Transmission Line i

UNIT I

Introduction to Metallic Transmission

Lines

Transverse EM Waves

◘ Longitudinal

- propagation of electrical power along a transmission line occurs in the form of transverse electromagnetic (TEM) waves.

- with longitudinal waves, the displacement (amplitude) is in the direction of propagation.

Two basic kinds of Waves:

◘ Transverse

Longitudinal Waves

Transverse Waves

Characteristics of EM Waves

◘ Wave Velocity - waves travel at various speeds, depending on the

type of wave and the characteristics of the propagation medium

◘ Frequency- it is the rate at which the periodic wave repeats.

◘ Wavelength

- it is the distance of one cycle occurring in space.

For free space propagation:

Where:λ = wavelengthc = speed of light =

3x108 m/s f = frequency

Wavelength in feet or inches:

Transmission Lines

• defined as the conductive connections between the system elements which carry signal power

• Metallic conductor system that is used to guide or transfer electrical energy from one point to another.

• Transfer of output rf energy of a transmitter to an antenna• The used of transmission line is due to that antenna cannot be

connected directly to the transmitter since it is located some distance away.

The transmission line is connected to a source which is called INPUT END.The input INPUT END is also called as Transmitter End, Sending End or Source.The other end is called the OUTPUT END or Receiving End or Sink.

Describing transmission line in terms of impedance

1. INPUT IMPEDANCE • Ratio of voltage to current at the input end• Impedance presented to the transmitter by the transmission line

and the load2. OUTPUT IMPEDANCE• Ratio of the voltage to current at the output end• Impedance presented to the load by the transmission line and the

source.3. CHARACTERISTICS IMPEDANCE• Impedance at the infinitely long transmission line • Ratio od the voltage and current at any point in the rf line

Types of Transmission Lines

◘ Balanced Transmission Lines

- with two wire balanced lines, both conductors carry current- also called as differential signal transmission

◘ Unbalanced Transmission Lines

- also called as single ended signal transmission- one wire is at ground potential, whereas the other wire is at signal potential.

◘ Baluns- stands for balanced to unbalanced

- a device used to connect a balanced transmission line to an unbalanced load.

Metallic Transmission Lines

◘ Parallel-conductor- are comprised of two or more metallic conductors separated

by a nonconductive insulating material called dielectric.

Most common parallel-conductor transmission lines:• Open-wire

transmission line - are two wire parallel conductors - consist simply of two parallel wires, closely spaced and separated by air.

- consist of two wires that are generally spaced from 0.25 to 6 inches apart. - sometimes used as a transmission line between antenna and transmitter or antenna and receiver. - advantage of this type is its simple construction. - principal disadvantage are the high radiation losses and noise pick up due to the lack of shielding

• Twin lead

- is another form of two wire parallel conductor - is essentially the same as open wire transmission line except that the spacers between the two conductors are replaced with a continuous solid dielectric. - essentially the same as the two wire open line except that uniform spacing is assured by embedding the wires in a low loss dielectric, usually polyethylene.

• Twisted-pair transmission lines

- is formed by twisting two insulated conductors around each other - are often stranded in units, and the units are then cabled into cores containing up to 3000 pairs of wires. - consist of two insulated wires, twisted to form a flexible line without the use of spacers. - not used for high frequencies due to the high losses that occur in the rubber insulation. - LAN are often wired using twisted pair.

• Shielded Pair transmission lines

- consist of parallel conductors separated from each other and surrounded by solid dielectric. - the conductor are contained within a copper braid tubing that acts as a shield. - the principal advantage is that the conductors are balanced to the ground - the copper braid shield isolates the conductors from external noise pick up.

◘ Coaxial or Concentric

- used for high data transmission rates to reduce losses and isolate transmission path.

• Rigid (Air) Coaxial Line

- consist of a wire mounted inside of and coaxially with a tubular outer conductor. - the inner conductor is insulated from the outer conductor by insulating spacers or beads at regular intervals. - the main advantage of this is to minimize radiation losses

• Solid Flexible Coaxial Line

- are made with an inner conductor that consists of flexible wire insulated from the outer conductor by a solid, continuous insulating material.

