7e Applied EM by Ulaby and Ravaioli 2. Transmission Lines 7e Applied EM by Ulaby and Ravaioli

Transmission Lines = roads for a wave to travel A transmission line connects a generator to a load Transmission lines include: Two parallel wires Coaxial cable Microstrip line Optical fiber Waveguide etc.

Types of Transmission Modes

Dispersion

Example of TEM Mode fc (cutoff frequency): f > fc = travel, f < fc = blocked TEM (transverse electromagnetic) mode: Ez = 0, Hz = 0, # of conductors > 1 quasi-TEM: TEM with mixed dielectric, fc (cutoff frequency) = 0 TE (transverse electric) mode: Ez = 0, fc > 0 TM (transverse magnetic) mode: Hz = 0, fc > 0 Hybrid mode: TE+TM, fc > 0

Electric and Magnetic Fields in A Transmission Line Voltage and Current from E and H Voltage and Current: obtained from E and H

Transmission Line Circuit Model

Expressions will be derived in later chapters

Transmission-Line Equations ac signals: use phasors Telegrapher’s equations

Phase constant complex propagation constant attenuation constant (전파상수) (감쇠정수) (위상정수)

(특성임피던스)

Solution of Wave Equations (cont.) In general: wave along +z because coefficients of t and z have opposite signs wave along –z because coefficients of t and z have the same sign

Example 2-1: Air Line

Microstrip Line Phase velocity in dielectric: Phase velocity for microstrip: Quasi-TEM : Ez & Hz very small

Microstrip (cont.) s = w/h

Lossless Transmission Line If Then: