UNIT 1
PART-A
1. What is communication and mention the three essential things necessary or any
communication?
Communication is the process of establishing connection (or link) between two points
for information exchange
2. Define signal to noise ratio?
Signal to noise power ratio is the ratio of the signal power level to the noise power
level
S/N = Ps/Pn
Where Ps = Signal power(watts)
Pn= Noise power(watts)
Signal to noise power ratio is often expressed as a logarithmic function with the
decimal unit
S/N(db) = 10log Ps/Pn
3. What are the three primary characteristics of a transmission line?
Wave velocity
Frequency
Wavelength
4. What is transmission line?
Transmission line is a metallic conductor system used to transfer electrical energy
from one point to another using electrical flow.
5. Mention the disadvantage of an unbalanced transmission line?
The primary disadvantage is its reduced immunity to common mode signals such as
noise and other interference.
6. Mention the disadvantage of an open wire transmission line?
There is no shielding so the radiation losses are high
The cable is susceptible to picking up signals through mutual induction, which
produces cross talk.
7. What are the different types of losses involved in a transmission line?
Conductor loss
Dielectric heating loss
Radiation loss
Coupling loss
Corona
8. What are standing waves?
With mismatched line there are two electromagnetic waves travelling in an opposite
direction, present on the line at the same time. These waves are in fact called
travelling waves. Two travelling wave setup an interference pattern known as
standing wave.
9. Define critical frequency?
Critical frequency is defined as the highest frequency that can be propagated directly
upward and still be returned to the earth by the ionosphere.
10. What is Maximum Usable Frequency?
MUF is the highest frequency that can be used for sky wave propagation between two
specific points on earth’s surface.
PART-B
1. What are the types of transmission line and their respective losses?
Transmission lines
Coaxial transmission line with one source and one load
Impedance bridging is unsuitable for RF connections, because it causes power to be
reflected back to the source from the boundary between the high and the low impedances.
The reflection creates a standing wave if there is reflection at both ends of the
transmission line, which leads to further power waste and may cause frequencydependent loss. In these systems, impedance matching is desirable.
In electrical systems involving transmission lines (such as radio and fiber optics)—where
the length of the line is long compared to the wavelength of the signal (the signal changes
rapidly compared to the time it takes to travel from source to load)— the impedances at
each end of the line must be matched to the transmission line's characteristic impedance (
) to prevent reflections of the signal at the ends of the line. (When the length of the
line is short compared to the wavelength, impedance mismatch is the basis of
transmission-line impedance transformers; see previous section.) In radio-frequency (RF)
systems, a common value for source and load impedances is 50 ohms. A typical RF load
is a quarter-wave ground plane antenna (37 ohms with an ideal ground plane; it can be
matched to 50 ohms by using a modified ground plane or a coaxial matching section, i.e.,
part or all the feeder of higher impedance).
The general form of the voltage reflection coefficient for a wave moving from medium 1
to medium 2 is given by
while the voltage reflection coefficient for a wave moving from medium 2 to medium 1 is
so the reflection coefficient is the same (except for sign), no matter from which direction
the wave approaches the boundary.
There is also a current reflection coefficient; it is the same as the voltage coefficient,
except that it has an opposite sign. If the wave encounters an open at the load end,
positive voltage and negative current pulses are transmitted back toward the source
(negative current means the current is going the opposite direction). Thus, at each
boundary there are four reflection coefficients (voltage and current on one side, and
voltage and current on the other side). All four are the same, except that two are positive
and two are negative. The voltage reflection coefficient and current reflection coefficient
on the same side have opposite signs. Voltage reflection coefficients on opposite sides of
the boundary have opposite signs.
