Showing posts with label Electrical Conductors. Show all posts
Showing posts with label Electrical Conductors. Show all posts

Sunday, July 2, 2017

How to Calculate the Inductance of an Electric Cable
July 02, 2017

How to Calculate the Inductance of an Electric Cable

The inductance, L , per core of a 3-core cable or of three single-core cables comprises two parts namely the self-inductance of the conductor and the mutual inductance with other cores. 

The formula for calculating the Inductance of a cable is given by:

$L = K + 0.2Log_e{\frac{2S}{d}}$                    (Hm/Km)

Where:
L  =  Inductance of cable in (Hm/Km)
K  =  a constant relating to the conductor formation (see table below)
S  =  axial spacing between conductors within the cable (mm) or axial spacing between 
       Conductors of a trefoil group of single core cables (mm) or 
   =  1.26 x phase spacing for a flat formation of three single-core cables (mm)
d =  conductor diameter or for shaped designs the diameter of an equivalent circular     
        conductor (mm)

For 2-core, 3-core and 4-core cables, the inductance obtained from the formula should be multiplied by 1.02 if the conductors are circular or sector-shaped, and by 0.97 for 3-core oval conductors.

Typical Values for K for Different Stranded Conductors (at 50Hz)


Number of Wires in Conductor
K
3
0.0778
9
0.0642
7
0.0554
37
0.0528
61 and Over
0.0514
1 (Solid)
0.0500
Hollow core conductor, 12mm duct
0.0383


0
By at No comments:
Labels:
Electrical and Physical Properties of Common Metals Used in Manufacturing Cables
July 02, 2017

Electrical and Physical Properties of Common Metals Used in Manufacturing Cables

The tables below indicate the electrical and physical properties of metals commonly used in the manufacture of electric cables in the electrical industry. Familiarity with these properties is required to fully grasp the key advantages and disadvantages of the various materials used and to understand from a practical standpoint why they are applied in the area they are used.

Electrical Properties
The table below indicates the electrical properties of the common metals used in cables. Taking price into consideration the below listed properties, Copper and Aluminium are clearly the best choice for conductors the manufacture of all manner of electric cables although there has been experimentation with other metals for example Sodium in certain applications:

Metals
Relative Conductivity (Copper = 100)
Electrical Resistivity at 20�C (Om, 10-8)
Temperature Coefficient of Resistance (per �C)
Silver 106 1.626 0.0041
Copper (HC, anealed) 100 1.724 0.0039
Copper (HC, Hard drawn) 97 1.777 0.0039
Tinned Copper 95 - 99 1.741 - 1.814 0.0039
Aluminium (EC grade, Soft) 61 2.803 0.0040
Aluminium (EC grade,         1/2H - H)                            61 2.826 0.0040
Sodium 35 4.926 0.0054
Mild Steel 12 13.80 0.0045
Lead 8 21.4 0.0040


Physical Properties of Metals Used in Electric Cables
The physical properties of metals used for conductors and sheaths are given in the table below:

Property
Unit
Aluminium
Copper
Lead
Density at 20�C
Kg/m3
 8890 2703 11370
Coefficient of thermal expansion per �C
x 10-6
 17 23 29
Melting point oC 1083 659 327
Thermal Conductivity
W/cm oC
 3.8 2.4 0.34
Ultimate Tensile Stress



Soft temper MN/m2 225 70 - 90    -
3/4H to H MN/m2 385 125 - 205    -
Elastic Modulus MN/m2 26 14    - 
Hardness



Soft DPHN 50 20 - 25  5
3/4H to H DPHN 115 30 - 40     -
Stress Fatigue Endurance Limit (Approximate) MN/m2
�65
 �40 �2.8

Except for conductors of self-supporting overhead cables, Copper is invariably used in the annealed condition. Solid Aluminium conductors are also mainly used in a soft condition but stranded Aluminium conductors are 3H (hard) to H. Aluminium sheaths are now extruded directly onto cables and hence of soft temper but a small amount of work hardening occurs during corrugation.
0
By at No comments:
Labels:

