Vibrator Power Supply Design - Development of Basic Transformer - I
Development of Basic Transformer - I
Development of Basic Transformer Formula with Design Examples
The procedure for the design of vibrator transformers will require reference to the general information of the preceding chapters and especially to the graphs and data sheets in Chapter VII. For simplification it will be limited initially to an input voltage of 6 volts as obtained from the storage battery of an automobile, since a majority of the applications are for this type of service. This basic information will then be expanded to include other input voltages.
I. Auto Radio Power Units
The 6-volt electrical system of automobiles includes a battery which has considerable reserve capacity, and a charging generator for maintaining the charge in the battery. Therefore, the efficiency of the vibrator system is not too important from the viewpoint of battery drain. The charging system creates the problem of a widely varying input voltage. When the charging system is not operating, the input voltage may be as low as 5.5 volts. When a voltage-regulated generator is charging at a maximum rate under adverse conditions, the input voltage may be as high as 8 volts. The power supply must be designed to operate satisfactorily over this entire range of voltages.
Most power supplies for automobile radio equipment, supply loads of medium to heavy values, from the standpoint of vibrator loading, and thus are quite representative of vibrator supplies in general. When used on 6-volt batteries without chargers, such as for home receivers, portable receivers, etc., they usually supply a much lighter load, and more consideration must be given to overall efficiency and other factors than is the case with automobile units. Therefore, these latter applications will be discussed later.
The two important differences between a sine-wave input voltage and that of the vibrator-input voltage to the transformer are (1), the wave form of the voltage, and (2), the discontinuity of the applied voltage caused by the switching interval required in the vibrator operation. The form factor of a sine-wave is 1.11 while that of the square-topped vibrator wave is approximately 
= time efficiency of the interrupter contacts expressed as a decimal.) Thus, for a time efficiency of 85 %, or .85, the form factor is .922/.85 =1.085. The form factor will differ with other values of wt. This requires a different equation for the calculation of flux-density and other related factors for a vibrator transformer than for a sine-wave transformer. The values of the various voltages are as follows:
The development of the voltage equation for a vibrator transformer is quite similar to that for a sine-wave transformer. The induced voltage is determined by the rate of change of flux-linkages such that
Since the rate of change of flux must be constant or linear to induce a constant opposing voltage and as it has already been shown in the preceding chapter that to make this induced voltage equal to the input voltage, the flux value must change from a minus maximum to a positive maximum, it can then be written
Substituting equation (3) for "t" in equation (2) then
The factor Kc is necessary as there will always be some air space between the laminations used in making up the core. This factor then represents the percent of iron in the core and will depend upon how tight the laminations are compressed. Substituting in equation (4)
Assuming that the operating condition is at no load, in order to simplify the consideration, the battery voltage Ei can be assumed to be equal to the induced voltage ei as the primary IR voltage drop can be considered as being negligible. Then
It must be remembered that in a vibrator transformer the primary is center-tapped and only one-half of the winding is active during each half cycle so that the total primary turns is twice that of N, given above. From the above, the flux-density in lines per square inch can be determined as,
The above formula is approximate but is sufficiently accurate for vibrator transformer work. Experience shows that E2 as determined is always lower than the secondary voltage produced by the actual transformer. This is an advantage as any revision found necessary in the transformer design is in the nature of reducing secondary turns so that it is never necessary to increase the transformer size.
Where a self-rectifying type of vibrator is used, the value of time efficiency (wt) for the rectifier contacts will be lower than that of the interrupter contacts. Therefore, it is necessary to use this value in figuring equation (14). However, if an interrupter type of vibrator is being used, the governing time efficiency will be that of the interrupter contacts. Also, in the latter case, the secondary voltage-drop must include the voltage drop of the rectifier tube in addition to voltage drop of the transformer secondary.