Because they are all the same except for sign it is traditional to interpret the reflection
coefficient as the voltage reflection coefficient (unless otherwise indicated). Either end
(or both ends) of a transmission line can be a source or a load (or both), so there is no
inherent preference for which side of the boundary is medium 1 and which side is
medium 2. With a single transmission line it is customary to define the voltage reflection
coefficient for a wave incident on the boundary from the transmission line side,
regardless of whether a source or load is connected on the other side.
a)imbalanced transmission line
ii.unbalanced transmission line
b) Baluns
c) Metallic transmission line
i.parallel conductor
• Open wire
•twin lead
• Twisted pair
d) co-axial transmission line
Losses
a) Conductor loss
b) Dielectric heating loss
c) Radiatin loss
d) Coupling loss
e) Corona loss
2. Equivalent circuit of transmission line?
a)equivalent circuit for a single section transmission line terminated in a load equal to
Zo.
R-resistance
L-self inductance
c-capacitance
The four terminal model
For the purposes of analysis, an electrical transmission line can be modelled as a two-port
network (also called a quadrapole network), as follows:
In the simplest case, the network is assumed to be linear (i.e. the complex voltage across
either port is proportional to the complex current flowing into it when there are no
reflections), and the two ports are assumed to be interchangeable. If the transmission line
is uniform along its length, then its behaviour is largely described by a single parameter
called the characteristic impedance, symbol Z0. This is the ratio of the complex voltage of
a given wave to the complex current of the same wave at any point on the line. Typical
values of Z0 are 50 or 75 ohms for a coaxial cable, about 100 ohms for a twisted pair of
wires, and about 300 ohms for a common type of untwisted pair used in radio
transmission.
When sending power down a transmission line, it is usually desirable that as much power
as possible will be absorbed by the load and as little as possible will be reflected back to
the source. This can be ensured by making the load impedance equal to Z 0, in which case
the transmission line is said to be matched.
A transmission line is drawn as two black wires. At a distance x into the line, there is
current I(x) traveling through each wire, and there is a voltage difference V(x) between
the wires. If the current and voltage come from a single wave (with no reflection), then
V(x) / I(x) = Z0, where Z0 is the characteristic impedance of the line.
Some of the power that is fed into a transmission line is lost because of its resistance.
This effect is called ohmic or resistive loss. At high frequencies, another effect called
dielectric loss becomes significant, adding to the losses caused by resistance. Dielectric
loss is caused when the insulating material inside the transmission line absorbs energy
from the alternating electric field and converts it to heat. The transmission line is
modeled with a resistance (R) and inductance (L) in series with a capacitance (C) and
conductance (G) in parallel. The resistance and conductance contribute to the loss in a
transmission line.
The total loss of power in a transmission line is often specified in decibels per metre
(dB/m), and usually depends on the frequency of the signal. The manufacturer often
supplies a chart showing the loss in dB/m at a range of frequencies. A loss of 3 dB
corresponds approximately to a halving of the power.
High-frequency transmission lines can be defined as those designed to carry
electromagnetic waves whose wavelengths are shorter than or comparable to the length
of the line. Under these conditions, the approximations useful for calculations at lower
frequencies are no longer accurate.
Telegrapher's equations
The telegrapher's equations (or just telegraph equations) are a pair of linear
differential equations which describe the voltage and current on an electrical transmission
line with distance and time.
Schematic representation of the elementary component of a transmission line.
3. Explain in detail about transmission line model?
The transmission line model represents the transmission line as an infinite series of twoport elementary components, each representing an infinitesimally short segment of the
transmission line:
The distributed resistance
of the conductors is represented by a series resistor
(expressed in ohms per unit length).
The distributed inductance
(due to the magnetic field around the wires, self
inductance, etc.) is represented by a series inductor (henries per unit length).
The capacitance between the two conductors is represented by a shunt capacitor C
(farads per unit length).
The conductance
of the dielectric material separating the two conductors is
represented by a shunt resistor between the signal wire and the return wire (Siemens per
unit length).
The model consists of an infinite series of the elements shown in the figure, and that the
values of the components are specified per unit length so the picture of the component
can be misleading.
, , , and may also be functions of frequency. An alternative
notation is to use
,
,
and
to emphasize that the values are derivatives with
respect to length. These quantities can also be known as the primary line constants to
distinguish from the secondary line constants derived from them, these being the
propagation constant, attenuation constant and phase constant.
