chap0 introduction

1

Theory of Guided WavesTheory of Guided Waves

Ruey-Beei Wu

Rm. 340, Dept. Electrical Engineering

E-mail: [email protected]

Website: http://cc.ee.ntu.edu.tw/~rbwu

國立台灣大學National Taiwan University

Main Focus

• to give a theoretical treatment of wave-guiding structures

and related phenomenon along with the development of

analytical methods for the solution of important

engineering problems.

• to deal with three basic guides structures, including

transmission lines, metallic waveguides, (and dielectric

waveguides).

• to address various guiding characteristics, including

propagation, excitation, discontinuities, and periodical

structures.

• why we revisit these topics?

2


Introduction to Waves

• Unguided waves:

– Propagation, scattering, radiation (antennas)

� IEEE Antennas and Propagation

– Inverse scattering, remote sensing

� IEEE Geoscience & Remote Sensing

• Guided waves:

– Waveguides, discontinuities, circuit components

� IEEE Microwave Theory and Techniques

– Interconnections, packaging, transients

�IEEE Advanced Packaging

• Interactions between guided/unguided waves

� IEEE Electromagnetic Compatibility


Applications

• Power transmission:– Low frequencies (50 or 60Hz)

• Communications:– High frequencies

• Microwave (0.1-1000GHz)

• Optical Spectrum (µm)

• Radar

• Remote sensing

• Microelectronics– VLSI, Computers, Consumer Electgonics

• Electro-Optics

3

WaveguidesWaveguides


Guided Waves

• Transverse electromagnetics (TEM) waves,

– Ez = Hz = 0

• Transverse electric (TE) waves,

– Ez = 0, Hz ≠ 0

• Transverse magnetic (TM) waves,

– Hz = 0, Ez ≠ 0

• Hybrid (HB) waves,

– Ez ≠ 0, Hz ≠ 0

• Cutoff frequency fc

– TEM: fc = 0

– TE, TM, fc ≠ 0

– HB

z

4


Waveguides -1

A) Transmission lines (No. of conductors ≥ 2)

– Non-planar structures • Two-wire or multi-wire lines

• Coaxial lines (circular, rectangular)

TEM, fc =0, 0 ~ GHz

HB, fc ≠ 0

– Quasi-planar structures• Finline

– Planar structures• Strip lines, TEM

• Microstrip lines (MS), HB

h w Striplinebw


Metallic Waveguides -2

– Uni-planar structures• Coplanar waveguides (CPW)

– 文正 (C. P. Wen), 1969, Microwave Application Award 1995

• Slotlines (SL), Cohn 1969

• Coplanar striplines (CPS), 1975

– Notes• Planar ~ uni-planar structures

• Hybrid ~ Quasi TEM

• Microwave

– Microwave integrated circuit (MIC)

B) Hollow Cylindrical Waveguides– Rectangular waveguides

– Circular waveguides

– Elliptical waveguides

TE, TM, HB: fc ≠ 0

Microwave

w1w2

5


Waveguides -3

C) Dielectric Waveguides

– Planar (slab) dielectric waveguides

– Optical integrated circuits

– Rectangular dielectric waveguides

– Circular dielectric waveguides• Optical fibers

– Notes• TE, TM, HB

• Optical spectrum


Periodic Structures

• Floquet’s Theorem

• Example 1: Lossless Microwave Quadrupoles

– Propagation in an Infinite Periodic Structure

– Terminated Periodic Structure

• Example 2: Capacitive Loaded Rectangular W/G

– Power flow and Bandgap

6

Why Revisit?Why Revisit?

國立台灣大學National Taiwan UniversityIntroduction – Richard Mellitz

Solution Spheres – Level & Influence

Solution with Solution with

analytic aideanalytic aide

Solution with Solution with

parametric studyparametric study

Simulation by Simulation by

SoftwareSoftware

7

國立台灣大學National Taiwan UniversityIntroduction – Richard Mellitz

#1: Solution Paradigms

• Point Solution

– Applies to a given instance of a structure or specimen

• Parametric Solution

– Applies to any single given structure

– Encompasses a locus of specific solutions.

