Microwave Engineering Transmission Lines - Microwave Engineering

What is Microwave Engineering Transmission Lines?

A transmission line is a connector which transfers energy from one point to another. The reading of transmission line theory is useful in the real usage of power and equipment.

There are essentially four types of transmission lines −

  • Two-wire parallel transmission lines
  • Coaxial lines
  • Strip type substrate transmission lines
  • Waveguides

While transmitting or while getting, the energy transfer has to be done efficiently, without the excess of power. To accomplish this, there are certain significant parameters which have to be measured.

Main Parameters of a Transmission Line

The significant parameters of a broadcast line are resistance, inductance, capacitance and conductance.
Resistance and inductance collected are called as transmission line impedance.

Capacitance and conductance together are called as admittance.

Resistance

The resistance presented by the material out of which the transmission lines are made, will be of substantial amount, particularly for shorter lines. As the line current increases, the ohmic loss (I2Rloss)(I2Rloss) also increases.

The resistance RR of a conductor of length "ll" and cross-section "aa" is represented as

METL

Where


�ρ = resistivity of the conductor material, which is constant.

Temperature and the incidence of the current are the chief factors that affect the resistance of a line. The resistance of a conductor differs linearly with the modification in temperature. While, if the frequency of the current rises, the current mass towards the surface of the conductor also rises. Else, the current density towards the center of the conductor rises.

This means, more the current flows in the direction of the surface of the conductor, it flows less towards the center, which is known as the Skin Effect.

Inductance

In an AC transmission line, the current runs sinusoidally. This current makes a magnetic field perpendicular to the electric field, which also differs sinusoidally. This is well known as Faraday's law. The fields are portrayed in the resulting figure.
inductance

This changing magnetic field makes some EMF into the electrode. Now this induced voltage or EMF runs in the opposite direction to the current flowing initially. This EMF flowing in the opposite direction is consistently shown by a parameter known as Inductance, which is the property to compete with the shift in the current.

It is denoted by "L". The unit of measurement is "Henry(H)".

Conductance

There will be an outflow current among the transmission line and the ground, and also among the phase conductors. This minor amount of outflow current usually flows over the surface of the insulator. Opposite of this outflow current is termed as Conductance. It is denoted by "G".
The flow of line current is related with inductance and the voltage change between the two points is related with capacitance. Inductance is related with the magnetic field, while capacitance is associated with the electric field.

Capacitance

The voltage alteration among the Phase conductors gives growth to an electric field between the conductors. The two conductors are just like similar plates and the air in among them develops dielectric. This pattern gives rise to the capacitance effect between the conductors.

Characteristic Impedance

If an unchanging lossless transmission line is measured, for a wave travelling in one direction, the ratio of the amplitudes of voltage and current along that line, which has no reflections, is called as Characteristic impedance.
It is denoted by Z0

image

Where L & C are the inductance and capacitance per unit lengths

Impedance Matching

To achieve maximum power transfer to the load, impedance matching has to be done. To achieve this impedance matching, the following conditions are to be met.

The resistance of the load should be equal to that of the source.

RL=RS

The reactance of the load should be equal to that of the source but opposite in sign.

XL=−XS

Which means, if the source is inductive, the load should be capacitive and vice versa.

Reflection Co-efficient

The parameter that states the amount of replicated energy due to impedance incompatibility in a transmission line is called as Reflection coefficient. It is indicated by ρ (rho).

It can be stated as "the ratio of reflected voltage to the incident voltage at the load terminals".

equation


If the impedance among the device and the transmission line don't match with each other, then the energy gets reflected. The higher the energy gets reflected, the greater will be the value of ρ reflection coefficient.

Voltage Standing Wave Ratio (VSWR)

The standing wave is shaped when the incident wave becomes replicated. The standing wave which is shaped covers some voltage. The magnitude of standing waves can be measured in terms of standing wave ratios.

The ratio of maximum voltage to the minimum voltage in a standing wave can be defined as Voltage Standing Wave Ratio (VSWR). It is denoted by "S".

equation

VSWR defines the voltage standing wave pattern that is present in the transmission line due to phase addition and subtraction of the incident and reflected waves.

Hence, it can also be written as

equation
The larger the impedance mismatch, the higher will be the amplitude of the standing wave. Therefore, if the impedance is matched perfectly,

Vmax:Vmin=1:1

equation
Hence, the value for VSWR is unity, which means the transmission is perfect.

Efficiency of Transmission Lines

The efficiency of transmission lines is defined as the ratio of the output power to the input power.

equation

Voltage Regulation

Voltage regulation is defined as the change in the magnitude of the voltage between the sending and receiving ends of the transmission line.%voltageregulation=sendingendvoltagereceivingendvoltagesendingendvoltage×100

equation
Losses due to Impedance Mismatch

The transmission line, if not ended with a matched load, happens in losses. These losses are numerous kinds such as attenuation loss, reflection loss, transmission loss, return loss, insertion loss, etc.

Attenuation Loss

The loss that happens due to the immersion of the signal in the transmission line is termed as Attenuation loss, which is represented as

equation

Attenuationloss(dB)=10log10[EiErEt]
Where

  • Ei= the input energy
  • Er= the reflected energy from the load to the input
  • Et= the transmitted energy to the load

Reflection Loss

The loss that happens due to the replication of the signal due to impedance mismatch of the transmission line is termed as Reflection loss, which is represented asReflectionloss(dB)=10log10[EiEiEr]

equation
Where

  • Ei= the input energy
  • Er= the reflected energy from the load

Transmission Loss

The loss that occurs while transmission through the transmission line is termed as Transmission loss, which is represented as

equation

10EiEt
Where

  • Ei= the input energy

  • Et= the transmitted energy

Return Loss

The measure of the power reflected by the transmission line is termed as Return loss, which is represented as
g10
EiEr

equation
Where

  • Ei= the input energy

  • Er= the reflected energy

Insertion Loss

The loss that happens due to the energy transmission using a transmission line likened to energy transfer without a transmission line is termed as Insertion loss, which is represented asE1E2

equation
Where

  • E1= the energy received by the load when directly connected to the source, without a transmission line.

  • E2= the energy received by the load when the transmission line is connected between the load and the source.

Stub Matching

If the load impedance mismatches the source impedance, a method called "Stub Matching" is occasionally used to attain matching.

The process of linking the units of open or short circuit lines called stubs in the shunt with the main line at some point or points can be termed as Stub Matching.

At higher microwave incidences, essentially two stub matching techniques are employed.

Single Stub Matching

In Single stub matching, a stub of certain fixed length is positioned at some distance from the load. It is used simply for a static frequency, because for any modification in frequency, the location of the stub has to be altered, which is not done. This method is not appropriate for coaxial lines.

Double Stub Matching

In double stud matching, two stubs of variable length are fixed at certain positions. As the load changes, only the lengths of the stubs are adjusted to achieve matching. This is widely used in laboratory practice as a single frequency matching device.

The following figures show how the stub matchings look.
double_stub_matching

The single stub matching and double stub matching, as revealed in the above figures, are done in the transmission lines to attain impedance matching.

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