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by
Lotis P. Patunob, M.Eng., ECE
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Microwaves
An electromagnetic waves with frequencies that ranges
from approximately 500 MHz to 300 GHz or more. And
its wavelengths fall between 1cm and 60 cm.
Wavelength
The distance between
repeating units of apropagating wave of a
given frequency.
Designated by lambda
().
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Categories of Microwave Systems:
A. Short haul used to carry information for relatively
short distances, e.i. between cities within the same state.
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Categories of Microwave Systems:
A. Long haul used to carry information for relatively
long distances, such as interstate.
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Advantages of Microwave Radio:
1. Radio systems do not require a right-of-way
acquisition between stations.
2. Each station requires the purchase or lease of only asmall area of land.
3. Because of their high operating frequencies,
microwave radio systems can carry large quantities of
information.
4. Short wavelengths, require relatively small antennas.
5. Radio signals are more easily propagated around
physical obstacles, such as high mountains
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Disadvantages of Microwave Radio:
1. It is more difficult to analyze and design circuits at
microwave frequencies.
2. Measuring techniques are more difficult to perfectand implement at microwave frequencies.
3. It is difficult to implement conventional circuit
components at microwave frequencies.
4. Transient time is more critical at microwave
frequencies.
5. Microwave frequencies propagate in a straight line,
which limits their use to line-of-sight applications.
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Applications of Microwave:
1. Telephone communications.
2. Radar
3. Space Communications
4. Heating
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Microwave Parameters:
It is the loss that would be obtained between two
isotropic antennas in free space, where there are noground influences or obstructions.
A. Free Space Path Loss, LFS
It is defined as a loss incurred by an electromagnetic
wave as it propagates in a straight line through a
vacuum with no absorption or reflection of energy fromnearby objects.
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Note: signal strength is 1/
distance; & antenna gain
aperture.
24
dFSL
)(10)(10 log20log204.32 kmMHz dfFSL
)(10)(10 log20log204.92 kmGHz dfFSL
)(10)(10 log20log206.36 miMHz dfFSL
)(10)(10 log20log206.96 miGHz dfFSL
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Microwave Parameters:
General Equation:
B. Parabolic Antenna Gain, G
where: D = antenna diameter in m
= signal wavelength in m
= efficiency
2
DG
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Microwave Parameters:
Antenna Gain for Typical Values of (0.55 to 0.75):
Parabolic Antenna Gain for Typical Values of (0.55
to 0.75) in Metric system:
2
6
D
G
)(10)(10 log20log204.42 mMHz DfG
)(10)(10 log20log208.17 mGHz DfG
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Microwave Parameters:
Parabolic Antenna Gain for Typical Values of (0.55
to 0.75) in English system:
)(10)(10 log20log206.52 ftMHz DfG
)(10)(10log20log205.7
ftGHzDfG
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Microwave Parameters:
C. Fade Margin, FM
It is an attenuation allowance so that anticipated
fading will still keep the signal above specified
minimum RF input.
It considers the nonideal and less predictable
characteristics of a radio wave propagation such as
multipath propagation and terrain sensitivity.
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Microwave Parameters:
Fade Margin in Metric system:
)1(log10)6(log10log3013010)(10)(10
RabfdFMMHzkm
)1(log10)6(log10log307010)(10)(10
RabfdFMGHzkm
Fade Margin in English system:
)1(log10)6(log10log308.123 10)(10)(10 RabfdFM MHzmi
)1(log10)6(log10log308.6310)(10)(10
RabfdFMGHzmi
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Microwave Parameters:
where: R = propagation reliability
Values for a Description
4.0 for very smooth terrain,
over water, flat desert
1.0 for average terrain with
some roughness
0.25 for mountainous, very
rough, or very dry terrain
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Microwave Parameters:
Values for b Description
0.50 for hot, humid coastal areas
0.25 for normal, interior
temperate or sub-arctic area
0.125 for mountainous, very drybut non-reflective areas
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Microwave Parameters:
D. System Reliability Estimates
D.1. Propagation Reliability for Non-diversity Systems:
%1001 xUndpR where: Undp = the path unavailability or
fade probability
10/635.1 10)1025.1( FMxxdabfUndp
where: d = path length in mi
f = frequency in GHz
FM = fade margin in dB
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Diversity
It suggests that there is more than one transmission path
or method of transmission available bet. a transmitter
and a receiver. Its purpose is to increase the reliability of
the system by increasing its availability
Frequency diversity
It simply modulates two different RF carrier frequencies
with the same information. At the destination, both aredemodulated but the one yields the better quality is
selected.
