Size versus Rating

Core area depends upon voltage, induction, frequency, and turns. For a given frequency and grade of core material, core area depends upon the applied voltage. Window area depends upon coil size, or for a given voltage upon the current drawn. Since window area and core area determine size, there is a relation between size and v-a rating.

With other factors, such as frequency and grade of iron, constant, the larger transformers dissipate less heat per unit volume than the smaller ones. This is true because dissipation area increases as the square of the equivalent spherical radius, whereas volume increases as its cube. Therefore larger units are more commonly of the open type, whereas smaller units are totally enclosed. Where enclosure is feasible, it tends to cause size increase by limiting the heat dissipation. Figure 43 shows the relation between size and rating for small, enclosed, low-voltage, two-winding, 60-cycle transformers having Hipersil cores and class A insulation and operating continuously in a 40°C ambient.

Fig. 43. Size of enclosed 60-cycle transformers.

The size increases for the same volt-amperes over that in Fig. 43 for any of the following reasons:

High voltage	Silicon-steel cores
High ambient temperature	Low regulation
Lower frequency	More windings

The size decreases for

Higher frequencies	Open-type units
Class B insulation	Intermittent operation

If low-voltage insulation is assumed, two secondary windings reduce the rating of a typical size by 10 per cent; six secondaries by 50 per cent. The decreased rating is due partly to space occupied by insulation and partly to poorer space factor. The effects of voltage, temperature, and core steel on size have been discussed in preceding sections. Frequency and regulation will be considered separately in succeeding chapters.

Open-type transformers like those in Fig. 8 have better heat dissipation than enclosed units. The lamination-stacking dimension can be made to suit the rating, so that one size of lamination may cover a range of v-a ratings. Heat dissipation from the end cases is independent of the stacking dimension, but that from the laminations is directly proportional to it. This is shown in Fig. 44 for several lamination sizes.

Fig. 44. Heat dissipation from open-type transformers with end cases.

For each size the horizontal line represents heat dissipation from the end cases; the sloping line represents dissipation from end cases, plus that from the lamination edges which is proportional to the stacking dimension. At ordinary working temperature, heat is dissipated at the rate of 0.008 watt per square inch per centigrade degree rise. In Fig. 44 the watts per centigrade degree of temperature rise are given as a function of lamination stack. This refers to temperature rise at the core surface only. In addition, there is a temperature gradient between coil and core which is given in similar manner in Fig. 45.

Fig. 45. Winding-to-core gradient for open-type transformers with end oases. For lamination sizes, see Fig. 44.

To find the average coil temperature rise, divide the copper loss by the watts per centigrade degree from the sloping line of Fig. 45. To this add the total of copper and iron losses divided by the appropriate ordinate from Fig. 44. That is, the total coil temperature rise is equal to the sum of the temperature drop across the insulation (marked Cu-Fe gradient in Fig. 45) and the temperature drop from the core to the ambient air.

Data like those in Figs. 44 and 45 can be established for any lamination by making a heat run on two transformers, one having a core stack near the minimum and one near the maximum that is likely to be used. Usually stacking dimensions lie between the extremes of 1/2 to 3 times the lamination tongue width, and poor use of space results from stacking outside these limits. If end cases are omitted, coil dissipation is improved as much as 50 per cent.

The same method can be used for figuring type C Hipersil core designs; here the strip width takes the place of the stacking dimension of punched laminations, and the build-up corresponds to the tongue width. When two cores are used, as in Fig. 14, the heating can be approximated by using data for the nearest punching.

For irregular or unknown heat dissipation surfaces, an approximation to the temperature rise can be found from the transformer weight, as derived in the next section.