Curves of Fig. 42 are for pressboard or Micarta under oil. Some kinds of porcelain have less creepage strength than these materials. On the other hand, some grades of glass and polystyrene are much better and withstand 150 kv for 1 minute with 2 in. of creepage path.

INCHES THICKNESS 4 5 6 7 8 9 Ю

40 50

.4 .5 .6 .7,8 .9

INCHES THICKNESS

Fig. 42. Creepage curves of solid insulation under oil.

In high-voltage low-current power supplies, these special materials are used to save weight and space. At 50 kv or more, sharp edges and points should be avoided by the use of round terminals, leads, and coils.

Only high grades of insulating oil are used for this purpose. Tests are run continually to check condition of the oil. Oil is stored in such a manner as to keep out moisture and dirt and avoid extremes of

temperature. Where very high voltages are used, as in X-ray apparatus, oil filling is done under vacuum to remove air bubbles, and containers are sealed afterwards to prevent moisture from entering. Mica insulation is not used in oil because oil dissolves flexible bonds.

Often a high-voltage transformer can be integrated with some other component, such as a tube socket, capacitor, or another transformer. This is desirable from the standpoint of space conservation, provided that adequate clearances to the case are maintained. Packaged power supplies are sometimes made in this fashion to facilitate assembly and repair.

22. 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. 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 В 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 sec-

tions. 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

>-

о

о

100

zi о

2 UJ

о

>

40 80 120 160 200

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

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. 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 ivliich is proportional to the stacking dimension. At ordinary working temperature, heat is dis-

Ш

о

i-<

о

<

2 4

LAMINATION DIMENSIONS - INCHES

01 234 5678 9 10 il 12 LAMINATION STACK - INCHES

Fif!. 44. Heat dissipation from open-Lype transformers with end cases.

gradient between coil and core which is given in similar manner in Fig. 45.

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 ex-

sipated 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

tremes of У2 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 С 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

о

о о

о

(л

ь

Fig. 45.

4 5 6 7 8 9 LAMINATION STACK-INCHES

Ю

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

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.

23. Intermittent Ratings. It often happens that electronic equipment is operated for repeated short lengths of time, between which the power is off. In such cases the average power determines the heating and size. Transformers operating intermittently can be built smaller than if they were operated continuously at full rating.

Intermittent operation affects size only if the on periods are short compared to the thermal time constant of the transformer; that is, small transformers have less heat storage capacity and hence rise to final

temperature more quickly than do large ones. It is important, therefore, to know the relation between size and thermal time constant, or the time that would be required to bring a transformer to 63 per cent of the temperature to which it would finally rise if the power were applied continuously.

The exact determination of temperature rise time in objects such as transformers, having irregular shapes and non-homogeneous materials, has not yet been attempted. Even in simple shapes of homogeneous material, and after further simplifying assumptions have been made, the solution is too complicated for rapid calculation. However, under certain conditions, a spherical object can be shown to cool according to the simple law:

в = вое vc- (28)

where В = temperature above ambient at any instant t во = initial temperature above ambient

E = emissivity in calories per second per centigrade degree per

square centimeter p = density of material с = specific heat of material r = radius of sphere e = 2.718.

The conditions involved in this formula are that the sphere is so small or the cooling so slow that the temperature at any time is sensibly uniform throughout the whole volume. Mathematically, this is fulfilled when the expression Er/k (where к is the thermal conductivity of the material) is small compared to unity. Knowing the various properties of the transformer material, we can tell (1) whether the required conditions are met, and (2) what the thermal time constant is. The latter is arrived at by the relation

= pcrJSE (29)

where Ге is the radius of the equivalent sphere.

In order to convert the non-homogeneous transformer into a homogeneous sphere the aл'erage product of density and specific heat pc is

1 See The Mathematical Theory of Heat Conduction, by L. R. Ingersoll and O. J. Zobe], Ginn and Co., Boston, 1913, p. 142.

2 Ingersoll and Zobel, op. cit., p. 143.

found. Figures on widely different transformers show a variation from 0.862 to 0.879 in this product; hence an average value of 0.87 can be taken, with only 1 per cent deviation in any individual case.

Since the densities of iron and copper do not differ greatly, and insulation brings the coil density closer to that of iron, it may be further assumed that the transformer has material of uniform density 7.8 throughout. The equivalent spherical radius can then be found from

r, = (Weight/1.073)

(30)

where is in inches and weight is in pounds. The time constant is plotted from equations 29 and 30 in terms of weight in Fig. 46.

