Dispersion for a Rectangular WG
Consider 2 k 2 kc2 .
i)
If f<fc, j and 2 k 2 kc2
kc2 k 2
2
2 2
c
2
2
1 1
2
c
2
c
ii)
k
1
kc
2
c
2
2
f
1
fc
2
If f>fc, is real and k 2 2 kc2 .
DEGENERATE MODES
In WGs, several modes with different conf
THE SMITH CHART
The Smith chart developed in 1939 by P. Smith, in the Bell Telephone laboratories, is a graphical
procedure for solving impedance transformation problems to reduce the computational effort required.
This is important in analysis.
In practi
TRANSMISSION LINES AND WAVEGUIDES
Uniformity along the Direction of Propagation
Definition: Transmission Line
TL is the term to describe transmission systems with two or
more metallic conductors electrically insulated from each
other.
Definition: Waveguid
FINITE LENGTH LINE TERMINATED IN A GENERAL z L
Reflections occur when Z L Z0 .
V ( z ) V0e z V0e z V V
I ( z ) I 0e z I 0e z I I
Reflection Coefficient:
Re flected Voltage (or Current ) at pt. z V I
Forward Voltage (or Current ) at pt. z V
I
The load
WAVE PROPAGATION ON A TL
The second order equations for V(z) and I(z) are:
d 2V ( z )
2
V ( z) 0
2
dz
d 2 I ( z)
2
I ( z) 0
2
dz
The solution for V(z) is:
z
0
V ( z) V e
z
0
V e
V
Where 0 is a constant of voltage waves traveling
V
in the forward directi
TRANSMISSION LINE THEORY
(TEM Line)
A uniform transmission line is defined as the one
whose dimensions and electrical properties are
identical at all planes transverse to the direction of
propagation.
Circuit Representation of TLs
A uniform TL may be mode
INTRODUCTION
APPLICATION AREAS OF MICROWAVES
1 RADAR
Surveillance (air traffic control)
Navigation (direction finding)
Meteorology
2 MEDICINE
Treatment of Diseases
Microwave Imaging
3 SURVEYING LAND
4 HEATING
5 INDUSTRIAL QUALITY CONTROL
6 RADI
GENERAL BACKGROUND
Frequency Definition: The frequency range extending from 300 MHz up to 300
GHz is generally known as microwaves. These limits are to some extent arbitrary.
Wavelength Definition: From c f (in vacuum), is between 1m and1mm .
Energy of a
GENERAL IMPEDANCE TRANSFORMATION EQUATION
V
The reflection coefficient is a function of position along the TL. Since we
V
1
have Z Z 0
.
1
Z is also a function of position along the line.
1
1 Le2 z '
e z ' Le z '
Z Z0
Z0
Z0 z '
1
1 Le2 z
e L e z
L
STRIPLINES
A stripline is a planar type transmission line which is well suited for
microwave integrated circuitry and photolithographic fabrication.
It is usually constructed by etching the center conductor of width w , on
a substrate of thickness b and t
IMPEDANCE MATCHING
We can define two types of impedance matching.
Conjugate Matching: The matching of load impedance, to a generator for maximum transfer of power.

Maximum power is delivered to a load when Z L Z *g Rg jX g . For this condition, the powe
MICROWAVE NETWORK ANALYSIS
At microwave frequencies, equivalent reactive and resistive elements
may be connected to form a microwave circuit. In placed of connecting
wires, transmission lines and waveguides are used. The lengths, of the
connecting links a
GENERAL IMPEDANCE TRANSFORMATION EQUATION
The reflection coefficient
V
V
along the TL. Since we have
is a function of position
Z Z0
1
.
1
Z is also a function of position along the line.
1
1 Le2 z '
e z ' Le z '
Z Z0
Z0
Z0 z '
2 z
1
1 Le
e L e z
L
PLANAR TRANSMISSION LINES
Definition: A planar TL is a TL with conducting metal strips that lie
entirely in parallel planes. The most common structure is one or
more parallel metal strips placed on a dielectric substrate material
adjacent to a conducting