This document discusses transmission lines and waveguides. It begins by defining key concepts like electrons, energy transfer through current and waves, and how the system used for energy transfer depends on frequency. It then covers topics like transmission lines, coaxial lines, parallel plate waveguides, various waveguide modes, and how circuit theory breaks down at high frequencies due to effects like skin effect. Filters and network analysis are also summarized. The document aims to provide an overview of guided communication systems ranging from circuits to optical fibers.
international workshop accelerator based neutron sources for medical industrial and scientific applications torino eurosea international workshop accelerator based neutron sources for medical industrial and scientific applications torino eurosea
Analysis and optimization of wireless power transfer linkAjay Kumar Sah
In this paper, a high efficiency Gallium nitride (GaN), HEMT (High Electron Mobility Transistor) class-E power amplifier for the wireless power transfer link is designed and simulated on PSpice. A four-coil wireless power transfer link is modeled for maximum power transfer efficiency on ADS (Advanced Design System) and frequency splitting phenomenon is demonstrated, explained and analyzed. Two resonant coupling structures, series & mixed, are presented and compared. The efficiency performance of the link is studied using spiral and helical antennas of different wire make. In addition, techniques for improving efficiency of the wireless power transfer systems with changing coupling coefficient viz. frequency splitting phenomenon of the coils are proposed.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
Event Management System Vb Net Project Report.pdfKamal Acharya
In present era, the scopes of information technology growing with a very fast .We do not see any are untouched from this industry. The scope of information technology has become wider includes: Business and industry. Household Business, Communication, Education, Entertainment, Science, Medicine, Engineering, Distance Learning, Weather Forecasting. Carrier Searching and so on.
My project named “Event Management System” is software that store and maintained all events coordinated in college. It also helpful to print related reports. My project will help to record the events coordinated by faculties with their Name, Event subject, date & details in an efficient & effective ways.
In my system we have to make a system by which a user can record all events coordinated by a particular faculty. In our proposed system some more featured are added which differs it from the existing system such as security.
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CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
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It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
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In present era, the scopes of information technology growing with a very fast .We do not see any are untouched from this industry. The scope of information technology has become wider includes: Business and industry. Household Business, Communication, Education, Entertainment, Science, Medicine, Engineering, Distance Learning, Weather Forecasting. Carrier Searching and so on.
My project named “Event Management System” is software that store and maintained all events coordinated in college. It also helpful to print related reports. My project will help to record the events coordinated by faculties with their Name, Event subject, date & details in an efficient & effective ways.
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2. Energy Transfer
All the systems are designed to carryout the
following jobs:
1.Energy generation.
2. Energy transportation.
3. Energy consumption.
Here we are concerned with energy transfer.
3. Electrons
Electron is part of everything on earth. Electrons
are the driving force for every activity on earth.
Electron is a energy packet, Source of energy,
capable of doing any work.
Electron accumulation = Voltage
Electron flow = current
Electrons’ oscillation = Wave
Electron transfer = Light
Electron emission = Heat.
4. No mass ;
No inertia;
Highly mobile;
No wear and tear;
No splitting of
electron;
No shortage;
Excellent service
under wider
different conditions:
Vacuum, gas, solid;
6. Energy = Electron - Wave
Energy is transferred from place to by two
means:
1.Current : Flow of electrons through
conductors.
2. Wave : Wave propagation in space, using
guiding systems or unguided system (free
space).
In this subject, except free space energy
transfer, other means are discussed.
41. Energy
V = Voltage = Size of energy packet / electron.
I = Current = Number of energy packet flow / sec
Total energy flow / sec = V X I
42. System Power Flow Medium
Circuits P = V x I Conductor
Transmission Lines P = E x H Free space
Coaxial Lines P = E x H Free space
Waveguides P = E x H Free space
Optical Fiber P = E x H Glass
43. Quantum of energy E = h f; h =6.626x10-34 J-s
Quantum physics states the EM waves are
composed of packets of energy called photons.
At high frequencies each photon has more energy.
Photons of infrared, visible, and higher frequencies
have enough energy to affect the vibrational and
rotational states of molecules and electrons in the
orbits of atoms in the materials.
