HIPOT,Lorenz,etc.doc

7/31/2019 HIPOT,Lorenz,etc.doc

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Test method for HIPOT Test

Hipot testers usually connect one side of the supply to safety ground (Earth ground). The other side of the supplyis connected to the conductor being tested. With the supply connected like this there are two places a givenconductor can be connected: high voltage or ground.

When you have more than two contacts to be hipot tested you connect one contact to high voltage and connect allother contacts to ground. Testing a contact in this fashion makes sure it is isolated from all other contacts.

If the insulation between the two is adequate, then the application of a large voltage difference between the twoconductors separated by the insulator would result in the flow of a very small current. Although this small currentis acceptable, no breakdown of either the air insulation or the solid insulation should take place. Therefore, thecurrent of interest is the current that is the result of a partial discharge or breakdown, rather than the current due tocapacitive coupling.

Time Duration for HIPOT Test

The test duration must be in accordance with the safety standard being used. The test time for most standards,including products covered under IEC 60950, is 1 minute.

A typical rule of thumb is 110 to 120% of 2U + 1000 V for 12 seconds.

Current Setting for HIPOT Test

Most modern hipot testers allow the user to set the current limit. However, if the actual leakage current of the product is known, then the hipot test current can be predicted.

The best way to identify the trip level is to test some product samples and establish an average hipot current. Oncethis has been achieved, then the leakage current trip level should be set to a slightly higher value than the averagefigure.

Another method of establishing the current trip level would be to use the following mathematical formula:

E(Hipot) / E(Leakage) = I(Hipot) / 2XI(Leakage)

The hipot tester current trip level should be set high enough to avoid nuisance failure related to leakage current

and, at the same time, low enough not to overlook a true breakdown in insulation.Test Voltage for HIPOT Test

The majority of safety standards allow the use of either ac or dc voltage for a hipot test.

When using ac test voltage, the insulation in question is being stressed most when the voltage is at its peak, i.e.,either at the positive or negative peak of the sine wave.

Therefore, if we use dc test voltage, we ensure that the dc test voltage is under root 2 (or 1.414) times the actest voltage, so the value of the dc voltage is equal to the ac voltage peaks.

For example, for a 1500-V-ac voltage, the equivalent dc voltage to produce the same amount of stress on theinsulation would be 1500 x 1.414 or 2121 V dc.

Advantages and Disadvantages of use DC Voltage for Hipot Test

One of the advantages of using a dc test voltage is that the leakage current trip can be set to a much lower valuethan that of an ac test voltage. This would allow a manufacturer to filter those products that have marginalinsulation, which would have been passed by an ac tester.

When using a dc hipot tester, the capacitors in the circuit could be highly charged and, therefore, a safe-dischargedevice or setup is needed. However, it is a good practice to always ensure that a product is discharged, regardlessof the test voltage or its nature, before it is handled.


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It applies the voltage gradually. By monitoring the current flow as voltages increase, an operator can detect a potential insulation breakdown before it occurs. A minor disadvantage of the dc hipot tester is that because dc testvoltages are more difficult to generate, the cost of a dc tester may be slightly higher than that of an ac tester.

The main advantage of the dc test is DC Voltage does not produce harmful discharge as readily occur in AC.

It can be applied at higher levels without risk or injuring good insulation. This higher potential can literallysweep-out far more local defects.

The simple series circuit path of a local defect is more easily carbonized or reduced in resistance by the dc leakagecurrent than by ac, and the lower the fault path resistance becomes, the more the leakage current increased, thus

producing a snow balling effect which leads to the small visible dielectric puncture usually observed. Since thedc is free of capacitive division, it is more effective in picking out mechanical damage as well as inclusions or areas in the dielectric which have lower resistance.

Advantages and Disadvantages of use AC Voltage for Hipot Test

One of the advantages of an ac hipot test is that it can check both voltage polarities, whereas a dc test charges theinsulation in only one polarity. This may become a concern for products that actually use ac voltage for their normal operation. The test setup and procedures are identical for both ac and dc hipot tests.

A minor disadvantage of the ac hipot tester is that if the circuit under test has large values of Y capacitors, then,

depending on the current trip setting of the hipot tester, the ac tester could indicate a failure. Most safety standardsallow the user to disconnect the Y capacitors prior to testing or, alternatively, to use a dc hipot tester.

The dc hipot tester would not indicate the failure of a unit even with high Y capacitors because the Y capacitorssee the voltage but dont pass any current.

Step for HIPOT Testing Only electrically qualified workers may perform this testing. Open circuit breakers or switches to isolate the circuit or Cable that will be hi-pot tested. Confirm that all equipment or Cable that is not to be tested is isolated from the circuit under test. The limited approach boundary for this hi-pot procedure at 1000 volts is 5 ft. (1.53m) so place barriers

around the terminations of cables and equipment under test to prevent unqualified persons from crossingthis boundary.

Connect the ground lead of the HIPOT Tester to a suitable building ground or grounding electrodeconductor. Attach the high voltage lead to one of the isolated circuit phase conductors.

Switch on the HIPOT Tester. Set the meter to 1000 Volts or pre decide DC Voltage. Push the Test button on the meter and after one minute observe the resistance reading. Record the reading for reference.

At the end of the one minute test, switch the HIPOT Tester from the high potential test mode to the voltagemeasuring mode to confirm that the circuit phase conductor and voltage of HIPOT Tester are now readingzero volts.

Repeat this test procedure for all circuit phase conductors testing each phase to ground and each phase toeach phase.

When testing is completed disconnect the HIPOT Tester from the circuits under test and confirm that thecircuits are clear to be re-connected and re-energized.

To PASS the unit or Cable under Test must be exposed to a minimum Stress of pre decide Voltage for 1minute without any Indication of Breakdown. For Equipments with total area less than 0.1 m2, theinsulation resistance shall not be less than 400 M. For Equipment with total area larger than 0.1 m2 themeasured insulation resistance times the area of the module shall not be less than 40 M m2.


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Safety precautions during HIPOT Test

During a HIPOT Test, There may be at some risk so to minimize risk of injury from electrical shock make sureHIPOT equipment follows these guidelines:

1. The total charge you can receive in a shock should not exceed 45 uC.

2. The total hipot energy should not exceed 350 mJ .3. The total current should not exceed 5 mA peak (3.5 mA rms)4. The fault current should not stay on longer than 10 mS .5. If the tester doesnt meet these requirements then make sure it has a safety interlock system that guarantees

you cannot contact the cable while it is being hipot tested.

For Cable:

1. Verify the correct operation of the safety circuits in the equipment every time you calibrate it.

2. Dont touch the cable during hipot testing.3. Allow the hipot testing to complete before removing the cable.4. Wear insulating gloves.5. Dont allow children to use the equipment.6. If you have any electronic implants then dont use the equipment.

Megger Tests

The insulation resistance meter test method for determining the condition of electrical insulation has been widelyused for many years as a general nondestructive test method.

A serious limitation of this test is that its operating voltage of 500 to 1,000 volts will not always detect insulation punctures, whereas the higher voltages used by the high-voltage, DC testers will detect these punctures.

The insulation resistance meter test will show following parameters:

(a) Relative amount of moisture in the insulation ,(b) (b) Leakage current over dirty or moist surfaces of the insulation, and(c) (c) Winding deterioration or faults by means of insulation resistance versus time curves.


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Description of Test

A dc voltage of 500 or 1,000 volts is applied to the insulation and readings are taken to the insulation resistanceversus time. Data should be recorded at the 1-and 10-minute intervals and at several other intermediate times.

Test Equipment

The hand-cranked insulation resistance meter has been the standard instrument for many years for checkinginsulation resistance. The hand- cranked instrument is satisfactory for spot checks but is not recommended for routine dielectric absorption tests, because very few men can continue cranking for 10 minutes without tiring andslowing up the cranking speed toward the end of the period. Motor driven or electronic insulation resistancetesters operating from a 115-volt, ac source or a self-contained battery are available and should be used for this

purpose. Because the value of insulation resistance varies with applied voltage, it is important that the testinstrument have sufficient capacity to maintain its rated output voltage for the largest winding being tested, andthe output voltage be constant over the 10-minute test period.

For this reason, some of the smaller test instruments may not be suitable for tests on large generators or transformers which draw a large dielectric absorption current.