The primary resistance voltage-drop should also include the voltage drop of interrupter contacts which is appreciable at the currents normally handled. This is somewhat variable, more or less unpredictable, and injects an unfavorable factor into the design. Judgment, based upon experience and empirical determinations, must be used in the equations since factual data is not available. Sufficient laboratory tests, involving the use of special instruments, have been concluded to determine the value of this contact-resistance under a given set of conditions. The value of contact resistance existing under operating conditions (dynamic values) are not the same as those measured under static conditions. The static condition refers to contact resistance measurements made when the reed is maintained in a deflected position by the same deflection as attained in operation. Tests have been conducted under dynamic conditions with the contacts carrying an average current of 5.0 amperes, as measured with a DC meter in the battery lead. For these conditions, the average contact-resistance per contact pair for several series of Mallory vibrators are given below:
After the input voltage and vibrator characteristics are known, the design of the transformer consists primarily in determining suitable values for the Number of Primary Turns, Core Area, and Flux Density. Following the determination of these factors, the next step is to determine the required wire sizes, the core size required to contain the necessary copper, and the build necessary to provide the required cross-sectional area, "A."
Primary Turns
The number of primary turns necessary may be determined from formula (9) after the Core Area and the Flux Density have been selected.
In using the above formula the factor E i should represent the highest input voltage to be encountered in the application. Also Nj represents only one-half of the primary as was pointed out previously.
Core Area
The core area is determined by computing the required primary watts and basing the area necessary upon previous experience. However, the following formula may be used as a close approximation:
Flux Density
Since the ideal condition of a linear relationship cannot be economically achieved, the upper limit of flux density must be held to such a value that no undue hardship is imposed upon the vibrator. Originally this upper limit was found to be very satisfactory when set at 65,000 lines per square inch with a 9-volt input. This resulted in a lower limit of 39,700 for 5.5 volts. For "Dynamo" (Allegheny) grade of steel, the respective values of "H" for the above flux densities would be 4.0 and 2.0. Thus "H" increases 2 times for an increase in flux density of 1.64 times.
While transformers designed around the above values of flux density had become more or less a standard of comparison and had performed excellently, the trend was to design smaller and more compact auto receivers. Thus it became necessary to design smaller and lower cost component parts, including the power supply components. At the same time, most of these newer receivers were used on automobiles having voltage-regulated charging systems, which permitted setting the upper limit of operation around 8.0 volts instead of 9.0 volts as had formerly been the case. This, in turn, reduced the spread between low and high-voltage operation compared to the previous condition.
This has resulted in the revision of the maximum flux density at maximum input voltage. Now it has been found possible to set the maximum limit of approximately 65,000 lines per square inch at 8.0 volts input instead of 9.0 volts as formerly used. This actually increases the maximum flux density allowable. Under the former conditions, the flux density at 8.0 volts was approximately 58,000 lines per square inch. Under this revised condition, the values of "H" corresponding to values of "B" of 65,000 and 44,700 are 4.0 and 2.2 respectively for "Dynamo" (Allegheny) grade of steel. In this case "H" (Ampere-turns) increases by 1.82 times where "B" increases by 1.45 times.
Another factor which allowed satisfactory vibrator performance at higher flux densities is that connected with the small shift in vibrator characteristics occurring with a change of input voltage from the low to the high value. With an increase in input voltage, the driving power of the vibrator is increased, the exact amount being determined by the design. This increased driving power causes a small increase in frequency and a small increase in percentage of time efficiency. The increase in frequency will cause a slight decrease in flux density and the increase in percentage of time efficiency will tend to increase the flux density, and in this way the two changes tend to counteract each other. However, the comparatively small percentage increase in time efficiency results in an equal percentage decrease in the "off-contact" time interval. The ratio of the new "off-contact" time interval to the old is, however, much greater than is the ratio of the old time efficiency value to the new. This effect aids in matching the single value of timing capacitor to the two extremes of input voltage operation. This can be illustrated by the following values:
Again, the full effect of this point will be understood after the discussion of timing capacitors in a later chapter.
Wire Size
The wire sizes must also be large enough to prevent the over-heating of the coil and a subsequent failure of insulation through charring. When figuring the heating effect of the current in the windings, it should be remembered that both the primary and the secondary coils are center-tapped, and that each half of each coil only carries current during one-half of each cycle.
