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Electrical Characteristics of Transmission Lines

Figure 1: Replacement circuit diagram of transmission lines

Vierpol- Ersatzschaltbild einer Leitung:
	in Längsrichtung wirkt der Ohmsche Längswiderstand R und eine Induktivität L,
	parallel wirkt der Isolationsleitwert G und die Leitungskapazität C. series resistance inductance parallel resistance parallel capacitance

Figure 1: Replacement circuit diagram of transmission lines

Conductions still have especially another task than only energy transport, for example the message transmission in the communication electronics at the telephone.

After more than 100 km on a conduction a message doesn't reach the receiver unchangedly. During the transport the message is subject to many influences. This affects the signal form.

Comparing the output signal of a conduction with the input signal, then we will establish alterations which have the following causes:

Since every conduction shows different qualities but all conductions are subject to the same influences, a replacement circuit diagram can be drawn for a conduction.

Figure 2: Calculation of the resistance of a round wire

Calculation of the resistance of a round wire

Figure 2: Calculation of the resistance of a round wire

Series Resistance R

Every conductor pits a resistance against the electric current since the mobile electrons always meet atom trunks and are braked therefore.

With a formula the resistance can be described so:

R = ρ· l in [Ω] R = series resistance in [Ω]
l = length of the conductor in [m]
A = cross-sectional area of the conductor in [mm²]
ρ = spezific resistance in [Ω·mm²/m]
(1)

A

The characteristic quantity is indicated of e.g. 1 km and then described as specific series resistance R' in data sheets for a defined conductor length. The series resistance is calculated with the following formula:

R' = R in Ω (2)


l km
Inductance L

A magnetic field builds itself up around any conductor current flowed through. The magnetic field changes proportionally to the calculated alternating voltage. Through this a tension which counteracts her cause is induced in the conductor. This induced voltage weakens the current flux with that. The value of the inductor L depends on the following parameters:

The characteristic quantity is indicated of e.g. 1 km and then described as specific inductance per unit length L' in data sheets for a defined conductor length. The inductance per unit length is calculated with the following formula:

L' = L in mH (3)


l km
Parallel Resistance G

In the practice there isn't any ideal insulator which is without any electric current. A certain leak current which flows about the insulation between the two wires therefore always appears at an isolated two-wire line, too. The value of the conducting ability is marked by G and sometimes also is called cross resistance or derivation. As a measurement unit for the conductance the S ("Siemens") is used.

G = 1 in [S] (4)

R

The characteristic quantity is indicated of e.g. 1 km and then described as conductance G' in data sheets for a defined conductor length. The conductance is calculated with the following formula:

G' = G in S (5)


l km
Parallel Capacity C

Every electric consumer has an inner resistance at which the voltage is exhausted. If this voltage is here led by a conduction to the consumer, a different potential arises between the two wires.

Figure 3: Rising of the parallel capacity

Rising of the parallel capacity

Figure 3: Rising of the parallel capacity

way there way back customer

Therefore both wires work like the plates of a condenser. This coupling over the electric field is described with the capacity C.

Capacitance C' is the measurement of energy absorbed by the cable. It is related to the inner and outer conductor sizes and the core dielectric constant. In a given cable design, capacitance and impedance are inversely proportional. The fewer the picofarad per foot, the better the cable performance. The characteristic quantity is indicated of (e.g. 1 km or 1 ft) and then described in data sheets for a defined conductor length. The capacitance is determined by the formula:

C' = C in nF (6)


l km
Impedance

Characteristic impedance is a measurement of resistance to the electrical current being carried in a cable. It is measured in units called Ohms (Ω) and is directly related to the ratio between inner conductor dimension and the outer conductor dimension, and inversely related to the dielectric constant of the cable core. Unlike conductor resistance, impedance does not vary with cable length.

For a system to work at maximum efficiency, the nominal impedance of the transmitter, receiver and cable must precisely match. An incorrect match will produce reflection loss. Nominal impedance is determined by the formula:

Where:

Z is the impedance of the cable
ε is the dielectric constant of the cable core
D is the dielectric diameter
d is the conductor diameter