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Space diversity
The output of a transmitter is fed to two or more
antennas that are physically separated by anappreciable number of wavelengths.
Diversity
Receiver diversity
It is using more than one receiver for a single RFchannel.
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Microwave Parameters:
D. System Reliability Estimates
D.2. Propagation Reliability for Diversity Systems:
where: Udiv = the path unavailability or
fade probability
where: Idiv = the diversity improvement factor
%100)1( xUdivR
di v
ndp
di v I
UU
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Microwave Parameters:
D. System Reliability Estimates
D.3. Equipment Reliability:
where: U = unavailability or probability of outage
where: MTTR = mean time to repair
MTBF = mean time before failure
%100)1( xUR
MTBFMTTRU
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Microwave Parameters:
E. Received Signal Level, RSL
RXRFSTTXLGLGLPRSL dBmo )(
It is the difference from the nominal transmitter
output, antenna transmit and receive gain, from thatof the fixed losses of transmit and receive side and its
path loss.
where: LTX and LRX = transmitter and receiver
total insertion losses in dB
GT and GR = transmit and receive antenna
gains in dB
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Microwave Parameters:
RSL = FM + Threshold (receiver)
where:
FM = Fade Margin in dB
Threshold (receiver) = receiver minimum RF
input in dBm; Cmin
where: LFS = Free Space Loss in dB
Po(dBm) = Transmitter Output Power in dBm
KTBN;min NN
CC
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Microwave Parameters:
F. System Gain, Gs (dB)
It is the difference between the nominal output power
of a transmitter and the minimum rf input power to areceiver.
)()()( .min dBmdBmodBS inputRFPG
gainslossesPdBmo
(dBm))(
inputRF.min
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Microwave Parameters:
)()()()()()( dBRdBTdBbdBfdBFSdBdBs GGLLLFMG
where: Lf(dB) = transmission line loss bet. thedistribution network and
its respective antenna (dB)
Lb(dB) = total coupling or branching loss
in the distribution network bet.the output of a transmitter or
receiver and the transmission line
(dB)
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G. Fresnel Zone and Fresnel Radius
Fresnel zone the area where the interference is
constructive.
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If a reflected signal is bounced within an odd-
numbered Fresnel zone, it would arrive at the receiver
in phaseaddition with the direct signal.
G. Fresnel Zone and Fresnel Radius
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Fresnel zones are a series of concentric ellipsoids that
surround the path from the transmitter to the receiver.
)()(
)(2)(1)(1 1.547
kmMHz
kmkmm
Df
ddF
Fresnel zone radius, (F1)
in Metric System:
)()(
)(2)(1
)(1 3.17kmMHz
kmkmm
Df
ddF
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)()(
)(2)(1
)(1 2280
miMHz
mimi
ft
Df
ddF
Fresnel zone radius, (F1) in English System:
)()(
)(2)(1)(1 1.72
miGHz
mimift
Df
ddF
nFFn 1nth Fresnel zone radius (Fn):
Fresnel zone clearance (Fc)- it takes into account the
unusual conditions that
occur in the atmosphere.
