Transmission Media 2

04/17/23 By S.Naiman

Transmission media

TE411 Microwave Communication

LECTURE TWO

In this lecture you will learn:

• Transmission media

• Transmission line equations


LECTURE TWO

Transmission media


Transmission Media• To be sent from one location to another, a signal must travel

along a physical path

• The physical path that is used to carry a signal between a signal transmitter and a signal receiver is called the transmission medium

• There are two types of transmission media: 1. Guided2. Unguided


TRANSMISSION MEDIA

• Guided media - transmissions material manufactured so that signals will be confined to a narrow path and will behave predictably

• Unguided media – no wires– Examples include microwaves, infrared light waves,

and radio waves


GUIDED MEDIA• The three most common types of guided

media include twisted-pair wiring, coaxial cable, and fiber optic cable


Other GUIDED MEDIA are

• Two-wire open line• Unshielded twisted pair (UTP)• Shielded Pair• Balanced/Unbalanced lines• Parallel plate line• Strip line• Microstrip line• Rectangular waveguide

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Unshielded Twisted Pair (UTP) CAT5

Eg. Category 5 computer networking cable capable of handling a 100MHz bandwidth. Most often used in LANs

Transmit data at rated up to 100Mbps for a length of 100m

CategoriesCAT 3 Class C Telephone linesCAT5 Class D Computer networksCAT5e Computer networksCAT6 Class E up to 250MHzCAT7 Class F up to 600MHz

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Coaxial Cable Coaxial cable - cable that can carry a wide range

of frequencies with low signal loss

Consists of a metallic shield with a single wire placed along the center of a shield and isolated from the shield by an insulator, The dielectric may be air, plastic or ceramic

Coaxial cable is divided into two different types: 1. Thinnet coaxial cable - similar to the cable used by

cable television companies2. Thicknet coaxial cable - similar to thinnet except that it

is larger in diameter

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Types Rigid or air coaxial line Flexible or solid coaxial line Electrical configuration of both is the same

Air coaxial: cable with washer insulator.

Flexible coaxial.

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Fiber Optic Cable Fiber optic (or "optical fiber") - the technology

associated with the transmission of information as light impulses along a glass or plastic wire or fiber

Optical fiber cable can transmit data over long distances with little loss in data integrity

Optical fiber is not subject to interference

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Cable Summary

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UNGUIDED MEDIA

Unguided media – no wires– Examples include microwaves, infrared light

waves, and radio waves, Cellular transmitters etc

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Microwave Transmitters Microwave transmitters and receivers - commonly

used to transmit network signals over great distances

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Infrared and Laser Transmitters

Infrared and laser transmitters - similar to microwave systems: they use the atmosphere and outer space as transmission media

They require a line-of-sight transmission path

Useful for signaling across short distances where it is impractical to lay cable

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Cellular Transmitters

Cellular transmitters - radio transmissions and therefore have the advantage of being able to penetrate solid objects

A cellular base station is at the center of each cell

Cellular devices are configured to operate at low power to avoid interfering with other cellular devices in the area

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Unguided Media Summary

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Definition :A transmission lines are means of conveying signals or power from one point to another

A transmission line is the part of the circuit that provides the direct link between generator and load.

A transmission line is the conductive connection between system elements that carry signal power

This “conductor” may at first appear to be a short circuit, but in fact will react differently when high frequencies are propagated along the line.

Transmission line (TL)

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The electrical energy transmitted could be: microwave signals between antennas and stations, television signals, radio signals telephone and telegraph signals digital signals in computer networks electrical power distribution.


• A typical engineering problem involves the transmission of a signal from a generator to a load.

• For simplicity, we will use the parallel-wire line to represent circuit connections, but the theory applies to all types of transmission lines.


• Remember low frequency circuits, you are used to treat all lines connecting the various circuit elements as perfect wires, with no voltage drop and no impedance associated to them (lumped impedance circuits).

•This is a reasonable procedure as long as the length of the wires is much smaller than the wavelength of the signal.


Example: The electricity supplied to households consists of high power sinusoidal signals, with frequency of 60Hz or 50Hz, depending on the country. Assuming that the insulator between wires is air (ε0), the wavelength for 60Hz is:

which is the about the distance between Cape Town (SA) and Cairo! Let’s compare to a frequency in the microwave range, for instance 60 GHz. The wavelength is given by

which is comparable to the size of a microprocessor chip.Which conclusions do you draw?


For sufficiently high frequencies the wavelength is comparable with the length of conductors in a transmission line. The signal propagates as a wave of voltage and current along the line, because it cannot change instantaneously at all locations. Therefore, we cannot neglect the impedance properties of the wires (distributed impedance circuits).


