propagate? Movement, variance Importance of two curl equations E = B H = J + D tt6EM Wave Lab 7. Microwave Engineering1. Wave equationEM simulatorsCST: MWS Ansoft: EnsembleAnsoft: HFSSHP: ADS7EM Wave Lab 8. Microwave Engineering1. Wave equationComplex number: time Circuit theory- e jt , = 2fEM theory2- e j (t kz ) = cos(t kz ) + j sin(t kz ), k = jte = j e j t t 8EM Wave Lab 9. Microwave Engineering1. Wave equationSignal representation using phasor jt e = j e j t t 9EM Wave Lab 10. Microwave Engineering2. Plane waveEM power Poynting vector - EH = S k = k EM power -( EH S) dS = P,VI = P Example of plane wave:E = x cos(vt z ) Approximation ( )10EM Wave Lab 11. Microwave Engineering2. Plane waveWave impedance Ratio of E and H - E / H = = [ ] Resistance - V /I =R[ ] 11EM Wave Lab 12. Microwave Engineering2. Plane waveReflection and transmission Incident wave e jk 0 z- E = xe jk 0 z , H =y ii0 Reflected wave- E = xe jk 0 z , H = y ejk 0 z r r 0 Transmitted wave jkz- Te jkz Et = xTe, Ht = y Er / Ei = , Et / Ei = T12 EM Wave Lab 13. Microwave Engineering2. Plane waveVisualization of reflection, transmission 13 EM Wave Lab 14. Microwave Engineering2. Plane waveBoundary conditions E continuity at z = 0- E +E =Ei rt H continuity at z = 0- H +H =Hir t Reflection and transmission coefficient- = 0 , T = 1 + + 0 14EM Wave Lab 15. Microwave Engineering2. Plane waveTransparency ( ) No reflection: transparency- = 0 = 0 Total reflection- = 0 = 1 : PEC (Electric Conductor)- = = 1 : PMC (Magnetic Conductor)15 EM Wave Lab 16. Microwave Engineering2. Plane waveLossy media Ohms law: induced current density- J = E , V = IR Complex permittivity(- H = + j ) E = j E - = 1 + = Re( ) j Im( ) j Stealth16 EM Wave Lab 17. Microwave Engineering2. Plane waveSkin depth Conductor - >> , = 1 + j Skin depth: - Wavenumber: k = = j 1 - == 2 Water 17EM Wave Lab 18. Microwave Engineering2. Plane wavePolarization: direction of E field LP: Linear Polarization CP: Circular Polarization EP: Elliptic Polarization Vertical LP Horizontal LP 18EM Wave Lab