The above description and Figure 18 apply to the "steady-state" (stable) operating conditions existing following the starting interval of the vibrator. The vibrator starting characteristics are quite important to the transformer but are often neglected. A serious transient condition may be imposed on the transformer by the vibrator during the first few cycles until the full operating frequency of the vibrator is attained. Such a condition does not exist in AC sine-wave transformers.

Vibrators do not start instantly at normal frequency and time efficiency. The moving parts possess mass and inertia, and a certain length of time is required to accelerate the parts to full amplitude and speed. Thus a transient condition arises. Some vibrator designs are better than others with regard to the rapidity with which they attain normal running characteristics. Even within any one design group, considerable variation in this characteristic exists as the result of required manufacturing tolerances and ever-changing conditions during life.

During the first few cycles of operation following the first energization of the driving coil, the amplitude of the reed is low, the frequency is low, and the balance between the pull and inertia half cycles is often poor with respect to the length of contact-dwell time. The time efficiency of the vibrator during these first cycles is lower than the normal value. As the amplitude of the reed increases these factors improve—with the frequency increasing and the balance and time efficiency improving until normal operation is attained. Some vibrator designs tested at nominal voltage, showed that only 2 to 2 1/2  cycles were required to reach normal operating conditions, while others required up to 7 or 8 cycles. Similar tests made during "life tests" indicate that the starting conditions become worse with age. Again, some designs being better than others in this respect.

The effects of these temporary vibrator characteristics upon the transformer are such that the operation at low frequency causes an increase in the maximum fluxdensity. This is partially counteracted by the lower time efficiency existing during this period. The degree to which one factor offsets the other depends upon the relative decrease in time efficiency with the decrease in effective frequency. Tests have indicated the decrease in time efficiency exceeds the decrease in frequency.

The matter of poor balance in time efficiency between successive half-cycles of operation is much more serious. When a vibrator does not operate in a full wave manner, generally during the starting cycle, it is said to be "single footing." It "buzzes" at low reed amplitude and makes contact only on the pull swing of the reed. This may be caused by several conditions, which are not of immediate concern, but the effect is to impress upon the core of the transformer a polarized magnetizing action which quickly builds the flux-density to a value approaching saturation. This in turn necessitates the supplying of a high magnetization current from the battery which the vibrator contacts must commutate. The result is a rapid deterioration of the contacts and possible voltage-breakdown of the transformer insulation and associated capacitors. This is the extreme condition, and a situation of unbalance falling in between "single footing" and equal balance merely reduces the seriousness of the above effects depending upon the degree of unbalance.

Since the timing capacitor value is selected for best performance of the vibrator-transformer combination under normal running conditions, it will seldom match the combination during these starting cycles. The loading upon the transformer (which includes the timing capacitor) has been observed to have a definite effect upon the ability of some vibrators to start successfully, especially after wear occasioned by age. Under the low-frequency and low-time efficiency condition existing at starting, the value of timing-capacity required to match the existing conditions would need to be much larger than that required for normal running. This would materially reduce the vibrator life and is not recognized as good engineering practice.

Another transient condition occasioned by starting is the effect of residual core magnetism upon the value of magnetization current drawn from the source during the starting cycles. This condition is common to both AC sine-wave transformers and vibrator transformers. It is a well-known fact that the current drawn immediately upon connecting a transformer to the sine-wave power source may have a peak value many times higher than the normal running value, the peak value depending upon the polarity of the residual flux and its magnitude with respect to the initial polarity of the applied voltage when the connection is made.

When the circuit is broken with the AC voltage at the positive peak value, the magnetizing current (and flux wave) lags behind the applied voltage by 90 electrical degrees. The circuit would open with a zero value of flux in the core and no residual magnetism would be present. If the circuit is closed again at the zero point of the positive half-cycle of the voltage wave, the required flux to satisfy the counter e.m.f. induction will have to vary from a zero value to 2Bmax. However, if the steady circuit is broken with the AC voltage at zero value at the finish of the positive half-cycle, the value of the flux in the core would be a positive maximum. The residual magnetism in the usual grades of silicon steel has been given as approximately 80 % of the maximum value existing at the time of removal of the magnetizing force. Under these conditions, if the circuit is again closed with the AC voltage at the zero point of the positive half-cycle, the flux would have to vary from a plus 0.8 to a plus 2.8 Bmax to satisfy the counter e.m.f. induction.