The line voltage
as
and the current
can be expressed in the frequency domain
When the elements and are negligibly small the transmission line is considered as a
lossless structure. In this hypothetical case, the model depends only on the and
elements which greatly simplifies the analysis. For a lossless transmission line, the
second order steady-state Telegrapher's equations are:
These are wave equations which have plane waves with equal propagation speed in the
forward and reverse directions as solutions. The physical significance of this is that
electromagnetic waves propagate down transmission lines and in general, there is a
reflected component that interferes with the original signal. These equations are
fundamental to transmission line theory.
If
and
are not neglected, the Telegrapher's equations become:
where
and the characteristic impedance is:
The solutions for
and
are:
The constants
pulse
and
, starting at
transmitted pulse
Transform,
must be determined from boundary conditions. For a voltage
and moving in the positive
at position
, of
-direction, then the
can be obtained by computing the Fourier
, attenuating each frequency component by
,
advancing its phase by
, and taking the inverse Fourier Transform. The real
and imaginary parts of can be computed as
For small losses and high frequencies, to first order in
Noting that an advance in phase by
can be simply computed as
and
is equivalent to a time delay by
one obtains
,
Input impedance of lossless transmission line
Looking towards a load through a length l of lossless transmission line, the impedance
changes as l increases, following the blue circle on this impedance smith chart. (This
impedance is characterized by its reflection coefficient Vreflected / Vincident.) The blue circle,
centered within the chart, is sometimes called an SWR circle (short for constant standing
wave ratio.
The characteristic impedance
of a transmission line is the ratio of the amplitude of a
single voltage wave to its current wave. Since most transmission lines also have a
reflected wave, the characteristic impedance is generally not the impedance that is
measured on the line.
For a lossless transmission line, it can be shown that the impedance measured at a given
position from the load impedance
is
where
is the wave number.
In calculating , the wavelength is generally different inside the transmission line to
what it would be in free-space and the velocity constant of the material the transmission
line is made of needs to be taken into account when doing such a calculation.
Special cases
Half wave length
For the special case where
where n is an integer (meaning that the length of
the line is a multiple of half a wavelength), the expression reduces to the load impedance
so that
for all . This includes the case when
, meaning that the length of the
transmission line is negligibly small compared to the wavelength. The physical
significance of this is that the transmission line can be ignored (i.e. treated as a wire) in
either case.
Quarter wave length
For the case where the length of the line is one quarter wavelength long, or an odd
multiple of a quarter wavelength long, the input impedance becomes
Matched load
Another special case is when the load impedance is equal to the characteristic impedance
of the line (i.e. the line is matched), in which case the impedance reduces to the
characteristic impedance of the line so that
for all and all
Short
.
Standing waves on a transmission line with an open-circuit load (top), and a short-circuit
load (bottom). Colors represent voltages, and black dots represent electrons.
For the case of a shorted load (i.e.
), the input impedance is purely imaginary
and a periodic function of position and wavelength (frequency)
Open
For the case of an open load (i.e.
imaginary and periodic
), the input impedance is once again
Stepped transmission line
A simple example of stepped transmission line consisting of three segments.
A stepped transmission line is used for broad range impedance matching. It can be
considered as multiple transmission line segments connected in series, with the
characteristic impedance of each individual element to be Z0,i. The input impedance can
be obtained from the successive application of the chain relation
where is the wave number of the ith transmission line segment and li is the length of
this segment, and Zi is the front-end impedance that loads the ith segment.
The impedance transformation circle along a transmission line whose characteristic
impedance Z0,i is smaller than that of the input cable Z0. And as a result, the impedance
curve is off-centered towards the -x axis. Conversely, if Z0,i > Z0, the impedance curve
should be off-centered towards the +x axis.
Because the characteristic impedance of each transmission line segment Z 0,i is often
different from that of the input cable Z 0, the impedance transformation circle is off
centered along the x axis of the Smith Chart whose impedance representation is usually
normalized against Z0.