– Ex.: filter design by microstrip coupled lines structure

• General Solution

– Applies to many structures of a given type

– Encompasses an explanation with analytic solutions

– Ex: locus of all solutions for a filter with any desired specification.


#2: Train of Analytical Thinking

• Statement of Problems

– Identify structure features for desired performance

– Ex. Wave guides -> infinitely long structures of

identical cross section

• Problem Abstraction

– Find mathematically simplest structure but it still keeps

key features -> Canonical problem

– Ex. TEM wave in Tx-line -> Parallel plate line

• Formulation & Derivation

– Express problem into mathematical description

• Analytical Solutions

8


# 3: Canonical Problems Repeat# 3: Canonical Problems Repeat

LTCC Multilayer LTCC Multilayer

StructureStructure


Vertically Stacked LTCC Filters

multilayer construction + Stacked cavities

Traditional hollow waveguide

4-pole quasi-elliptic fully stacked-cavity filter4-pole quasi-elliptic fully stacked-cavity filter

� short-ckt CPW feed lines to

realize cross coupling for

non-adjacent resonators

� 27-33GHz with 20dB return

loss at pass band

� 0.72 × 0.47 × 0.16λg

SIW ConceptSIW Concept

Resonator 1

Resonator 2

Resonator 3

Resonator 4

SIW SIW –– Miniature mmWave PassivesMiniature mmWave Passives

NTUNTU--NCTUNCTU--ITRIITRI

T.-M. Shen, C.-F. Chen, T.-Y. Huang, and R.-B. Wu, “Design of vertically stacked waveguide filters in

LTCC,” IEEE MTT-55, pp. 1771-1779, Aug 2007

9


Transition from MS to SIW

C. K. Yau, T. Y. Huang, T. M. Shen, H. Y. Chien, and R. B. Wu, “Design of 30GHz transition

between microstrip line and substrate integrated waveguide,” APMC, Dec. 2007.

國立台灣大學National Taiwan UniversityT.-L. Wu, Y.-H. Lin, T.-K. Wang, C.-C. Wang, and S.-T. Chen, “Electromagnetic bandgap power/ground planes for wideband

suppression of ground bounce noise and radiated emission in high-speed circuits,” IEEE MTT-53, No. 9, pp. 2935 - 2942, Sept. 2005

Reference EMI performance

Power integrity performance

Geometry

� Wide-band suppression of P/GBN and radiated emission

Long-Period-Coplanar EBG P/G Planes

10

Course ContentsCourse Contents


Course Organization – EM Group

工程數學物理數學(微方、複變)

電磁學

電磁波實驗微波工程微波系統導論天線與傳播電磁理論微波電路天線光電電磁學

數值電磁學導波理論高速數位系統電磁設計微波單晶積體電路

電磁相容濾波器設計天線專題微波積電專題無線通訊功率放大器設計T-AdvP

T-EMC

T-LT

T-AP

T-MTT

T-AP, T-MTT

必修複選必修

選修核心課程專業課程進階課程

大學部研究所

11


Purpose

• Propagation

– TEM wave

– TE/TM wave

• Excitation

– TE/TM wave excited by Tx-line

• Discontinuities

– Circuit components

• Periodical structures


Outline

• Basic Theory (2 weeks)Introduction and Basics, Equivalence, Reciprocity, and Green’s

Functions

• Transmission Lines (2 weeks)Basics, Parameter Extraction

• Waveguides (4 weeks)Metallic Waveguide, Modal Orthogonality, inhomogeneously filled

waveguides

• Waveguide Excitation (3 weeks)Probe, Loop, Aperture Coupling

• Waveguide Discontinuities (2 weeks)Variational Methods, Capacitive Diaphragm

• Periodic Structures (1 weeks)Floquet’s Thm, Periodic loaded waveguides

12


References & Scores

• Textbook:

– R. E. Collins, Field Theory of Guided Waves, 2nd ed.,

IEEE Press, 1991. (民全書局有，絕版書)

• Scores & evaluation

– Mid-Term Exam., 40%

– Final Exam., 40%

– Exercise, 20%


Basics

• A. Time Harmonic Fields

• B. Maxwell Equations

• C. Poynting Vector

• D. Solution of Helmholtz Eq.