16.0 FFc
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H. Passive Repeater
Gain of a Passive Repeater
2)(cos4
log20
A
G dBp
where: A = the actual area of the passive repeater in (ft2 )
= wavelength = c/f in (ft)
= alpha, the angle bet. the incident wave and the
reflected wave in ()
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I. Net Path Loss, NPL:
It is the total loss of the system.
RFSpFSTdB GLGLGNPL 21)(
Example:
A plane passive reflector 10x16 ft is erected
21 miles from one active site and only 1 mile from
the other and = 50. The operating frequency is2000 MHz. Determine the net path loss of the
system.
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Example:
In a microwave communication system with a
normal temperate and average terrain has the
following parameters:
a. Operating frequency = 4 GHzb. Path length = 25 mi
c. Tx/Rx antenna diameter = 3 ft.
d. Transmitter Output Power = 1 W
e. Threshold(receiver) = - 80 dBmf. Tx total insertion loss = 5 dB
g. Rx total insertion loss = 4 dB
Deermine: LFS(dB) , FM(dB) & % Reliability
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Waveguides
It is a conducting tube through which the energy is
transmitted, in the form of electromagnetic waves.
It is an alternative to cable for frequency of 1 Ghz andabove.
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Electromagnetic Wave
It is made up of magnetic and electric fields that are at
right angles to each other and at right angles to the
direction of propagation. It travels in a straight line at
approximately the speed of light.
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Modes of Propagation - the possible direction of
distribution of energy
1. Transverse Electric (TE) has the electric field
transverse the direction of propagation, while the
magnetic field is along the propagation direction
2. Transverse Magnetic (TM0) has the magnetic field atright angles to the direction of propagation along the
guide, and the electric field in the direction of
propagation.
Classification of Modes of Propagation:
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Format: TEm,n
where: n = indicates the no. of half wave variation
of the electric field along the y or b
(height) dimension.
m = indicates the no. of half wave variation
of the electric field along the x or a
(width) dimension.
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where: arrows = represent the E field perpendicular to
the sides of the guide.
xs = represent the H field that is going into
the waveguide.
dots = represent the H field that is coming out
of the waveguide.
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Types of Waveguides:
A. Rectangular used when energy must be coupled
from the source to a load and both are fixed in place
since they are smaller than circular waveguides for a
given wavelength.
General formula for
cut off wavelength, c:
22
2
y
n
x
m
c
Cut off wavelength for
TEm,0:
m
x
c
2
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Cut off wavelength for TE1,0:
xc
2
where: TE1,0 = called the dominant mode, the mode for
the lowest frequency that can be
propagated in a waveguide
x = the width of the waveguide
y = the height of the waveguide
Note: x /2 for dominant mode means no propagation
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B. Circular used for rotating systems such as radar
antenna
K
r
c
2
where: K = 1.84 for dominant mode
Example:
What is the cut off wavelength that a 2.5 cm widewaveguide will support the dominant mode (m = 1)?
How about for the next mode (m = 2)?
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Key wavelength formula for rectangular/circularwaveguide:
Rectangular Circular
Cut off wavelength 2x 3.41r
Longest transmitted
with little attenuation
1.6x 3.2r
Shortest before next
mode is possible
1.1x 2.8r
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Group Velocity, Vg
The actual speed at which
a signal travels down the
guide.
2
1
ccg VV
Phase Velocity, Vp
The rate at which the
wave appears to move
along the wall of theguide.
2
1
c
cp
VV
Note: VgVp = Vc2
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Waveguide Characteristic Impedance:
TE mode:
20
1
377
c
Z
TM mode:
20
1
377
c
Z
Example:
A 6 GHz signal is to be propagated in a waveguidewhose width is 7.5 cm. Calculate the characteristic
impedance for TE1,0 mode and TM1,1 mode if the
thickness is 3.75 cm.
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Example:
A 6 GHz signal is to be propagated in the dominant
mode in a rectangular waveguide if its group velocity
is to be 90% of the speed of light, what must be width
of the guide?
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