Transmission Lines

Lecture 10

Types of transmission lines

Open-wire transmission lineThis simply consists of two parallel wires,closely

spaced and separated by air. Nonconductive spacers are used to keep the distance between the two wires constant. The distance between the wires is between 2 and 6 inches. The real advantage: it is simple to construct. Because there is no shielding, radiation losses are high and can easily pick up noise.

Twin lead This is similar to the open wire, except that

instead of spacers a solid dielectric is used along the whole length of the wire. This provides uniform spacing along the entire length. The distance between the wires is about 5/16 inch. Common dielectrics used include teflon and polyethylene.

Twisted pair cable

In this two insulated conductors are twisted together

Shielded pair

Two parallel wires separated by a solid dielectric material are enclosed in a conductive metal braid, which is connected to ground and hence acts as a shield. The braid also prevents signals from radiating beyond its boundaries. It also stops electromagnetic interference from reaching the wires

Coaxial

Parallel transmission lines are suitable for low frequency applications. At high frequencies, their radiation and dielectric losses become excessive. Coaxial cables are therefore used at high frequencies. The basic coaxial is made of a centre conductor surrounded by an outer concentric conductor.

There can be two types rigid air filled or solid flexible lines. The rigid air filled lines can be expensive to manufacture and the air insulator must be moisture free.

The equivalent circuit of transmission line

For any given transmission line, resistance and inductance will occur along the line and capacitance and conductance will occur between the lines. These are called primary constants and are uniformly distributed along the length of the line. To make analysis simple these parameters are lumped together per unit length to form an artificial electrical model of the line.

At radio frequencies the inductive reactance is much larger than the resistance, the capacitive susceptance is also much larger than the conductance. Both R and G may therefore be ignored resulting in what is called a lossless line

Transmission Characteristics

These are called the secondary constants and are determined from the primary characteristics. They are the:

characteristic impedance and

the propagation constant

Characteristic impedance

Maximum power transfer is only possible if the load matches the characteristic impedance of the line. This is the impedance measure at the input of a transmission line when its length is infinite.

The relationship between the capacitance and the inductance per unit length and the characteristic impedance is given as

C

LZo

Propagation Constant

This is used to express the attenuation and phase shift per unit length of the transmission line. This can be expressed as

is the propagation constant is attenuation coefficient is the phase shift coefficient

j

Reflected Wave and standing wave ratio

When a transmission line terminates in a load that does not match the characteristic impedance of the line then reflected waves result. A summation of the incident and reflected waves at different points along the line will give rise to different rms voltage (current) values along the line. The ratio of the largest rms value to the smallest is called standing wave ratio. It is an indication of how close we are to transmitting maximum power to the load.

min rms

max rms

min rms

max rms

I

I

V

V

Z

ZSWR

o

L

Reflection Coefficient This is defined as reflected voltage

(current) divided by the incident voltage (current).

This coefficient can also be expressed in terms of the SWR or the load resistance and characteristic impedance

inc

refl

inc

refl

I

I

V

VKr

r

r

1

1

K

KSWR

oL

oLr ZZ

ZZK

Antenna resistance

Reflected Power The reflected power is given as

The incident power is given as

L

2

R

VP refl

refl

L

2

R

VP inc

inc 2

2

2

r

inc

refl

inc

refl KV

V

P

P

Quarter-wave matching A quarter wavelength section of a

transmission line can be used to match a load to a transmission line. The value of the characteristic impedance of quarter wavelength section can found as follows:

L

2

Z

ZZ o

T

Microwave frequencies are from 1 to 300 GHz. At these frequencies the wavelength is very small and these can a serious effect on the circuit. The circuits at these frequencies are extremely short and for such circuits, coaxial cable parallel open and other forms of transmission lines are impractical. In this case microstrip lines are used. The tracks or traces on the circuit board are varied to produce the desired characteristic impedance. Different configurations are in common use; examples of these are:

Microstrip Lines

hcb

tZo

8.067.0

4ln

60

Single-conductor microstrip

cb

hZo

8.0

98.5ln

41.1

87

Parallel coupled microstrip)

cb

hZo

ln

120

Advantages of fiber optic

systems Bandwidth.

One of the most significant advantages that fiber has over copper or other transmission media is bandwidth. Bandwidth is directly related to the amount of information that can be transmitted per unit time. Today's advanced fiber‑optic systems are capable of transmitting several gigabits per second over hundreds of kilometers. Thousands of voice channels can now be multiplexed together and sent over a single fiber strand.

Less Loss. Currently, fiber is being manufactured to exhibit less than a few tenths of a decibel of loss per kilometer. Imagine glass so pure that you could see through a window over 75 miles (120 km) thick! Repeaters can now be spaced 50 to 75 miles apart from each other.

Noise Immunity and Safety

Since fiber is constructed of dielectric material, it is immune to

inductive coupling or crosstalk from adjacent copper or fiber

channels. In other words, it is not affected by electromagnetic

interference (EMI) or electrostatic interference. This includes

environments where there are electric motors, relays, and even

lightning. Likewise, since fiber‑optic cables transmit light instead of

current, they do not emit electrical noise, nor do they arc when there

is an intermittent in the link. Thus they are useful in areas where

EMI must be kept to a minimum. With the telecommunications

highways of the air as congested as they are, the use of fiber is an

attractive alternative.

