Comm3Le_1

TRANSMISSION LINE- medium that is used to transfer signal or power from one point to

another- can be used to propagate dc or low-frequency ac (such as 60-Hz

electrical power and audio signals, and very high frequencies (such as IF and RF)

- All practical transmission lines are arranged in some uniform pattern to simplify calculation, reduce costs and increase convenience.

- There is a difference between a transmission line and a conductor Conductor – a material that guides flow of current

(All conductors are transmission lines, but not all transmission lines are conductors)

THREE IMPORTANT REQUIREMENTS OF TRANSMISSION LINE> There must be minimum loss (line losses attenuate the signal

because of power dissipation in the conductors> Reflection of signal on the line must be avoided> There should be no stray radiation or pick-up of signal by the line

itself

TRANSMISSION LINES

TRANSMISSION LINE

• Any physical structure that will guide an electromagnetic wave from place to place

• Transmission of digital and analog signals between two points occurs over a pair of parallel conductors

• is a metallic conductor system that is used to transfer electrical energy from one point to another.

TRANSMISSION LINES

TRANSMISSION LINE

• Consists most frequently of two conductors

• Are rare electromagnetic systems that can also be analyzed by circuit-theory tools

• (Popovic. 2000. Introductory Electromagnetics p.320)

• Guide electromagnetic signals

TRANSMISSION LINES

DIFFERENCE BETWEEN CIRCUIT THEORY AND TRANSMISSION LINE THEORY

• The key difference between circuit theory and transmission line theory is electrical size.

• Circuit analysis assumes that the physical dimensions of a network are much smaller than the electrical wavelength, while transmission lines may be a considerable fraction of a wavelength, or many wavelengths, in size.

• Thus a transmission line is a distributed-parameter network, where voltages and currents can vary in magnitude and phase over its length. (Pozar. Microwave Engineering. P49)

TRANSMISSION LINES

TYPES OF TRANSMISSION LINE

> BALANCED LINE (PARALLEL WIRE) - the two wires have the same capacitance to ground - each wire carries same current but are 180° out of phase (currents for

each wire are equal, only in opposite direction) - OPEN-WIRE TRANSMISSION LINE - TWIN LEAD TRANSMISSION LINE - TWISTED-PAIR CABLE - SHIELDED CABLE PAIR

> UNBALANCED LINE (COAXIAL) - one wire is at ground potential, while the other wire is at signal potential - COAXIAL/CONCENTRIC TRANSMISSION LINE - BALUNS

INTRODUCTION

OPEN-WIRE TRANSMISSION LINE

- Consists of two parallel wires,closely spaced and separated by air

- Nonconductive spacers are used at periodic intervals as support to keep

the distance between the two wires constant (spacing: 2 - 6 inches)

- Advantage: simple construction

- Disadvantage: high radiation losses and noise susceptibility

INTRODUCTION

TWIN LEAD TRANSMISSION LINE

- Similar to the open wire, except that instead of spacers a solid dielectric is

used along the whole length of the wire which provides uniform spacing along

the entire length

- Also termed as ribbon cable

- Typical distance between the wires is about 5/16 inch

- Common dielectrics are teflon and polyethylene

INTRODUCTION

TWISTED-PAIR CABLE

- Two insulated wires twisted to form a flexible line without the use of spacers

- Advantage: flexibility

- Disadvantage: not suitbale for high frequencies because of high loss due

to insulation

INTRODUCTION

SHIELDED CABLE PAIR - Consists of parallel conductors separated from each other and surrounded by a solid dielectric. - Conductors are contained within a copper braid tubing that acts like a shield - Assembly is covered by a rubber coating for protection from elements and mechanical damage - Advantage: less radiation loss and interference

INTRODUCTION

COAXIAL/CONCENTRIC TRANSMISSION LINE - The basic coaxial is made of a centre conductor surrounded by an outer concentric conductor. - Extensively used for high frequencies (parallel transmission lines are suitable for low frequency applications since their radiation and dielectric losses become excessive at high frequencies) - Two types:

Rigid air filled - insulating material is air - Advantage: ability to minimize the radiation losses - Noise pick up is also prevented - Disadvantage: expensive and high-maintenance (moisture sensitive)

Solid flexible lines - inner conductor consists of flexible wire insulated from the braided outer

conductor by a solid continuous insulating material - polyethylene plastic as well as Teflon, is used to separate the two

conductors - Advantage: less expensive, easier to construct and install, less

maintenance - Disadvantage: higher dielectric loss

INTRODUCTION

COAXIAL/CONCENTRIC TRANSMISSION LINE

INTRODUCTION

Rigid Air-filled Coaxial Cable

Solid Flexible Coaxial Cable

BALUN - a circuit device used to connect a balanced transmission line to an unbalanced transmission line