Photons at radio waves do not have enough energy
to affect the bound electrons in the materials.
44. System Energy Flow
Circuits Inside Conductor
Transmission Lines TEM mode
Coaxial Lines TEM mode
Waveguides TE and TM modes
Optical Fiber TE and TM modes
45. Problems at high frequency operation
1.Circuits radiates and accept radiation : Information
loss. Conductors become guides, current’s flow
becomes field flow
2.EMI-EMC problems: Aggressor – Victim problems
3.Links in circuit behave as distributed parameters.
4. Links become transmission Line: Z0 , ρ, .
5.Delay – Phase shift-Retardation.
6. Digital circuits involves high frequency problems.
7. High energy particle behaviour.
46. High Frequency Effects
1.Skin effect
2.Transit time –
3.Moving electron induce current
4. Delay
5. Retardation-.Radiation
6.Phase reversal of fields.
7.Displacement current.
8.Cavity
47. High Frequency effects
1.Fields inside the conductor is zero.
2.Energy radiates from the conductors.
3.Conductor no longer behaves as simple
conductor with R=0
4.Conductor offers R, L, G, C along its length.
5.Signal gets delayed or phase shifted.
48. Skin Effect
Skin effect makes the current flow simply a surface
phenomenon. No current that vary with time can
penetrate a perfect conducting medium. Iac = 0
The penetration of Electric field into the conducting
medium is zero because of induced voltage effect.
Thus inside the perfect conductor E = 0
The penetration of magnetic field into the conducting
medium is zero since current exists only at the
surface. H=0.
56. •
Frequency f Wavelength
50 Hz 6,000 Km
3 KHz 100 Km
30 KHz 10 Km
300 KHz 1 Km
3 MHz 100 m
30 MHz 10 m
300 MHz 1 m
3 GHz 10 cm
30 GHz 1 cm
300 GHz 1 mm
57.
V= V0 sin (0 )
V= V0 sin (90)
V= V0 sin (180)
V= V0 sin (360)
58. Circuit domain :Dimension <<
C= f x = 300,000 km/sec
Given f = 30 kHz ; = 10 km
Hence circuit dimensions << = 10 km
Medium = Conducting medium.
= Conductors in circuits.
Electrons = Energy Packet
Energy E = eV electron volts; W= V X I
62. D < ; D <<
• When circuit dimension is very small
compared to operating wavelength ( D << ) ,
circuit theory approximation can be made.
• No phase shift the signal undergoes by virtue
of distance travelled in a circuit.
• Circuit / circuit components/ devices/ links will
not radiate or radiation is very negligible.
63. Field domain : Dimension
C= f x = 300,000 km/sec
Given f = 3000 MHz ; = 10 cm
Hence circuit dimensions = 10 cm
Dielectric medium – Free space
Waves = E/H fieldes
Energy E = h.f joules
Total radiated power W = EXH ds joules
64. Lumped circuit Model
• Electric circuits are modeled by means of lumped
elements and Kirchhoff’s law.
• The circuit elements R, L, C are given values in
those lumped circuit models, for example R=10
K, L = 10 H c= 10 pf.
• These models are physical elements and hence
the element values depend on the structure and
dimensions of the physical elements.
68. Frequency dependent parasitic elements
At high frequency operation all ideal
components deviate from their ideal behavior
mainly due to parasitic capacitance and
parasitic inductance.
Any two conductors separated by some
dielectric will have capacitor between them.
Any conductor carrying current will have an
inductance.
69. Reactance XC and XL
fC
j
XC
2
fL
j
XL
2
Parasitic capacitance and parasitic inductance
create reactance that varies with frequency
At DC, capacitance impedance is infinity; an open
circuit. The capacitive reactance decreases with
frequency. At DC an inductive impedance is zero; a
short circuit. The impedance of inductive reactance
increase with frequency.
Thus these real components behave different at high
frequency operation.
70. Cp =Parasitic capacitance due to leads of resistor,
parallel to R. At high frequency it shunts the resistor
reducing its value.
Llead = Due to resistor and material of resistor.
High value R are not recommended for high frequency
operation.
Caution: Minimize the lead size, Use surface mounted
device.
71. Llead = Lead inductance
Rlead = Lead resistance
RDC = Dielectric leakage
RAC =Dielectric Frictional loss due to polarization.
At high frequency operation, the component acts as
L. Large values of C are not useful at high frequency
operation.
77. 0o 180o 360o
At 3 KHz No Phase variation across the Resistor
For f =3 KHz, = 10 Km
= 10 Km
R
78. Circuit Theory
Connecting wires introduces no drop and no delay. The wires
between the componenets are of same potential. Shape and
size of wires are ignored.
79. 0o 180o 360o
Resistor
For f =30 GHz, = 1cm
0o 180o 360o
= 1cm
At 30GHz 360o Phase variation across the Resistor
84. The T section as derived from
unsymmetrical L-sections, showing notation
used in symmetrical network analysis
85. The section as derived from
unsymmetrical L-sections, showing notation
used in symmetrical network analysis
86. Examples of Transmission Line
Transmission Line in communication carry
1)Telephone signals
2)Computer data in LAN
3)TV signals in cable TV network
4)Telegraph signals
5)Antenna to transmitter link
87. TRASMISSION LINE
• It is a set of Conductors used for transmitting
electrical signals.
• Every connection in an electrical circuit is a
transmission line.
• Eg: Coaxial line, Twisted-wire
• Parallel wire pairs
• Strip line , Microstrip
98. Resonant circuit and Filter
Resonant circuits select relatively narrow band
of frequencies and reject others.
Reactive networks, called filters, are designed
to pass desired band of frequencies while
totally suppressing other band of frequencies.
The performance of filter circuits can be
represented in terms of Input current to output
current ratios.
99. Image Impedance Non-Symmetry Network
i
i
i
in
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
2
3
2
2
2
1
1
1
1
)
(
Input impedance at the 1,1 terminal
i
in Z
Z 1
1
100. Likewise, the impedance looking into the 2,2
terminal is required to be
i
Z2
i
i
i
Z
Z
Z
Z
Z
Z
Z
Z
1
3
1
1
1
3
2
2
)
(
Upon solving for i
iandZ
Z 2
1
3
2
1
3
3
2
2
1
3
1
1
)
)(
(
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z i
3
1
1
3
3
2
2
1
3
2
2
)
)(
(
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z i
102. 2
1
2
1
V
V
I
I
(1)
Then the voltage ratios and current ratios can
be represented by
i
i Z
Z 2
1
o
o
i
i
I
V
I
V
2
2
1
1
then
If the image impedances are equal
104. Performance parameters of a Network
(Active or Passive)
1. Gain of Loss of signal due to the Network
in terms of Voltage or Current ratios.
B
I
I
A
V
V
2
1
2
1
2. Delay of phase shift of the signal due to
network.
105. Performance of a N networks in
cascade
If several networks are used in succession as in
fig., the overall performance may be
appreciated as a
n
n
n
V
V
V
V
X
V
V
X
V
V
X
V
V 1
1
4
3
3
2
2
1
.....
(2)
106. Which may also me stated as
4
3
2
1
4
3
2
1 .
1
.
. A
A
A
A
A
A
A
A
Both the processes employing multiplication of
magnitudes. In general the process of addition or
subtraction may be carried out with greater ease
than the process of multiplication and division. It is
therefore of interest to note that
n
c
b
a
n
c
b
e
e
x
xe
xe
e
....
.....
Is an application in which addition is
substituted for multiplication.
107. If the voltage ratios are defined as
etc
e
V
V
e
V
V
e
V
V c
b
a
;.......
;
;
4
3
3
2
2
1
Eq. (2) becomes
n
c
b
a
n
e
V
V
........
1
If the natural logarithm (ln) of both sides is
taken, then
(3)
n
d
c
b
a
V
V
..........
ln
2
1
108. Thus it is common to define under conditions
of equal impedance associated with input and
output circuits.
N
e
I
I
V
V
2
1
2
1 (4)
The unit of “N” has been given the name
nepers and defined as
N
nepers
2
1
2
1
ln
ln
I
I
V
V
(5)
Two voltages, or two currents, differ by one
neper when one of them is “e” times as large as
the other.
109. Obviously, ratios of input to output power may
also may also be expressed In this fashion. That
is,
N
e
P
P 2
2
1
The number of nepers represents a convenient
measure of power loss or power gain of a
network.
Losses or gains of successive
110. Transmission Line
1.It provided guided communication to distance
with reasonable minimum attenuation
2.It overcomes the parasitic effects of lumped
elements due to high frequency operation.
3. High frequency operation introduces
distributed parameter effect.
4.Due to high frequency operation, energy
carried by fields rather than voltage and
currents.
111. 5. Operation remains outside conductors.
6. Radiation and phase shift (delay) play
important roles.
7. Radiation effects are much reduced or
prevented by special arrangements.
8. Treating Tr.Line as infinite infinitesimal
symmetrical networks, network theory analysis
is adopted.
112. Analysis of Transmission line ( N
networks in cascade) based on
basic symmetrical T and
networks
116. Resonant circuit and Filter
Resonant circuits select relatively narrow band
of frequencies and reject others.
Reactive networks, called filters, are designed
to pass desired band of frequencies while
totally suppressing other band of frequencies.
The performance of filter circuits can be
represented in terms of Input current to output
current ratios.
117. Image Impedance Non-Symmetry Network
i
i
i
in
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
2
3
2
2
2
1
1
1
1
)
(
Input impedance at the 1,1 terminal
i
in Z
Z 1
1
118. Likewise, the impedance looking into the 2,2
terminal is required to be
i
Z2
i
i
i
Z
Z
Z
Z
Z
Z
Z
Z
1
3
1
1
1
3
2
2
)
(
Upon solving for i
iandZ
Z 2
1
3
2
1
3
3
2
2
1
3
1
1
)
)(
(
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z i
3
1
1
3
3
2
2
1
3
2
2
)
)(
(
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z i
120. 2
1
2
1
V
V
I
I
(1)
Then the voltage ratios and current ratios can
be represented by
i
i Z
Z 2
1
o
o
i
i
I
V
I
V
2
2
1
1
then
If the image impedances are equal
126. Filters -Resonant circuits
Resonant circuits will select relatively narrow
bands of frequencies and reject others.
Reactive networks are available that will freely
pass desired band of frequencies while almost
suppressing other bands of frequencies.
Such reactive networks are called filters.
.
127.
128. Ideal Filter
An ideal filter will pass all frequencies in a given
band without (attenuation) reduction in
magnitude, and totally suppress all other
frequencies. Such an ideal performance is not
possible but can be approached with complex
design.
Filter circuits are widely used and vary in
complexity from relatively simple power supply
filter of a.c. operated radio receiver to complex
filter sets used to separate the various voice
channels in carrier frequency telephone
circuits.
129. Application of Filter circuit
Whenever alternating currents occupying
different frequency bands are to be
separated, filter circuits have an application.
130. Neper - Decibel
In filter circuits the performance Indicator is
current
Output
current
Input
e
Performanc
If the ratios of voltage to current at input and
output of the network are equal then
2
1
2
1
V
V
I
I
(1)
131. If several networks are used in cascade as
shown if figure the overall performance will
become
n
n
n
V
V
V
V
X
V
V
X
V
V
X
V
V 1
1
4
3
3
2
2
1
.....
(2)
132. Which may also me stated as
4
3
2
1
4
3
2
1 .
1
.
. A
A
A
A
A
A
A
A
Both the processes employing multiplication of
magnitudes. In general the process of addition or
subtraction may be carried out with greater ease
than the process of multiplication and division. It is
therefore of interest to note that
n
c
b
a
n
c
b
e
e
e
e
e
....
.....
is an application in which addition is
substituted for multiplication.
133. If the voltage ratios are defined as
etc
e
V
V
e
V
V
e
V
V c
b
a
;.......