Tuesday, December 20, 2016

December 20, 2016

Basics of Coaxial Cables Used in Electronic and Computer Systems

A coaxial cable consists of four basic parts:

  • Inner conductor (center conductor)
  • Outer conductor (shield)
  • Dielectric, which separates the inner and outer conductors
  • Jacket, which is the outer polymer layer protecting the parts inside



Parts of a Typical Coaxial Cable Photo Credit : ANIXTER CABLES

The following characteristics/properties help to define a coaxial cable as applied in electronic systems and Computer Systems:
1. Characteristic impedance
2. Voltage Standing-Wave Ratio (VSWR)
3. Velocity of Propagation
4. Voltage Rating
5. Operating Temperature

Characteristic Impedance
The characteristic impedance of a coaxial cable is a function of its geometry and materials. Characteristic impedance is independent of length and typically ranges from 35 to 185 ohms. The most common values are 50, 75 and 93 ohms. The characteristic impedance of a cable is not the same as the  impedance of the conductors in a cable, which is dependent on length.
The most efficient transfer of energy from a source to a load occurs when all parts of the system have the same characteristic impedance. To have better performance with coaxial cable, there is need for impedance matching especially critical at higher frequencies, where the consequences of mismatches are more severe.

Voltage Standing - Wave Ratio (VSWR)
The voltage standing-wave ratio (VSWR) is a measure of the standing waves that result from reflections. It expresses the uniformity or quality of a cable�s characteristic impedance. Uniformity is also measured as structural return loss (SRL).

Velocity of Propagation
Velocity of propagation is the speed at which electromagnetic energy travels along the cable. In free space or air, electromagnetic energy travels at the speed of light, which is 186,000 miles per second. In other materials, however, the energy travels slower, depending on the dielectric constant of the material. Velocity of propagation is expressed as a percentage of the speed of light. For example, a velocity of 65 percent means that the energy travels at 120,900 miles per second � or 35 percent slower than in free space. The dielectric (insulation) separating the two conductors determines the velocity of propagation. Although the electromagnetic energy travels in the dielectric, the current associated with the energy travels primarily on the outside of the center conductor and the inside of the outer conductor (shield).

The two conductors bind the energy within the cable. Consequently, the quality of the dielectric is important to efficient, speedy transfer of energy. Speed is important to engineers who must know the transit time of signals for digital transmission.

Voltage Rating
This is the maximum voltage the cable is designed to handle.

Operating Temperature Range
These are the minimum and maximum temperatures at which the cable can operate.

Types of Coaxial Cables
There are many types of coaxial cables but four types are commonly used namely:
1. Flexible Coax
2. Semirigid Coax
3. Triaxial 
4. Dual Coax
There is also Twinaxial (Twinax) Cable used in high-speed, balanced-mode multiplexed transmission in large computer systems.

Flexible Coax
The most common type, flexible coax has a braided outer conductor (shield) of extremely fine wires. While the braid makes the cable flexible, it does not provide complete shielding � energy (RF signals) can leak through the shield via minute gaps in the braid. To combat this, many cables have several layers in the outer conductor. In addition, thin foils are sometimes used to supplement the braid to provide better coverage for greater shielding effectiveness. The greater the coverage, the better the shield

Semirigid Coax
Semirigid coax has a solid, tubular metallic outer conductor, similar to a pipe. This construction gives the cable a very uniform characteristic impedance (low VSWR) and excellent shielding, but at the expense of flexibility.

Triaxial Cable (Triax)
This coax has two outer conductors (shields) separated by a dielectric layer. One outer conductor (shield) serves as a signal ground, while the other serves as earth ground, providing better noise immunity and shielding. One caution: Do not confuse a flexible cable having a multilayer outer shield with triaxial cable.

Dual Coax
This cable contains two individual coaxial cables surrounded by a common outer jacket.
Shown below are the four basic types of coaxial cables commonly used
Common Types of Coaxial Cables - Photo Credit : ANIXTER CABLES

Twinaxial Cable (Twinax)
Twinax has a pair of insulated conductors encased in a common outer conductor (shield). The center conductors may be either twisted or run parallel to one another. In appearance, the cable is often like a shielded twisted pair, but it is held to the tighter tolerances common to fixed-impedance coaxial cable. A common use of twinax is high-speed, balanced-mode multiplexed transmission in large computer systems. Balanced mode means that the signal is carried on both conductors, which provides greater noise immunity.

A Typical Twinaxial Cable - Photo Credit: ANIXTER CABLE

0
By at No comments:
Labels:

Thursday, January 14, 2016

Resistance and Reactance per km of Copper and Aluminium cables
January 14, 2016

Resistance and Reactance per km of Copper and Aluminium cables

For the purpose of calculating voltage drop within a cable, the table below gives the reactance and resistance values for Copper and Aluminium cables:

Values for Copper Cables


Cable Size, S (mm2) Single - Core Cable Two - Core/Three Core Cables
R(O/km) @ 80�C X (O/km) @ 80�C R(O/km) @ 80�C X(O/km) @ 80�C
1.5 14.8 0.168 15.1 0.118
2.5 8.91 0.156 9.08 0.109
4 5.57 0.143 5.68 0.101
6 3.71 0.135 3.78 0.0955
10 2.24 0.119 2.27 0.0861
16 1.41 0.112 1.43 0.0817
25 0.889 0.106 0.907 0.0813
35 0.641 0.101 0.654 0.0783
50 0.473 0.101 0.483 0.0779
70 0.328 0.0965 0.334 0.0751
95 0.326 0.0975 0.241 0.0762
120 0.188 0.0939 0.191 0.074
150 0.153 0.0928 0.157 0.0745
185 0.123 0.0908 0.125 0.0742
240 0.0943 0.0902 0.0966 0.0752
300 0.0761 0.0895 0.078 0.075

Values for
Aluminium Cables


Cable Size, S (mm2) Single - Core Cable Two - Core/Three Core Cables
R(O/km) @ 80�C X (O/km) @ 80�C R(O/km) @ 80�C X(O/km) @ 80�C
1.5 24.384 0.168 24.878 0.118
2.5 14.680 0.156 14.960 0.109
4 9.177 0.143 9.358 0.101
6 6.112 0.135 6.228 0.0955
10 3.691 0.119 3.740 0.0861
16 2.323 0.112 2.356 0.0817
25 1.465 0.106 1.494 0.0813
35 1.056 0.101 1.077 0.0783
50 0.779 0.101 0.796 0.0779
70 0.540 0.0965 0.550 0.0751
95 0.389 0.0975 0.397 0.0762
120 0.310 0.0939 0.315 0.074
150 0.252 0.0928 0.259 0.0745
185 0.203 0.0908 0.206 0.0742
240 0.155 0.0902 0.159 0.0752
300 0.125 0.0895 0.129 0.075
0
By at No comments:
Labels:

Saturday, December 26, 2015

Ampacity Correction Factors for All Cables
December 26, 2015

Ampacity Correction Factors for All Cables

As already discussed in Ampacity of a Conductor, the ampacity of a conductor depends on temperature. Any change in ambient temperature affects the ampacity of an electrical cable. When this happens, correction factors are applied to get new ratings for such a conductor.
The approximate ampacity correction factors for all cables under different ambient temperature conditions for cables whose insulation is rated 90 degree C are given below:


Ambient Temperature  Correction Factors for Cable Insulation Rated At:
(�C) 90�C
10 1.26
20 1.18
30 1.10
40 1.00
50 0.90
0
By at No comments:
Labels:
Thermal Properties of Cable Polymers
December 26, 2015

Thermal Properties of Cable Polymers

Often times in the application of electrical cables, we neglect the thermal characteristics of  the polymers used in the cable insulation. Here is a list of the temperature range each of the common electrical cable polymers can withstand while in service or operation:


Cable Insulation/Polymer  Designed Temperature Range (�C)
PVC (Standard) -20 - 80
PVC (Premium) -55 - 105
Polyethylene -60 - 80
Polypropylene -40 - 105
Cross-Linked Polyethylene -40 -130
Ethylene Propylene Rubber -60 - 150
CSPE -40-105
Ethylene Vinyl Acetate (EVA) -40 - 105
CPE -40- 105
Silicone Braidless -65 - 150
Silicone with Braid -65 � 200
Teflon -70 - 260
0
By at No comments:
Labels:

Sunday, December 20, 2015

How to Calculate Conductor Diameter from Wire Diameter
December 20, 2015

How to Calculate Conductor Diameter from Wire Diameter

To calculate the nominal diameter of any concentric-lay-stranded conductor made from round wires of uniform diameters, multiply the diameter of an individual wire by the applicable factors listed below:

Number of Wires in Conductor Factor to Calculate Conductor Diameter
3 2.155
7 3.000
12 4.155
19 5.000
37 7.000
61 9.000
91 11.000
127 13.000
169 15.000
217 17.000
271 19.000
For a greater number of wires use the formula:
Conductor Diameter = Wire Diameter x SQRT (1.332 x No. of Wires)
0
By at No comments:
Labels:

Saturday, December 12, 2015

December 12, 2015

How to Determine Temperature Correction Factors for Resistance: Copper Conductors

The DC resistance of copper wire increases with increasing temperature in accordance with the formula:

On the basis of the above formula, we now generate a table of correction factors for copper conductors in operating in the temperature range 25 � 200 degree celsius:


Temperature (0C)
Multiplying Factor
25
1.000
40
1.058
50
1.096
55
1.116
60
1.135
65
1.154
70
1.173
75
1.193
80
1.212
85
1.231
90
1.250
100
1.289
105
1.308
125
1.385
130
1.404
150
1.482
200
1.674
0
By at No comments:
Labels:

Saturday, August 2, 2014

NEMA Insulation Classes for Transformers
August 02, 2014

NEMA Insulation Classes for Transformers

The capacity or rating of a transformer is limited by the temperature that the insulation can tolerate.  The life of a transformer can be extended by making sure it is not operated over and above the temperature rating of the insulation system on a continuous basis. A guiding rule of thumb would be that the useful operating life of the transformer halves for every 10�C  rise above its rated temperature. 

The insulation system of a transformer is rated in degrees Celsius at its maximum temperature rating:

The class number  = the maximum �C of the transformer insulation

NEMA (National Manufacturer�s Association) has the following thermal or insulation classification as regards transformers (dry type):


NEMA Insulation Class
NEMA Letter Designation
Ambient
Temperature
Maximum Allowable Temperature Rise
Maximum Allowable Operating Temperature
�C 
�F
�C 
�F
105
A
40�C 
50
122
105
221
130
B
80
176
130
226
155
F
105
221
155
311
180
H
125
257
180
356
220
R
150
302
220
428

Note  that a transformer with a Class 220 insulation system can be designed for a maximum temperature rise that is lower than the standard 150�C . It can be designed for either 125 or 80�C rise. Also, a Class 180 insulation transformer can be designed with 80�C rise. Class 155 and 105 transformers are not typically designed for other than their standard temperature rise

The maximum operating temperature is determined by by adding the rated ambient temperature of the device which is normally 40�C, the maximum temperature rise, and a 10�C hot-spot allowance:
Maximum operating Temperature 
= Ambient Temperature + Maximum Temperature Rise + 10�C hot-spot allowance.

0
By at No comments:
Labels: ,

Thursday, July 3, 2014

July 03, 2014

Ampacity of a Conductor

Ampacity is the current carrying capacity of a conductor. Ampacity calculation should take into account natural variables such as solar warming, wind and air density, viscosity, and thermal conductivity. Ampacity is a temperature rating. In order words, as temperature changes, the ampacity of a conductor changes. 

Increase in ambient/surrounding/medium temperature can significantly limit the current carrying capacities of cables. As cable temperature increases, its resistance increases thereby reducing the amount of current that can be carried. 
According to the National Electrical Code, article 310.15(C), the ampacities of conductors can be calculated by the following general formula:
Where:
TC    =  Conductor temperature in degree Celsius
TA    =  Ambient temperature in degree Celsius
?TD  = Dielectric loss temperature rise
RDC  = DC resistance of conductor at temperature TC
YC    =  Component AC resistance resulting from skin effect and proximity effect
RCA  = Effective thermal resistance between conductor and surrounding ambient.
The NEC specifies that the above formula can only be applied under engineering supervision. 

