barcode printing using vb.net Coefficient of coupling in Software

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Coefficient of coupling
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The coefficient of coupling, specified by the letter k, is a number ranging from 0 (no coupling) to 1 (maximum possible coupling). Two coils that are separated by a sheet of solid iron would have essentially k 0; two coils wound on the same form, one right over the other, would have practically k 1.
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Mutual inductance
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The mutual inductance is specified by the letter M and is expressed in the same units as inductance: henrys, millihenrys, microhenrys, or nanohenrys. The value of M is a function of the values of the inductors, and also of the coefficient of coupling. For two inductors, having values of L1 and L2 (both expressed in the same size units), and with a coefficient of coupling k, the mutual inductance M is found by multiplying the inductance values, taking the square root of the result, and then multiplying by k. Mathematically, M k (L1L2)1/2
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Effects of mutual inductance
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Mutual inductance can operate either to increase the inductance of a pair of series connected inductors, or to decrease it. This is because the magnetic fields might reinforce each other, or they might act against each other. When two inductors are connected in series, and there is reinforcing mutual inductance between them, the total inductance L is given in the formula: L L1 L2 2M
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where L1 and L2 are the values of the individual inductors, and M is the mutual inductance. All inductances must be expressed in the same size units.
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Problem 10-5
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Suppose two coils, having values of 30 H and 50 H, are connected in series so that their fields reinforce, as shown in Fig. 10-5, and that the coefficient of coupling is 0.5. What is the total inductance of the combination First, calculate M from k. According to the formula for this, given above, M .5(50 30)1/ 2 19.4 H. Then the total inductance is equal to L L1 L2 2M 30 50 38.8 118.8 H, rounded to 120 H because only two significant digits are justified. When two inductors are connected in series and the mutual inductance is in opposition, the total inductance L is given by the formula L L1 L2 2M
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where, again, L1 and L2 are the values of the individual inductors.
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Air-core coils 189
10-5
Illustration for Problem 10-5.
Problem 10-6
There are two coils with values L1 835 H and L2 2.44 mH. They are connected in series so that their coefficient of coupling is 0.922, acting so that the coils oppose each other, as shown in Fig. 10-6. What is the net inductance of the pair
10-6 Illustration for Problem 10-6.
First, calculate M. Notice that the coil inductances are specified in different units. Convert them both to microhenrys, so that L2 becomes 2440 H. Then M 0.922(835 2440)1/ 2 1316 H. The total inductance is therefore L L1 L2 2M 835 2440 2632 643 H. It is possible for mutual inductance to increase the total series inductance of a pair of coils by as much as a factor of 2, if the coupling is total and if the flux reinforces. Conversely, it is possible for the inductances of two coils to cancel each other. If two equal-valued inductors are connected in series so that their fluxes oppose, the result will be theoretically zero inductance.
Air-core coils
The simplest inductors (besides plain, straight lengths of wire) are coils. A coil can be wound on a plastic, wooden or other nonferromagnetic material, and it will work very well, although no air-core inductor can have very much inductance. In practice, the maximum attainable inductance for such coils is about 1 mH. Air-core coils are used mostly at radio frequencies, in transmitters, receivers, and antenna networks. In general, the higher the frequency of an alternating current, the less inductance is needed to produce significant effects. Air-core coils can be made to have
190 Inductance almost unlimited current-carrying capacity, just by using heavy-gauge wire and making the radius of the coil large. Air does not dissipate much energy in the form of heat; it is almost lossless. For these reasons, air-core coils can be made highly efficient.
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