ELECTROMAGNETICS AND APPLICATIONS Lecture 11 RF & Microwave TEM Lines Luca Daniel

L10-2 Review of Fundamental Electromagnetic Laws Electromagnetic Waves in Media and Interfaces Digital & Analog Communications oTEM transmission lines (cables and IC/PCB traces) oDigital communications (transients) oRF communications (matching loads to amplifiers)  Telegrapher equations in complex notation (frequency domain)  TEM terminated by short circuit in frequency domain  Voltage/Current Standing waves on TEM line  Line Impedance and Reflection Coefficient along the line  Smith Chart  Voltage Standing Wave Ratio oRLC and TEM resonators Today’s Outline Today

L10-3 Course Outline and Motivations Electromagnetics: –How to transport signals and power on “guided systems” Applications –digital electronics: e.g. analyze transients when you send a signal from the CPU chip to the GPU chip, or from your keyboard to your iPad –analog and biomedical electronics: e.g. match load of RF cables bringing signal from power amplifier to MRI coil antennas to avoid reflections CPU RAM GPU A/D D/A PA

RF / Microwave Systems Generic System Architecture: Signal Processing Guide Antenna Guide Amplification Microwave or optical tuning, resonance coupling waveguides microwave integrated circuits matching transitions Detection

Review Maxwell vs. Telegrapher’s Eqns - Phasors Electromagnetic Fields in the medium inside TEM line Corresponding Voltages and Currents on guiding metals (induced by boundary conditions) Solutions:      x y z V+V+ V-V-

Voltage Standing Waves – Electric Fields Normal incidence on perfect conductor c == x z 0 c x z 0 TEM line terminated by short circuit c E = 0 every half wavelength for any tV = 0 every half wavelength for any t Electric/Voltage Standing Waves oscillate without moving or Every half wavelength the TEM line behaves like a short circuit! z 0 x

Current Standing Waves - Magnetic Fields z 0 y or Every half wavelength the TEM line behaves like an open circuit! Magnetic/Current Standing Waves oscillate without moving Normal incidence on perfect conductor c == x z 0 TEM line terminated by short circuit c x z 0 c

Line Impedance Z(z) Definition: Line Impedance Definition: Reflection Coefficient  (z) Equivalent circuit Z(z) V(z) I(z) ZoZo + - z Example:  L = 0  Z(z) = Z o 0 Note: the line impedance depends very much on the load ZLZL

Examples of Z(z) transformations Example: half-wave and quarter-wave lines: ZoZo 0 z ? ZLZL