• E. Equivalence Principle

• F. Duality & Babinet’s Principle

• G. Reciprocity Theorem

13


TEM Waves and Transmission Lines

• 1.1 TEM Waves

• 1.2 Transmission Lines

• 1.3 Circuit theory for Lossy Lines

• 1.4 Field Theory for Lossless Transmission Lines

• 1.5 Power Loss in Planar Conductors

• 1.6 Field Theory for Lossy Lines

• 1.7 General Two-Conductor Lines

• 1.8 Transmission Line Parameters

• 1.9 Conformal Mapping Method

• 1.10 Variational Method

• 1.11 Problems


Cylindrical Waveguides

• 2.0 Introduction (0-1)

• 2.1 Auxiliary Potential Functions (1-9)

• 2.2 General Properties of Cylindrical Waveguides (2-11)

• 2.3 Orthogonal Properties of Modes (3-9)

• 2.4 Complex Poynting Theorem (4-3)

• 2.5 Power (5-6)

• 2.6 Energy (6-6)

• 2.7 Lossy Waveguides (7-6)

• 2.8 Problems

14


Excitation of Waveguides -1

• 3.0 Introduction

• 3.1 Green’s Functions (1-4)

• 3.2 Green’s Functions for Hn0 Modes in Rectangular Guide (2-4)

• 3.3 Dyadics (3-5)

• 3.4 Dyadic Green’s Functions (4-3)

• 3.5 Infinity-Space Dyadic Green’s Functions (5-5)

• 3.6 Lorentz Reciprocity Theorem (6-3)

• 3.7 Love’s Field Equivalence Principle (7-2)

• 3.8 Probe Antenna (8-22)

• 3.9 Radiation in Cylindrical Waveguides (9-10)

• 3.10 Antenna Input Impedance (10-5)

• 3.11 Image Theory (11-1)


Excitation of Waveguides -2

• 3.12 Vector Potentials (12-10)

• 3.13 Fields of Magnetic Dipole Sources (13-2)

• 3.14 Loop Antenna (14-17)

• 3.15 Field Equivalence Principle (15-5)

• 3.16 Coupling by Small Apertures (16-31)– 3.16.1 Original Aperture Coupling Problem 16-1)

– 3.16.2 Auxiliary Problems 16-2

– 3.16.3 Equivalent Problem 16-16

– 3.16.4 Original Aperture Coupling Problem 16-19

– 3.16.5 Dipole Moments of Elliptic Disk 16-25

– 3.16.6 Aperture Coupling in Rectangular Waveguides 16-28

• 3.17 General Aperture Coupling Problems (17-7)

• 3.18 Problems

15


Waveguide Discontinuities

• 4.0 Introduction (0-2)

• 4.1 Inhomogeneously Filled Waveguides (1-6)

• 4.2 Variational Methods (2-22)

– 4.2.1 Junction Problem 2-1

– 4.2.2 Input Admittance of Junction 2-11

• 4.3 Capacitive Diaphragm (3-21)

– 4.3.1 Formulation 3-2

– 4.3 2 Variational Expression for Shunt Susceptance B 3-9

– 4.3.3 Approximate Evaluation of B 3-14


Periodic Structures

• 5.1 Floquet’s theorem

• 5.2 Lossless microwave quadrupoles

• 5.3 Propagation in an infinite periodic structures

• 5.4 Terminated periodic structure

• 5.5 Capacitively loaded rectangular waveguides

• 5.6 Energy and power flow

chap0 introduction

Documents