INTRODUCTION

http://en.wikipedia.org/wiki/File:2_Balun_matching_transformers.jpg

http://en.wikipedia.org/wiki/File:Tvbalun.jpg

LOSSES IN TRANSMISSION LINE RESISTIVE OR CONDUCTOR HEATING (I2R LOSS)

- proportional to current and therefore inversely proportional to characteristic impedance

- this loss also increases with frequency because of skin effectWays to minimize skin effect: a. increase wire diameter b. silver plate the conductor

DIELECTRIC HEATING- proportional to the voltage across the dielectric and inversely

proportional to the characteristic impedance for any power transmitted- comes from the leakage current that flows through the dielectric

RADIATION LOSS- result when the line cannot restrain all of the signal enerrgy to stray

within the shield- also occurs if the transmission line acts as an antenna

TRANSMISSION LINES

TRANSMISSION LINE EQUIVALENT CIRCUIT



**Since each conductor has a certain length and diameter, it will have a RESISTANCE (R) and INDUCTANCE (L).**Since there are two wires close to each other, there will be CAPACITANCE (C) between them.**The wires are separated by a certain dielectric which cannot be perfect insulation, the leakage current through it can be represented by shunt CONDUCTANCE (G).**R, L, C, and G are all measured per unit length because they occur periodically along the line

TRANSMISSION LINES

TRANSVERSE ELECTROMAGNETIC MODE (TEM)

Lumped Element Model• A transmission line shall be represented by a

parallel wire configuration regardless of the specific shape of the line under consideration

• The representation of transmission line is called the LUMPED ELEMENT MODEL

• Transmission Line Parameters– Resistance ( R )– Inductance ( I )– Conductance ( G )– Capacitance ( C )

TRANSVERSE ELECTROMAGNETIC MODE (TEM)

Coaxial Line a = outer radius of the inner conductor (m) b = inner radius of outer conductor (m)

TRANSMISSION LINE PARAMETERS

Rs = surface resistance of the conductor known as the INTRINSIC RESISTANCENOTE: Rs depends not only on the material but property of the conductor (conductivity and permeability but also on the frequency traveling) REMEMBER:Perfect conductor = σc = ∞Perfect dielectric = σ = 0


Two – Wire Line a = radius of each wire ( m ) d = spacing between wires’ centers ( m )


Parallel Plate Line w = width of each plate ( m ) d = thickness of insulation between plates ( m )



NOTE: If the insulating material between the conductor is air the transmission line is called AIR LINEFor Air Lineε = εo = 8.854 x 10-12 F/mμ = μ o = 4pi x 10-7 H/mσ = 0 and G’ = 0

TRANSMISSION LINE RELATIONS

• General Characteristics of Transmission Line– Propagation delay per unit length (T0) { time/distance} [s/m]

• Or Velocity (v0) {distance/ time} [s/m]– Characteristic Impedance (Z’) (– Per-unit-length Capacitance (C’) [F/m]– Per-unit-length Inductance (L’) [H/m]– Per-unit-length (Series) Resistance (R’) [/m]– Per-unit-length (Parallel) Conductance (G’ ) [S/m]

lL’lR’

lC’l G’

T- LINE EQUIVALENT CIRCUIT

• Ideal (lossless) Characteristics of Transmission Line– Ideal TL assumes:

• Uniform line• Perfect (lossless) conductor (R’0)• Perfect (lossless) dielectric (G’0)

– We only consider T0, Z’, C’, and L’.

• A transmission line can be represented by a cascaded network (subsections) of these equivalent models. – The smaller the subsection the more accurate the model

– The delay for each subsection should be no larger than 1/10th the signal rise time.

Ll’

lC’

IDEAL T- LINE EQUIVALENT CIRCUIT

• Knowing any two out of Z0, Td, C0, and L0, the other two can be calculated.

• C0 and L0 are reciprocal functions of the line cross-sectional dimensions and are related by constant me.

• is electric permittivity 0= 8.85 X 10-12 F/m (free space)

ri s relative dielectric constant

• is magnetic permeability 0= 4pi X 10-7 H/m (free space)

r is relative permeability

.;

;;1

;;

;;

00

000

0000

00

00d0

00

rr

LCv

TZLZ

TC

CLTC

LZ

Don’t forget these relationships and what they mean!Don’t forget these relationships and what they mean!

