The Technician Explains

Radio Record, Volume III, Issue 17, 8 November 1929, Page 27

The Technician Explains

Inductance Coil Design

(By

CATHODE

an 3 THIRD INSTALMENT, BH have now dealt both with the: number of turns required: to obtain a given inductance and with the best or "optimum". diameter of wire for any given broadcast coil. It will be anpropridte now to consider the dimensions and shape likely to produce the best results’ from such a coil under differing circumstances. In Figs 1, 2, and. 3 are given the theoretical high-frequency resistances of the coils previously discussed when wound with the optimum diameter of Wire. It will be remembered that we discussed this question of optimum wire diameter in the issue#of September 27, and that the optimum diameter was there given for a series: of coils for which the required number of turns was given alongside; this previous paper should be referred to in order to gain a complete understanding of the present one, A tremendous amount of information can be gained from these charts by the experienced designer. For the present, however, we are only concerned with a comparison of efficiencies; a little later the charts will be put to a more fitting use in’ assisting in the design of the primary of radio-frequency transformers. .It is for this latter purpose that the high-frequency resistance + for radio-frequency resistance) has been given at two frequencies-one would have sufficed:-for our present purposes. Note, in passing, that the resistance increases with the applied frequency of 1000 kilocycles per second (corresponding to a wavelength of 300: metres) is gubstantially higher than that presented to an applied frequency of 640 kilocycles per second. The reason for this increase in resistance with increasing frequency is, as may have been guessed, that the "skin effect" and "proximity factor’ discussed in the last paper both increase in a most decided fashion with the frequency. In~-dealing with very high frequencies (e.g., short-wave reception) these phenomena -render it very difficult indeed to design coils having any pretentions to. efficiency, the most promising results being obtained with windings of copper ribbon or a gumber of parallel wires flat-wise wound: Both these expedients aim at reducing the "skin effect," the scheme of winding with a number of parallel wires also assisting in reducing the proximity factor by reason of the two outer stands shielding the inner ones from the a.e. field of the adjacent turns. The first of the two points which, for the present, arise out of the resistance charts, is that of the best, or "optimum" ratio of length to diameter. Here it is necessary to explode another little theory which has at various times held sway in quarters where it should _, not have. been entertained for one mo- \ ment. The theory reférred to is one arising out of the fact that, in windIng a wire of given length into a ‘coil of given diameter, the greatest inductance ‘will. be reached when the diameter is 2.46 times the winding length. ‘ From this fact it was injudiciously assumed that a coil fulfilling this ratio

of length to diameter would be of the greatest possible efficiency. Nothing could be further from the case. So far is this*assumption from the truth, ‘indeed, that if wé double the winding if we more than double it, making it equal to the coil diameter, we have still not reached the optimum ratio of length to diameter. As a matter of fact, thére is no constant ratio ‘of length to diameter giving maximum efficiency. So far as the broadcast band is’ concerned, however,

we can gain some idea of what ratio is desirable from. a study of Figs. 1, 2, and 3, From these it will be seen that there is.practically no advantage in increasing the winding length beyond 1 1-8 or 14. times. the coil. diameter. In- practice, the increase: in resistance involved by a reduction of the winding -length- until. it equals. the

diameter is likely to be more than compensated by the less extended magnetic field of the smaller coil and the consequent reduction of, absorption losses occasioned by surrounding apparatus. Thus it would seem that, so far as a single coil is concerned, there is: every reason for so designing it that its winding length is approximately equal to its diameter. If anything, the winding length should be less than the diameter rather than more, as. the increase in resistance will be but slight provided the length is not made less than threequarters the diameter, while the reduction in incidental losses by reason of the smaller field may be substantial. It is not always that a single coil is used for coupling, the principal instances of this form of coupling ~in present-day practice, being a tunedplate or a parallel-feed coupling following a screened-grid valve. Both tuned-plate coupling and parallel feed are too familiar to the- average constructor to merit description here, parallel feed in particular having been treated by the writer in a simple analysis in these columns quite recently ‘(The Efficiency Parallel Feed, "Radio Record," October 4, 1929). When two coupled coils are concerned, as in the case of a radio-frequency transformer following ‘a three or fourelectrode valve, the problem is somewhat complicated by the necessity of securing a high coupling-factor. It would seem, however, that this subject can most appropriately be treated in a future article dealing -generally with the design of the primary. For the present it will be sufficient to mention that the desirability of a high coupling-factor usually refders it desirable to reduce the winding length still further; where efficiency is aimed at, however, it should never be reduced to less than half the diameter.