This is obviously a much worse magnetizing condition than the steady-state condition with the flux-density being far above the "knee" of the "B-H" curve and well into the saturation region. Actually, the regulation of the circuit limits the maximum magnetization current to a value considerably below this calculated value. For other combinations of magnetic residual polarity and initial voltage polarity, the value of maximum flux-density and current is lower than the above, the lowest peak value occurring with the maximum residual magnetism at one polarity and the initial voltage at the opposite polarity in the correct phase relationship. Here the flux-density change required is from a minus 0.8 to a positive 1.2 Bmox. Usually quite a few cycles are required before the steady-state condition is reached. AC power sources can readily absorb this temporary overload without damage, and since there is no commutation necessary, the occurrence of this transient condition causes no damage and usually goes unnoticed.

These circumstances can also exist in the operation of vibrator transformers, but the results are far more serious than they are in sine-wave transformers. Figure 19 illustrates the two extremes that could arise in the starting of a vibrator power supply. The heavy solid-line curve represents the steady-state flux-wave, in the same manner as shown in Figure 18 and is again plotted with reference to the effective alternating DC input voltage pulses. For purposes of illustration it is assumed that the time efficiency and frequency remain constant for the starting cycles and are the same values as for the steady-state cycles. While this condition does not actually exist, the assumption is made for clarity. It is also quite possible for the transient transformer condition to last for a few cycles longer than it takes the vibrator to assume a normal running condition. The lower of the two dashed-line curves parallels the solid curve at a value slightly above the latter, and represents the initial condition of maximum opposing residual magnetism (80% of nominal maximum). The upper dashed-line curve again parallels the solid curve, but represents the other extreme of initial residual magnetism, where the polarity of the residual magnetism adds to rather than subtracts from the resultant maximum flux-density.

Because of its mechanical design the vibrator will always start with the initial contact-closure in the direction of the same polarity, although the opening of the battery circuit when stopping may occur on either polarity. This condition, combined with the fact that the vibrator starts with a complete half-cycle every time, reduces the possible combinations of residual polarity and starting polarity to the extent that it is far more probable that a detrimental combination will be encountered with a vibrator transformer than it is with an AC sine-wave transformer. In addition, the high magnetization current must be broken by the vibrator contacts at its peak value, which often is damaging, or even destructive, to the contacts.

The arbitrary values of magnetization currents corresponding to the several starting conditions are also plotted in Figure 19 and are in their proper phase relationship to the corresponding voltage and flux waves. The steady-state condition is also shown. The scale is only relative to show the effect and the spread of actual values would usually be much greater under the conditions described.
Figure 20 is similar to that of Figure 19, except that in this instance the variation in frequency and time efficiency during the starting cycles is considered. This variation was described earlier in this chapter. The input transformer voltage is shown at the bottom of the diagram. It is plotted to show a hypothetical starting condition and is for illustration only. Six cycles are shown, with gradually increasing frequency from the first through the fourth, and with a poor time efficiency and balance condition in the first that improves through the fourth. Cycles five and six are duplicates of the fourth, representing the eventual steady-state condition of the vibrator.

The steady-state magnetic flux-wave necessary to induce the required counter e.m.f. is shown at the right-hand end of the zero line of flux-density. The slope of the vertical portions represents the required "rate of change of flux." Since the number of primary turns and the cross-sectional area of the core remain constant, the rate of change of flux will also remain constant regardless of the position of the flux-wave so long as the input voltage is constant. Therefore, this slope of the curve is used to project a new flux-wave curve which is matched to the transient starting condition just described. This is shown in the upper part of the diagram, where the starting point is with a residual magnetism of a positive 80 % value, the most adverse condition. Under the combination of conditions shown, the maximum flux-density would reach about 435% of the normal maximum during the transient, if no limiting factors intervened. From this maximum the core steel would slowly return to a more or less neutral, or steady-state, magnetic condition. The time interval required is much longer than that required by the vibrator to reach its steady operating state.

A theoretical value of 283,000 lines per square inch would be indicated by 435% of a normal Bma* of 65,000 lines and the corresponding magnetizing current would be ridiculously high. The core steel curves do not extend to such extreme figures, but it is obvious that by estimating an extension of the curves that a magnetizing force of approximately 10,000 ampere-turns per inch would be required; this compares to 4 ampere turns for the normal Bma* of 65,000. The increase, therefore, is roughly 2,500 times. Assuming an average value of 0.5 ampere for the normal condition, this would amount to a value of 1,250 amperes for the peak condition.

