{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# Lecture5 - Lecture 5 Notes 95.658 Spring 2012...

This preview shows pages 1–3. Sign up to view the full content.

Lecture 5 Notes, 95.658, Spring 2012, Electromagnetic Theory II Dr. Christopher S. Baird, UMass Lowell 1. Waveguides Continued - In the previous lecture we made the assumption that the wave is free in the z dimension but stays general in the other dimensions, and has a harmonic time dependence. - From this simple set-up, we were able to find the transverse fields in terms of the parallel fields: t E t =− i k E z t B t =− i k B z ̂ z ⋅(∇ t × E t )= i ω B z ̂ z ⋅(∇ t × B t )=− i μ ϵω E z E t = i μ ϵω 2 k 2 ( k t E z −ω ̂ z ×∇ t B z ) B t = i μ ϵω 2 k 2 ( k t B z +μ ϵω ̂ z ×∇ t E z ) - Looking at the two bottom equations, we realize that each is a superposition of two particular solutions. - If the parallel component of the electric field is zero, E z = 0, but the transverse components of the electric field E t are non-zero, and all components of the magnetic field are non-zero, then the wave is known as a “Transverse Electric” wave or “TE” wave. - If the parallel component of the magnetic field is zero, B z = 0, but the transverse components of the electric field B t are non-zero, and all components of the electric field are non-zero, then the wave is known as a “Transverse Magnetic” wave or “TM” wave. - The solution presented in the equations above can be thought of as a superposition of a TM wave and a TE wave. TRANSVERSE ELECTRIC (TE) WAVE: E t = i ω μ ϵω 2 k 2 ( ̂ z ×∇ t B z ) B t = i k μ ϵω 2 k 2 ( t B z ) TRANSVERSE MAGNETIC (TM) WAVE: E t = i k μ ϵω 2 k 2 ( t E z ) B t = i μ ϵω μ ϵω 2 k 2 ( ̂ z ×∇ t E z ) z x y B z B t E t z x y B t E z E t

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

View Full Document
- There is a special case where both the electric field and the magnetic field are completely transverse, that is B z = 0 and E z = 0. This is called a transverse electromagnetic (TEM) wave. - A TEM wave is not supported in simple hollow metal waveguides. A plane wave in free space or in an infinite uniform material exists in the TEM 00 mode. TEM waves are the dominant ones in coaxial cables. - The problem has been reduced to finding the parallel components of the fields, and then the transverse components follow immediately. - Let us now use the divergence equations at the top of the first page and plug in the solution for the transverse fields: TM: t i k    2 k 2 t E z =− i k E z TE: t i k   2 k 2 t B z =− i k B z - After multiplying through: TM: t 2 E z =−(μϵ ω 2 k 2 ) E z TE: t 2 B z =−(μ ϵω 2 k 2 ) B z - Solving for the waves inside any waveguide reduces to solving the above equations and applying appropriate boundary conditions.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 7

Lecture5 - Lecture 5 Notes 95.658 Spring 2012...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online