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# 課程大綱 - PowerPoint PPT Presentation

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• Introduction of Electromagnetic Theory (1)
• Transmission Line Theory (2)
• Transmission Line (3, 10.5)
• Microwave Network Analysis (4)
• Impedance Matching and Tuning (5)
• Microwave resonators (6)

ps. 括弧中之數字代表所對應教科書之章節

• D.M. Pozar, Microwave Engineering, 3nd. Ed. John Wiley & Sons, 2005.

• Lecture Note by Prof.T.S. Horng, E.E. Dept. NSYSU.
• T.C. Edwards and M.B. Steer, Foundations of Interconnect and Microstrip Design, 3nd. Ed. John Wiley & Sons, 2000.

• 簡答題
• 重點敘述
• 課本內容之Point of Interest
• 設計及計算題
• 範例及問題
• 習題

• 期中考 40%
• 期末考 40%
• 二次(模擬)作業 20%

• The term microwave (微波) refers to alternating current signals with frequencies between 300 MHz (3108 Hz) and 30 GHz (31010 Hz), with a corresponding electrical wavelength between 1 m and 1 cm. (Pozar defines the range from 300 MHz to 300 GHz)
• The term millimeter wave (毫米波) refers to alternating current signals with frequencies between 30 GHz (31010 Hz) to 300 GHz (31011 Hz), with a corresponding electrical wavelength between 1 cm to 1 mm.
• The termRF (射頻) is an abbreviation for the “Radio Frequency”. It refers to alternating current signals that are generally applied to radio applications, with a wide electromagnetic spectrum covering from several hundreds of kHz to millimeter waves.
Functional Block Diagram of a Communication System

Input signal

(Audio, Video, Data)

Input Transducer

Transmitter

Wire

or

Wireless

Channel

Output signal

(Audio, Video, Data)

Output Transducer

Electrical System

Antenna and Wave Propagation

Microwave & Millimeter Wave

Satellite

communication

Ionsphere

Sky Wave

Repeaters(Terrestrial communication)

50Km@25fts antenna

Direct Wave

Surface Wave

Receiving Antenna

Transmitting Antenna

Earth

Absorption by the atmosphere

Remote sensing:

20 or 55

GHz

Spacecraft Communication:

60 GHz

Communication

Windows:

35.94and 135

GHz , below 10 GHz

IEEE Standard C95.1-1991 recommended power density limits for human exposure to RF and microwave electromagnetic fields

Coaxial Cable

Wireline

Fiber

Waveguide

1 GHz

1 MHz

10 GHz

1 kHz

1014 Hz

1015 Hz

10 MHz

100 kHz

10 kHz

100 GHz

100 MHz

Wireline and Fiber Optic Channels

RF

Millimeter

wave

Microwave

Guided Structures at RF Frequencies

Planar Transmission Lines and Waveguides

Conventional Transmission Lines and Waveguides

Good for Microwave Integrated Circuit (MIC) Applications

Good for Long Distance Communication

Coaxial Cable

Wireline

Fiber

Waveguide

1 GHz

1 MHz

10 GHz

1 kHz

1014 Hz

1015 Hz

10 MHz

100 kHz

10 kHz

100 GHz

100 MHz

Theory

Conventional Circuit Theory

Microwave Engineering

Optics

l >> 

l << 

l 

Transmission Line

RF and Microwave ICs and Systems

RF and Microwave Active and Nonlinear Components

RF and Microwave Passive Components

Microwave Resonator

Microwave Network

Impedance Matching

Transmission Line

Circuit Theory, Electronics, Electromagnetics

RF & Microwave Background Build-Up

Goal for this course

### Chapter 1

Electromagnetic Theory

History of Microwave Engineering
• J.C. Maxwell (1831-1879) formulated EM theory in 1873.
• O. Heaviside (1850-1925) introduced vector notation and provided an analysis foundation for guided waves and transmission lines from 1885 to 1887.
• H. Hertz (1857-1894) verified the EM propagation along wire experimentally from 1887 to 1891
• G. Marconi (1874-1937) invented the idea of wireless communication and developed the first practical commercial radio communication system in 1896.
• E.H. Armstrong (1890-1954) invented superheterodyne architecure and frequency modulation (FM) in 1917.
• N. Marcuvitz, I.I. Rabi, J.S. Schwinger, H.A. Bethe, E.M. Purcell, C.G. Montgomery, and R.H. Dicke built up radar theory and practice at MIT in 1940s (World War II).

ps. The names underlined were Nobel Prize winners.

Maxwell’s Equations
• Equations in point (differential) form of time-varying
• Equations in integral form
• Generally, EM fields and sources vary with space (x, y, z) and time (t) coordinates.

Time-Harmonic Fields

When steady-state condition is considered, phasor representations of Maxwell’s equations can be written as : (time dependence by multiply e -jt )

• Where MKS system of units is used, and
• E : electric field intensity, in V/m.
• H : magnetic field intensity, in A/m.
• D : electric flux density, in Coul/m2.
• B : magnetic flux density, in Wb/m2.
• M : (fictitious) magnetic current density, in V/m2.
• J : electric current density, in A/m2.
• ρ: electric charge density, in Coul/m3.
• ultimate source of the electromagnetic field.

Q : total charge contained in closed surface S.

I : total electric current flow through surface S.

In free space

• In istropic materials

(e.g. Crystal structure and ionized gases)

where 0 = 8.85410-12 farad/m is the permittivity of free space.

μ0 = 410-7 Henry/m is the permeability of free space.

Question:2(6) equations are not enough to solve 4(12) unknown

field components

• Constitutive Relations

Complex and 

where Pe is electric polarization, Pm is magnetic polarization,

e is electric susceptibility, and m is magnetic susceptibility.

• The negative imaginary part of  and  account for loss in medium (heat).

where  is conductivity (conductor loss),

ω’’ is loss due to dielectric damping,

(ω’’ + ) can be seen as the total effective conductivity,

 is loss angle.

• In a lossless medium,  and  are real numbers.
• Microwave materials are usually characterized by specifying the real permittivity, ’=r0,and the loss tangent at a certain frequency.
• It is useful to note that, after a problem has been solved assuming a lossless dielectric, loss can easily be introduced by replaced the real  with a complex .

Example1.1 : In a source-free region, the electric field intensity is given as follow. Find the signal frequency?

Solution :

Boundary Conditions

• Fields at a dielectric interface
• Fields at the interface with a perfect conductor (Electric Wall)
• It is analogous to the relations between voltage and current at the end of a short-circuited transmission line.
• Magnetic Wallboundary condition (not really exist)
• It is analogous to the relations between voltage and current at the end of a open-circuited transmission line.

Helmholtz (Vector) Wave Equation

• In a source-free, linear, isotropic, and homogeneous

medium

• Solutions of above wave equations
• Plane wave in a lossless medium

is defined the wavenumber, or propagation constant

, of the medium; its unit are 1/m.

is wave impedance, intrinsic impedance of medium.

In free space, 0=377.

In free space, vp=c=2.998108 m/s.

is wavelength, defined as the distance between two successive maximum (or minima) on the wave.

In wave equations, jk for following conditions.

• Plane wave in a general lossy medium
• Good conductor

Condition: (1)  >>ω or (2) ’’>>’

is skin depth or penetration depth, defined as the amplitude of fields in the conductor decay by an amount 1/e or 36.8%, after traveling a distance of one skin depth.