For occasional checks on the calibration and proper function of insulation test instruments, it is recommended thata resistor in the 100-megohm range be attached to the inside of the instrument cover for use as checking standard.It is recommended that the same test instrument be used for each periodic test on a certain piece of equipment, asdifferences in instrument output characteristics may affect the shape of the dielectric absorption curves, especiallyat the lower end.

Dielectric Absorption Curve

Insulation resistance is not a definite measure of the voltage an insulation will withstand, but when properlyinterpreted affords a useful indication of the suitability of the winding for continued service. It should beremembered that values of insulation resistance, even on identical machines and for identical conditions, may varyover a wide range. Changes occurring in insulation resistance are more significant than certain absolutemagnitudes. This curve is called the curve of dielectric absorption.

The test voltage should be applied for a standard period of 10 minutes, with readings taken at intervals of 1 minuteor less.

Any such curve which reaches a constant and lower than normal value in about 3 minutes or less, indicates highleakage current (due to the leakage current being large in proportion to the absorption current), and the windingshould be thoroughly cleaned and retested or further investigated. Such cleaning should preferably precede allinsulation resistance tests. In case of very damp insulation, the dielectric absorption curve may start upward andthen droop to a value lower than at the start of the test.

Minimum Values of Machine Insulation Resistance

Recommended Practice for Testing Insulation Resistance of Rotating Machinery, IEEE Standard No. 43, November 1974, indicates the recommended minimum insulation resistance Rm for armature and field windingsof ac and dc machines can be determined by the equation:

where:Rm = recommended minimum insulation resistance in megohms at 40 C of the entire machine windingVt = rated machine terminal to terminal potential, in rms kilovolts

The winding insulation resistance obtained by applying direct potential to the entire winding for 1 minute must becorrected to 40 C to be used for comparison with the recommended minimum value Rm. The insulationresistance of one phase of a three-phase armature winding with the other two phases grounded is approximatelytwice that of the entire winding. Therefore, the resistance of each phase, when the phases are tested separately,should be divided by two to obtain a value which, after correction for temperature, may be compared with Rm. If guard circuits are used on the two phases not under test when each phase is tested separately, the observedresistance of each phase should be divided by three to obtain a value which, after correction for temperature, may


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be compared with Rm. For insulation in good condition, insulation resistance readings of 10 to 100 times thevalue of Rm are not uncommon.

It should be remembered, however, that decreasing values of insulation resistance obtained from periodic tests aremore indicative of deterioration of the insulation than low values. Machines rated at 10,000 kV-A or less shouldhave either the polarization index or the insulation resistance (at 40 C) at least as large as the minimumrecommended values to be considered in suitable condition for operating or for overpotential tests. Machines ratedabove 10,000 kVCA should have both the polarization index and the insulation resis-tance above the minimumrecommended values.

When the end turns of a machine are treated with a semiconducting material for corona elimination purposes, theinsulation resistance may be somewhat lower than without such treatment.

Transformer Insulation Resistance

Although the foregoing paragraphs apply more specifically to generator and motor windings, they also apply, ingeneral, to transformers, except that no insulation values have been established for transformers. Also, thetechnique of measuring transformer insulation resistance is not well known or standardized. If the transformer windings are not immersed in oil, the insulation resistance will behave much like generator insulation resistance.The insulation resistance will be less after adding the oil, because the insulation resistance of the oil is in parallelwith part of the solid insulation. Therefore, insulation resistance readings alone cannot be used to indicate the

progress of dry out of the winding because the winding and the oil resistances cannot be separated.Tests should run on oil samples as specified in Facilities Instructions, Standards, & Techniques Volume 3-5 at thesame time as the test of the transformer winding, and the oil then filtered, if necessary, to remove the moisture.The change of insulation resistance with temperature when the transformer windings are oil-immersed is similar tothat in generators, and curves similar to those of figure 3 are useful for temperature standardizing. Whether theslope of these temperature correction curves is affected by moisture content in the oil is not fully known. At the

present state of the art, it is believed that the power factor test gives a better indication of transformer insulationcondition than the insulation resistance test. Tests should be made between each winding, between each windingand ground with the other windings grounded, and between each winding and ground with the guard circuitconnected to the other windings but not grounded.

Cable Insulation Resistance

The most frequently used test on high-voltage cables is insulation resistance measured by means of an insulationresistance meter. The most informative test for high-voltage cables is the dc, high-voltage test modified tocombine a modest voltage withstand with insulation current/voltage measurement.Insulation resistance testing of cable differs from the testing of apparatus windings mainly because of the highcapacitance, if the cable is long, which takes a longer time to charge, and in the difficulty of obtaining asatisfactory temperature measurement, insulation resistance measurements are of value for comparison rather thanfor conformance to stated minimums. The temperature of the cable is important and should be recorded with theinsulation resistance. This will be difficult if the cable is partly indoors and partly outdoors, partly underground,

partly above ground, partly exposed, and partly in conduits.

It may be necessary to estimate the temperature of the various lengths, and a weighted average computed. Testsshould be made between each conductor, between each conductor and ground with other conductors grounded,and between each conductor and ground with other conductors connected to the guard circuit but not grounded.

SOURCE: TESTING SOLID INSULATION OF ELECTRICAL EQUIPMENT VOL.3-1


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ANEXO A

Moisture Effect On Insulation Of Generator

Moisture, which can enter the insulation of a generator or motor winding from damp air or which can enter thewinding of a transformer from wet oil, will make a surprisingly large difference in the insulation resistance. Thisis clearly shown by the curves of figure 2 for a Grand Coulee generator.

Curve A was taken shortly after the generator was placed in service, at a temperature of 36 EC. Curve C wastaken after a dry-out run of 168 hours on the generator.

Figure 2. - Dielectric absorption curves before and after initial dryout for Grand Couleeunit L-6 108,000-kVA, 120-r/min, 13.8-kV, 60-Hz generator.

The generator winding was, therefore, more thoroughly dried out in curve C than in curve A, althoughevaporation of the volatile content of the insulation or other curing or aging effect may have had an appreciableeffect. Low insulation resistance resulting from exposure to moisture does not mean that the insulation isunsuitable for operation, particularly if the insulation resistance value is comparable to that obtained from recent

periodic tests.

Dry out of thermosetting insulation is not as big a factor, and is sometimes not done, except to cure field appliedinsulation.


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ANEXO B

Grounded Systems

Grounded systems are equipped with a grounded conductor that is required per NEC Section 250- 23(b) to be runto each service disconnecting means. The grounded conductor can be used as a current-carrying conductor toaccommodate all neutral related loads.

It can also be used as an equipment grounding conductor to clear ground faults per NEC Section 250-61(a).

Figure 1. A grounded system is equipped with a grounded (neutral) conductor routed between the supply transformer and the service equipment.

A network of equipment grounding conductors is routed from the service equipment enclosure to all metalenclosures throughout the electrical system. The equipment grounding conductor carries fault currents from the

point of the fault to the grounded bus in the service equipment where it is transferred to the grounded conductor.The grounded conductor carries the fault current back to the source and returns over the faulted phase and tripsopen the overcurrent protection device.

Note: A system is considered grounded if the supplying source such as a transformer, generator, etc., is grounded,in addition to the grounding means on the supply side of the service equipment disconnecting device per NECSections 250-23(a) or 250-26 for seperately derived systems.

The neutral of any grounded system serves two main purposes: (1) it permits the utilization of lineto-neutralvoltage and thus will serve as a current-carrying conductor to carry any unbalanced current, and (2) it plays a vitalrole in providing a low-impedance path for the flow of fault currents to facilitate the operation of the overcurrentdevices in the circuit. ( See Figure 1. )

Consideration should be given to the sizing of the neutral conductor for certain loads due to the presence of harmonic currents (See NEC Sections 210-4 and 310-10).

SOURCE: DOE HANDBOOK ELECTRICAL SAFETY


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ANEXO C

American wire gauge (AWG ),

Also known as the Brown & Sharpe wire gauge (Brown & Sharpe is a division of Hexagon Metrology, Inc., amultinational corporation focused mainly on metrological tools and technology. During the 19th and 20thcenturies, Brown & Sharpe was one of the most well-known and influential firms in the machine tool industry. Itsinfluence throughout mechanical engineering was such that its name is often synonymous with certain industrialstandards that it established, including: The American wire gauge (AWG) standards for wire; The Brown &Sharpe taper in machine tool spindle tapers; and The Brown & Sharpe worm thread form for worms. Since beingacquired by Hexagon Metrology in 2001, Brown and Sharpe has concentrated exclusively on metrologyequipment), is a standardized wire gauge system used since 1857 predominantly in the United States and Canadafor the diameters of round, solid, nonferrous, electrically conducting wire. [1] The cross-sectional area of eachgauge is an important factor for determining its current-carrying capacity.