Optimum Coil Diameter. . HAVING disposed of the ratio of winding length to diameter for the present, we arrive at the next problem, that of the optimum coil diameter in any particular circumstances. There are so many different factors to be considered in making a decision regarding this question that it is impracticable to lay down any set rules, The most that can be done is to indicate the factors which should receive attention, showing their relative effect and perhaps making one or two guiding suggestions; for the rest the individual designer must make his own decision. This much is clear: that, within the limits ordinarily encountered, the greater the coil diameter, the greater the efficiency. It can readily be seen from Figs. 1, 2, and 3, that a-coil having a diameter of 3 inches has a substantially less resistance than one (of the same inductance and shape) ‘having a diameter of 2 inches. Thus. if coil efficiency were the only thing to be considered, there would be little object in contemplating the -usé of coils

of a less diameter than 8 inches, als | though coils of greater diameter might be objected to on account of their bulk. It is, in fact, the case that in a re« ceiver employing only one coil, or, where wide separation can be readily. obtained, two coils, the greatest sensitivity can be secured with coils have ing a diameter of 3 inches or more, provided that no further apparatus or screening is mounted adjacent to the coils to introduce absorption losses; this is at least one thing that can be stated. definitely. It is unfortunately the case that such conditions are sele dom encountered. More often. we wish to mount two or more coils in fairly close proximity without encountering instability, or we are anxious to make our receiver compact, or to screen each stage in a metal shield, or to use screens ed coils, or to do some other thing which, were coils of larger diameter to be used, would result in either exces sive losses or instability. Causes of Instability.. INCE instability is the thing prine cipally to be avoided, it may be dealt with first. In a receiver employing for high-fre« quency amplification either a screens grid valve or a neutralised three-elece trode valve, instability can result only from magnetic coupling between a. coil in the plate circuit of. the amplifying valve and one in its grid circuit-or, what is the same thing,:one in the plate circuit of the preceding valve; the. measure .of this coupling is the mutual induetance of the two coils. In case the term "mutual inducts "ance" should not be a familiar one, it may be explained that where two coils are mounted so, that their magnetie fields interlink, the total inductance of the two coils is not merely the sum of their separate inductances, but is greater or less than this by twice the "mutual inductance," which may be either aiding, that is, adding to the sum of the separate inductances, or opposing, that is, subtracting therefrom. It is this "mutual inductance" forming, as it does, a part of both plate and grid inductances, which is responsible for the feed-back causing instability; therefore, in arranging a 2 high-frequency amplifier without screening, it is necessary to ensure that the mutual inductance is too low to provide adequate feedback to sus~ tain a condition of oscillation, A number of experiments served to show that, even with fairly efficient © broadeast coils, a reduction of the

coupling to the point where the mutual inductance was of the order of microhenry, was sufficient to ensure stability of a two-stage high-frequency amplifier. To attain this low figure with coils having a diameter of three inches ‘entailed a spacing so great as to militate against compactness; coils of diameter 24"inches, however, could fairly readily be arranged to have a mutual inductance of less than one microhenry by spacing them 4a reasonable distance apart and positioning them so that their axes were mutually perpendicular-that is to say, the first coil might be mounted vertically, the second horizontally, and the third also horizontally, but at right angles to the second. With coils having a diameter of 2 inches, it is a comparatively easy matter to reduce the coupling to the on quired point. As an example, Fig. 4 gives in graph from the mutual inductance between two 2-inch coils mounted

vertically and at varying distances one from the other. It will be seen that, mounted with centres 5 inches distant, the coupling was reduced to the required one microhenry. Furthermore, having all coils vertically mounted reduces the possibility of impairing their performance by mounting metallic objects within the intense part of their field; any coll of solenoid form has a comparatively weak field at the side of the eoil, the major field being concentrated at the ends-thus, with horizontallymounted coils, the woes of the designer are added to by the necessity of keeping other apparatus well away from the ends of the coil. Where more than two high-frequen-cy stages are purposed, it becomes impossible to mount the necessary four or more coils with their axes mutually perpendicular, so that we are more or less forced to the use of small diameter coils, It must not be forgotten, however, that unless the dictates of efficiency are departed from by introducing resistance or other losses into ap-~ propriate points in the circuit (e¢g., stabilising grid resistance between the grid of the radio-frequency valve and the preceding radio-frequency transformer, the coupling must be reduced below the 1 microhenry mentioned as being sufficiently low for a two-stage amplifier. The problem may be solved either by increasing the spacing or reducing the dimensions of the coil. In practice, however, increasing the spacing is undesirable, owing to the huge dimensions attained by the finished re-

ceiver, while reducing the coil diameter below '2 inches also reduces its efficiency disproportionately and ‘impairs selectivity; the best compromise is the use of series grid resistances, (To be concluded next week.)