3. UNIT:1
Introduction to Microwaves
• Microwaves refer to the electromagnetic
waves with frequencies between 1GHz and
300GHz in the electromagnetic spectrum.
• The word microwave here implies that that
wavelength of the signal in the microwave
band are much smaller compared to HF/VHF
signals and does not mean it is in
micrometers.
SEC1405-RF And microwave Engineering
4. Microwaves??
Microwave is a form of electromagnetic radiation
with wavelengths ranging from about one meter to
one millimeter
Frequencies between 300 MHz (1 m) and 300 GHz
(1 mm).
Different sources define different frequency ranges
as microwaves
Which includes both UHF and EHF (millimeter
wave) bands.
SECA1701-Microwave and Optical
communication
8. Microwave Band Classification
Letter
Designation
Frequency
Range
Wavelength Range
L band 1 to 2 GHz 15 cm to 30 cm
super high
frequency
(SHF)
(3-30 GHz)
Microwaves
(1-30GHz)
S band 2 to 4 GHz 7.5 cm to 15 cm
C band 4 to 8 GHz 3.75 cm to 7.5 cm
X band 8 to 12 GHz 25 mm to 37.5 cm
Ku band 12 to 18 GHz 16.7 mm to 25 mm
K band 18 to 26.5 GHz 11.3 mm to 16.7 mm
Ka band 26.5 to 40 GHz 5.0 mm to 11.3 mm
Q band 33 to 50 GHz 6.0 mm to 9.0 mm
extremely high
frequency
(EHF) (30-300
GHz).
mmWaves
(30GHz-
U band 40 to 60 GHz 5.0 mm to 7.5 mm
V band 50 to 75 GHz 4.0 mm to 6.0 mm
W band 75 to 110 GHz 2.7 mm to 4.0 mm
F band 90 to 110 GHz 2.1 mm to 3.3 mm
SECA1701-Microwave and Optical
communication
9. Microwave Properties
Microwaves are the waves that radiate electromagnetic
energy with shorter wavelength.
Microwaves are not reflected by Ionosphere.
Microwaves travel in a straight line and are reflected by the
conducting surfaces.
Microwaves are easily attenuated within shorter distances.
Microwave currents can flow through a thin layer of a cable
SEC1405-RF And microwave Engineering
10. Disadvantages of Microwaves
Cost of equipment or installation cost is
high.
They are hefty and occupy more space.
Electromagnetic interference may occur.
Variations in dielectric properties with
temperatures may occur.
Inefficiency of electric power
SECA1701-Microwave and Optical
communication
11. Applications of Microwaves
• The application areas are many can be categories
in different ways.
• Telecom
• Point-to-point communication, Satellite, Cellular
access technologies
• Deep Space Communication
• Sensing/Spectroscopy, Radio astronomy
• Diagnostics, imaging, and treatment applications.
• Defense
• Radar, Satellite Communication
SECA1701-Microwave and Optical
communication
12. Applications of Microwaves
• There are a wide variety of applications for Microwaves, which are not possible for other radiations.
Wireless Communications
For long distance telephone calls
Bluetooth, WIMAX operations
Outdoor broadcasting transmissions
Remote pickup unit
Studio/transmitter link
Direct Broadcast Satellite
Personal Communication Systems
Cellular Video
Electronics
Phase shifters
HF generation
Tuning elements
Spread spectrum systems
Direct Broadcast Satellite DBS
SECA1701-Microwave and Optical
communication
14. Applications of Microwaves(cond..)
Commercial Uses
• Burglar alarms
• Police speed detectors
• Identification by non-contact methods
• Cell phones, pagers, wireless LANs
• Satellite television, XM radio
• Motion detectors
• Remote sensing
Navigation
Global navigation satellite systems
Global Positioning System
Military and Radar
Radars to detect the range and speed of the target.