The steel industry does not use AWG and prefers a number of other wire gauges. These include W&M WireGauge, US Steel Wire Gauge, and Music Wire Gauge.

Increasing gauge numbers give decreasing wire diameters, which is similar to many other non-metric gaugingsystems. This gauge system originated in the number of drawing operations ( Wire drawing is a metalworkingprocess used to reduce the cross-section of a wire by pulling the wire through a single, or series of,drawing dies ), used to produce a given gauge of wire. Very fine wire (for example, 30 gauge) required more

passes through the drawing dies than did 0 gauge wire. Manufacturers of wire formerly had proprietary wiregauge systems; the development of standardized wire gauges rationalized selection of wire for a particular

purpose.

The AWG tables are for a single, solid, round conductor. The AWG of a stranded wire is determined by the totalcross-sectional area of the conductor, which determines its current-carrying capacity and electrical resistance.Because there are also small gaps between the strands, a stranded wire will always have a slightly larger overalldiameter than a solid wire with the same AWG.

AWG is also commonly used to specify body piercing jewelry sizes (especially smaller sizes), even when the

material is not metallic.[2]

Formula

By definition, No.36 AWG is 0.0050 inches in diameter, and No.0000 is 0.4600 inches in diameter. The ratio of these diameters is 92, and there are 40 gauge sizes from No.36 to No.0000, or 39 steps. Using this common ratio,wire gauge sizes vary geometrically according to the following formula: The diameter of a No. n AWG wire is

or equivalently

The gauge can be calculated from the diameter using

[3]

and the cross-section area is
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The ASTM B 258-02 standard defines the ratio between successive sizes to be the 39th root of 92, or approximately 1.1229322. [4] ASTM B 258-02 also dictates that wire diameters should be tabulated with no morethan 4 significant figures, with a resolution of no more than 0.0001 inches (0.1 mils) for wires larger than No. 44AWG, and 0.00001 inches (0.01 mils) for wires No. 45 AWG and smaller.

Sizes with multiple zeros are successively larger than No. 0 and can be denoted using " number of zeros /0", forexample 4/0 for 0000. For an m/0 AWG wire, use n = ( m1) = 1 m in the above formulas. For instance, for No.0000 or 4/0, use n = 3.

Rules of thumb

The sixth power of this ratio is very close to 2, [5] which leads to the following rules of thumb: When the diameter of a wire is doubled, the AWG will decrease by 6. (e.g., No.2 AWG is about twice the

diameter of No.8 AWG.) When the cross-sectional area of a wire is doubled, the AWG will decrease by 3. (e.g., Two No.14 AWG

wires have about the same cross-sectional area as a single No.11 AWG wire.)

Additionally, a decrease of ten gauge numbers, for example from No.10 to 1/0, multiplies the area and weight by

approximately 10 and reduces the resistance by a factor of approximately 10.Tables of AWG wire sizes

The table below shows various data including both the resistance of the various wire gauges and the allowablecurrent (ampacity) based on plastic insulation. The diameter information in the table applies to solid wires.Stranded wires are calculated by calculating the equivalent cross sectional copper area . Fusing Current (meltingwire) is estimated based on 25C ambient temperature. The table below assumes DC, or AC frequencies equal toor less than 60 Hz, and does not take skin effect into account. Turns of wire is an upper limit for wire with noinsulation.

AWGDiameter Turns of wire Area Copper

resistance [6] NEC copper wire

ampacity with60/75/90 C

insulation (A) [7]

Approximatestandard metricequivalents

Fusing Current

(copper) [8][9]

(inch) (mm) (per in) (per cm) (kcmil) (mm 2) (/km)(m/m)(/kFT)(m/ft)

Preece(~10s)

Onderdonk (1s)

Onderdonk (32ms)

0000 (4/0) 0.4600 11.684 2.17 0.856 212 107 0.1608 0.04901 195 / 230 / 260 31 kA 173 kA000 (3/0) 0.4096 10.404 2.44 0.961 168 85.0 0.2028 0.06180 165 / 200 / 225 24.5 kA 137 kA00 (2/0) 0.3648 9.266 2.74 1.08 133 67.4 0.2557 0.07793 145 / 175 / 195 19.5 kA 109 kA0 (1/0) 0.3249 8.252 3.08 1.21 106 53.5 0.3224 0.09827 125 / 150 / 170 1.9 kA 15.5 kA 87 kA

1 0.2893 7.348 3.46 1.36 83.7 42.4 0.4066 0.1239 110 / 130 / 150 1.6 kA 12 kA 68 kA2 0.2576 6.544 3.88 1.53 66.4 33.6 0.5127 0.1563 95 / 115 / 130 1.3 kA 9.7 kA 54 kA3 0.2294 5.827 4.36 1.72 52.6 26.7 0.6465 0.1970 85 / 100 / 110 196/0.4 1.1 kA 7.7 kA 43 kA4 0.2043 5.189 4.89 1.93 41.7 21.2 0.8152 0.2485 70 / 85 / 95 946 A 6.1 kA 34 kA5 0.1819 4.621 5.50 2.16 33.1 16.8 1.028 0.3133 126/0.4 795 A 4.8 kA 27 kA6 0.1620 4.115 6.17 2.43 26.3 13.3 1.296 0.3951 55 / 65 / 75 668 A 3.8 kA 21 kA7 0.1443 3.665 6.93 2.73 20.8 10.5 1.634 0.4982 80/0.4 561 A 3 kA 17 kA

8 0.1285 3.264 7.78 3.06 16.5 8.37 2.061 0.6282 40 / 50 / 55 472 A 2.4 kA 13.5 kA9 0.1144 2.906 8.74 3.44 13.1 6.63 2.599 0.7921

84/0.3396 A 1.9 kA 10.7 kA

10 0.1019 2.588 9.81 3.86 10.4 5.26 3.277 0.9989 30 / 35 / 40 333 A 1.5 kA 8.5 kA11 0.0907 2.305 11.0 4.34 8.23 4.17 4.132 1.260 56/0.3 280 A 1.2 kA 6.7 kA12 0.0808 2.053 12.4 4.87 6.53 3.31 5.211 1.588 25 / 25 / 30 235 A 955 A 5.3 kA13 0.0720 1.828 13.9 5.47 5.18 2.62 6.571 2.003 50/0.25 198 A 758 A 4.2 kA14 0.0641 1.628 15.6 6.14 4.11 2.08 8.286 2.525 20 / 20 / 25 166 A 601 A 3.3 kA15 0.0571 1.450 17.5 6.90 3.26 1.65 10.45 3.184

30/0.25140 A 477 A 2.7 kA

16 0.0508 1.291 19.7 7.75 2.58 1.31 13.17 4.016 / / 18 117 A 377 A 2.1 kA17 0.0453 1.150 22.1 8.70 2.05 1.04 16.61 5.064 32/0.2 99 A 300 A 1.7 kA18 0.0403 1.024 24.8 9.77 1.62 0.823 20.95 6.385 / / 14

24/0.283 A 237 A 1.3 kA

19 0.0359 0.912 27.9 11.0 1.29 0.653 26.42 8.051 70 A 189 A 1 kA20 0.0320 0.812 31.3 12.3 1.02 0.518 33.31 10.15 16/0.2 58.5 A 149 A 834 A
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21 0.0285 0.723 35.1 13.8 0.810 0.410 42.00 12.80 13/0.2 49 A 119 A 662 A22 0.0253 0.644 39.5 15.5 0.642 0.326 52.96 16.14 7/0.25 41 A 94 A 525 A23 0.0226 0.573 44.3 17.4 0.509 0.258 66.79 20.36 35 A 74 A 416 A24 0.0201 0.511 49.7 19.6 0.404 0.205 84.22 25.67 1/0.5, 7/0.2, 30/0.1 29 A 59 A 330 A25 0.0179 0.455 55.9 22.0 0.320 0.162 106.2 32.37 24 A 47 A 262 A26 0.0159 0.405 62.7 24.7 0.254 0.129 133.9 40.81 1/0.4, 7/0.15 20 A 37 A 208 A27 0.0142 0.361 70.4 27.7 0.202 0.102 168.9 51.4728 0.0126 0.321 79.1 31.1 0.160 0.0810 212.9 64.90 7/0.1229 0.0113 0.286 88.8 35.0 0.127 0.0642 268.5 81.8430 0.0100 0.255 99.7 39.3 0.101 0.0509 338.6 103.2 1/0.25, 7/0.1

31 0.00893 0.227 112 44.1 0.0797 0.0404 426.9 130.132 0.00795 0.202 126 49.5 0.0632 0.0320 538.3 164.1 1/0.2, 7/0.0833 0.00708 0.180 141 55.6 0.0501 0.0254 678.8 206.934 0.00630 0.160 159 62.4 0.0398 0.0201 856.0 260.935 0.00561 0.143 178 70.1 0.0315 0.0160 1079 329.036 0.00500 0.127 200 78.7 0.0250 0.0127 1361 414.837 0.00445 0.113 225 88.4 0.0198 0.0100 1716 523.138 0.00397 0.101 252 99.3 0.0157 0.00797 2164 659.639 0.00353 0.0897 283 111 0.0125 0.00632 2729 831.840 0.00314 0.0799 318 125 0.00989 0.00501 3441 1049

In the North American electrical industry, conductors larger than 4/0 AWG are generally identified by the area inthousands of circular mils ( kcmil ), where 1 kcmil = 0.5067 mm. The next wire size larger than 4/0 has a cross

section of 250 kcmil. A circular mil is the area of a wire one mil in diameter. One million circular mils is the areaof a circle with 1000 mil = 1 inch diameter. An older abbreviation for one thousand circular mils is MCM .

Stranded wire AWG sizes

Stranded wires are specified with three numbers, the overall AWG size, the number of strands, and the AWG sizeof a strand. The number of strands and the AWG of a strand are separated by a slash. For example, a 22 AWG7/30 stranded wire is a 22 AWG wire made from seven strands of 30 AWG wire.

NEC Code for Size of Cable for Motor

Motor terminal box

NEC Code 430.22 (Size of Cable for Single Motor)

Size of Cable for Branch circuit which has Single Motor connection is 125% of Motor Full Load CurrentCapacity.

Example

What is the minimum rating in amperes for Cables supplying 1 No of 5 hp, 415-volt, 3-phase motor at 0.8 Power Factor.
http://electrical-engineering-portal.com/nec-code-for-size-of-cable-for-motorhttp://electrical-engineering-portal.com/nec-code-for-size-of-cable-for-motor


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Full-load currents for 5 hp = 7Amp. Min Capacity of Cable= (7X125%) =8.75 Amp.

NEC Code 430.6 (A) (Size of Cable for Group of Motors or Elect.Load)

Cables or Feeder which is supplying more than one motors other load(s), shall have an ampacity not less than 125% of the full-load current rating of the highest rated motor plus the sum of the full-load current ratings of all theother motors in the group, as determined by 430.6(A).

For Calculating minimum Ampere Capacity of Main feeder and Cable is 125% of Highest Full Load Current +Sum of Full Load Current of remaining Motors.ExampleWhat is the minimum rating in amperes for Cables supplying 1 No of 5 hp, 415-volt, 3-phase motor at 0.8 Power Factor , 1 No of 10 hp, 415-volt, 3-phase motor at 0.8 Power Factor, 1 No of 15 hp, 415-volt, 3-phase motor at 0.8Power Factor and 1 No of 5hp, 230-volt, single-phase motor at 0.8 Power Factor?

Full-load currents for 5 hp = 7Amp Full-load currents for 10 hp = 13Amp Full-load currents for 15 hp = 19Amp Full-load currents for 10 hp (1 Ph) = 21Amp

Here Capacity wise Large Motor is 15 Hp but Highest Full Load current is 21Amp of 5hp Single PhaseMotor so 125% of Highest Full Load current is 21X125%=26.25Amp Min Capacity of Cable= (26.25+7+13+19) =65.25 Amp.

NEC Code 430.24 (Size of Cable for Group of Motors or Electrical Load)

As specified in 430.24, conductors supplying two or more motors must have an ampacity not less than 125 % of the full-load current rating of the highest rated motor + the sum of the full-load current ratings of all the other motors in the group or on the same phase.

It may not be necessary to include all the motors into the calculation. It is permissible to balance the motors asevenly as possible between phases before performing motor-load calculations.

Example

What is the minimum rating in amperes for conductors supplying 1No of 10 hp, 415-volt, 3-phase motor at 0.8 P.Fand 3 No of 3 hp, 230-volt, single-phase motors at 0.8 P.F.

The full-load current for a 10 hp, 415-volt, 3-phase motor is 13 amperes. The Full-load current for single-phase 3 hp motors is 12 amperes. Here for Load Balancing one Single Phase Motor is connected on R Phase Second in B Phase and third is

in Y Phase. Because the motors are balanced between phases, the full-load current on each phase is 25 amperes (13 +

12 = 25). Here multiply 13 amperes by 125 %=(13 125% = 16.25 Amp). Add to this value the full-load currents of

the other motor on the same phase (16.25 + 12 = 28.25 Amp ). The minimum rating in amperes for conductors supplying these motors is 28 amperes.

NEC 430/32 Size of Overload Protection for Motor

Overload protection (Heater or Thermal cut out protection) would be a device that thermally protects a givenmotor from damage due to heat when loaded too heavy with work.

All continuous duty motors rated more than 1HP must have some type of an approved overload device.

An overload shall be installed on each conductor that controls the running of the motor rated more than onehorsepower. NEC 430/37 plus the grounded leg of a three phase grounded system must contain an overload also.


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This Grounded leg of a three phase system is the only time you may install an overload or over current deviceon a grounded conductor that is supplying a motor.

To Find the motor running overload protection size that is required, you must multiply the F.L.C. (full loadcurrent) with the minimum or the maximum percentage ratings as follows;

Maximum Overload Maximum overload = F.L.C. (full load current of a motor) X allowable % of the maximum setting of an

overload, 130% for motors, found in NEC Article 430/34. Increase of 5% allowed if the marked temperature rise is not over 40 degrees or the marked service factor

is not less than 1.15.

Minimum Overload Minimum Overload = F.L.C. (full load current of a motor) X allowable % of the minimum setting of an

overload, 115% for motors found in NEC Article 430/32/B/1. Increase of 10% allowed to 125% if the marked temperature rise is not over 40 degrees or the marked

service factor is not less than 1.15.

Ampacity

Ampacity is a portmanteau for ampere capacity defined by National Electrical Safety Codes, in some NorthAmerican countries. Ampacity is defined as the maximum amount of electrical current a conductor or device cancarry before sustaining immediate or progressive deterioration. Also described as current rating or current-carrying capacity , ampacity is the RMS electric current which a device or conductor can continuously carrywhile remaining within its temperature rating.


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The ampacity of a conductor depends on:

its insulation temperature rating; the electrical resistance of the conductor material; frequency of the current, in the case of alternating current; ability to dissipate heat, which depends on conductor geometry and its surroundings; ambient temperature.

All electrical conductors have some resistance to the flow of electricity. Electric current flowing through themcauses voltage drop and power dissipation, which heats conductors. Copper or aluminum can conduct a largeamount of current without damage, but long before conductor damage, insulation would, typically, be damaged bythe resultant heat.

The ampacity for a conductor is based on physical and electrical properties of the material and construction of theconductor and of its insulation, ambient temperature, and environmental conditions adjacent to the conductor.Having a large overall surface area can dissipate heat well if the environment can absorb the heat.

In cables different conditions govern, and installation regulations normally specify that the most severe conditionalong the run will govern each cable conductor's rating. Cables run in wet or oily locations may carry a lower temperature rating than in a dry installation. Derating is necessary for multiple cables in close proximity. Whenmultiple cables are in close proximity, each contributes heat to the others and diminishes the amount of externalcooling affecting the individual cable conductors. The overall ampacity of insulated cable conductors in a bundleof more than three cables must also be derated, whether in a raceway or cable. Usually the derating factor istabulated in a nation's wiring regulations.

Depending on the type of insulating material, common maximum allowable temperatures at the surface of theconductor are 60, 75, and 90 C, often with an ambient air temperature of 30 C. In the United States, 105 C isallowed with ambient of 40 C, for larger power cables, especially those operating at more than 2 kV. Likewise,specific insulations are rated 150, 200, or 250 C.

