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Lowloss core material is essential for high Q. Nickeliron alloys are widely used; the lamination thickness depends on frequency. At frequencies up to 400 cycles, 0.014in.thick laminations are used, and at frequencies higher than 400 cycles, 0.005 in. thick. This is an approximate practical guide.
Figure 140 shows how loss varies with thickness, frequency, and flux density. At frequencies higher than 1,000 cycles, flux density must be quite small for low core loss. In the majority of audio applications, low flux density conditions prevail. Under such conditions, core loss is largely eddycurrent loss and may be treated as a linear resistance. Core gaps are used in filter reactors to obtain better Q. For any core, inductance per turn, and frequency, there is a maximum value of Q. The reason for this is that the ac resistance is composed of at least two elements: the winding resistance and the equivalent core loss. In previous chapters the core loss has been regarded as an equivalent resistance across a winding. But it can also be regarded as an equivalent resistance in series with the winding.
Figure 141 shows this equivalence, which may be stated:
For values of Q > 5,
where R_{sh} = equivalent shunt resistance The equivalence depends upon frequency. The formula for large Q may then be changed to
or Q is proportional to shunt resistance, the winding resistance being neglected. Thus Q can be increased by lowering L, and L is lowered by increasing core gap, but there are limits on the increase of Q that can be obtained in this way. First, the winding resistance is not negligible. With small gaps, maximum Q is obtained when winding resistance and equivalent series coreloss resistance are equal. For a given air gap there is a certain frequency f_{m} at which this maximum Q holds. At higher and lower frequencies, the manner in which Q falls below the maximum is found as follows: Let R_{c} be the coil winding resistance. Then
If for R_{ser} we substitute the value obtained from equation 84, we have, approximately,
Equation 86 therefore gives the relation of Q to frequency. When it is plotted on loglog coordinates with frequency as the independent variable,^{(1)} it is symmetrical about the frequency f_{m} for which Q is a maximum. If the core gap is changed, frequency f_{m} changes.
Figure 142 shows how the Q of a small inductor varies with frequency for several values of air gap in the core. All these curves have the same shape, a fact which suggests the use of a template for interpolating such curves. Another phenomenon that limits Q is the flux fringing at the core gap, the influence of which on inductance was discussed in Chapter 3. As the air gap increases, the flux across it fringes more and more, like that shown in Fig. 143, and L ceases to be inversely proportional to the gap.
Some of the fringing flux strikes the core perpendicular to the laminations and sets up eddy currents which cause additional loss. Accurate prediction of gap loss depends on the amount of fringing flux. For laminated cores it can be estimated from
where G = a constant (17 · 10 ^{10} for silicon steel) In Power Supply Frequency, it was shown that under certain conditions maximum transformer rating for a given size is obtained when core and winding losses are equal. The same would be true for inductors with zero core gap. Similarly it may be shown that, if the core gap is large enough to cause appreciable gap loss, maximum Q is obtained with core, winding, and gap losses equal. In a given design, if this triple equality does not result in the required Q, size must be increased. Losses may be compared by finding either the equivalent series resistances or the equivalent shunt resistances.


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