Note that the equivalent circuit of a generator consists of an ideal alternating voltage generator in series with its actual internal impedance. When the generator is open we have:


The simplest circuit problem that we can study consists of a voltage generator connected to a load through a uniform transmission line.

In general, the impedance seen by the generator is not the same as the impedance of the load, because of the presence of the transmission line, except for some very particular cases.

Our goal is to determine the equivalent impedance seen by the generator, that is, the input impedance of the line terminated by the load. Once that is known, standard circuit theory can be used.



Uniformly distributed Lines• The characteristics of a transmission lines are determined

by its electrical properties such as wire conductivity and insulator dielectric constant and its physical properties such as wire diameter and conductor spacing.

The impedance parameters L, R, C, and G represent:

L = series inductance per unit lengthR = series resistance per unit lengthC = shunt capacitance per unit lengthG = shunt conductance per unit length



• A uniform transmission line is a “distributed circuit” that we can describe as a cascade of identical cells with infinitesimal length.

• We use the concept of shunt conductance, rather than resistance, because it is more convenient for adding the parallel elements of the shunt.

• Uniform transmission line (general lossy line)


Each cell of the distributed circuit will have impedance elements with values: Ldz, Rdz, Cdz, and Gdz, where dz is the infinitesimal length of the cells.

If we can determine the differential behavior of an elementary cell of the distributed circuit, in terms of voltage and current, we can find a global differential equation that describes the entire transmission line.

So, all we need to do is to study how voltage and current vary in a single elementary cell of the distributed circuit.


Loss-less Transmission LineIn many cases, it is possible to neglect resistive effects in the line. In

this approximation there is no Joule effect loss because only reactive elements are present.


The series inductance determines the variation of the voltage from input to output of the cell, according to the sub-circuit below

The corresponding circuit equation is

which gives a first order differential equation for the voltage


The current flowing through the shunt capacitance determines the variation of the current from input to output of the cell.

The circuit equation for the sub-circuit above is

The second term (including dV dz) tends to zero very rapidly for infinitesimal length dz and can be ignored, giving a first order differential equation for the current


We have obtained a system of two coupled first order differential equations that describe the behavior of voltage and current on the uniform loss-less transmission line. The equations must be solved simultaneously.

These are often called “telegraphers’ equations” of the loss-less transmission line.


One can easily obtain a set of uncoupled equations by differentiating with respect to the space coordinate. The first order differential terms are eliminated by using the corresponding telegraphers’ equation

These are often called “telephonists’ equations”.


We have now two uncoupled second order differential equations for voltage and current, which give an equivalent description of the loss-less transmission line. Mathematically, these are wave equations and can be solved independently.The general solution for the voltage equation is

where the wave propagation constant is

Note that the complex exponential terms including have unitary magnitude and purely “imaginary” argument, therefore they only affect the “phase” of the wave in space.




Characteristics impedance (Zo)

• Characteristics impedance is defined as the impedance seen looking into an infinitely long line or the impedance seen looking into finite length of line which is terminated in a purely resistive load equal to the Characteristics impedance of the line.

• Is the ratio of voltage to current at any point along the line on which no reflected wave exists.


Question

• A lossless transmission line has a shunt capacitance of 100pF/m and a series inductance of 4µH/m. What is its characteristic impedance?

• Ans 200Ω





We have again a system of coupled first order differential equations that describe the behavior of voltage and current on the lossy transmission line

These are the “telegraphers’ equations” for the lossy transmission line case.


One can easily obtain a set of uncoupled equations bydifferentiating with respect to the coordinate z as done earlier

These are the “telephonists’ equations” for the lossy line.


The telephonists’ equations for the lossy transmission line are uncoupled second order differential equations and are again wave equations. The general solution for the voltage equation is

where the wave propagation constant is now the complex quantity

The real part of the propagation constant describes the attenuation of the signal due to resistive losses. The imaginary part describes the propagation properties of the signal waves as in loss-less lines.

The exponential terms including are “real”, therefore, they only affect the “magnitude” of the voltage phasor. The exponential terms including have unitary magnitude and purely “imaginary” argument, affecting only the “phase” of the waves in space.




Question

• The primary constants for transmission line are R =0.5 Ω/m, L=250nH/m, C=100pF/m and G=10-6 S/m.

• Calculate:

a. Characteristic impedance( Zo)

b. Wave propagation constant

c. Attenuation constant(α)

d. Phase shift coefficient(β)


What happen to the signal as it travels down a transmission line?

• Power loss due to attenuation.

• Reflections due to impedance mismatch.

• Dispersion: frequency dependent velocity

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Transmission Media 2

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