It is obvious that it would be impossible to even approach this value of current before the voltage-drop in the resistances of the source and of the primary circuit would equal the source voltage. As the effective voltage applied to the transformer primary is reduced by this voltage-drop, the required counter e.m.f. is reduced and the resultant rate of change of flux and maximum flux-density are also reduced proportionately. This results in a self-limiting condition, which affects the described theoretical graph. It will be necessary to refer to this section at a later point where the phenomenon just outlined has a definite bearing upon the performance of high-voltage input vibrators. It seems pertinent to point out, however, that this characteristic is also important to the success of attaining a good power supply design, and must be taken into account to insure satisfactory results.

Transformer Core Characteristics

Another vibrator transformer characteristic concerns the magnetic core. As a general rule, transformers for use with vibrators have always used the so-called "shell type" of core laminations. These consist of an assembly of "E" and "I" punchings, usually interleaved so that the "I's" are fitted across the open side of the "E's" between the closed sides of other adjacent "E's." Seldom are transformers made with the "core type" of laminations, which are assembled of interleaved "L" shaped units. Other variations of the "shell type" now in use are the "EE" laminations and the "split-wound-loop" type, exemplified by the "Hypersil" design. Figure 21 shows outline drawings of the above types of cores.

The general design practice for small sine-wave power transformers is to use cores having a "stack" or "build" of a sufficient quantity of laminations to result in a square cross-section in the leg over which the windings are placed. This results in an economical use of the copper in the windings and provides a shape of winding form which is better adapted to automatic winding machines than the rectangular shape which would occur with a larger or smaller core "stack." Each size of lamination then receives a nominal power rating of so many watts, and the design usually starts from this point. Most small AC applications are not too greatly limited as to space or to efficiency considerations, and these standardizations in transformer size work out rather well.

In vibrator applications, however, there is usually a very different situation existing. The greatest demand is for minimum size and weight (and, as a corollary, minimum cost), with the best possible efficiency and life. The "power rating" conception of core sizes must be discarded if this is to be accomplished. Quite often it is necessary, or desirable, to design around a core having a radical rectangular cross-section in order to meet some dimensional requirement. Or, in order to reduce the leakage inductance of the unit, the use of a greater amount of iron and fewer turns than would normally be used is justified. Therefore, no fixed rules on core sizes can be given for use in various applications. The effects upon the vibrator performance and life should always be the major consideration. In general, the ideal conditions are obtained when the vibrator transformer is designed so the iron losses equal the copper losses.

Another core characteristic concerns the method of stacking the laminations to produce the desired core thickness. The common method of assembly is the insertion of the "E's" from alternate ends of the coil and after all have been placed, to insert the "I's" in the vacant spaces between the ends of the "E's" so as to complete the magnetic circuit for each lamination through the butt-gap thus formed. The interleaving may be done singly, in groups of two, three, or four, but seldom in more than that number per group. The "I's" are tapped solidly into place and the core wedged, or clamped, to hold it tightly together until after impregnation. Often the clamps are left on the finished transformer.

The inductance of the windings and the necessary magnetization current are affected by the method of interleaving. With an assembly of laminations interleaved singly, the effective magnetic path will have the shortest length because of the reduction in the effective series air-gap in the core; thus, the magnetization current will be reduced to a minimum and the inductance will be made a maximum. The effects of stacking in groups of 2x2 is only slightly different from lxl, while the change is much more pronounced with 3x3, or greater. A butt-joint introduces a definite air-gap into' the magnetic circuit, and a resultant undesirable reduction in inductance. However, under certain unusual circumstances of operation, recent developments show that it is desirable to introduce a controlled small air gap condition. This is done to reduce the effects of steel saturation upon the required value of the timing capacitor when operating the transformer over a range of rather high values of flux-density. This will be covered and explained fully in a later chapter on Timing Capacitors.

Figure 22 is an illustration of the various methods of the interleaving the laminations and showing the resultant flux paths through the joints in the magnetic path. Illustrated are cores alternately interleaved in groups of one by one (1x1), two by two (2x2), three by three (3x3), and five by one (5x1). Regardless of the care exercised in the assembly of the laminations, the "I's" can never be made to join the open ends of the "E's" perfectly, and an air-gap results in the steel path. There are two joints in series in each path (see the dotted lines in Figure 21).

Because these air-gaps offer opposition to the flow of the magnetic flux, the latter will try to diverge and find a parallel path of lower reluctance in which to flow around the gaps. The bridging of the gap by an adjacent lamination furnishes such a parallel path of low reluctance. The air-gap between the parallel faces of the laminations is short when the assembly is clamped, usually being limited by oxide or finishes on the steel and by burrs occurring on the edges as a result of the punching process. The area of this air-gap is that of the parallel faces of the laminations, and obviously is much greater than that of the butt-joint cross-sectional area of the laminations. This combination of factors explains the low reluctance of the parallel path around the gap. Because the presence of surface scale or oxide on the lamination affects the parallel air-gap length, it has been the usual practice to specify that the laminations be cleaned before annealing. This removes the objectionable surface condition and improves the "stacking factor." The "stacking factor" refers to the percentage of actual steel present in a given cross-section of a laminated core to the amount it would contain if the core were solid.

