Yungui MA ( 马云贵 )E-mail: yungui@zju.edu.cn

Office: Room 209, East Building 5, Zijin’gang campus

Microwave Microwave FundamentalsFundamentals

Electromagnetic spectrum

Band P L S C X Ku K Ka

Freq (GHz)

0.23-1 1-2 2-4 4-8 8-12.5 12.5-18 18-26.5 26.5-40

300 MHz 3 GHz 30 GHz 300 GHz 3 THz 30 THz 300 THz

Photonic devices

Electronic devices

Microwaves THz gap visibleRadio waves UV

Microwave bands

Millimeter waves

Infrared

Microwave applicationsWireless communications (cell phones, WLAN,

…)Global positioning system (GPS)Computer engineering (bus systems, CPU, …)Microwave antennas (radar, communication,

remote sensing, …)Other applications (microwave heating, power

transfer, imaging, biological effect and safety)

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SyllabusChapter 1: Transmission line theory

Chapter 2: Transmission lines and waveguides

Chapter 3: Microwave network analysis

Chapter 4: Microwave resonators

Reference books ： 1.David M. Pozar, Microwave Engineering, third edition (Wiley, 2005)2.Robert E. Collin, Foundations for microwave engineering, second edition (Wiley, 2007) 3.J. A. Kong ， Electromagnetic theory (EMW, 2000)

Chapter 1: Transmission line theory 1.1 Why from lumped to distributed

theory?

1.2 Examples of transmission lines

1.3 Distributed network for a

transmission line

1.4 Field analysis of transmission lines

1.5 The terminated lossless

transmission line

1.6 Sourced and loaded transmission

lines

1.1 Why from lumped to distributed theory?

At low frequencies: Can simply use a wire to connect two components

f =50 HZ, wavelength = 6 x 106m;

At high frequencies: Cannot simply use a wire to connect two components

f =500 MHZ, wavelength = 0.6 m;

1.1 Why from lumped to distributed theory?

1.1 Why from lumped to distributed theory?

E field

H field

Microwave component: electric size << the operating wavelength

R = series resistance per unit length, for both conductors, in /m;L = series inductance per unit length, for both conductors, in H/m;G = parallel conductance per unit length, in S/m;C = parallel capacitance per unit length, in F/m.

Loss: R (due to the finite conductivity) + G (due to the dielectric loss)

Transmission line theory

Transmission line theory

Bridges the gap between field analysis and basic circuit theory

Extension from lumped to distributed theoryA specialization of Maxwell’s equationsSignificant importance in microwave network

analysis

The key difference between circuit theory and transmission line theory is electrical size. Circuit analysis assumes that the physical dimensions of a network are much smaller than the electrical wavelength, while transmission lines may be a considerable fraction of a wavelength, or many wavelengths, in size. Thus a transmission line is a distributed-parameter network, where voltages and currents can vary in magnitude and phase over its length.

1.2 Examples of transmission lines

(2) Coaxial line

Magnetic field

(dashed lines)

Electric field

(solid lines)

(3) Microstrip line

(1)Two-wire line

Review: Kerchhoff’s law

1.3 Distributed network for a transmission line

KCL: 01

n

kki KVL: 0

1

n

kkv

1.3 Distributed network for a transmission line

1.3 Distributed network for a transmission line

Derivation of differential transmission line equation

KVL:

Derivation of differential transmission line equation

KCL:

Derivation of differential transmission line equation

Phasor form of sinusoid haromic wave

Time factor convention

Derivation of differential transmission line equation

ki, Phase constant, rad/m

kr, attenuation constant, nep/m

Impedance, wavelength and phase velocity

Wavelength:

Phase velocity:

)cos()cos(),( 00 zktVzktVtzv ii

Voltage in the time domain:

ik/2

fk

vi

p

Characteristic impedance:

TL current:

Characteristic impedance:

Phase velocity:

Wavelength: (what happens if exchange L and C ?)

LC /2

LCvp /1

Propagation constant: