# What are Transmission Lines : Types, Equation and Applications

Transmission lines became out of crafted by James Clerk Maxwell (13 June 1831 – 5 Nov 1879) was a Scottish researcher, Lord Kelvin (26 June 1824 – 17 Dec 1907) and Oliver Heaviside was conceived on 18 May 1850 and kicked the bucket on 3 Feb 1925. In North America first transmission line is worked at 4000V in 1889 June-3. A portion of the force transmission and circulation organizations in India are NTPC in New Delhi, Tata Power in Mumbai, NLC India in China, Orient Green in Chennai, Neueon Towers or Sujana Towers Ltd in Hyderabad, Aster Transmission line development, L.J.Technologies in cherlapalli, Mpower Infratech private constrained in Hyderabad.

The transmission lines are a piece of the framework that gets power from the force stations to homes and it is comprised of aluminum since it is progressively plentiful, less expensive and less thick than copper. It conveys electromagnetic vitality starting with one point then onto the next point and it comprises of two conductors that are utilized to transmit electromagnetic waves over a long separation among transmitter and beneficiary are called transmission lines. There are both AC (Alternating Current) and DC (Direct Current) transmission lines. The AC transmission lines are utilized to transmits rotating current over a long separation utilizing three conductors and the DC transmission lines are utilizes two conductors to transmit direct current over a long separation.

Let us take the comparable circuit of the transmission line, for this we are going to take the least difficult type of transmission line which is two wirelines. This two wireline is comprised of two transmitters isolated by a dielectric medium typically air medium, which is appeared in the beneath figure

two_wireline_conductor

two_wireline_conductor

On the off chance that we pass a current (I) through the channel 1, will find that there is an attractive field around the current-conveying wire of a conveyor 1 and the attractive field can be outlined utilizing arrangement inductor because of the present stream in the conduit 1, there ought to be a voltage drop over the transmitter 1, which can be represented by a progression of obstruction and inductor. The arrangement of the two wireline channel can be made to a capacitor. The capacitor in the figure will consistently be loosy to outline that we have included conductor G. The all out arrangement i.e, arrangement obstruction an inductor, parallel capacitor, and conductor make up an identical circuit of a transmission line.

equivalent_circuit_of_a_transmission_line_1

equivalent_circuit_of_a_transmission_line_1

The inductor and obstruction set up together in the above figure can be called as arrangement impedance, which is communicated as

Z = R+jωL

The parallel blend of capacitance and conductor n the above figure can be communicated as

Y = G+jωc

equivalent_circuit_of_transmission_line_2

equivalent_circuit_of_transmission_line_2

Where l – length

Is – Sending end current

Versus – Sending end voltage

dx – component length

x – a separation of dx from sending end

At a point, 'p' take current(I) and voltage(v) and at a point, 'Q' take I+dV and V+dV

The adjustment in voltage for the length PQ is the

V-(V + dV) = (R + jωL) dx * I

V-V-dv = (R + jωL) dx * I

- dv/dx = (R + jωL) * I … . eq(1)

I-(I + dI) = (G + jωc)dx * V

I – I+dI = (G + jωc)dx * V

- dI/dx = (G + jωc) * V … . eq(2)

Separating eq(1) and (2) as for dx will get

- d2v/dx2 = (R + jωL) * dI/dx … . eq(3)

- d2I/dx2 = (G + jωc) * dV/dx … . eq(4)

Subbing eq(1) and (2) in eq(3) and (4) will get

- d2v/dx2 = (R + jωL) (G + jωc) V … . eq(5)

- d2I/dx2 = (G + jωc) (R + jωL) I … . eq(6)

Let P2 = (R + jωL) (G + jωc) … . eq(7)

Where P – propogation steady

Substitute d/dx = P in eq(6) and (7)

- d2v/dx2 = P2V … . eq(8)

- d2I/dx2 = P2I … . eq(9)

General arrangement is

V = Aepx + Be-px … . eq(10)

I = Cepx + De-px … . eq(11)

Where A, B C and D are constants

Separating eq(10) and (11) regarding 'x' will get

- dv/dx = P (Aepx – Be-px ) … . eq(12)

- dI/dx = P (Cepx – De-px) … . eq(13)

Substitute eq(1) and (2) in eq(12) and (13) will get

- (R + jωL) * I = P ( Aepx + Be-px ) … . eq(14)

- ( G + jωc) * V = P (Cepx + De-px ) … . eq(15)

Substitute 'p' esteem in eq(14) and (15) will get

I = - p/R + jωL * (Aepx + Be-px)

= √G + jωc/R + jωL * (Aepx + Be-px) … . eq(16)

V = - p/G + jωc * (Cepx + De-px )

= √R + jωL/G + jωc * (Cepx + De-px ) … . eq(17)

Let Z0= √R + jωL/G + jωc

Where Z0is the trademark impedenc

Substitute limit conditions x=0, V=VS and I=IS in eq(16) and (17) will get

IS = A+B … . eq(18)

Versus = C+D … . eq(19)

ISZ0= - A+B … . eq(20)

Versus/Z0 = - C+D … . eq(21)

From (20) will get An and B esteems

A = VS - IS Z0

B =VS +IS Z0

From eq(21) will get C and D esteems

C = (IS – VS/Z0)/2

D = (IS + VS/Z0)/2

Substitute A, B, C and D esteems in eq(10) and (11)

V= (VS - IS Z0) epx + (VS +IS Z0)e-px

= VS (epx +e-px/2) – IS Z¬0(epx - e-px/2)

= VS coshx – IS Z0 sinhx

Likewise

I= (IS - VS Z0) epx + (VS/Z0+IS/2)e-px

=IS (epx+e-px/2) – VS/Z0 (epx - e-px/2)

=IS coshx – VS/Z0 sinhx

In this way V = VS coshx – IS Z0 sinhx

I = IS coshx – VS/Z0 sinhx

Condition of transmission line regarding sending end parameters are inferred

Effectiveness of Transmission Lines

The effectiveness of the transmission line is characterized as a proportion of got power by transmitted force.

Proficiency = got power (Pr)/transmitted force (Pt) * 100%

Sorts of Transmission Lines

The various sorts of transmission lines incorporate the accompanying.

1). Open Wire Transmission Line

It comprises pair of parallel directing wires isolated by a uniform separation. The two-wire transmission lines are extremely basic, minimal effort and simple to keep up over short separations and these lines are utilized around 100 MHz The another name of an open-wire transmission line is a parallel wire transmission line.

2). Coaxial Transmission Line

The two transmitters put coaxially and loaded up with dielectric materials, for example, air, gas or strong. The recurrence increments when misfortunes in the dielectric builds, the dielectric is polyethylene. The coaxial links are utilized something like 1 GHz. It is a sort of wire which conveys high-recurrence signals with low misfortunes and these links are utilized in CCTV frameworks, advanced sounds, in PC organize associations, in web associations, in TV links, and so on.

sorts of-transmission-lines

sorts of-transmission-lines

3). Optic Fiber Transmission Line

The primary optical fiber concocted by Narender Singh in 1952. It is comprised of silicon oxide or silica, which is utilized to send flags over a long separation with little misfortune in signal and at the speed of light. The optic fiber links utilized as light aides, imaging instruments, lasers for medical procedures, utilized for information transmission and furthermore utilized in a wide assortment of enterprises and applications.

4). Microstrip Transmission Lines

The microstrip transmission line is a Transverse Electromagnetic (TEM) transmission line imagined by Robert Barrett in 1950.

5). Wave Guides

Waveguides are utilized to transmit electromagnetic vitality starting with one spot then onto the next spot and they are normally working in predominant mode. The different latent segments, for example, channel, coupler, divider, horn, recieving wires, tee intersection, and so on. Waveguides are utilized in logical instruments to gauge optical, acoustic promotion flexible properties of materials and items. There are two sorts of waveguides are Metal waveguides and dielectric waveguides. The waveguides are utilized in optical fiber correspondence, microwaves, space makes, and so forth.

Applications

The utilizations of transmission line are

Force transmission line

Phone lines

Printed circuit board

Links

The transmission line conditions as far as sending end parameters are inferred, applications and arrangement of transmission lines are examined and, Here is an inquiry for you what are the consistent voltages in AC and DC transmission lines?

## What are Transmission Lines?

The transmission lines are a piece of the framework that gets power from the force stations to homes and it is comprised of aluminum since it is progressively plentiful, less expensive and less thick than copper. It conveys electromagnetic vitality starting with one point then onto the next point and it comprises of two conductors that are utilized to transmit electromagnetic waves over a long separation among transmitter and beneficiary are called transmission lines. There are both AC (Alternating Current) and DC (Direct Current) transmission lines. The AC transmission lines are utilized to transmits rotating current over a long separation utilizing three conductors and the DC transmission lines are utilizes two conductors to transmit direct current over a long separation.

## Transmission Line Equation

Let us take the comparable circuit of the transmission line, for this we are going to take the least difficult type of transmission line which is two wirelines. This two wireline is comprised of two transmitters isolated by a dielectric medium typically air medium, which is appeared in the beneath figure

two_wireline_conductor

two_wireline_conductor

On the off chance that we pass a current (I) through the channel 1, will find that there is an attractive field around the current-conveying wire of a conveyor 1 and the attractive field can be outlined utilizing arrangement inductor because of the present stream in the conduit 1, there ought to be a voltage drop over the transmitter 1, which can be represented by a progression of obstruction and inductor. The arrangement of the two wireline channel can be made to a capacitor. The capacitor in the figure will consistently be loosy to outline that we have included conductor G. The all out arrangement i.e, arrangement obstruction an inductor, parallel capacitor, and conductor make up an identical circuit of a transmission line.

equivalent_circuit_of_a_transmission_line_1

equivalent_circuit_of_a_transmission_line_1

The inductor and obstruction set up together in the above figure can be called as arrangement impedance, which is communicated as

Z = R+jωL

The parallel blend of capacitance and conductor n the above figure can be communicated as

Y = G+jωc

equivalent_circuit_of_transmission_line_2

equivalent_circuit_of_transmission_line_2

Where l – length

Is – Sending end current

Versus – Sending end voltage

dx – component length

x – a separation of dx from sending end

At a point, 'p' take current(I) and voltage(v) and at a point, 'Q' take I+dV and V+dV

The adjustment in voltage for the length PQ is the

V-(V + dV) = (R + jωL) dx * I

V-V-dv = (R + jωL) dx * I

- dv/dx = (R + jωL) * I … . eq(1)

I-(I + dI) = (G + jωc)dx * V

I – I+dI = (G + jωc)dx * V

- dI/dx = (G + jωc) * V … . eq(2)

Separating eq(1) and (2) as for dx will get

- d2v/dx2 = (R + jωL) * dI/dx … . eq(3)

- d2I/dx2 = (G + jωc) * dV/dx … . eq(4)

Subbing eq(1) and (2) in eq(3) and (4) will get

- d2v/dx2 = (R + jωL) (G + jωc) V … . eq(5)

- d2I/dx2 = (G + jωc) (R + jωL) I … . eq(6)

Let P2 = (R + jωL) (G + jωc) … . eq(7)

Where P – propogation steady

Substitute d/dx = P in eq(6) and (7)

- d2v/dx2 = P2V … . eq(8)

- d2I/dx2 = P2I … . eq(9)

General arrangement is

V = Aepx + Be-px … . eq(10)

I = Cepx + De-px … . eq(11)

Where A, B C and D are constants

Separating eq(10) and (11) regarding 'x' will get

- dv/dx = P (Aepx – Be-px ) … . eq(12)

- dI/dx = P (Cepx – De-px) … . eq(13)

Substitute eq(1) and (2) in eq(12) and (13) will get

- (R + jωL) * I = P ( Aepx + Be-px ) … . eq(14)

- ( G + jωc) * V = P (Cepx + De-px ) … . eq(15)

Substitute 'p' esteem in eq(14) and (15) will get

I = - p/R + jωL * (Aepx + Be-px)

= √G + jωc/R + jωL * (Aepx + Be-px) … . eq(16)

V = - p/G + jωc * (Cepx + De-px )

= √R + jωL/G + jωc * (Cepx + De-px ) … . eq(17)

Let Z0= √R + jωL/G + jωc

Where Z0is the trademark impedenc

Substitute limit conditions x=0, V=VS and I=IS in eq(16) and (17) will get

IS = A+B … . eq(18)

Versus = C+D … . eq(19)

ISZ0= - A+B … . eq(20)

Versus/Z0 = - C+D … . eq(21)

From (20) will get An and B esteems

A = VS - IS Z0

B =VS +IS Z0

From eq(21) will get C and D esteems

C = (IS – VS/Z0)/2

D = (IS + VS/Z0)/2

Substitute A, B, C and D esteems in eq(10) and (11)

V= (VS - IS Z0) epx + (VS +IS Z0)e-px

= VS (epx +e-px/2) – IS Z¬0(epx - e-px/2)

= VS coshx – IS Z0 sinhx

Likewise

I= (IS - VS Z0) epx + (VS/Z0+IS/2)e-px

=IS (epx+e-px/2) – VS/Z0 (epx - e-px/2)

=IS coshx – VS/Z0 sinhx

In this way V = VS coshx – IS Z0 sinhx

I = IS coshx – VS/Z0 sinhx

Condition of transmission line regarding sending end parameters are inferred

Effectiveness of Transmission Lines

The effectiveness of the transmission line is characterized as a proportion of got power by transmitted force.

Proficiency = got power (Pr)/transmitted force (Pt) * 100%

Sorts of Transmission Lines

The various sorts of transmission lines incorporate the accompanying.

1). Open Wire Transmission Line

It comprises pair of parallel directing wires isolated by a uniform separation. The two-wire transmission lines are extremely basic, minimal effort and simple to keep up over short separations and these lines are utilized around 100 MHz The another name of an open-wire transmission line is a parallel wire transmission line.

2). Coaxial Transmission Line

The two transmitters put coaxially and loaded up with dielectric materials, for example, air, gas or strong. The recurrence increments when misfortunes in the dielectric builds, the dielectric is polyethylene. The coaxial links are utilized something like 1 GHz. It is a sort of wire which conveys high-recurrence signals with low misfortunes and these links are utilized in CCTV frameworks, advanced sounds, in PC organize associations, in web associations, in TV links, and so on.

sorts of-transmission-lines

sorts of-transmission-lines

3). Optic Fiber Transmission Line

The primary optical fiber concocted by Narender Singh in 1952. It is comprised of silicon oxide or silica, which is utilized to send flags over a long separation with little misfortune in signal and at the speed of light. The optic fiber links utilized as light aides, imaging instruments, lasers for medical procedures, utilized for information transmission and furthermore utilized in a wide assortment of enterprises and applications.

4). Microstrip Transmission Lines

The microstrip transmission line is a Transverse Electromagnetic (TEM) transmission line imagined by Robert Barrett in 1950.

5). Wave Guides

Waveguides are utilized to transmit electromagnetic vitality starting with one spot then onto the next spot and they are normally working in predominant mode. The different latent segments, for example, channel, coupler, divider, horn, recieving wires, tee intersection, and so on. Waveguides are utilized in logical instruments to gauge optical, acoustic promotion flexible properties of materials and items. There are two sorts of waveguides are Metal waveguides and dielectric waveguides. The waveguides are utilized in optical fiber correspondence, microwaves, space makes, and so forth.

Applications

The utilizations of transmission line are

Force transmission line

Phone lines

Printed circuit board

Links

## Connectors (PCI, USB)

The transmission line conditions as far as sending end parameters are inferred, applications and arrangement of transmission lines are examined and, Here is an inquiry for you what are the consistent voltages in AC and DC transmission lines?

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