IDEAL TRANSMISSION LINE PARAMETERS

TRANSMISSION LINE EQUIVALENT CIRCUIT PRIMARY CONSTANTS:

R Ω / unit lengthL H / unit lengthC F / unit lengthG S / unit length

SECONDARY CONSTANTS

Characteristic ImpedancePropagation Constant

CHARACTERISTIC IMPEDANCE - the impedance measured at the input of a transmission line when its length is infinite - ration of maximum voltage to maximum current at any point on such line - Mathematically, Zo = √Z/Y or where: Z series impedance per section

R + jωL

Zo = R + jωL Y shunt admittance perr section

G + jωC G + jωC

TRANSMISSION LINES

CHARACTERISTIC IMPEDANCE BASED ON GEOMETRY

PARALLEL-WIRE LINE

Zo =

COAXIAL LINE

TRANSMISSION LINES

d

D2log

276

r

r

D

d d

d D

PROPAGATION CONSTANT (PROPAGATION COEFFICIENT) - used to express the attenuation and phase shift per unit length of the transmission line - determines the variation of current or voltage with distance S along the line

γ = √ZY = √(R + jωL)(G + jωC) = α + jβ

Since a phase shift of 2π rad occurs over a distance of one wavelength,2πλ

At IF and RF, ωL > R, and ωC > G, thus, R GZo and β = ω√LC the line is

considered lossless2Zo 2

TRANSMISSION LINES

j(nepers / unit length)

(radians / unit length)

β =

α = +

The current and voltage distribution along a transmission line that is terminated in a load equal to its characteristic impedance (matched line) are determined from the formula:

I = Ise-lγ V = Vse-lγ

Is = current at the source end of the line Vs = voltage at the source end of the line γ = propagation constant l = distance from the source at which the current or voltage is

determined

For a matched load ZL = Zo, and for a given length of cable, l, the loss in signal voltage or current is the real part of γl, and the phase shift is the imaginary part.

TRANSMISSION LINES

INCIDENT AND REFLECTED WAVES An ordinary transmission line is bidirectional, that is, power can propagate equally well in both directions.

INCIDENT VOLTAGE – voltage that propagates from the source toward the load

REFLECTED VOLTAGE – voltage that propagates from the load toward the source

INCIDENT CURRENT – current that propagates from the source toward the load

REFLECTED CURRENT – current that propagates from the load toward the source

**For infinitely long lines, all incident power is stored in the line, thus, there is no reflected power;**For purely resistive load equal to Zo, the load absorbs all the incident power

REFLECTED POWER – portion of the incident power that is not absorbed by the load (Pr < Pi)

TRANSMISSION LINES

Using Kirchhoffs’ Law

TRANSMISSION LINE EQUATION

• Dividing and rearranging the equation

• Setting the limit for delta z as it approaches 0

• Application of Kirchhoff’s current law at point N+1

• Dividing all terms by delta z and taking the as it approaches to 0



• Consider the following sinusoidal steady state equation

• Thus the following transmission line equation will be derived also known as the telegraph equation

REFLECTION COEFFICIENT- also called Coefficient of Reflection- vector quantity that represents the ratio of reflected voltage to

incident voltage; or reflected current to incident current

Γ = Er / Ei or Γ = Ir / Ii

(Worst case : Γ = 1; Ideal: Γ = 0)

STANDING WAVE RATIOSTANDING WAVE – interference pattern caused by the two traveling

waves (incident wave and reflected wave) - stationary waves that appear to remain in a fixed position in the

line, varying only in amplitude

STANDING WAVE RATIO – ratio of the maximum voltage to the minimum voltage or the maximum current to the minimum current of a standing wave on transmission line

- often called as VSWR (Voltage Standing Wave Ratio) - is essentially a measure of the mismatch between ZL and Zo

TRANSMISSION LINES

ZL – ZO

ZL + ZO

Γ =

STANDING WAVE RATIO

Vmax

Vmin

where Vmax = Ei + Er

Vmin = Ei – Er

1 + Γ1 – Γ

Consequently,

SWR – 1SWR + 1

Example: For a transmission line with an incident voltage of 5V and reflected voltage of 3V, determine the reflection coefficient and SWR.

TRANSMISSION LINES

SWR =

SWR =

Γ =

STANDING WAVE ON OPEN LINE STANDING WAVE ON SHORTED LINE

TRANSMISSION LINES

Documents

Comm3Le_1