Transmission line Totally Explained

Everything about Transmission Line totally explained

A transmission line is the material medium or structure that forms all or part of a path from one place to another for directing the transmission of energy, such as electromagnetic waves or acoustic waves, as well as electric power transmission.Components of transmission lines include wires, coaxial cables, dielectric slabs, optical fibers, electric power lines, and waveguides.

History

Mathematical analysis of the behaviour of electrical transmission lines grew out of the work of James Clerk Maxwell, Lord Kelvin and Oliver Heaviside. In 1855 Lord Kelvin formulated a diffusion model of the current in a submarine cable. The model correctly predicted the poor performance of the 1858 trans-Atlantic submarine telegraph cable. In 1885 Heaviside published the first papers that described his analysis of propagation in cables and the modern form of the telegrapher's equations.

Transmission line vs wire

In many electric circuits, the length of the wires connecting the components can for the most part be ignored. That is, the voltage on the wire at a given time can be assumed to be the same at all points. However, when the voltage changes in a time interval comparable to the time it takes for the signal to travel down the wire, the length becomes important and the wire must be treated as a transmission line. Stated another way, the length of the wire is important when the signal includes frequency components with corresponding wavelengths comparable to or less than the length of the wire.
A common rule of thumb (justified in the input impedance section) is that the cable or wire should be treated as a transmission line if the length is greater than 1/10 of the wavelength. At this length the phase delay and the interference of any reflections on the line become important and can lead to unpredictable behavior in systems which have not been carefully designed using transmission line theory.

The four terminal model

For the purposes of analysis, an electrical transmission line can be modelled as a two-port network (also called a quadrupole network), as follows:
In the simplest case, the network is assumed to be linear (for example the complex voltage across either port is proportional to the complex current flowing into it when there are no reflections), and the two ports are assumed to be interchangeable. If the transmission line is uniform along its length, then its behaviour is largely described by a single parameter called the characteristic impedance, symbol Z₀. This is the ratio of the complex voltage of a given wave to the complex current of the same wave at any point on the line. Typical values of Z₀ are 50 or 75 ohms for a coaxial cable, about 100 ohms for a twisted pair of wires, and about 300 ohms for a common type of untwisted pair used in radio transmission.
   When sending power down a transmission line, it's usually desirable that as much power as possible will be absorbed by the load and as little as possible will be reflected back to the source. This can be ensured by making the source and load impedances equal to Z₀, in which case the transmission line is said to be matched.
   Some of the power that's fed into a transmission line is lost because of its resistance. This effect is called ohmic or resistive loss (see ohmic heating). At high frequencies, another effect called dielectric loss becomes significant, adding to the losses caused by resistance. Dielectric loss is caused when the insulating material inside the transmission line absorbs energy from the alternating electric field and converts it to heat (see dielectric heating).
   The total loss of power in a transmission line is often specified in decibels per metre (dB/m), and usually depends on the frequency of the signal. The manufacturer often supplies a chart showing the loss in dB/m at a range of frequencies. A loss of 3 dB corresponds approximately to a halving of the power.
   High-frequency transmission lines can be defined as transmission lines that are designed to carry electromagnetic waves whose wavelengths are shorter than or comparable to the length of the line. Under these conditions, the approximations useful for calculations at lower frequencies are no longer accurate. This often occurs with radio, microwave and optical signals, and with the signals found in high-speed digital circuits.

Telegrapher's equations

The Telegrapher's Equations (or just Telegraph Equations) are a pair of linear differential equations which describe the voltage and current on an electrical transmission line with distance and time. They were developed by Oliver Heaviside who created the transmission line model, and are based on Maxwell's Equations. The transmission line model represents the transmission line as an infinite series of two-port elementary components, each representing an infinitesimally short segment of the transmission line:

The distributed resistance $R$ of the conductors is represented by a series resistor (expressed in ohms per unit length).
The distributed inductance $L$ (due to the magnetic field around the wires, self-inductance, etc.) is represented by a series inductor (henries per unit length).
The capacitance $C$ between the two conductors is represented by a shunt capacitor C (farads per unit length).
The conductance $G$ of the dielectric material separating the two conductors is represented by a conductance G shunted between the signal wire and the return wire (siemens per unit length).