Two types of Coaxial cable connectors:• BNC connector

- Bayonet Neill – Concelman. It is a common type of RF connector used for a coaxial cable. - are made to match the characteristic impedance of cable at either 50 ohms or 75 ohms. It is usually applied for frequencies below 3 GHz and voltages below 500 Volts.

• Type N connector

-is a threaded RF connector used to join coaxial cables. It was one of the first connectors capable of carrying microwave-frequency signals, and was invented in the 1940s by Paul Neill of Bell Labs, after whom the connector is named.

Waveguide

- Classified as a transmission line- Used to guide energy from one point to another but the usage is

limited to mean a hollow metal tube- The EM wave travelling down the waveguide is somewhat slower

than the EM Wave travelling in free space.

Types of Waveguide

BASED ON THE CROSS SECTION1. Rectangular2. Elliptical3. Circular

BASED ON THE MATERIAL1. Metallic2. Dielectric

- The installation of waveguide is difficult compare to the other types of transmission line. Radius of bends must measure than two wavelengths at the operating frequency to avoid attenuation.

Transmission Line Losses

◘ Copper Losses

◘ Radiation Losses

◘ Dielectric Heating Losses

◘ Coupling Losses

◘ Corona

- Is a luminous discharge that destroys the transmission line

• A type of copper loss is Power Loss.

• It occurs whenever the current flows through one of the conductors, and dissipate energy in the form of heat.

• Another type of copper loss is due to Skin Effect. But can be reduced using Litzendrant Wire.

• SKIN EFFECT – current in the center of the wire becomes smaller and most of the electron flow is in the surface

A difference of potential bet. Two conductors of a metallic transmission line

- It is the energy radiated caused by the fields surrounding the conductors

When two section of transmission line are connected together.

◘ Length of Transmission Line- A transmission line is considered to or is defined as

long if its length exceeds 1/16th of a wavelength, otherwise it is considered short.

NOTE- When a power is applied to a short transmission line

practically it reaches at the output end of end of the line.- Since most transmission lines are electrically long, the

properties of the line should be considered. Example is the voltage necessary to drive the current.

EXAMPLE:A line that has a physical length of 3 meters is considered short if it transmits a radio frequency of 30 kilohertz. On the other hand, the same transmission line is considered electrically long if it transmits 30000 Megahertz.

To show the difference in physical and electrical lengths of the lines, compute the wavelength of the two frequencies.

◘ Transmission Line Equivalent Circuit

◘ Lumped ConstantsA transmission line has the properties of inductance, capacitance, and resistance just as more conventional circuits have. But in conventional circuits they are lumped into a single device or component.

1. Coil of Wire2. Two metal plates separated by small space3. Fixed Resistor

But a transmission line constants are distributed. Meaning all lumped constants are lumped together.

• Series Inductance

◘ Distributed Parameters

When current flows through a wire, a magnetic lines of force are set up around the wire. As the current increase or decrease, the field expands and collapse that tends to keep the current in the same direction

• Shunt Capacitance

◘ Distributed Parameters

The two parallel wires act as a plates of capacitor and that air between them is serving as a dielectric material.

◘ Distributed Parameters• Series

Resistance

The transmission line has a electrical resistance along its length.

◘ Distributed Parameters• Shunt

Conductance

Since Dielectric, even air is not a perfect insulator, a small current known as LEAKAGE CURRENT flows between two wires. It acts as a resistor parallel between to wires permitting the flow of current. The property is called CONDUCTANCE.

◘ Electromagnetic Fields about a Transmission Line

Distributed constants are basic properties common to all transmission line and exist whether or not current flows. But as soon as current and voltage already exist in a transmission line, another property becomes evident. The EM field.

Two kinds of field:1. Electric field - field associated

with voltage. It exerts force to a charge that placed on it.

2. Magnetic Field – field associated with current, because it tends to exert magnetic force on the poles.

Transmission Characteristics

- are called secondary constants and are determined from the four primary constant.

◘ Characteristic Impedance

- sometimes called surge impedance is defined as the impedance seen looking into an infinitely long line or the impedance seen looking into a finite length of line that is terminated in a purely resistive load with a resistance equal to the characteristic impedance of the line.

- ratio of E to I at every point in the transmission line

◘Velocity Wave Propagation - The inductance of a line delays the charging of the line

capacitance. Therefore the velocity of propagation is related to the values of L and C.