1.0 0.8

0.3 -

a to

60 80 100

Fig. 46. Transformer time constant, or time required to reach 63 per cent of final

temperature.

The condition that Er/k be small compared to unity is approximated by assuming that к is the conductivity of iron-a safe assumption, because the conductivity of copper is 7 to 10 times that of iron. A transformer weighing as much as 60 lb has = 5.45 in., E = 0.00028 cal per sec per sq cm/°C, and к = 0.11. Changing Ге to metric units

0.9 0.8

I г 3

TIME IN MULTIPLES OF THERMAL TIME CONSTANT Tj.

Fig. 47. Transformer temperature rise time.

gether with the exponential law which is во - в, where в is the temperature of equation 28. The actual rise is less at first than that of the foregoing simplified theory, then more rapid, and with a more pronounced knee. The 63 per cent of final temperature is reached in about 70 per cent of the theoretical time constant tc for transformers weighing between 5 and 200 lb. This average correction factor is included in Fig. 46 also.

If a transformer is operated for a short time and then allowed to cool to room temperature before operating again, the temperature rise can be found from Figs. 46 and 47. As an example, suppose that the continuously operated final coil temperature rise is 100 centigrade degrees, the total weight is 5 lb, and operating duty is infrequent periods of 2 hr. From Fig. 46, the transformer has a thermal time constant of 0.85 hr. This corresponds to tc = 1 in Fig. 47. Two hours are therefore 2 0.85 - 2.35 times t and the transformer rises to 90 per cent of final temperature, or a coil temperature rise of 90 centigrade degrees, in 2 hr.

If, on the other hand, the transformer has regular off and on intervals, the average watts dissipated over a long period of time govern the

gives Er/k = (0.00028 X 5.45 X 2.54)/0.11 = 0.34, which is small enough to meet the necessary condition of equation 28.

It will be noticed that equation 28 is a law for cooling, not temperature rise. But if the source of heat is steady (as it nearly is) the equation can be inverted to the form во - 0 for temperature rise, and во becomes the final temperature.

Temperature rise of a typical transformer is shown in Fig. 47, to-

/Total weight in poundsV \ 1.073 /

where во is the final temperature rise in centigrade degrees. This equation is subject to the same approximations as equation 28; test results show that it is most reliable for transformers weighing 20 lb or more, with 55°C temperature rise at 40°C ambient.

temperature rise. A transformer is never so small that it heats up more in the first operating interval than at the end of many intervals.

From equation 30 can be found a relation between weight, losses, and final temperature rise. For, since heat is dissipated at 0.008 watt per sq in./°C rise, and the area As of the equivalent sphere is 47гг/,

Total watts loss Total watts loss

во =-=- (31)

0.008A,5 /Total weight in poundsX

3. RECTIFIER TRANSFORMERS AND REACTORS

Fig. 48. High-vacuum rectifier voltage-current curve.

Rectifiers are used to convert alternating into direct current. The tubes generally have two electrodes, the cathode and the anode. Both high vacuum and gas-filled tubes are used. Sometimes for control purposes the gas-filled tubes have grids, which are discussed in Chapter 8.

A high-vacuum rectifier tube characteristic voltage-current curve is shown in Fig. 48. Current flows only when the anode is positive with respect to the cathode. The voltage on this curve is the internal potential drop in the tube when current is drawn through it. This voltage divided by the current gives effective tube resistance at any point. Tube resistance decreases as current increases, up to the emission limit, where all the electrons available from the cathode are used. Filament voltage governs the emission limit and must be closely controlled. If the filament voltage is too high, the tube life is shortened; if too low, the tube will not deliver rated current at the proper voltage.

Gas-filled rectifier tubes have internal voltage drop which is virtually constant and independent of current. Usually this voltage drop is much lower than that of high vacuum tubes. Consequently, gas-filled tubes are used in high power rectifiers, where high efficiency and 1ол¥ regulation are important. In some rectifiers, silicon or germanium crystals or selenium disks are used as the rectifying elements.

In this chapter, the rectifier circuits are summarized and then rectifier transformers and reactors are discussed.

24. Rectifiers with Reactor-Input Filters. Table VII gives commonly used rectifier circuits, together with current and voltage relations in the associated transformers. This table is based on the use of a reactor-input filter to reduce ripple. The inductance of the choke is assumed to be great enough to keep the output direct current constant. AVith any finite inductance there is always some superposed