SONAR applications, Weather forecasting, Navigation of ships, Speed limit enforcement , Air traffic
control
Military uses microwave frequencies for communications and for the above mentioned applications.
SECA1701-Microwave and Optical
communication
16. Applications of Microwaves(cond..)
Research Applications
Atomic resonances
Nuclear resonances
Radio Astronomy
Mark cosmic microwave background radiation
Detection of powerful waves in the universe
Detection of many radiations in the universe and earth’s atmosphere
Food Industry
Microwave ovens used for reheating and cooking
Food processing applications
Pre-cooking
Roasting food grains/beans
Drying potato chips
Moisture levelling
Absorbing water molecules
SECA1701-Microwave and Optical
communication
20. Applications of Microwaves(cond..)
Industrial Uses
Vulcanizing rubber, Analytical chemistry applications. Drying and reaction processes
Processing ceramics, Polymer matrix, Surface modification
Powder processing
Sterilizing pharmaceuticals
Medical Applications
Monitoring heartbeat
Lung water detection
Tumor detection
Hyperthermia treatment
Microwave tomography
Microwave Acoustic imaging
For any wave to propagate, there is the need of a medium. Free space transmission and transmission lines,
which are of different types, are used for the propagation of Microwaves.
SECA1701-Microwave and Optical
communication
23. Advantages of Microwaves
Supports larger bandwidth and hence more information is
transmitted. Hence this reason, microwaves are used for
point-to-point communications.
More antenna gain is possible.
Higher data rates are transmitted as the bandwidth is more.
Antenna size gets reduced, as the frequencies are higher.
Low power consumption as the signals are of higher
frequencies.
Effect of fading gets reduced by using line of sight
propagation.
Provides effective reflection area in the radar systems.
Satellite and terrestrial communications with high capacities
are possible.
Low-cost miniature microwave components can be developed.
Effective spectrum usage with wide variety of applications in
all available
frequency ranges of operation.
SECA1701-Microwave and Optical
communication
24. Advantages of Microwaves
• Large Bandwidth: The Bandwidth of Microwaves is larger than the
common low frequency radio waves. Thus more information can be
transmitted using Microwaves. It is very good advantage, because of this,
Microwaves are used for Point to Point Communications.
• Better Directivity: At Microwave Frequencies, there are better directive
properties. This is due to the relation that As Frequency Increases,
Wavelength decreases and as Wavelength decreases Directivity Increases
and Beam width decreases. So it is easier to design and fabricate high gain
antenna in Microwaves.
• Small Size Antenna: The antenna size can be smaller as the size of antenna
is inversely proportional to the transmitted frequency. Thus in
Microwaves, we have waves of much higher frequencies and hence the
higher the frequency, the smaller the size of antenna.
• Low Power Consumption: The power required to transmit a high
frequency signal is lesser than the power required in transmission of low
frequency signals. As Microwaves have high frequency thus requires very
less power.
• Effect Of Fading: The effect of fading is minimized by using Line Of Sight
propagation technique at Microwave Frequencies. While at low frequency
signals, the layers around the earth causes fading of the signal.
SECA1701-Microwave and Optical
communication
25. Health Hazards of Microwaves
SECA1701-Microwave and Optical
communication
29. Single port, Two port and Multiport networks
Basic current and voltage definitions for single, two port and
Multiport network are shown in the figure.
SECA1701-Microwave and Optical
communication
30. Low frequency network parameters
• At low frequencies, two port networks or circuits can
be characterized by the following parameters:
• Impedance (z) Parameter
• Admittance (Y) Parameter
• Hybrid (h) Parameter
• Inverse Hybrid (g) Parameter
• ABCD Parameter
• Inverse ABCD Parameter
Note: Calculation of all these parameters involves the
measurement of currents and voltages in the networks.
SECA1701-Microwave and Optical
communication
31. Z-Parameters
The impedance or Z parameter of a two port network is
defined by
Z11 and Z22 give the relationship between
voltages and currents at port 1–1′ and 2–2′.