Q = IT (The total charge is equal to the current multiplied by the time it flows)

Q = CE (The total charge on a capacitor is equal to capacitance multiplied by E on the capacitor.

Since non e of the charge is lost, the total charge leaving the battery is equal to the total charge on the line.

- Since the capacitor is charge equal to CE, the voltage across each inductor must also change

◘Determining the Characteristic Impedance

Formulas:Based on equivalent ckt.:

For extremely low frequency:

For extremely high frequency:

Basic formula of Impedance:

For two parallel transmission line:

For concentric coaxial cable:

Example 1:

Determine the characteristic impedance for an air dielectric two wire parallel transmission line with a D/r ratio of 12.22.

Ans. 300 ohms

Example 2:

Determine the characteristic impedance for an RG-59A coaxial cable with the following specs: d= 0.025 in., D= 0.15in. and Єr= 2.23.

Ans. 71.9 ohms

Example 3:

Determine the characteristic impedance for an RG-59A coaxial cable with the following specs: L= 0.118 µH/ft and C= 21pF/ft.

Ans. 75 ohms

◘ Propagation Constant

- is used to express the attenuation and the phase shift per unit length of a transmission line.

Formulas:

Propagation constant:

Phase shift:

Intermediate and radio frequency:

Current and Voltage distribution:

Wave Propagation on a Metallic

Transmission Line

◘ Velocity and Dielectric Constant

- is defined simply as the ratio of the actual velocity of the propagation of an electromagnetic wave through a given medium to the velocity of propagation through a vacuum.

• Velocity Factor

• Dielectric constant

- is simply the relative permittivity of the material.

Where:Vp = velocity factorVP = actual velocity of propagationc = velocity of propagation through the vacuum

Rearranging the equation gives the Vf = VP x c

The velocity at which the electromagnetic waves travels through transmission line depends on the dielectric constant of the insulating material separating the two conductors.

VP =

Example:

For a given length of RG 8A/U coaxial cable with distributed capacitance C = 96.6pF/meter, a distributed inductance L = 241.56nH/meter and a relative dielectric constant of Єr = 2.3, determine the velocity of propagation and the velocity factor.

Ans. 2.07x108m/s, 0.69 or 0.66

◘ Electrical length of a transmission line

- the length of a transmission line is relative to the length of the wave propagating.

◘ Delay Lines

- are transmission line design to intentionally introduce a time delay in the path of an electromagnetic wave.

td = LC (seconds)

◘ INCIDENT AND REFLECTED WAVES

An ordinary transmission line is bidirectional; power can propagate well in both directions. Voltage that propagates from the source.

Voltage that propagates from the source toward the load is called INCIDENT VOLTAGE.Voltage that propagates from the load towards the source is called REFLECTED VOLTAGE.

◘ REFLECTION COEFFICIENT

The reflection of coefficient is a vector quantity that represents the ratio of reflected voltage to incident voltage or reflected current to incident current.

or where reflection coefficient = incident voltage = reflected voltage = reflected current = incident current

◘ STANDING WAVES

When Zo = ZL , all the incident power is absorbed by the

load. This is called a 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 UNMATCHED LINE OR MISMATCHED LINE.

◘ STANDING WAVES

When there is a mismatched line, there are two electromagnetic waves, travelling in opposite direction, present on the line at the same time. These are called TRAVELING WAVES.The two traveling waves set up an interference pattern called a STANDING WAVE.

◘ STANDING WAVE RATIO

The standing-wave ratio (SWR) is defined as the ratio of the maximum voltage to the minimum voltage or the maximum current to the minimum current of a standing wave on a transmission line. (Voltage Standing Wave Ratio).

SWR = =

Vmax = Ei + Er = occur when the incident and reflected waves are in phase Vmin = Ei – Er = occur when the incident and reflected waves are 180 out of phase.

◘ STANDING WAVE RATIO

SWR = SWR =

Substituting the formula from the original SWR equation

◘ STANDING WAVE ON AN OPEN LINE

When an incident wave waves of voltage and current reach an open termination, none of the power is absorbed; it all reflected back to the source .

It can be seen that the voltage standing wave has a maximum value of at the open end and a minimum value one quarter wavelength from the open.

The current standing wave

THE END of PART 1