Standing wave
When Zo =ZL all the incident power is absorbed by the load.this is called as matched
line.when Zo≠ZL some of the incident power is absorbed by the load,and some is
returned to the source.this is called an unmatched or mismatched line.with a mismatched
line,there are two electromagnetic waves,traveling in opposite direction,present on the
line at the same time.the two traveling waves set up an interference pattern known as a
standing wave.
4. Give short notes about ground wave propagation and space wave propogation?
Radio waves in the VLF Very low frequency band propagate in a ground, or surface
wave. The wave is confined between the surface of the earth and to the ionosphere. The
ground wave can propagate a considerable distance over the earth's surface and in the low
frequency and medium frequency portion of the radio spectrum. Ground wave radio
propagation is used to provide relatively local radio communications coverage, especially
by radio broadcast stations that require to cover a particular locality.
The radio waves having high frequencies are basically called as space waves. These
waves have the ability to propagate through atmosphere, from transmitter antenna to
receiver antenna. These waves can travel directly or can travel after reflecting from
earth’s surface to the troposphere surface of earth. So, it is also called as Tropospherical
Propagation. In the diagram of medium wave propagation, c shows the space wave
propagation. Basically the technique of space wave propagation is used in bands having
very high frequencies. E.g. V.H.F. band, U.H.F band etc
5. Give short notes about Maximum Usable Frequency?
In radio transmission maximum usable frequency (MUF) is the highest radio frequency
that can be used for transmission between two points via reflection from the ionosphere (
skywave or "skip" propagation) at a specified time, independent of transmitter power.
This index is especially useful in regard to short wave transmissions.
In short wave radio communication, a major mode of long distance propagation is for the
radio waves to reflect off the ionized layers of the atmosphere and return diagonally back
to Earth. In this way radio waves can travel beyond the horizon, around the curve of the
Earth. However the refractive index of the ionosphere decreases with increasing
frequency, so there is an upper limit to the frequency which can be used. Above this
frequency the radio waves are not reflected by the ionosphere but are transmitted through
it into space.
The ionization of the atmosphere varies with time of day and season as well as with solar
conditions, so the upper frequency limit for skywave communication varies on an hourly
basis. MUF is a median frequency, defined as the highest frequency at which skywave
communication is possible 50% of the days in a month, as opposed to the (LUF) which is
the frequency at which communication is possible 90% of the days, and the frequency o
optimum transmission (FOT).
Typically the MUF is a predicted number. Given the maximum observed frequency
(MOF) for a mode on each day of the month at a given hour, the MUF is the highest
frequency for which an ionospheric communications path is predicted on 50% of the days
of the month.
On a given day, communications may or may not succeed at the MUF. Commonly, the
optimal operating frequency for a given path is estimated at 80 to 90% of the MUF. As a
rule of thumb the MUF is approximately 3 times the critical frequency.
It is the highest frequency that can be used for sky wave propagation between specific two
points on earth surface.
Mathematically muf=critical frequency/
6.
Explain in detail about Transmission line impedance matching?
In electronics, impedance matching is the practice of designing the input impedance of an
electrical load (or the output impedance of its corresponding signal source) to maximize the
power transfer or minimize reflections from the load.
In the case of a complex source impedance ZS and load impedance ZL, maximum power
transfer is obtained when
where * indicates the complex conjugate. Minimum reflection is obtained when
Reflection-less matching
Impedance matching to minimize reflections is achieved by making the load impedance equal
to the source impedance. Ideally, the source and load impedances should be purely resistive:
in this special case reflection-less matching is the same as maximum power transfer matching.
A transmission line connecting the source and load together must also be the same impedance:
Zload = Zline = Zsource, where Zline is the characteristic impedance of the transmission line. The
transmission line characteristic impedance should also ideally be purely resistive. Cable
makers try to get as close to this ideal as possible and transmission lines are often assumed to
have a purely real characteristic impedance in calculations, however, it is conventional to still
use the term characteristic impedance rather than characteristic resistance.
Complex conjugate matching
Complex conjugate matching is used when maximum power transfer is required. This is
different from reflection-less matching only when the source or load have a reactive
component.
