Microwave Fundamentals
Dr. Yungui MA (马云贵)
E-mail: yungui@zju.edu.cn
Office: Room 209, East Building 5, Zijin’gang campus
Electromagnetic spectrum
Millimeter waves
Radio waves
Microwaves
300 MHz
3 GHz
UV
THz gap
30 GHz
300 GHz
Infrared
3 THz
Electronic devices
30 THz
visible
300 THz
Photonic devices
Microwave bands
Band
Freq
(GHz)
P
L
0.23 1-2
-1
S
C
2-4 4-8
X
Ku
8- 12.512.5 18
K
Ka
1826.5
26.540
Microwave applications
 Wireless 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)
http://mypage.zju.edu.cn/mayungui/640892.html
Syllabus
 Chapter 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
1.7 Introduction of the Smith chart
Transmission line theory
 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 infinite conductivity) + G (due to the dielectric loss)
Transmission line theory
 Bridges the gap between field analysis and basic
circuit theory
 Extension from lumped to distributed theory
 A specialization of Maxwell’s equations
 Significant 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.
1.1 Why from lumped to distributed theory?
1.1 Why from lumped to distributed theory?
1.2 Examples of transmission lines
(1)Two-wire line
Electric field
(solid lines)
Magnetic field
(dashed lines)
(3) Microstrip line
(2) Coaxial line
1.3 Distributed network for a transmission line
Review: Kerchhoff’s law
n
KCL:
i
k 1
k
0
n
KVL:
v
k 1
k
0
1.3 Distributed network for a transmission line
1.3 Distributed network for a transmission line
1.3 Distributed network for a transmission line
(Telegrapher
equations)
1.3 Distributed network for a transmission line
1.3 Distributed network for a transmission line
Impedance, wavelength and phase velocity
TL current:
Characteristic
impedance:
Voltage in the time domain:
v( z, t )  V0 cos(t  ki z    )  V0 cos(t  ki z    )
  2 / ki

 f
Phase velocity: v p 
Wavelength:
ki
1.3 Distributed network for a transmission line
Propagation constant:
= iw LC
Characteristic impedance: Z0 = L / C
Wavelength:   2 /  LC
Phase velocity: v p  1 / LC
(what happens if
exchange L and C ?)