;
;
4
3
3
2
2
1
Eq. (2) becomes
n
c
b
a
n
e
V
V
........
1
If the natural logarithm (ln) of both sides is
taken, then
(3)
n
d
c
b
a
V
V
..........
ln
2
1
134. Consequently if the ratio of each individual
network is given as “ n “ to an exponent, the
logarithm of the current or voltage ratios for all
the networks in series is very easily obtained as
the simple sum of the various exponents. It has
become common, for this reason, to define
N
e
I
I
V
V
2
1
2
1
(4)
under condition of equal impedance
associated with input and output circuits
135. The unit of “N” has been given the name
nepers and defined as
N
nepers
2
1
2
1
ln
ln
I
I
V
V
(5)
Two voltages, or two currents, differ by one
neper when one of them is “e” times as large as
the other.
136. Obviously, ratios of input to output power may
also may also be expressed In this fashion. That
is,
N
e
P
P 2
2
1
The number of nepers represents a convenient
measure of power loss or power gain of a
network.
Loses or gains of successive networks then
may be introduced by addition or subtraction of
their appropriate N values.
137. “ bel “ - “ decibel “
The telephone industry proposed and has
popularized a similar unit based on logarithm
to the base 10, naming the unit “ bel “ for
Alexander Graham Bell
The “bel” is defined as the logarithm of a
power ratio,
number of bels =
2
1
P
P
log
It has been found that a unit, one-tenth as large,
is more convenient, and the smaller unit is called
the decibel, abbreviated “db” , defined as
138. 2
1
P
P
log
10
dB (6)
In case of equal impedance in input and output
circuits,
2
1
2
1
V
V
log
20
I
I
log
20
dB (7)
Equating the values for the power ratios,
10
10
2 dB
N
e
Taking logarithm on both sides
139. 8.686 N = dB
Or 1 neper = 8.686 dB
Is obtained as the relation between nepers
and decibel.
The ears hear sound intensities on a
logarithmically and not on a linear one.
141. Performance parameters of a
“series of identical networks”.
1.Characteristic Impedance
2. Propagation constant
0
Z
For efficient propagation, the network is to be
terminated by Z0 and the propagation
constant should be imaginary.
142. We should also attempt to express these
two performance constants in terms of
network components Z1 and Z2 .
146. Both T and networks can be considered as
built of unsymmetrical L half sections, connected
together
in one fashion for T
and oppositely for the network.
A series connection of several T or networks
leads to so-called “ladder networks”
which are indistinguishable one from the other
except for the end or terminating L half section
as shown.
149. For a symmetrical network:
the image impedance and are
equal to each other and the image impedance
is then called characteristic impedance or
iterative impedance, .
i
Z1 i
Z2
i
i Z
Z 2
1
o
it
i
i Z
Z
Z
Z
2
1
150. That is , if a symmetrical T network is
terminated in , its input impedance will
also be , or the impedance transformation
ration is unity.
0
Z
0
Z
0
i
0
R then Z
Z
If Z
Z
0
Z
ZR
0
Z
Zi
151. The term iterative impedance is apparent if the
terminating impedance is considered as
the input impedance of a chain of similar
networks in which case is iterated at the
input to each network.
0
Z
0
Z
in
it
R Z
Z
Z
Z
0
154. Characteristic Impedance
for a symmetrical T section
2
1
2
1
2
1
2
1
0
4
1
(
4 Z
Z
Z
Z
Z
Z
Z
Z T
Characteristic impedance is that
impedance, if it terminates a symmetrical
network, its input impedance will also be
0
Z
0
Z
0
Z is fully decided by the network’s intrinsic
properties, such as physical dimensions and
electrical properties of network.
(!0)
158. propagation constant
The magnitude ratio does not express the
complete network performance , the phase
angle between the currents being needed as
well.
N
e
I
I
V
V
2
1
2
1
The use of exponential can be extended to
include the phasor current ratio.
e
I
I
2
1
(14)
159.
j
Where is a complex number defined by
Hence
j
e
e
I
I
2
1
If
A
I
I
2
1
e
I
I
A
2
1
j
e
(15)
160. With Z0 termination, it is also true,
e
V
V
2
1
The term has been given the name
propagation constant
= attenuation constant, it determines
the magnitude ratio between input and
output quantities.