The table below gives the ampacities for portable power cables at 90 degree Celsius insulation and under an ambient temperature of 40 degrees Celsius. When the temperature changes as discussed above, correction factors are applied to determine the true ampacity of the cable at the new temperature. Correction factors normally applied are given here



0
By at No comments:
Labels:
July 03, 2014

AC Resistance of a Conductor

A conductor offers a greater resistance to the flow of alternating current(AC) than it does to direct current(DC). The magnitude of the increase is usually expressed as an �AC/DC � ratio. The reasons for the increase include:
  1. Skin effect, 
  2. Proximity effect, 
  3. Hysteresis and eddy current losses in nearby ferromagnetic materials, and
  4. Induced losses in short-circuited nearby non-ferromagnetic materials
Skin Effect
Skin Effect describes the phenomena of alternating current flowing more densely near the surface of a conductor. The net effect is a reduction in effective area and an increase in the resistance. To calculate skin effect in tubular conductors made of solid wire to an infinitely thin tube, the curves of Ewan are used.
The parameter is:
The table below gives the factors for skin effect ratio R/R0 as a function of X, where R is the AC resistance and R0 is the DC resistance. Note that from the table, R/R0 is the resistance ratio due to skin effect. L/L0 is the inductance ratio due to skin effect. X is as defined by the formula above.

For conductors larger than 1,500,000 circular mils,other calculation formulas must be used for accuracy. The non-uniform cross-sectional distribution of current also affects the inductance, the value of which is less than if the current density were uniform. The table of skin effect ratios above, therefore, lists the inductance ratio L/L0 where L is the inductance due to a non-uniform current density and L0 is the inductance assuming uniform current density.

Proximity Effect:
Proximity effect is the distortion of the cross-sectional current distribution of the conductor due to nearby currents. To calculate approximately the proximity effect, use the following formula:
Where:
fp       = The factor to account for proximity effect
GMR = The geometric mean radius of the equal conductors
GMD = Geometric mean spacing of the conductors
R/R0  = Skin effect ratio

After determining skin and proximity effect, the effective resistance of a conductor taking these two factors into effect is then given by:
Where:
R/R0 = Skin effect ratio
fp      = Factor accounting for proximity effect 


0
By at No comments:
Labels:
July 03, 2014

DC Resistance of a Conductor

The DC resistance of a conductor or cable is that defined by ohms law. It is a function of many factors including temperature which greatly affects the resistance of a given material. Copper and Aluminium are the most widely used conductors. Their resistance (DC) increases with increasing temperature. 

The DC resistance of copper wire at 20 degree Celsius(68 degree Fahrenheit) is given below:

The copper wire resistance in the above table are at 20 degree Celsius. To get the resistance at any other temperature above this, we use the equation:

Actual values of a depends on the composition of the material in addition to temperature. For copper and aluminium, taking, a = 0.0039 will give reasonable accuracy for most conductor calculations

0
By at No comments:
Labels:
July 03, 2014

American Wire Gauge (AWG)

Wire size is expressed in circular mils(CM). A mil is one-thousandth of an inch. In the United States, the American Wire Gauge is used. It is a scale of even numbers that start with the number 40 and descend. The cross-sectional area becomes larger as the numbers on this scale get smaller. 

For wires larger than No.2 wire, a scale of 1/0, 2/0, 3/0 and 4/0 is used. For even larger wires, thousands of circular mils is used �MCM or Kcmil

AWG Conversions
Copper conductor size conversions are determined using;

Circular mils = sq in. x 1,273,240 = sq mm x 1,973.5

For conductor cross-sectional forms other than circular, where S is the cross-sectional area in square inches, the conversions are:

The table below shows a quick guide to AWG wire conversions:

0
By at No comments:
Labels: