# emw - Electromagnetic Waves EEL3472 EEL3472 Spherical...

This preview shows pages 1–6. Sign up to view the full content.

EEL 3472 EEL 3472 Electromagnetic Electromagnetic Waves Waves

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
EEL 3472 EEL 3472 2 Electromagnetic Waves Electromagnetic Waves Spherical Wavefront Direction of Propagation Plane-wave approximation
EEL 3472 EEL 3472 3 Electromagnetic Waves In the case of              (fields inside a good insulator such as air or vacuum) we have  vector  Helmholtz    equation This equation has a rich variety of solutions. Let us assume that     has only an x component and varies  only in the z direction.   In this case the vector Helmholtz  equation simplifies to scalar  Helmholtz equation The latter equation is similar to the voltage wave equation for a lossless transmission line.  E j j E E ) ( 2 ϖε σ ϖ μ + = ϖε << σ E E 0 2 2 = + E E με ϖ 0 2 2 2 = + x E z x E Electromagnetic Waves Electromagnetic Waves

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
EEL 3472 EEL 3472 4 The solution of the scalar Helmholtz equation is where                 , to be found from boundary conditions;  the minus and the plus correspond to waves moving in the +z and –z directions, respectively. In terms of propagation constant k  The position of a field maximum is given by    z z j o x e E e E E γ με ϖ ± ± = = 0 o j e A E φ 0 0 = ) cos( ] Re[ ) , ( o o t j z j o x z t A e e E t z E + - = = - με ϖ φ + με = = φ + με ϖ - ϖ o max o max t z 0 z t 1 max = = dt dz U p s / m 10 x 99793 . 2 / 1 c U   ,    If 8 o o p o o = ε μ = = ε = ε μ = μ ) cos( ) , ( o o x kz t A t z E + - = με ϖ = k Electromagnetic Waves Electromagnetic Waves k
EEL 3472 EEL 3472 5 Characteristics of  Plane Waves For a plane wave which propagates in the +z direction and  has an electric field directed in the x direction where  The time-varying electric field of the wave must, according  to Faraday’s law, be accompanied by a magnetic field.      Thus, when                              and is called the characteristic impedance of vacuum. x jkz o e e E E - = λ π = με ϖ = / 2 k y jkz o y x e e E jk e z E E H j - - = = × = ϖ μ - y jkz e e E H - = η 0 = η μ = μ ε = ε 377      , o o ε μ η= wave impedance (intrinsic impedance of  the medium ( 29 dt dB - Electromagnetic Waves Electromagnetic Waves

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 26

emw - Electromagnetic Waves EEL3472 EEL3472 Spherical...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online