= It is the attenuation produced in
passing the network.
Units of attenuation is nepers
161. = phase constant. It determines the phase
angle between input and output
quantities.
= the phase shift introduced by the
network.
= The delay undergone by the signal as it
passes through the network.
= If phase shift occurs, it indicates the
propagation of signal through the network.
The unit of phase shift is radians.
162. If a number of sections all having a common Z
n
I
I
I
I
I
I
I
I 1
4
3
3
2
2
1
........
from which
n
e
e
e
e
........
3
2
1
and taking the natural logarithm,
the ratio of currents is
n
........
..........
4
3
2
1
Thus the overall propagation constant is equal to
the sum of the individual propagation constants.
(16)
163. and of symmetrical networks
Use the definition of and the introduction of
as the ratio of currents for a
termination leads to useful results
e
0
Z
0
Z
164.
e
Z
Z
Z
Z
I
I
2
0
2
1
2
1 2
The T network in figure is considered
equivalent to any connected symmetrical
network terminated in a termination.
From the mesh equations the current ratio
can be shown as
0
Z
Where the characteristic impedance is given
as
2
1
2
1
2
0
4
Z
Z
Z
Z
(30)
(32)
168. SC
OCZ
Z
Z
0
Thus the propagation constant and the
characteristic impedance Z0 can be evaluated
using measurable parameters
OC
SC Z
and
Z
From these these two equations it can be
shown that
OC
SC
Z
Z
tanh
(42)
169. Filter fundamentals
Pass band – Stop band:
The propagation constant is
j
For = 0 or
There is no attenuation , only phase shift occurs.
It is pass band.
2
1 I
I
band
Stop
-
occurs;
n
attenuatio
,
I
ve;
when 2
1 I
170. Is conveniently studied by use of the
expression.
2
1
4
2
sinh
Z
Z
It is assumed that the network contains only
pure reactance and thus will be real
and either positive or negative, depending on
the type of reactance used for
Expanding the above expression
2
1
4Z
Z
2
1 Z
and
Z
172. The attenuation will be given by
2
1
1
4
sinh
2
Z
Z
then
reactances
type
opposite
Z
and
Z
If 2
1 are
imaginary.
is
radical
or the
0
4 2
1
Z
Z
This results in the following conclusion for
pass band.
0
4
1
2
1
Z
Z
173. The phase angle in this pass band will be
given by
2
1
1
4
sin
2
Z
Z
1
4Z
Z
when
2
1
Another condition for stop band is given as
follows:
175. Cut-off frequency
The frequency at which the network changes
from pass band to stop band, or vice versa,
are called cut-off frequencies.
These frequencies occur when
0
or Z
0
4
1
2
1
Z
Z
2
1
2
1
4
or Z
1
4
Z
Z
Z
(48)
.
reactances
of
types
opposite
are
Z
&
Z
where 2
1
176. Since may have number of
combinations, as L and C elements, or as
parallel and series combinations, a variety of
types of performance are possible.
2
1 Z
and
Z
177. Constant k- type low pass filter
(a) Low pass filter section; (b) reactance curves
demonstrating that (a) is a low pass section or has pass
band between Z1 = 0 and Z1 = - 4 Z2
178. If of a reactance network are unlike
reactance arms, then
2
1 Z
and
Z
2
2
1 k
Z
Z
where k is a constant independent of
frequency. Networks or filter circuits for which
this relation holds good are called constant-k
filters.