The presence of burrs on the edges of the laminations has the same effect as the scale on the surface and, therefore, is a detriment to the best construction and performance. The burrs also present sharp edges to adjacent laminations which undesirably provides a good electrical contact between the laminations and results in an increase in eddy-current losses. Therefore, the specifications should call for laminations that have been annealed following punching, which (1) reduces the height and sharpness of the burrs; (2) provides a very thin coating of oxide on the lamination surfaces which acts as an electrical insulator, thereby reducing the eddy-currents; (3) returns the magnetic characteristics of the steel to their original condition, thus assuring uniformity in the final assembly.

Good manufacturing practice provides that the lamination punching dies be constructed so that only very small burrs are produced. These dies should be re-sharpened whenever the burrs exceed certain maximum heights. Silicon steels are among the most difficult metals to punch satisfactorily. The dies should be inspected frequently since their life is comparatively short. Steels having higher silicon content are more difficult to punch. The recommendations of the steel manufacturer should be followed closely in the construction of punching dies and in specifying the burr limits.

Figure 22 shows that where there is an adjacent lamination bridging the butt-joint air-gap, the flux divides. Part of the flux crosses the air-gap and the remainder by-passes the air-gap by crossing into the adjacent lamination ahead of the joint and leaving it beyond the joint where the flux returns to its original lamination. Since the adjacent lamination steel is already carrying its share of the flux, this additional by-passing flux crowded into this short portion of the magnetic circuit raises the flux-density considerably, thereby tending to saturate the steel in this section. These factors of air-gaps and spot saturation create intangibles which result in errors in subsequent calculations. About all that can be done in attaining greater accuracy is to control all of the factors as closely as possible in order to make the errors insignificant.

Interleaving the laminations 1x1 will place a bridging lamination on each side of the butt-joint air-gap. Interleaving 2x2 results in a bridging lamination on one side only of each air-gap, but experience has shown that this construction is more practical and gives almost the same results as the 1x1 stacking. However, with an interleaving of 3x3, or more, only the outside butt-joints are directly bridged by adjacent laminations, and the effect of the air-gap becomes much more pronounced in proportion to the number of unbridged joints in the assembly. The introduction of an air-gap requires a considerably higher magnetization current to produce the required flux-density, but straightens out the effective "B-H" curve of the combined steel air-path and overcomes some of the saturation effects. To accomplish this straightening to a complete degree requires a much longer air-gap than occurs under these interleaving methods.

During the recent years a new type of core construction has been developed which is based on the directional orientation of the steel molecules. When silicon steel sheets are rolled to secure the desired thickness, certain magnetic characteristics are imparted to the sheet because of the alignment or orientation of the grain structure during the process. When the "E" laminations are punched from this sheet, part of the magnetic path is along a portion of the steel in the direction of rolling and part of it is across the direction of rolling. It so happens that the permeability of the steel is much higher in the direction of the grain alignment than across this alignment and, therefore, the "E" lamination does not provide maximum permeability, or minimum reluctance, for the entire magnetic flux-path.

The "Hyper-sil" core is based on this orientation principle. The core is made by cutting a long ribbon of steel in the direction of rolling and grain alignment and winding upon a mandrel to form a compact core. The laminated assembly of wound ribbon is then impregnated with a high-temperature binder and baked to bind the laminations together. This core is then removed from the mandrel and cut into two parts, usually two open "C" cores. The faces of the cut sections are then ground smooth and parallel, and the two halves assembled through a pre-wound coil in the usual manner. Straps are fastened around the core, drawn snug and anchored, in a manner that holds parallel faces of the joints tightly together. The effective total air-gap of this arrangement is approximately .001 inches in length.

Because the flux-path is now entirely in the direction of the grain of the metal, the effective permeability of the core is much higher than for the usual laminated core. This means that the magnetization current for a given flux-density is lower. In addition, the losses in the core are reduced for a given flux-density and frequency, over those of the common laminated core, and the method of assembly lends itself very well to the use of very thin material. Therefore, the use of "Hyper-sil" core material would result in a transformer of smaller size than could be obtained with standard "E" and "I" laminations. This material may be used to advantage when size and weight are of prime importance.