They are called driving point impedances.
Z12 and Z21 give the relationship between
voltages and currents at different ports. They
are called transfer impedance.
Z parameters are called as open circuit
impedance parameters SECA1701-Microwave and Optical
communication
32. Y-Parameters
The impedance or Z parameter of a two port network is
defined by
•Y11 and Y22 are driving point input and
output admittances.
•Y21 and Y12 are forward and reverse
transfer admittances.
•Y parameters are called as short-circuited
admittance parameters.
SECA1701-Microwave and Optical
communication
33. H-Parameters
• H-parameter is the combination of Z and Y parameter
defined by
SECA1701-Microwave and Optical
communication
34. ABCD-Parameters
The impedance or Z parameter of a two port network is
defined by
A = VS / VR open circuit reverse voltage ratio
B = VS / IR short circuit reverse transfer
impedance
C = IS / VR open circuit reverse transfer
admittance (mho)
D = IS / IR short circuit reverse current
transfer ratio
SECA1701-Microwave and Optical
communication
35. Drawbacks of Low frequency parameters
Z,H,Y and ABCD parameters cannot be measured at microwave
frequencies due to the following reasons.
Equipment is not readily available to measure total voltage and total current
at the port of the network.
Short circuit and open circuit are difficult to achieve over a wide range of
frequencies.
Presence of active devices such as power transistors and tunnel diodes,
makes the circuit unusable for short (or) open circuit.
Based on these observations, the Z,Y,H and ABCD-parameters cannot
be accurately measured at Microwave frequencies.
SECA1701-Microwave and Optical
communication
36. Scattering or S-Parameters
A linear network can be characterized by a set of simultaneous
equations describing the exiting waves from each port in terms
of incident waves and are called as S-parameters.
S11 = b1 / a1 - Reflection coefficient at port1
S21 = b2 / a1 - Forward Transmission coefficient
S12 = b1 / a2 - Reverse Transmission coefficient
S22 = b2 / a2 - Reflection coefficient at port2
•S21 describes the forward transmission coefficient
(responding port 1st!)
SECA1701-Microwave and Optical
communication
37. S-parameters are measured by sending a single frequency signal
into the network or “black box” and detecting what waves exit
from each port.
Measurement of S-Parameters
Power, voltage and current
can be considered to be in
the form of waves travelling
in both directions.
For a wave incident on Port 1,
some part of this signal
reflects back out of that port
and some portion of the signal
exits other ports.
a1
b1
a2
SECA1701-Microwave and Optical
communication
38. Measuring S11 and S21
S11 refers to the signal reflected at Port1 for the signal incident at Port 1.
S21 refers to the signal exiting at Port 2 for the signal incident at
Port1. Scattering parameter (S21) is the ratio of the two
waves b2/a1.
Note: S-parameter convention always refers to the responding port first!
SECA1701-Microwave and Optical
communication
39. Measuring S22 and S12
S-parameters are complex (i.e. they have magnitude and angle)
because both the magnitude and phase of the input signal are
changed by the network.
SECA1701-Microwave and Optical
communication
41. S-Parameter Matrix of 1 port, 2 port
and 4 port network
SECA1701-Microwave and Optical
communication
42. Properties of S-Matrix
• [S] is always a square matrix of order (nxn)
• [S] is a symmetric matrix i.e., Sij=Sji
• [S] is a unitary matrix i.e., [S][S∗] =I
• The sum of the products of each term of any row or
column multiplied by the complex conjugate of the
corresponding terms of any other row or column is zero.
i.e.,
SECA1701-Microwave and Optical
communication
43. Isolator
• An isolator is a two-
port device that
transmits microwave
or radio frequency
power in one direction
only.
• Due to internal
behavior, the
propagation in one
direction is allowed
while the other
direction is blocked
SECA1701-Microwave and Optical
communication
44. ISOLATOR
• An isolator is a non-reciprocal device, with a non-
symmetric scattering matrix.