Less Weight and Volume Fiber‑optic cables are substantially lighter in weight and

occupy much less volume than copper cables with the same information capacity. Fiberoptic cables are being used to relieve congested underground ducts in metropolitan and suburban areas. For example, a 3‑in. diameter telephone cable consisting of 900 twistedpair wires can be replaced with a single fiber strand 0.005 in. in diameter (approximately the diameter of a hair strand) and retain the same information‑carrying capacity. Even with a rugged protective jacket surrounding the fiber, it occupies enormously less space and weighs considerably less.

Since light does not radiate from a fiber‑optic cable, it is nearly impossible to secretly tap into it without detection. For this reason, several applications requiring communications security employ fiber‑optic systems. Military information, for example, can be transmitted over fiber to prevent eavesdropping. In addition, fiber‑optic cables cannot be detected by metal detectors unless they are manufactured with steel reinforcement for strength.

Security

Flexibility We normally think of glass as being extremely brittle. If one

were to attempt to bend a 1/8 in. thick glass window, it would certainly break at some point. One reason for this is that the glass we are familiar with has a considerable amount of surface flaws, although it appears polished. The outer surface of the glass would bend considerably more than the inside. The surface flaws would initiate the crack in the same manner that long scratches are intentionally used to crack and form glass windows. The surface of glass fiber is much more refined than ordinary glass. This, coupled with its small diameter, allows it to be flexible enough to wrap around a pencil. In terms of strength, if enough pressure is applied against it, a 0.005‑in. strand of fiber is strong enough to cut one's finger before it breaks.

EconomicsPresently, the cost of fiber is comparable to copper, at approximately $0.20 to $0.50 per yard, and is expected to drop as it becomes more widely used. Since transmission losses are considerably less than for coaxial cable, expensive repeaters can be spaced farther apart. Fewer repeaters means a reduction in overall system costs and enhanced reliability.

ReliabilityOnce installed, a longer life span is expected with fiber over its metallic counterparts since it is more resistant to corrosion caused by environmental extremes such as temperature, corrosive gases, and liquids. Many coating systems made of lacquer, silicons, and ultraviolet‑cured acrylates have been developed to maintain fiber strength and longevity.

DISADVANTAGES OF FiBER‑OPTIC SYSTEMS

In spite of the numerous advantages that fiber‑optic systems have over conventional methods of transmission, there are some disadvantages, particularly because of its newness. Many of these disadvantages are being overcome with new and competitive technology.

Interfacing Costs Electronic facilities must be converted to optics

to interface to fiber. Often these costs are initially overlooked. Fiber‑optic transmitters, receivers, couplers, and connectors, for example, must be employed as part of the communication system. Test and repair equipment is costly. If the fiber‑optic cable breaks, splicing can be a costly and tedious task. Manufacturers, however, are continuously introducing new and improved field repair kits.

Strength

Fiber, by itself, has a tensile strength of approximately 1 lb, as compared to coaxial cable at 180 lb (RG591J). Surrounding the fiber with stranded KevIar* and a protective PVC jacket can increase the pulling strength up to 500 lb. Installations requiring greater tensile strengths can be achieved with steel reinforcement.

Remote Powering of Devices

Occasionally it is necessary to provide electrical power to a remote device. Since this cannot be achieved through the fiber, metallic conductors are often included in the cable assembly. Several manufacturers now offer a complete line of cable types, including cables manufactured with both copper wire and fiber.

Propagation Modes

The term mode is important in fibre optics, it describes the propagation characteristics of an electromagnetic wave as it travels through a particular type of fibre. Mathematically it can be said to be the spatial distribution of energy of the electromagnetic wave. Two modes of transmission can be distinguished in a fibre.

Single Mode

When there is only one path along which the ray of light travels, along the centre axis of the fibre, then that fibre is said to be a single mode fibre.

Multimode

Where there are a number of paths along which the ray may travel then the fibre is said to be multimode fibre.

The number of modes a fibre can support is a function of the wavelength as well as the diameter of the fibre and the index of refraction. Mathematically it can be described using the following equation:

No. of Modes 2

2

2

2

2

1

nn

d

Multimode step index

Useful in local applications that do not require great transmission speeds. Core diameter range between 50 – 1000 m. It is this large core size that supports many modes and permits the use of simple and inexpensive LED transmitters. Light pulses in this type of fibre tend to broaden as they reach their destination. This is known as modal dispersion

Single mode step index

In this the core of the fibre is made much smaller. The index of refraction is also reduced. This leads to an increase in the critical angle. Light rays tend to travel along the same path hence reducing modal dispersion. They offer the best performance in terms of information capacity and distance

Multimode graded index

The refractive index is graded from the core outwards. This produces a bending effect on the rays and helps them arrive at end at the same time.

Flexibility

Cells and Cellular traffic

Introduction to Wireless Systems by P. M. ShankarCopyright © 2002 John Wiley and Sons. All rights reserved

Splitting of thegeographical regioninto “cells.” Thefrequency fc1 is usedin multiple cellsseparated by a fixeddistance.

Introduction to Wireless Systems by P. M. ShankarCopyright © 2002 John Wiley and Sons. All rights reserved

The power from the primary channel and the totalpower from the co-channels in the cell subscribing tothe primary channel.

Introduction to Wireless Systems by P. M. ShankarCopyright © 2002 John Wiley and Sons. All rights reserved

Figure 4.3.Different geometrical shapesfor cells.(a) Square.(b) Triangular.(c) Circular.(d) Hexagonal, where R isthe “radius” of the hexagon.