Most common types of transmission line which support TEM waves are:a) Parallel-plate transmission line- it consists of two parallel conducting plates separated
by a dielectric slab of a uniform thickness as shown in Fig.1.1. At microwaves
frequencies, th
Power in Electrical Circuits
Electrical Power, (P) in a circuit is the amount of energy that is absorbed or produced within the
circuit. A source of energy such as a voltage will produce or deliver power while the connected
load absorbs it. The quantity s
Nortons Theorem
Nortons Theorem
In some ways Norton's Theorem can be thought of as the opposite to "Thevenins Theorem", in
that Thevenin reduces his circuit down to a single resistance in series with a single voltage.
Norton on the other hand reduces his
Resistance.
The Resistance of a circuit is its ability to resist or prevent the flow of current (electron flow)
through it making it necessary to apply a bigger voltage to the circuit to cause the current to flow
again. Resistance is measured in Ohms, Gre
Ohms Law Triangle
Then by using Ohms Law we can see that a voltage of 1V applied to a resistor of 1 will cause a
current of 1A to flow and the greater the resistance, the less current will flow for any applied
voltage. Any Electrical device or component t
Summary
This relationship between Voltage, Current and Resistance forms the basis of Ohms Law which
is discussed in the next tutorial and a basic summary of the three units is given below.
Voltage or potential difference is the measure of potential energy
1. General Transmission-Line Equation
These are equations that govern a general two-conductor uniform transmission lines.
Transmission lines differ from ordinary electric networks in that its physical dimensions
are a fraction of the operating wavelengt
LINES WITH ARBITRARY TERMINATION
Let the terminating impedance be . Assume the voltage standing wave on the line to be as
shown Fig. 3.2.
Thus, nether a nor appear at . will occur at an extra distance i.e. is where its suppose to be if
the original termin
Transmission lines
INTRODUCTION
A transmission line consists of two or more parallel conductors used to transmit electric
energy and signals from one point to another, specifically from a source to a load e.g.
1. The connection between a transmitter and
1. Low-Loss Line ()
This conditions are usually satisfied at very high frequencies.
a) Propagation constant:
[51]
since
Hence,
[52]
[53]
b) Phase velocity:
[54]
c) Characteristic impedance:
[55]
[56]
1) Short-circuit termination.
Here, equ. [108] reduces to
[111]
Since can range from to , the input impedance of a short-circuited lossless line can also
be either purely inductive or capacitive, depending on the value of . A graph of is as
shown in Fig.3
Nodal Voltage Analysis
Nodal Voltage Analysis
As well as using Mesh Analysis to solve the currents flowing around complex circuits it is also
possible to use Nodal Analysis methods too. Nodal Voltage Analysis complements Mesh
Analysis in that it is equall
1) Quarter-wave section.
When the length of the line is an odd multiple of i.e. , , then
and
Thus, equ. [108] becomes
[113]
Hence, a quarter-wave lossless line transforms the load impedance to the input
terminals as its inverse multiplied by the square of
Page Summary.
This "look-see" method of circuit analysis is probably the best of all the circuit analysis methods
with the basic procedure for solving Mesh Current Anaysis equations is as follows:
1. Label all the internal loops with circulating currents.
Transformer Impedance Matching
One very useful application of impedance matching to provide maximum power transfer is in
the output stages of amplifier circuits, where the speakers impedance is matched to the
amplifier output impedance to obtain maximum s
TRANSMISSION-LINE PARAMETERS
The electrical properties of a transmission line at a given frequency are completely
characterized by its four distributed parameters R,L,G and C.
For parallel-plate transmission line, these parameters have been obtained abo
[P = I2 x R]
P (watts) = I2 (amps) x R ()
The Power Triangle
One other point about Power, if the calculated power is positive in value for any formula the
component absorbs the power, but if the calculated power is negative in value the component
produces
WAVE CHARACTERISTICS ON FINITE TRANSMISSION LINE
The general solutions for the time-harmonic one-dimension Helmholtz equaitions are
[91a]
[91b]
where
[92]
As mention above, the reflected component is zero for infinite lines. For a finite the same can
be
LINES WITH RESISTIVE TERMINATION
When a line is terminated in a load impedance, both an incident wave and reflected wave
exist. Equ. [96a] gives the phasors expression for the voltage at any distance from the load
end.
NB: the termrepresents the inciden
Open circuit line
Standing wave is similar to a resistance terminated line with , except that and curves are
magnitudes of sinusoidal functions of the distance from the load. This can be verified by
letting in equ. [136a] and [136b]. i.e. and . Thus,
[14
Short-circuited line
The standing-waves are similar to those on a resistance-terminated line with . Here, , and is
finite. Hence, equ. [136a] and [136b] reduces to
[143a]
[143b]
Typical standing waves for open- and short-circuited lines are shown in Fig.
Ohms Law and Power
Ohms Law
The relationship between Voltage, Current and Resistance in any DC electrical circuit was firstly
discovered by the German physicist Georg Ohm, (1787 - 1854). Georg Ohm found that, at a
constant temperature, the electrical curr
MICROSTRIP LINE
Microstrip line is a practical example of a parallel-plate transmission as shown in Fig.1.6.
The analysis done earlier assumed that the two conduction plates on each side of the
substrate are of the same size as the substrate, therefore,
TRANSMISSION LINES AS CIRCUIT ELEMENTS
Transmission lines at ultrahigh frequencies (frequencies from 300 MHz to 3 GHz),
wavelength from 1 m t0 0.1 m, they serve as circuit elements. At these frequencies, ordinary
lumped-circuit elements are difficult to
Example
The measured attenuation of an air-dielectric coaxial transmission line at 400 MHz is .
Determine the Q and the half-power bandwidth of a quarter-wavelength section of the line with a
short-circuit termination.
Solution:
Given ,
Therefore,
The hal
Example 3
A lossless transmission line is 80 cm long and operates at a frequency of 600 MHz. The
line parameters are and Find the characteristic impedance, the phase constant, and the
phase velocity.
Solution
For a lossless line, the characteristic impeda
a) Coaxial transmission line
A cross-section of a coaxial cable is as shown in Fig. 2.5.
Assuming a current I flows in the inner conductor and returns through the outer conductor in
the other direction, the due symmetry, magnetic flux density, , has only
Equs.[39] and [43] are the general expressions for the propagation constant and
characteristic impedance. For three special cases of transmission lines, the expressions
changes as follows:
1. Lossless line (),
a) Propagation constant:
[44]
,
[45]
[46]
b)
Equations [32] and [35] are the general transmission-line equations or telegraphists
equations
The most important case for practical problem is when and varies sinusoidally with time.
Thus we can write them as:
[36a]
[36b]
where and are complex amplitu
Example 2
It is found that the attenuation on a 50 distortionless transmission line is The line has a
capacitance of
a) Find the resistance, inductance, and conductance per meter of the line
b) Find the velocity of wave propagation
c) Determine the percen