Zload = Zsource*
(where * indicates the complex conjugate).
If the source has a reactive component, but the load is purely resistive then matching can be
achieved by adding a reactance of the opposite sign to the load. This simple matching network
consisting of a single element will usually only achieve a perfect match at a single frequency.
This is because the added element will either be a capacitor or an inductor, both of which are
frequency dependent and will not, in general, follow the frequency dependence of the source
impedance. For wide bandwidth applications a more complex network needs to be designed.
Power transfer
Whenever a source of power with a fixed output impedance such as an electrical signal source,
a radio transmitter or a mechanical sound (e.g., a loudspeaker) operates into a load, the
maximum possible power is delivered to the load when the impedance of the load (load
impedance or input impedance) is equal to the complex conjugate of the impedance of the
source (that is, its internal impedance or output impedance). For two impedances to be
complex conjugates their resistances must be equal, and their reactances must be equal in
magnitude but of opposite signs. In low-frequency or DC systems (or systems with purely
resistive sources and loads) the reactances are zero, or small enough to be ignored. In this
case, maximum power transfer occurs when the resistance of the load is equal to the resistance
of the source.
Impedance matching is not always necessary. For example, if a source with a low impedance
is connected to a load with a high impedance the power that can pass through the connection
is limited by the higher impedance. This maximum-voltage connection is a common
configuration called impedance bridging or voltage bridging, and is widely used in signal
processing. In such applications, delivering a high voltage (to minimize signal degradation
during transmission or to consume less power by reducing currents) is often more important
than maximum power transfer.
In older audio systems (reliant on transformers and passive filter networks, and based on the
telephone system), the source and load resistances were matched at 600 ohms. One reason for
this was to maximize power transfer, as there were no amplifiers available that could restore
lost signal. Another reason was to ensure correct operation of the hybrid transformers used at
central exchange equipment to separate outgoing from incoming speech, so these could be
amplified or fed to a four-wire circuit. Most modern audio circuits, on the other hand, use
active amplification and filtering and can use voltage-bridging connections for greatest
accuracy. Strictly speaking, impedance matching only applies when both source and load
devices are linear; however, matching may be obtained between nonlinear devices within
certain operating ranges.
Impedance-matching devices
Adjusting the source impedance or the load impedance, in general, is called "impedance
matching". There are three ways to improve an impedance mismatch, all of which are called
"impedance matching":
Devices intended to present an apparent load to the source of Zload = Zsource* (complex
conjugate matching). Given a source with a fixed voltage and fixed source impedance,
the maximum power theorem says this is the only way to extract the maximum power
from the source.
Devices intended to present an apparent load of Zload = Zline (complex impedance
matching), to avoid echoes. Given a transmission line source with a fixed source
impedance, this "reflectionless impedance matching" at the end of the transmission
line is the only way to avoid reflecting echoes back to the transmission line.
Devices intended to present an apparent source resistance as close to zero as possible,
or presenting an apparent source voltage as high as possible. This is the only way to
maximize energy efficiency, and so it is used at the beginning of electrical power
lines. Such an impedance bridging connection also minimizes distortion and
electromagnetic interference; it is also used in modern audio amplifiers and signalprocessing devices.
There are a variety of devices used between a source of energy and a load that perform
"impedance matching". To match electrical impedances, engineers use combinations of
transformers, resistors, inductors, capacitors and transmission lines. These passive (and active)
impedance-matching devices are optimized for different applications and include baluns,
antenna tuners (sometimes called ATUs or roller-coasters, because of their appearance),
acoustic horns, matching networks, and terminators.
Transformers
Transformers are sometimes used to match the impedances of circuits. A transformer converts
alternating current at one voltage to the same waveform at another voltage. The power input to
the transformer and output from the transformer is the same (except for conversion losses).
The side with the lower voltage is at low impedance (because this has the lower number of
turns), and the side with the higher voltage is at a higher impedance (as it has more turns in its
coil).
