RF & Microwave EngineeringBETE-Spring 2009

Department of Electrical EngineeringAir University

Waveguides

TEM,TE & TM Modes

Lecture No. 13

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

Introduction

• There are several ways by which electromagnetic waves can propagate.

– Coaxial cable.

– Microstrip Lines

– Free Space (Unguided)

– Wave Guide Structures

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

Why Waveguides?

• Transmission Lines can only support TEM Waves.

• At high frequency attenuation, skin effect, and power handling capability limits the use of Transmission Lines.

• Wave Guides are the solution at microwave frequencies giving us:– Medium to Large bandwidth – Lower signal Attenuation– Greater power handling capacity

A waveguide is a metallic hollow structure of meaningful

shape which is used for guided wave propagation at high frequencies in an efficient manner.

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

Types of Waveguides

• Rectangular

• Circular

• Elliptical

In this course, we will only focus on rectangular waveguides.

Theory of waveguides requires an understanding of

Maxwell Equations and basic calculus!!

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

Rectangular Waveguide

It is assumed that the waveguide is filled with a material of permittivity ε and permeability µ.

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

Concept of Modes

• We will first develop an extremely important property of EM waves that propagate in homogenous waveguides.

• This will lead to the concept of different “modes” that travel inside a waveguide

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

Solution of Maxwell’s Equations

Electric and Magnetic field components along x,y,zcoordinates

Ex,Ey and Hx,Hy are transverse components

Ez, Hz are longitudinal/axial components

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

Solution of Maxwell’s Equations

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

Solution of Maxwell’s Equations

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

Solution of Maxwell’s Equations

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

Solution of Maxwell’s Equations

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

Wave Modes

• Transverse Electric and Magnetic (TEM)

• Transverse Electric (TE)

• Transverse Magnetic (TM)

• In a given waveguide at a given frequency, several field configurations may satisfy Maxwell’s equations. These field configurations are called wave modes.

• Every mode has its own propagation characteristics: velocity, attenuation, and cutoff frequency.

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

Waveguide Modes

• TE mode• TM mode• TEM mode

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

TE Mode

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

Wavenumber

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

Wavenumber

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

Cuttoff Frequency

Waveguides always operate above a certain frequency called the “cut off frequency”. At a frequency below cutoff frequency, field attenuates very rapidly and no wave can propagate.

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

X-Band Waveguide

WR 90

Waveguide

in the lab!

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

TM Modes

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

TM Modes Cutoff frequency

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

TEM Mode

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

Mode Distributions