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Power Supply Frequency

Foregoing examples were based on a 60-cycle supply. Twenty-five-cycle transformer losses are lower for a given induction. It follows that induction can be increased somewhat over the 60-cycle value, but saturation currents prevent a decided increase. Larger size results, nearly 2:1 in volume. Otherwise 25-cycle transformers are not appreciably different from 60-cycle transformers.

Power supply frequencies of 400 and 800 cycles are used mainly in aircraft and portable equipment to save weight and space. Silicon-steel core materials 0.005 in. thick are principally used at these frequencies to reduce eddy currents. Losses at 400 and 800 cycles for three core materials are shown in Fig. 62.

Fig. 62. Silicon-steel core loss at 400 and 800 cycles.

These losses can be the controlling factors in determining transformer size, because a given material saturates at nearly the same induction whether the frequency is 60 cycles or 800 cycles, but the core loss is so high at 800 cycles that the core material cannot be used near the saturation density. The higher the induction the higher the core heating. For this reason, class B insulation can be used in many 400- and 800-cycle designs to reduce size still further. If advantage is taken of both the core material and insulation, 800-cycle transformers can be reduced to 1.0 per cent of the size of 60-cycle transformers of the same rating. Typical combinations of grain-oriented core material and insulation are as follows:

B-GaussClass of
600.01415,000A95 °C

In very small units, these flux densities may be used at lower temperatures and with class A insulation because of regulation. The special 4-mil steel developed for 400 cycles makes possible size reduction comparable to that for 800 cycles. The necessity for small dimensions, especially in aircraft apparatus, continually increases the tendency to use materials at their fullest capabilities.

Many small 60-cycle transformers have core loss which is small compared to winding or copper loss. This condition occurs because inductance is limited by exciting current rather than by core loss. As size or frequency increases, this limitation disappears, and core loss is limited only by design considerations. Under such circumstances, the ratio of core to copper loss for maximum rating in a given size may be found as follows. Let

We = core loss

Ws = copper loss

K1, K2, etc. = constants

E = secondary voltage

I = secondary current

For a transformer with a given core, winding, volt-ampere rating, and frequency, We K1E2. For a given winding, Ws = K2I2. Also, for a given size, We + Ws = K3, a quantity determined by the permissible temperature rise. Hence the transformer volt-ampere rating is approximately

For a maximum, the rating may be differentiated with respect to We, and the derivative equated to zero:

0 = K3 - 2We


We = K3/2

so that WS = K3/2, or copper and core losses are equal for maximum rating.

Although this equality is not critical, and is subject to many limitations such as core shape, voltage rating, and method of cooling, it does serve as a guidepost to the designer. If a transformer design is such that a large disparity exists between core and copper losses, size or temperature rise often may be reduced by a redesign in the direction of equal losses.

Last Update: 2011-01-24