One example of this method involves a television balun transformer. This transformer
converts a balanced signal from the antenna (via 300-ohm twin-lead) into an unbalanced
signal (75-ohm coaxial cable such as RG-6). To match the impedances of both devices, both
cables must be connected to a matching transformer with a turns ratio of 2 (such as a 2:1
transformer). In this example, the 75-ohm cable is connected to the transformer side with
fewer turns; the 300-ohm line is connected to the transformer side with more turns. The
formula for calculating the transformer turns ratio for this example is:
Resistive network
Resistive impedance matches are easiest to design and can be achieved with a simple L pad
consisting of two resistors. Power loss is an unavoidable consequence of using resistive
networks, and they are only (usually) used to transfer line level signals.
Stepped transmission line
Most lumped-element devices can match a specific range of load impedances. For example, in
order to match an inductive load into a real impedance, a capacitor needs to be used. If the
load impedance becomes capacitive, the matching element must be replaced by an inductor. In
many cases, there is a need to use the same circuit to match a broad range of load impedance
and thus simplify the circuit design. This issue was addressed by the stepped transmission
line, where multiple, serially placed, quarter-wave dielectric slugs are used to vary a
transmission line's characteristic impedance. By controlling the position of each element, a
broad range of load impedances can be matched without having to reconnect the circuit.
Filters
Filters are frequently used to achieve impedance matching in telecommunications and radio
engineering. In general, it is not theoretically possible to achieve perfect impedance matching
at all frequencies with a network of discrete components. Impedance matching networks are
designed with a definite bandwidth, take the form of a filter, and use filter theory in their
design.
Applications requiring only a narrow bandwidth, such as radio tuners and transmitters, might
use a simple tuned filter such as a stub. This would provide a perfect match at one specific
frequency only. Wide bandwidth matching requires filters with multiple sections.
L-section
L networks for narrowband matching a source or load impedance Z to a transmission line with
characteristic impedance Z0. X and B may each be either positive (inductor) or negative
(capacitor). If Z/Z0 is inside the 1+jx circle on the Smith chart (i.e. if Re(Z/Z0)>1), network (a)
can be used; otherwise network (b) can be used.
A simple electrical impedance-matching network requires one capacitor and one inductor.
One reactance is in parallel with the source (or load), and the other is in series with the load
(or source). If a reactance is in parallel with the source, the effective network matches from
high to low impedance. The L-section is inherently a narrow band matching network.
The analysis is as follows. Consider a real source impedance of
and real load impedance
of
. If a reactance
is in parallel with the source impedance, the combined impedance
can be written as:
If the imaginary part of the above impedance is canceled by the series reactance, the real part
is
Solving for
If
the above equation can be approximated as
The inverse connection (impedance step-up) is simply the reverse—for example, reactance in
series with the source. The magnitude of the impedance ratio is limited by reactance losses
such as the Q of the inductor. Multiple L-sections can be wired in cascade to achieve higher
impedance ratios or greater bandwidth. Transmission line matching networks can be modeled
as infinitely many L-sections wired in cascade. Optimal matching circuits can be designed for
a particular system using smith charts.
Power factor correction
These devices are intended to cancel the reactive and nonlinear characteristics of a load at the
end of a power line. This causes the load seen by the power line to be purely resistive. For a
given true power required by a load this minimizes the true current supplied through the
power lines, and minimizes power wasted in the resistance of those power lines. For example,
a maximum power point tracker is used to extract the maximum power from a solar panel and
efficiently transfer it to batteries, the power grid or other loads. The maximum power theorem
applies to its "upstream" connection to the solar panel, so it emulates a load resistance equal to
the solar panel source resistance. However, the maximum power theorem does not apply to its
"downstream" connection. That connection is an impedance bridging connection; it emulates a
high-voltage, low-resistance source to maximize efficiency.
On the power grid the overall load is usually inductive. Consequently, power factor
correction is most commonly achieved with banks of capacitors. It is only necessary for
correction to be achieved at one single frequency, the frequency of the supply. Complex
networks are only required when a band of frequencies must be matched and this is the reason
why simple capacitors are all that is usually required for power factor correction.