The allowed current in a conductor generally needs to be decreased (derated) when conductors are in a groupingor cable, enclosed in conduit, or an enclosure restricting heat dissipation. e.g. The United States National ElectricCode, Table 310-16, specifies that up to three 8 AWG copper wires having a common insulating material(THWN) in a raceway, cable, or direct burial has an ampacity of 50 A when the ambient air is 30C, the conductor surface temperature allowed to be 75C. A single insulated conductor in free air has 70 A rating.

Ampacity rating is normally for continuous current, and short periods of overcurrent occur without harm in mostcabling systems. The acceptable magnitude and duration of overcurrent is a more complex topic than ampacity.

When designing an electrical system, one will normally need to know the current rating for the following:

WiresPrinted Circuit Board traces, where includedFusesCircuit breakersAll or nearly all components used

Some devices are limited by power rating, and when this power rating occurs below their current limit, it is notnecessary to know the current limit to design a system. A common example of this is lightbulb holders.

Current rating
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For electronic components (such as transistors, voltage regulators, and the like), the term current rating is more-commonly used than ampacity, but the considerations are broadly similar. However the tolerance of short-termovercurrent is near zero for semiconductor devices, as their thermal capacities are extremely small.

Skin effect

Distribution of current flow in a cylindrical conductor, shown in cross section. For alternating current, most (63%)of the electrical current flows between the surface and the skin depth, , which depends on the frequency of thecurrent and the electrical and magnetic properties of the conductor.

The 3-wire bundles in this power transmission installation act as a single conductor. A single wire using the sameamount of metal per kilometer would have higher losses due to the skin effect.

Skin effect is the tendency of an alternating electric current (AC) to become distributed within a conductor suchthat the current density is largest near the surface of the conductor, and decreases with greater depths in theconductor. The electric current flows mainly at the "skin" of the conductor, between the outer surface and a levelcalled the skin depth . The skin effect causes the effective resistance of the conductor to increase at higher frequencies where the skin depth is smaller, thus reducing the effective cross-section of the conductor. The skineffect is due to opposing eddy currents induced by the changing magnetic field resulting from the alternatingcurrent. At 60 Hz in copper, the skin depth is about 8.5 mm. At high frequencies the skin depth becomes muchsmaller. Increased AC resistance due to the skin effect can be mitigated by using specially woven litz wire.Because the interior of a large conductor carries so little of the current, tubular conductors such as pipe can beused to save weight and cost.
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Cause

Skin depth is due to the circulating eddy currents (arising from a changing H field) cancelling the current flow in the center of a conductor and reinforcing it in the skin.

Conductors, typically in the form of wires, may be used to transmit electrical energy or signals using analternating current flowing through that conductor. The charge carriers constituting that current, usually electrons,are driven by an electric field due to the source of electrical energy. An alternating current in a conductor

produces an alternating magnetic field in and around the conductor. When the intensity of current in a conductor

changes, the magnetic field also changes. The change in the magnetic field, in turn, creates an electric field whichopposes the change in current intensity. This opposing electric field is called counter-electromotive force(counter EMF). The counter EMF is strongest at the center of the conductor, and forces the conducting electronsto the outside of the conductor, as shown in the diagram on the right.

An alternating current may also be induced in a conductor due to an alternating magnetic field according to thelaw of induction. An electromagnetic wave impinging on a conductor will therefore generally produce such acurrent; this explains the reflection of electromagnetic waves from metals.

Regardless of the driving force, the current density is found to be greatest at the conductor's surface, with areduced magnitude deeper in the conductor. That decline in current density is known as the skin effect and the skin

depth is a measure of the depth at which the current density falls to 1/e of its value near the surface. Over 98% of the current will flow within a layer 4 times the skin depth from the surface. This behavior is distinct from that of direct current which usually will be distributed evenly over the cross-section of the wire.

The effect was first described in a paper by Horace Lamb in 1883 for the case of spherical conductors, and wasgeneralised to conductors of any shape by Oliver Heaviside in 1885. The skin effect has practical consequences inthe analysis and design of radio-frequency and microwave circuits, transmission lines (or waveguides), andantennas. It is also important even at mains frequencies (50 60 Hz) in AC electrical power transmission anddistribution systems. Although the term "skin effect" is most often associated with applications involvingtransmission of electrical currents, the skin depth also describes the exponential decay of the electric and magnetic
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fields, as well as the density of induced currents, inside a bulk material when a plane wave impinges on it atnormal incidence.

Formula

The AC current density J in a conductor decreases exponentially from its value at the surface J S according to thedepth d from the surface, as follows:

where is called the skin depth . The skin depth is thus defined as the depth below the surface of the conductor atwhich the current density has fallen to 1/e (about 0.37) of J S. In normal cases it is well approximated as:

.

where

= resistivity of the conductor = angular frequency of current = 2 frequency = absolute magnetic permeability of the conductor [1]

A more general expression for skin depth which is more exact in the case of poor conductors (non-metals) at highfrequencies is: [2][3]

where is the electric permittivity of the material. Note that in the usual form for the skin effect, above, the effectof cancels out. This formula is valid away from strong atomic or molecular resonances (where would have alarge imaginary part) and at frequencies which are much below both the material's plasma frequency (dependenton the density of free electrons in the material) and the reciprocal of the mean time between collisions involvingthe conduction electrons. In good conductors such as metals all of those conditions are insured at least up tomicrowave frequencies, justifying this formula's validity.

This formula can be rearranged as follows to reveal departures from the normal approximation:

At frequencies much below the quantity inside the radical is close to unity and the standard formula applies.For instance, in the case of copper this would be true for frequencies much below Hz.

However in very poor conductors at sufficiently high frequencies, the factor on the right increases. At frequencies

much higher than it can be shown that the skin depth, rather than continuing to decrease, approaches anasymptotic value:


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This departure from the usual formula only applies for materials of rather low conductivity and at frequencieswhere the vacuum wavelength is not much much larger than the skin depth itself. For instance, bulk silicon(undoped) is a poor conductor and has a skin depth of about 40 meters at 100 kHz ( =3000m). However as thefrequency is increased well into the megahertz range, its skin depth never falls below the asymptotic value of 11

meters. The conclusion is that in poor solid conductors such as undoped silicon, the skin effect doesn't need to betaken into account in most practical situations: any current is equally distributed throughout the material's cross-section regardless of its frequency.

Resistance

The effective resistance due to a current confined near the surface of a large conductor (much thicker than ) can be solved as if the current flowed uniformly through a layer of thickness based on the DC resistivity of thatmaterial. We can therefore assume a cross-sectional area approximately equal to times the conductor'scircumference. Thus a long cylindrical conductor such as a wire, having a diameter D large compared to , has aresistance approximately that of a hollow tube with wall thickness carrying direct current. Using a material of resistivity we then find the AC resistance of a wire of length L to be:

The final approximation above assumes .

A convenient formula (attributed to F.E. Terman) for the diameter DW of a wire of circular cross-section whoseresistance will increase by 10% at frequency f is:

The increase in AC resistance described above is accurate only for an isolated wire. For a wire close to other wires, e.g. in a cable or a coil, the ac resistance is also affected by proximity effect, which often causes a muchmore severe increase in ac resistance.

Material effect on skin depth

In a good conductor, skin depth varies as the inverse square root of the conductivity. This means that better conductors have a reduced skin depth. The overall resistance of the better conductor remains lower even with thereduced skin depth. However the better conductor will show a higher ratio between its AC and DC resistance,when compared with a conductor of higher resistivity. For example, at 60 Hz, a 2000 MCM (1000 squaremillimetre) copper conductor has 23% more resistance than it does at DC. The same size conductor in aluminumhas only 10% more resistance with 60 Hz AC than it does with DC. [4]

Skin depth also varies as the inverse square root of the permeability of the conductor. In the case of iron, itsconductivity is about 1/7 that of copper. However being ferromagnetic its permeability is about 10,000 timesgreater. This reduces the skin depth for iron to about 1/38 that of copper, about 220 micrometres at 60 Hz. Iron
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wire is thus useless for A.C. power lines. The skin effect also reduces the effective thickness of laminations in power transformers, increasing their losses.

Iron rods work well for direct-current (DC) welding but it is impossible to use them at frequencies much higher than 60 Hz. At a few kilohertz, the welding rod will glow red hot as current flows through the greatly increasedA.C. resistance resulting from the skin effect, with relatively little power remaining for the arc itself. Only non-magnetic rods can be used for high-frequency welding.

Mitigation

A type of cable called litz wire (from the German Litzendraht , braided wire) is used to mitigate the skin effect for frequencies of a few kilohertz to about one megahertz. It consists of a number of insulated wire strands woventogether in a carefully designed pattern, so that the overall magnetic field acts equally on all the wires and causesthe total current to be distributed equally among them. With the skin effect having little effect on each of the thinstrands, the bundle does not suffer the same increase in AC resistance that a solid conductor of the same cross-sectional area would due to the skin effect. [5]

Litz wire is often used in the windings of high-frequency transformers to increase their efficiency by mitigating

both skin effect and proximity effect . Large power transformers are wound with stranded conductors of similar construction to litz wire, but employing a larger cross-section corresponding to the larger skin depth at mainsfrequencies. [6] Conductive threads composed of carbon nanotubes [7] have been demonstrated as conductors for antennas from medium wave to microwave frequencies. Unlike standard antenna conductors, the nanotubes aremuch smaller than the skin depth, allowing full utilization of the thread's cross-section resulting in an extremelylight antenna.

High-voltage, high-current overhead power transmission lines often use aluminum cable with a steel reinforcingcore ; the higher resistance of the steel core is of no consequence since it is located far below the skin depth whereessentially no AC current flows. In other applications, solid conductors are replaced by tubes, completelydispensing with the inner portion of the conductor where little current flows. This hardly affects the AC resistance

but considerably reduces the weight of the conductor.

Solid or tubular conductors may also be silver - plated to take advantage of silver's higher conductivity. Thistechnique is particularly used at VHF to microwave frequencies where the small skin depth requires only a verythin layer of silver, making the improvement in conductivity very cost effective. Silver or gold plating is similarlyused on the surface of waveguides used for transmission of microwaves. This reduces attenuation of the

propagating wave due to resistive losses affecting the accompanying eddy currents; the skin effect confines sucheddy currents to a very thin surface layer of the waveguide structure. The skin effect itself isn't actually combatedin these cases, but the distribution of currents near the conductor's surface makes the use of precious metals(having a lower resistivity) practical.

Examples
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Skin depth vs. frequency for some materials, red vertical line denotes 50 Hz frequency:Mn-Zn - magnetically soft ferriteAl - metallic aluminiumCu - metallic copper steel 410 - magnetic stainless steelFe-Si - grain-oriented electrical steelFe-Ni - high-permeability permalloy (80%Ni-20%Fe)

We can derive a practical formula for skin depth as follows:

where

the skin depth in metresthe relative permeability of the medium

the resistivity of the medium in m, also equal to the reciprocal of its conductivity: (for Copper, = 1.6810 -8 m)

the frequency of the current in Hz

Gold is a good conductor with a resistivity of 2.4410 -8 m and is essentially nonmagnetic: 1, so its skindepth at a frequency of 50 Hz is given by

Lead , in contrast, is a relatively poor conductor (among metals) with a resistivity of 2.210 -7 m, about 9 times

that of gold. Its skin depth at 50 Hz is likewise found to be about 33 mm, or times that of gold.
http://en.wikipedia.org/wiki/Ferritehttp://en.wikipedia.org/wiki/Ferritehttp://en.wikipedia.org/wiki/Aluminiumhttp://en.wikipedia.org/wiki/Aluminiumhttp://en.wikipedia.org/wiki/Copperhttp://en.wikipedia.org/wiki/Copperhttp://en.wikipedia.org/wiki/Stainless_steelhttp://en.wikipedia.org/wiki/Grain-oriented_electrical_steelhttp://en.wikipedia.org/wiki/Grain-oriented_electrical_steelhttp://en.wikipedia.org/wiki/Permalloyhttp://en.wikipedia.org/wiki/Permalloyhttp://en.wikipedia.org/wiki/Permeability_(electromagnetism)http://en.wikipedia.org/wiki/Permeability_(electromagnetism)http://en.wikipedia.org/wiki/Permeability_(electromagnetism)http://en.wikipedia.org/wiki/Goldhttp://en.wikipedia.org/wiki/Leadhttp://en.wikipedia.org/wiki/File:Skin_depth_by_Zureks.pnghttp://en.wikipedia.org/wiki/File:Skin_depth_by_Zureks.pnghttp://en.wikipedia.org/wiki/Ferritehttp://en.wikipedia.org/wiki/Aluminiumhttp://en.wikipedia.org/wiki/Copperhttp://en.wikipedia.org/wiki/Stainless_steelhttp://en.wikipedia.org/wiki/Grain-oriented_electrical_steelhttp://en.wikipedia.org/wiki/Permalloyhttp://en.wikipedia.org/wiki/Permeability_(electromagnetism)http://en.wikipedia.org/wiki/Goldhttp://en.wikipedia.org/wiki/Lead


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Highly magnetic materials have a reduced skin depth owing to their large permeability as was pointed outabove for the case of iron, despite its poorer conductivity. A practical consequence is seen by users of inductioncookers , where some types of stainless steel cookware are unusable because they are not ferromagnetic. [8]

At very high frequencies the skin depth for good conductors becomes tiny. For instance, the skin depths of somecommon metals at a frequency of 10 GHz (microwave region) are less than a micron:

Conductor Skin depth ( m )Aluminum 0.80Copper 0.65Gold 0.79Silver 0.64

Thus at microwave frequencies, most of the current flows in an extremely thin region near the surface. Ohmiclosses of waveguides at microwave frequencies are therefore only dependent on the surface coating of thematerial. A layer of silver 3 m thick evaporated on a piece of glass is thus an excellent conductor at suchfrequencies.

In copper, the skin depth can be seen to fall according to the square root of frequency:

Frequency Skin depth (m)60 Hz 847010 kHz 660100 kHz 2101 MHz 6610 MHz 21100 MHz 6.6

In Engineering Electromagnetics , Hayt points out that in a power station a bus bar for alternating current at 60 Hzwith a radius larger than one-third of an inch (8 mm) is a waste of copper, and in practice bus bars for heavy ACcurrent are rarely more than half an inch (12 mm) thick except for mechanical reasons.

Skin effect reduction of the self inductance of a conductor

Refer to the diagram below showing the inner and outer conductors of a coaxial cable. Since the skin effect causesa current at high frequencies to flow mainly at the surface of a conductor, it can be seen that this will reduce themagnetic field inside the wire, that is, beneath the depth at which the bulk of the current flows. It can be shownthat this will have a minor effect on the self inductance of the wire itself; see Skilling [9] or Hayt [10] for amathematical treatment of this phenomenon.

Note that the inductance considered in this context refers to a bare conductor, not the inductance of a coil used asa circuit element. The inductance of a coil is dominated by the mutual inductance between the turns of the coilwhich increases its inductance according to the square of the number of turns. However when only a single wire isinvolved, then in addition to the "external inductance" involving magnetic fields outside of the wire (due to thetotal current in the wire) as seen in the white region of the figure below, there is also a much smaller component of "internal inductance" due to the magnetic field inside the wire itself, the green region in figure B. In a single wirethe internal inductance becomes of little significance when the wire is much much longer than its diameter. The

presence of a second conductor in the case of a transmission line requires a different treatment as is discussed below.
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Due to the skin effect, at high frequencies the internal inductance of a wire vanishes, as can be seen in the case of a telephone twisted pair, below. In normal cases the effect of internal inductance is ignored in the design of coilsor calculating the properties of microstrips .

Inductance per length in a coaxial cable

Let the dimensions a, b, and c be the inner conductor radius, the shield (outer conductor) inside radius and theshield outer radius respectively, as seen in the crossection of figure A below.

Four stages of skin effect in a coax showing the effect on inductance. Diagrams show a cross-section of the coaxial cable. Color code: black=overall insulating sheath, tan=conductor, white=dielectric, green=current into thediagram, blue=current coming out of the diagram, dashed blue lines with arrowheads=magnetic flux (B). The widthof the dashed blue lines is intended to show relative strength of the magnetic field integrated over the circumference at that radius. The four stages, A, B, C, and D are non-energized, low frequency, middle frequency and high frequencyrespectively. There are three regions that may contain induced magnetic fields: the center conductor, the dielectricand the outer conductor. In stage B, current covers the conductors uniformly and there is a significant magnetic field in all three regions. As the frequency is increased and the skin effect takes hold (C and D) the magnetic field in thedielectric region is unchanged as it is proportional to the total current flowing in the center conductor. In C, however,there is a reduced magnetic field in the deeper sections of the inner conductor and the outer sections of the shield (outer conductor). Thus there is less energy stored in the magnetic field given the same total current, corresponding to

a reduced inductance. At an even higher frequency, D, the skin depth is tiny: all current is confined to the surface of the conductors. The only magnetic field is in the regions between the conductors; only the "external inductance" remains.

For a given current, the total energy stored in the magnetic fields must be the same as the calculated electricalenergy attributed to that current flowing through the inductance of the coax; that energy is proportional to thecable's measured inductance.

The magnetic field inside a coaxial cable can be divided into three regions, each of which will therefore contributeto the electrical inductance seen by a length of cable. [11]

The inductance is associated with the magnetic field in the region with radius , the region inside thecenter conductor.

The inductance is associated with the magnetic field in the region , the region between the twoconductors (containing a dielectric, possibly air).

The inductance is associated with the magnetic field in the region , the region inside the shieldconductor.

The net electrical inductance is due to all three contributions:
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is not changed by the skin effect and is given by the frequently cited formula for inductance L per length D ofa coaxial cable:

At low frequencies, all three inductances are fully present so that .

At high frequencies, only the dielectric region has magnetic flux, so that .

Most discussions of coaxial transmission lines assume they will be used for radio frequencies, so equations aresupplied corresponding only to the latter case.

As the skin effect increases, the currents are concentrated near the outside of the inner conductor ( r =a) and theinside of the shield ( r =b). Since there is essentially no current deeper in the inner conductor, there is no magneticfield beneath the surface of the inner conductor. Since the current in the inner conductor is balanced by theopposite current flowing on the inside of the outer conductor, there is no remaining magnetic field in the outer conductor itself where . Only contributes to the electrical inductance at these higher frequencies.

Although the geometry is different, a twisted pair used in telephone lines is similarly affected: at higher frequencies the inductance decreases by more than 20% as can be seen in the following table.

Characteristics of telephone cable as a function of frequency

Representative parameter data for 24 gauge PIC telephone cable at 21 C (70 F).

Frequency (Hz) R (/km) L (mH/km) G (S/km) C (nF/km)1 172.24 0.6129 0.000 51.571k 172.28 0.6125 0.072 51.5710k 172.70 0.6099 0.531 51.57100k 191.63 0.5807 3.327 51.571M 463.59 0.5062 29.111 51.572M 643.14 0.4862 53.205 51.575M 999.41 0.4675 118.074 51.57

More extensive tables and tables for other gauges, temperatures and types are available in Reeve. [12] Chen [13] givesthe same data in a parameterized form that he states is usable up to 50 MHz.

Chen [13] gives an equation of this form for telephone twisted pair:

Notes


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1. The permeability can be found from , the relative permeability of the material by multiplyingit by , the permeability of free space: .2. VanderVorst (2006)3. Jordan (1968, p. 130)4. Donald G. Fink, H. Wayne Beatty Standard Handbook for Electrical Engineers 11th Edition ,McGraw Hill, 1978 table 18-215. Xi Nan; Sullivan, C. R. (2005), "An equivalent complex permeability model for litz-wirewindings", Industry Applications Conference 3: 22292235, DOI :10.1109/IAS.2005.1518758, ISBN 0-7803-9208-6, ISSN 0197-26186. Central Electricity Generating Board (1982). Modern Power Station Practice . Pergamon Press.7. "Spinning Carbon Nanotubes Spawns New Wireless Applications". Sciencedaily.com. 2009-03-09. Retrieved 2011-11-08.8. If the permeability is low, the skin depth is so large that the resistance encountered by eddycurrents is too low to provide enough heat9. Skilling (1951, pp. 157159)10. Hayt (1981, pp. 434439)11. Hayt (1981, p. 434)12. Reeve (1995, p. 558)13. a b Chen (2004, p. 26)

References Chen, Walter Y. (2004), Home Networking Basics , Prentice Hall, ISBN 0-13-016511-5 Hayt, William (1981), Engineering Electromagnetics (4th ed.), McGraw-Hill, ISBN 0-07-027395-2 Hayt, William Hart. Engineering Electromagnetics Seventh Edition . New York: McGraw Hill, 2006. ISBN

0-07-310463-9. Nahin, Paul J. Oliver Heaviside: Sage in Solitude . New York: IEEE Press, 1988. ISBN 0-87942-238-6. Ramo, S., J. R. Whinnery, and T. Van Duzer. Fields and Waves in Communication Electronics . New

York: John Wiley & Sons, Inc., 1965. Ramo, Whinnery, Van Duzer (1994). Fields and Waves in Communications Electronics . John Wiley and

Sons. Reeve, Whitman D. (1995), Subscriber Loop Signaling and Transmission Handbook , IEEE Press, ISBN 0-

7803-0440-3 Skilling, Hugh H. (1951), Electric Transmission Lines , McGraw-Hill Terman, F. E. (1943), Radio Engineers' Handbook , New York: McGraw-Hill. For the Terman formula

mentioned above. Xi Nan; Sullivan, C. R. (2005), "An equivalent complex permeability model for litz-wire windings",

Industry Applications Conference 3: 22292235, DOI:10.1109/IAS.2005.1518758, ISBN 0-7803-9208-6,ISSN 0197-2618

Jordan, Edward (1968), Electromagnetic Waves and Radiating Systems , Prentice Hall, ISBN 978-0-13-249995-8

Eddy current
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Eddy currents (also called Foucault currents [1]) are electric currents induced in conductors when a conductor isexposed to a changing magnetic field; due to relative motion of the field source and conductor or due to variationsof the field with time. This can cause a circulating flow of electrons, or current, within the body of the conductor.These circulating eddies of current have inductance and thus induce magnetic fields. These fields can causerepulsive, attractive, [2] propulsion and drag effects. The stronger the applied magnetic field, or the greater theelectrical conductivity of the conductor, or the faster the field changes, then the greater the currents that aredeveloped and the greater the fields produced.

The term eddy current comes from analogous currents seen in water when dragging an oar breadthwise: localisedareas of turbulence known as eddies give rise to persistent vortices. Somewhat analogously, eddy currents cantake time to build up and can persist for very short times in conductors due to their inductance.

Eddy currents, like all electric currents, generate heat as well as electromagnetic forces. The heat can be harnessedfor induction heating. The electromagnetic forces can be used for levitation, creating movement, or to give astrong braking effect. Eddy currents can also have undesirable effects, for instance power loss in transformers. Inthis application, they are minimised with thin plates, by lamination of conductors or other details of conductor shape.

Self-induced eddy currents are responsible for the skin effect in conductors. [3] The latter can be used for non-

destructive testing of materials for geometry features, like micro-cracks. [4] A similar effect is the proximity effect,which is caused by externally-induced eddy currents. [5]

History

The first person to observe current eddies was Franois Arago (17861853), the 25th Prime Minister of France,who was also a mathematician, physicist and astronomer. In 1824 he observed what has been called rotatorymagnetism, and that most conductive bodies could be magnetized; these discoveries were completed andexplained by Michael Faraday (17911867).

In 1834, Heinrich Lenz stated Lenz's law , which says that the direction of induced current flow in an object will be such that its magnetic field will oppose the magnetic field that caused the current flow. Eddy currents developsecondary flux that cancels a part of the external flux.

French physicist Lon Foucault (18191868) is credited with having discovered Eddy currents. In September,1855, he discovered that the force required for the rotation of a copper disc becomes greater when it is made torotate with its rim between the poles of a magnet, the disc at the same time becoming heated by the eddy currentinduced in the metal. The first use of eddy current for non-destructive testing occurred in 1879 when David E.Hughes used the principles to conduct metallurgical sorting tests. [6]

Explanation
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As the circular plate moves down through a small region of constant magnetic field directed into the page, eddycurrents are induced in the plate. The direction of those currents is given by Lenz's law, i.e. so that the plate'smovement is hindered.

When a conductor moves relative to the field generated by a source, electromotive forces (EMFs) can begenerated around loops within the conductor. These EMFs acting on the resistivity of the material generate acurrent around the loop, in accordance with Faraday's law of induction. These currents dissipate energy, and createa magnetic field that tends to oppose changes in the current- they have inductance.

Eddy currents are created when a conductor experiences changes in the magnetic field. If either the conductor ismoving through a steady magnetic field, or the magnetic field is changing around a stationary conductor, eddycurrents will occur in the conductor. Both effects are present when a conductor moves through a varying magneticfield, as is the case at the top and bottom edges of the magnetized region shown in the diagram. Eddy currents will

be generated wherever a conducting object experiences a change in the intensity or direction of the magnetic fieldat any point within it, and not just at the boundaries.

The swirling current set up in the conductor is due to electrons experiencing a Lorentz force that is perpendicular to their motion. Hence, they veer to their right, or left, depending on the direction of the applied field and whether the strength of the field is increasing or declining. The resistivity of the conductor acts to damp the amplitude of the eddy currents, as well as straighten their paths. Lenz's law states that the current swirls in such a way as tocreate an induced magnetic field that opposes the phenomenon that created it. In the case of a varying appliedfield, the induced field will always be in the opposite direction to that applied. The same will be true when avarying external field is increasing in strength. However, when a varying field is falling in strength, the inducedfield will be in the same direction as that originally applied, in order to oppose the decline.

An object or part of an object experiences steady field intensity and direction where there is still relative motion of the field and the object (for example in the center of the field in the diagram), or unsteady fields where thecurrents cannot circulate due to the geometry of the conductor. In these situations charges collect on or within theobject and these charges then produce static electric potentials that oppose any further current. Currents may beinitially associated with the creation of static potentials, but these may be transitory and small.
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Lamination of conductors parallel to the field lines reduce eddy currents

Eddy currents generate resistive losses that transform some forms of energy, such as kinetic energy, into heat.This Joule heating reduces efficiency of iron-core transformers and electric motors and other devices that usechanging magnetic fields. Eddy currents are minimized in these devices by selecting magnetic core materials thathave low electrical conductivity (e.g., ferrites ) or by using thin sheets of magnetic material, known as laminations .Electrons cannot cross the insulating gap between the laminations and so are unable to circulate on wide arcs.

Charges gather at the lamination boundaries, in a process analogous to the Hall effect , producing electric fieldsthat oppose any further accumulation of charge and hence suppressing the eddy currents. The shorter the distance between adjacent laminations (i.e., the greater the number of laminations per unit area, perpendicular to theapplied field), the greater the suppression of eddy currents.

The conversion of input energy to heat is not always undesirable, however, as there are some practicalapplications. One is in the brakes of some trains known as eddy current brakes. During braking, the metal wheelsare exposed to a magnetic field from an electromagnet, generating eddy currents in the wheels. The eddy currentsmeet resistance as charges flow through the metal, thus dissipating energy as heat, and this acts to slow the wheelsdown. The faster the wheels are spinning, the stronger the effect, meaning that as the train slows the braking forceis reduced, producing a smooth stopping motion. Induction heating makes use of eddy currents to provide heatingof metal objects.

Strength of eddy currents

Under certain assumptions (uniform material, uniform magnetic field, no skin effect , etc.) the power lost due toeddy currents can be calculated from the following equation: [7]

where:

k ,o 1 for thin sheetso 2 for thin wires

P , power dissipation (W/kg) B p, peak flux density (T) d , thickness of the sheet or diameter of the wire (m) f , frequency (Hz) , resistivity (m) D, density (kg/m 3)
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It should be borne in mind that these equations are valid only under the so-called quasi-static conditions, wherethe frequency of magnetisation does not result in the skin effect; i.e., the electromagnetic wave fully penetrates thematerial.

Therefore, the following things usually increase the size and effects of eddy currents:

stronger magnetic fields, increases flux density B faster changing fields (due to faster relative speeds or otherwise), increases the frequency f thicker materials, increases the thickness d lower resistivity materials (aluminium, copper, silver etc.)

Some things reduce the effects:

weaker magnets, lower B slower changing fields (slower relative speeds), lower f thinner materials, lower d slotted materials so that currents cannot circulate, reduced d or coefficient in the denominator (6, 12, etc.) laminated materials so that currents cannot circulate, reduced d higher resistance materials (silicon rich iron, etc.)

Skin effect

In very fast changing fields due to skin effect the equations shown above are not valid because the magnetic fielddoes not penetrate the material uniformly. However, in any case increased frequency of the same value of fieldwill always increase eddy currents, even with non-uniform field penetration.

The penetration depth can be calculated from the following equation :[8]

where:

, penetration depth (m) ,[9] f , frequency (Hz) , magnetic permeability (H/m) , electrical conductivity (S/m)

Applications

Repulsive effects and levitation
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A cross section through a linear motor placed above a thick aluminium slab. As the linear induction motor ' s field pattern sweeps to the left, eddy currents are left behind in the metal and this causes the field lines to lean.

In a fast varying magnetic field the induced currents, in good conductors, particularly copper and aluminium,frequently exhibit diamagnetic-like repulsion effects on the magnetic field, and hence on the magnet and cancreate repulsive effects and even stable levitation, albeit with reasonably high power dissipation due to the highcurrents this entails.

They can thus be used to induce a magnetic field in aluminum cans , which allows them to be separated easilyfrom other recyclables (see also eddy current separator ). With a very strong handheld magnet, such as those madefrom neodymium , one can easily observe a very similar effect by rapidly sweeping the magnet over a coin withonly a small separation. Depending on the strength of the magnet, identity of the coin, and separation between themagnet and coin, one may induce the coin to be pushed slightly ahead of the magnet - even if the coin contains nomagnetic elements, such as the US penny . Another example involves dropping a strong magnet down a tube of copper [10] -- the magnet falls at a dramatically slow pace.

Perfect conductors allow lossless conduction that allows eddy currents to form on the surface of the conductor thatexactly cancel any changes in the magnetic field applied to the object after the material's resistance went to zero,thus allowing magnetic levitation . Superconductors are a subclass of perfect conductors in that they also exhibitthe Meissner Effect , an inherently quantum mechanical phenomenon that is responsible for expelling anymagnetic field lines present during the superconducting transition, thus making the magnetic field zero in the bulk of the superconductor.

Attractive effects

In some geometries the overall force of eddy currents can be attractive, for example, where the flux lines are past90 degrees to a surface, the induced currents in a nearby conductor cause a force that pushes a conductor towardsan electromagnet .[2]

Identification of metals

In coin operated vending machines , eddy currents are used to detect counterfeit coins, or slugs . The coin rolls pasta stationary magnet, and eddy currents slow its speed. The strength of the eddy currents, and thus the retardation,depends on the conductivity of the coin's metal. Slugs are slowed to a different degree than genuine coins, and thisis used to send them into the rejection slot.

Vibration | Position Sensing

Eddy currents are used in certain types of proximity sensors to observe the vibration and position of rotating shaftswithin their bearings. This technology was originally pioneered in the 1930s by researchers at General Electric using vacuum tube circuitry. In the late 1950s, solid-state versions were developed by Donald E. Bently at Bently

Nevada Corporation. These sensors are extremely sensitive to very small displacements making them well suited
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to observe the minute vibrations (on the order of several thousandths of an inch) in modern turbomachinery . Atypical proximity sensor used for vibration monitoring has a scale factor of 200 mV/mil. Widespread use of suchsensors in turbomachinery has led to development of industry standards that prescribe their use and application.Examples of such standards are American Petroleum Institute (API) Standard 670 and ISO 7919.

Electromagnetic braking

Main article: Eddy current brake

Braking forces resulting from eddy currents in a metal plate moving through an external magnetic field

Eddy currents are used for braking at the end of some roller coasters. This mechanism has no mechanical wear and produces a very precise braking force. Typically, heavy copper plates extending from the car are moved

between pairs of very strong permanent magnets. Electrical resistance within the plates causes a dragging effectanalogous to friction, which dissipates the kinetic energy of the car. The same technique is used inelectromagnetic brakes in railroad cars and to quickly stop the blades in power tools such as circular saws.

Structural testing

Eddy current techniques are commonly used for the nondestructive examination (NDE) and condition monitoringof a large variety of metallic structures, including heat exchanger tubes, aircraft fuselage, and aircraft structuralcomponents..

Side effects

Eddy currents are the root cause of the skin effect in conductors carrying AC current.

Lamination of magnetic cores in transformers greatly improves the efficiency by minimising eddy currents
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Similarly, in magnetic materials of finite conductivity eddy currents cause the confinement of the majority of themagnetic fields to only a couple skin depths of the surface of the material. This effect limits the flux linkage ininductors and transformers

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