• An ideal isolator transmits all the power entering port 1 to
port 2, while absorbing all the power entering port 2, so that
to within a phase-factor its S-matrix is:
SECA1701-Microwave and Optical
communication
45. Circulator
circulator is a passive,
non-reciprocal three- or
four-port device, in
which a microwave or
radio-frequency signal
entering any port is
transmitted to the next
port in rotation (only).
SECA1701-Microwave and Optical
communication
46. Circulator
The most common application of a circulator is as a duplexer. A duplexer allows the
transmitter and receiver in a radio or radar unit to share a common antenna
SECA1701-Microwave and Optical
communication
47. E-Plane Tee
A waveguide tee is a 3 port device
that is similar to a power divider.
When the axis of the side arm is
parallel to the Electric Field (E) of
the collinear, then the tee is called
a E-Plane Tee Junction
An E-Plane Tee junction
is formed by attaching a simple
waveguide to the broader dimension
of a rectangular waveguide, which
already has two ports.
As the axis of the side arm is
parallel to the electric field, this
junction is called E-Plane
Tee junction.
This is also called as Voltage or
Series junction.
SECA1701-Microwave and Optical
communication
48. S- Matrix of E-Plane Tee/Series Tee
• The arms of rectangular
waveguides create two
ports called collinear ports
i.e., Port1 and Port2, while
the new one, Port3 is called
as Side arm or E-arm.
• The ports 1 and 2 are 180°
out of phase with each
other.
• The properties of E-Plane
Tee can be defined by its
[S]3x3 matrix.
SECA1701-Microwave and Optical
communication
49. It is a 3×3 matrix as there are 3 possible inputs and 3 possible outputs.
Scattering coefficients S13 and S23 are out of phase by 180° with an inpu
at port 3. Port3 is perfectly matched so S33=0
From the symmetric property,
Considering equations 3 & 4, the [S] matrix can be written as,
SECA1701-Microwave and Optical
communication
50. So we have four unknowns, considering the symmetry property. From
the unitary property
Multiplying we get, (Noting R as row and C as column)
SECA1701-Microwave and Optical
communication
51. Equating the equations 6 & 7, we get
From Equation 8,
From Equation 9,
Using the equations 10, 11, and 12 in the equation 6,we get,
=0
SECA1701-Microwave and Optical
communication
52. Substituting the values from the above equations in [S][S] matrix,
We get,
We know that [b]= [S][a]
This is the scattering matrix for E-Plane Tee, which explains its
scattering properties. Because of mismatch at any 2 ports the VSWR at the
mismatch port of either E or H tee jn is very high
a & b are
respective matrix
of incident and
reflected wave
VSWR=1+
𝟏
𝟐
/1-
𝟏
𝟐
=3.0
SECA1701-Microwave and Optical
communication
53. H-plane Tee
An H-Plane Tee junction
is formed by attaching a
simple waveguide to a
rectangular waveguide
which already has two
ports. ...
This H-plane Tee is also
called as Shunt Tee. As
the axis of the side arm
is parallel to the
magnetic field, this
junction is called H-
Plane Tee junction.
SECA1701-Microwave and Optical
communication
54. • The arms of rectangular
waveguides make two
ports called collinear
ports i.e., Port1 and
Port2, while the new one,
Port3 is called as Side
arm or H-arm
• The properties of H-Plane
Tee can be defined by its
[S]3×3matrix.
• It is a 3×3 matrix as there
are 3 possible inputs and
3 possible outputs.
S- Matrix of H-Plane Tee/Shunt Tee
SECA1701-Microwave and Optical
communication
55. It is a 3×3 matrix as there are 3 possible inputs and 3 possible
outputs.
Scattering coefficients S13 and S23 are equal here as the junction is
symmetrical in plane. From the symmetric property,
The port S33is perfectly matched :
Now, the [S] matrix can be written as,
Because of plane
of symmetry of the
junction scattering
co-efficient s13
&S23 must be
equal, expressed
as
S13=S23
SECA1701-Microwave and Optical
communication
56. We can say that we have four unknowns, considering the symmetry
property. From the Unitary property
Multiplying we get, (Noting R as row and C as column)
SECA1701-Microwave and Optical
communication
57. From the Equation 6,
Since
Using these in equation 3, Since,
SECA1701-Microwave and Optical
communication
58. Substituting for S13, S11, S12 and S22 from equation 7 and 10, 11 and 12
in equation 2,We get,
We know that [b] = [s][a]
This is the scattering matrix for H-Plane Tee, which explains its
scattering properties.
SECA1701-Microwave and Optical
communication
59. Magic Tee
A Magic Tee or Hybrid Tee is a 4 port waveguide tee that is a
combination of an E-Plane and H-Plane Waveguide Tee.
• A magic tee has four ports:
• Port 1 - Co-linear
• Port 2 - Co-linear
• Port 3 - Difference Port
• Port 4 - Sum Port
• Operation of a Magic Tee:
• Case 1: When two signals of equal magnitude are fed
from port 1 and 2, we get a zero at port 3 and the sum
of the two signals at port 4.
• Case 2: When a signal is fed through port 4, it gets
divided equally between port 1 & 2 and both the
outputs are in phase. No output comes from port 3.
• Case 3: When a signal is fed through port 3, we get an
output of equal magnitude but opposite phase at port 1
& 2 (the signals are 180 degrees out of phase). Output
at port 4 is zero.
• A magic tee is ideally lossless. But the biggest
disadvantage of magic tee is that reflections arise within
it due to impedance mismatches, which causes some
level of power loss. These reflections can be minimized
by optimizing matching.
SECA1701-Microwave and Optical
communication
60. S-Parameters of Magic TEE
• A Magic Tee or Hybrid Tee is a 4 port waveguide tee that is a
combination of an E-Plane and H-Plane Waveguide Tee.
• A magic tee has four ports:
Port 1 and Port 2 - Co-linear
Port 3 - Difference Port; Port 4 - Sum Port
SECA1701-Microwave and Optical
communication
61. Operation of a Magic Tee
• Case 1: When two signals of equal magnitude are fed
from port 1 and 2, we get a zero at port 3 and the
sum of the two signals at port 4.
• Case 2: When a signal is fed through port 4, it gets
divided equally between port 1 & 2 and both the
outputs are in phase. No output comes from port 3.
• Case 3: When a signal is fed through port 3, we get
an output of equal magnitude but opposite phase at
port 1 & 2 (the signals are 180 degrees out of phase).
Output at port 4 is zero.
SECA1701-Microwave and Optical
communication
62. S-Matrix Calculation For Magic Tee
The S matrix of magic tee would be 4x4 matrix as shown in eq.1
-------(1)
• Because of H-plane Tee section, s23=s13 -----(2)
• Because of E-plane Tee section, s24=-s14 ----(3)
• Because of geometry of the junction on inputs at port 3 can’t come out of port 4
since they are isolated ports and vice-versa s34=s43=0 -------(4)
•From symmetric property sij = sji:
s12=s21; s13=s31;
s23=s32; s34=s43;
s24=s42; s41=s14; --------(5)
•In magic tee, If ports 3 and 4 are perfectly matched to the junction:
s33=s44=0 ---(6)
SECA1701-Microwave and Optical
communication
63. • Substitute properties in eq. 2 to eq.6 in equation (1)
we get:
From unity matrix property, [s].[s]*=[I]
S14=S41;S24=S42;S31=S13
-S23=-S32
S43=S34=0
S12=S21=0
S33=S44=0
SECA1701-Microwave and Optical
communication
64. From equation 10 and 11,
S13= 1/√2 — (12)
S14= 1/√2 — (13)
Subtracting equation (9) from (8), we get,
s11=s22 ------(14)
SECA1701-Microwave and Optical
communication
65. • Using these values from equation (12) and (13) and
substituting in equation (8), we get:
This means port 1 and port 2 are also perfectly matched to the junction.