If the average battery-lead current is measured with a DC ammeter as Ii, the peak battery-lead current will be:
The heating watts in the primary coil will be:
From (21) it will be seen that in figuring the required wire size to prevent overheating, the value of current to be employed in the calculations is related to the R.M.S. value by the reciprocal of the square-root of 2. For example, if the peak-value of battery current is found to be 1.0 ampere, the value used for calculating is .707 ampere. The high peak charging currents into the secondary filter condenser upset the exact calculations, but the above furnishes a very close approximation sufficient for average purposes.
The same procedure can be followed for determining the copper loss in the secondary.
For vibrators having a high value of time efficiency, only slight errors are introduced by using the average value of battery (or output) current, as measured by a DC ammeter, instead of the R.M.S. value shown above. As the time efficiency is reduced, however, the error becomes appreciable, as is shown in the following table:
In most cases of automobile receivers, as now designed, heating considerations are usually the limiting factors on wire sizes. The large majority of receivers use a single tube output power stage, with the current drain for the set being essentially constant with signal-input variations. A few models use a "push-pull" power output stage, some of which do have variable current drain with signal-input variations.
The cross-sectional area of round copper wire is usually expressed in units known as "circular-mils" (cm). One circular-mil is the area of a wire one mil (.001") in diameter. The area of any round wire in circular-mils is equal to the square of the bare diameter expressed in mils. For an example, #30 B & S Gauge wire is .010", or 10 mils, in diameter, and has an area of 100 cm.
An area of 1000 cm. per ampere has been considered desirable for a conservatively designed transformer. In many instances, considerably higher values have been used, especially when the use of a lower value involves a wire size so small that the difficulty of handling and cost of the wire make its use undesirable and expensive. This usually occurs when sizes from #40 up are involved, and since auto receiver loads seldom involve any such small wire sizes, it is only of academic interest at this moment. A value in the neighborhood of 1000 cm./amp. results in a larger overall size, greater cost, and increased use of materials, and for these reasons is seldom used in the automobile receiver industry.
The average design under present conditions centers around a value of 700 cm./ amp., which has proven to be a rather acceptable compromise between size and cost on the one extreme, and regulation and heating upon the other. Values on either side may be encountered, as other factors affect the exact size of wire that must be used in a given design.
Only under extreme conditions of space or cost requirements will values in the region between 500 and 600 cm./amp. be justified. And under these conditions it is reasonable to expect short transformer life, over-heating, and possibly shortened vibrator life. Where short operating periods of time are involved, or where unusual cooling means are available, the use of such values can also be justified. In test equipment, such as portable "meggers," cable testers, etc., these values would probably be satisfactory, since this sort of apparatus usually operates intermittently.
The above values are considered as starting points for initiating designs, and refer to the currents being handled at the rated input voltage of the unit—in other words, the input and output currents that are to be expected at the nominal input voltage at the transformer center-tap.
As an example, in an application requiring an output current of 50 ma. DC and an input current of 4.0 amperes, the wire sizes would be determined by the following calculations:
One difficulty, encountered in the use of a wire having too small a diameter, is that hot-spots will develop within the body of the winding which will cause rapid deterioration at that point, even though unusual cooling methods are used.
Another factor that affects the choice of wire size is the location of the coil with respect to the other coils. By placing the primary next to the core form (inside of the secondary), one size smaller wire can often be used, and still maintain the coil resistance at approximately the same value, than would be required when the primary is wound over the secondary coil. The current density would naturally increase with such a change, but other factors often make it desirable to take advantage of this arrangement. One of these is the fact that a few additional turns per layer can be used with the smaller wire size, and this is a big advantage in designing the primary, where large wire is necessary and the turns per layer are naturally limited. The secondary coil mean-length-of-turn, of course, is increased by this winding being placed over the primary, but this does not create a difficult situation to control since smaller wire sizes are involved. The increased resistance of this winding can usually be compensated for by a small increase in the number of secondary turns.
Another factor to be considered is that automatic coil-winding machines can, in general, handle wire sizes from #17 and smaller. Number 16 and larger sizes require hand-winding, or at least special handling, which increases the bulk and cost of designs in which these sizes are required. If, by placing the primary next to the core the wire size can be made #17, it is quite probable that the coils can be wound with the automatic machinery, whereas special handling would otherwise be required.
- planright's blog
- 630 reads
Post new comment