The model consists of an infinite series of the elements shown in the figure, and that the values of the components are specified per unit length so the picture of the component can be misleading.

R

L

C

, and

G

may also be functions of frequency. An alternative notation is to use

R'

L'

C'

and

G'

to emphasize that the values are derivatives with respect to length.
The line voltage

V(x)

and the current

I(x)

can be expressed in the frequency domain as ť

frac=Z_0

, for all

l

and all

lambda

.
In calculating

eta

, the wavelength is generally different inside the transmission line to what it would be in free-space and the velocity constant of the material the transmission line is made of needs to be taken into account when doing such a calculation.

Practical types of electrical transmission line

Coaxial cable

In radio-frequency applications up to a few gigahertz, the wave propagates in the transverse electric and magnetic mode (TEM), which means that the electric and magnetic fields are both perpendicular to the direction of propagation. However, above a certain frequency called the cutoff frequency, the cable behaves as a waveguide, and propagation switches to either a transverse electric (TE) or a transverse magnetic (TM) mode or a mixture of modes. This effect enables coaxial cables to be used at microwave frequencies, although they're not as efficient as the more expensive, purpose-built waveguides.
The most common use for coaxial cables is for television and other signals with bandwidth of multiple Megahertz. In the middle 20th Century they carried long distance telephone connections.

Microstrip

parallel to a ground plane. Microstrip can be made by having a strip of copper on one side of a printed circuit board (PCB) or ceramic substrate while the other side is a continuous ground plane. The width of the strip, the thickness of the insulating layer (PCB or ceramic) and the dielectric constant of the insulating layer determine the characteristic impedance.

Stripline

ť Main article : Stripline

A stripline circuit uses a flat strip of metal which is sandwiched between two parallel ground planes. The insulating material of the substrate forms a dielectric. The width of the strip, the thickness of the substrate and the relative permittivity of the substrate determine the characteristic impedance of the strip which is a transmission line.

Balanced lines

A balanced line is a transmission line, consisting of two conductors of the same type, and equal impedance to ground and other circuits.

Twin-lead

Twin-lead consists of a pair of conductors held apart by a continuous insulator.

Lecher lines

Lecher lines are a form of parallel conductor that can be used at UHF for creating resonant circuits. They are used at frequencies between HF/VHF where lumped components are used, and UHF/SHF where resonant cavities are more practical.

General applications of transmission lines

Transferring signals from one point to another

Electrical transmission lines are very widely used to transmit high frequency signals over long or short distances with minimum power loss. One familiar example is the down lead from a TV or radio aerial to the receiver.

Pulse generation

Transmission lines are also used as pulse generators. By charging the transmission line and then discharging it into a resistive load, a rectangular pulse equal in length to twice the electrical length of the line can be obtained, although with half the voltage. A Blumlein transmission line is a related pulse forming device that overcomes this limitation. These are sometimes used as the pulsed energy sources for radar transmitters and other devices.

Stub filters

If a short-circuited or open-circuited transmission line is wired in parallel with a line used to transfer signals from point A to point B, then it'll function as a filter. The method for making stubs is similar to the method for using Lecher lines for crude frequency measurement, but it's 'working backwards'. One method recommended in the RSGB's radiocommunication handbook is to take an open-circuited length of transmission line wired in parallel with the feeder delivering signals from an aerial. By cutting the free end of the transmission line, a minimum in the strength of the signal observed at a receiver can be found. At this stage the stub filter will reject this frequency and the odd harmonics, but if the free end of the stub is shorted then the stub will become a filter rejecting the even harmonics.

Acoustic transmission lines

Further Information

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