lS13l=
1
2
= lS14l
The scattering matrix
for an ideal hybrid Tee
may be stated in the
following form
SECA1701-Microwave and Optical
communication
66. We know that, [b]=[s] . [a], therefore the b matrix of magic tee is given as below:
b1= 1/√2(a3+a4)
b2= 1/√2(a3-a4) -----(18)
b3= 1/√2(a1+a2)
b4= 1/√2(a1-a2)
Hence in any 4 ports junction if any
ports are perfectly matched to the
junction then the remaining two ports
are automatically matched to the
junction. such a junction where in all
4 ports are perfectly matched to the
junction is called magic tee.
Applications:
1.Measurement of impedance
2.As duplexer
3.As mixer
4.As an isolator
A hybrid junction is a 4 port
network in which a signal
incident in any one of the
ports divides between 2
output ports with the
remaining port being isolated
SECA1701-Microwave and Optical
communication
67. Directional Coupler
• A Directional coupler is a device
that samples a small amount
of Microwave power for
measurement purposes. The power
measurements include incident
power, reflected power, VSWR
values, etc. ...
• Directional coupler is used to
couple the Microwave power which
may be unidirectional or bi-
directional.
SECA1701-Microwave and Optical
communication
68. Directional Coupler
Properties of Directional Coupler
• All the terminations are matched to the ports.
• When the power travels from Port 1 to Port 2, some portion of it gets
coupled to Port 4 but not to Port 3.
• As it is also a bi-directional coupler, when the power travels from Port 2
to Port 1, some portion of it gets coupled to Port 3 but not to Port 4.
• If the power is incident through Port 3, a portion of it is coupled to Port
2, but not to Port 1.
• If the power is incident through Port 4, a portion of it is coupled to Port
1, but not to Port 2.
• Port 1 and 3 are decoupled as are Port 2 and Port 4.
Pi = Incident power at Port 1
Pr = Received power at Port 2
Pf = Forward coupled power at Port 4
Pb = Back power at Port 3
SECA1701-Microwave and Optical
communication
69. 1. Directional coupler is 4-Port network. Hence [S] is a 4*4 matrix.
2. In a Directional coupler(DC) all four ports are perfectly matched
to the junction Hence the diagonal elements are zero.
3. From symmetric property Sij = Sji
SECA1701-Microwave and Optical
communication
70. • Substituting the values from 2 and 3 in eq.1, we get:
From unity matrix property: [s].[s]*=[I]
SECA1701-Microwave and Optical
communication
71. Multiplying rows and columns, we get:
R1c1:- |s12|2+|s14|2=1 –-------------(7)
R2c2:- |s12|2 +|s23|2=1 —-----------(8)
R3c3:- |s23|2 +|s34|2=1 --------------(9)
R1c3:- s12. s*23+ S14 s*34=0 --------(10)
Comparing or subtracting equation 7 and 8
S14=s23 -------(11)
Comparing or subtracting equation 8 and 9
S12=S34 -------(12)
• Let us assume that S12 is real and positive = 'P'
Therefore s12=s34=P=S*34 .........(13)
SECA1701-Microwave and Optical
communication
72. • Put equation 11 value in equation 10 i.e s14=s23
• From equation 10 & 13
P.s*23+s23.P=0
P[s23+s*23]=0
• Since P0, s23+s*23=0; s23=jy ; s*23=-jy
i.e. s23 must be imaginary
• Let s23=jq=s14 .........(14)
Therefore, s12=s34=P and s23=s14=jq; also p2+q2=1;
• Substituting these values, we get:
SECA1701-Microwave and Optical
communication
74. Striplines
• These are the planar transmission lines, used at frequencies from
100MHz to 100GHz.