C
j
L
j
Z
2
1 Z
and
2
2
1 k
C
L
R
Z
Z
(51)
179. (b) reactance curves demonstrating that (a) is a
low pass section or has pass band between Z1 =
0 and Z1 = - 4 Z2
180. Low pass filter
Pass band : 2
1
1 4Z
-
Z
to
0
Z
c
f
f
to
0
f
stopband
c
f
f
LC
c
f
1
C
f
f
j
2
sinh
181. Variation of and with frequency for the low
pass filter
183. Characteristic Impedance of T filter
2
1
C
OT
f
f
C
L
Z
2
1
C
K
OT
f
f
R
Z
ZOT varies throughout the pass band, reaching a
value of zero at cut-off, then becomes imaginary
in the attenuation band, rising to infinity
reactance at infinite frequency
185. Constant k high pass filter
(a) High pass filter; (b) reactance curves demonstrating
that (a) is a high pass filter or pass band between Z1 = 0
and Z1 = - 4Z2
186. m-derived T section
(a) Derivation of a low pass section having a
sharp cut-off section (b) reactance curves
for (a)
197. Circuit Model/Lumped constant
Model Approach
• Normal circuit consists of Lumped elements
such as R, L, C and devices.
• The interconnecting links are treated as good
conductors maintaining same potential over
the interconnecting links. Effectively links
behaves as short between components and
devices.
• Circuits obey voltage loop equation and
current node equation.
200. If the final section is terminated in its
characteristic impedance, the input impedance
at the first section is Z0. Since each section is
terminated by the input impedance of the
following section and the last section is
terminated by its Z0. , all sections are so
terminated.
Characteristic impedance of T section is known
as )
4
1
(
2
1
2
1
Z
Z
Z
Z
ZOT
There are n such terminated
section.
r
s I
I , = sending and receiving end currents
202. Certain the analysis developed for lumped
constants can be extended to distributed
components well.
The constants of an incremental length x of a
line are indicated.
Series constants:
R + j L
ohms/unit length
Shunt constants:
Y + jC
mhos/unit length
203. Thus one T section, representing an incremental
length x of the line has a series impedance Zx
ohms and a shunt admittance Yx mhos. The
characteristic impedance of all the incremental
sections are alike since the section are alike.
Thus the characteristic impedance of any small
section is that of the line as a whole.
Thus eqn. (1) gives the characteristic of the line
with distributed constant for one section is given
as
)
4
1
(
0
x
xY
Z
x
Y
x
Z
Z
204. )
4
1
(
2
0
x
ZY
Y
Z
Z
(4)
Allowing x to approach zero in the limit the value
of
Z0 for the line of distributed constant is obtained
as Y
Z
Z
0
Ohms
(5)
Z and Y are in terms unit length of the line. The
ration Z/Y in independent of the length units
chosen.
209. Characteristic or surge impedance
Since there no energy is coming back to the
source , there is no reactive effect.
Consequently the impedance of the line is pure
resistance.
This inherent line impedance is called the
characteristic impedance or surge impedance
of the line.
The characteristic impedance is determined by
the inductance and capacitance per unit
length .
These quantities are in turn depending upon the
size of the line conductors and spacing
210. Dimension of line decides line impedance
The closer the two conductors of the line and
greater their diameter, the higher the capacitance
and lower the inductance.
A line with large conductors closely spaced will
have low impedance.
A line with small conductors and widely spaced
will have relative large impedance.
The characteristic impedance of typical lines
ranges from a low of about 50 ohms in the coaxial
line type to a high of somewhat more than 600
ohms for a open wire type.
211. C
L
C
j
L
j
Z
0
Thus at high frequencies the characteristic
impedance Z0 of the transmission line
approaches a constant and is independent of
frequency.
Z0 depends only on L and C
Z0 is purely resistive in nature and absorb all
the power incident on it.
C
L
C
j
L
j
Z
0
50
2500
)
10
2200
(
)
10
5
.
5
(
12
6
x
x
213. 62
.
42
63
.
32
10
32
.
48
100
32
.
48
100
10
4
x
Z
With additional section added the input
impedance is decreasing further till it
reaches its characteristic impedance of
37. For a single section with
termination of 37
37
137
3700
10
37
100
37
100
10
1
0
X
Z
R
xZ
R
R
Z
Z
L
S
L
S
214. Transmission Line
Transmission line is a critical link in any
communication system.
Transmission lines behaves as follows:
a) Connecting link
b) R – L – C components
c)Resonant circuit
d)Reactance impedance
e) Impedance Transformer