• A Strip line consists of a central thin conducting strip of width ω which
is greater than its thickness t.
• It is placed inside the low loss dielectric (εr) substrate of thickness b/2
between two wide ground plates.
• The width of the ground plates is five times greater than the spacing
between the plates.
• The thickness of metallic central conductor and the thickness of
metallic ground planes are the same.
• The fundamental and dominant mode in Strip lines is TEM mode.
For b<λ/2, there will be no propagation in the transverse direction.
• The impedance of a strip line is inversely proportional to the ratio of
the width ω of the inner conductor to the distance b between the
ground planes.
SECA1701-Microwave and Optical
communication
75. Micro Strip Lines
• The strip line has a disadvantage that it is not accessible for
adjustment and tuning. This is avoided in micro strip lines, which
allows mounting of active or passive devices, and also allows
making minor adjustments after the circuit has been fabricated.
• A micro strip line is an unsymmetrical parallel plate transmission
line, having di-electric substrate which has a metallized ground on
the bottom and a thin conducting strip on top with thickness 't' and
width 'ω'.
• The characteristic impedance of a micro strip is a function of the
strip line width (ω), thickness (t) and the distance between the line
and the ground plane (h)
SECA1701-Microwave and Optical
communication
76. Coplanar strip line
• Coplanar strip line is formed by two
conducting strips with one strip grounded,
both being placed on the same substrate
surface, for convenient connections.
SECA1701-Microwave and Optical
communication
77. Coplanar waveguide
• A coplanar waveguide consists of a strip of thin
metallic film which is deposited on the surface of
a dielectric slab.
• This slab has two electrodes running adjacent
and parallel to the strip on to the same surface.
SECA1701-Microwave and Optical
communication
79. Losses in Microwave circuits
The transmission line, if not terminated with a
matched load, occurs in losses.
These losses are many types such as
attenuation loss, reflection loss,
transmission loss, return loss, insertion loss,
etc.
SECA1701-Microwave and Optical
communication
81. Waveguide Corners, Bends, twist
• The waveguide corner, bend and twist are shown in figure.
• These waveguide components are normally used to change the
direction of the guide through an arbitrary angle
SECA1701-Microwave and Optical
communication
83. In order to minimize reflections from the discontinues,it is
desirable to have the mean length L between continuities
equal to an odd number of quarter wavelengths that is
L=(2n+1)
ᆋg
4
Where n=0,1,2,3….and ᆋg is the wavelength in the wave
guide.
If the mean length L is an odd number of quarter
wavelengths, the reflected waves from both ends of the
waveguide section are completely cancelled. For the
waveguide bend, the minimum radius of curvature for a small
reflection is given by
R=1.5b for an E bend
R=1.5 a for a H-band
where a and b are the dimensions of the waveguide
bend as illustrated SECA1701-Microwave and Optical
communication
84. References
• David M. Pozar “Microwave Engineering”, John Wiley & Sons - 3rd
Edition, 2009.
• 2. Samuel Y Liao, “Microwave Devices & Circuits”, Prentice Hall of
India, 3rd Edition, 2008.
• 3. Kulkarni M, "Microwave and Radar Engineering", Umesh
Publication, 4th ed,2010..
• 4. Annapurna Das and Sisir K Das, “Microwave Engineering”, Tata
Mc Graw Hill Inc., 2004.
• 5. M.M.Radmanesh , “RF & Microwave Electronics Illustrated”,
Pearson Education, 2007
• 6. Robert E.Colin, 2ed “Foundations for Microwave Engineering”,
McGraw Hill, 2001
• 7. Reinhold.Ludwig and Pavel Bretshko “RF Circuit Design”, Pearson
Education, Inc., 2006
SECA1701-Microwave and Optical
communication