The Technician Explains

Radio Record, Volume III, Issue 6, 23 August 1929, Page 30

The Technician Explains

Design of Inductance Coils |

By

CATHODE

We commence this week a section which will be conducted by "Cathode" for the more advanced. While attacking radio from its fundamentals, the articles are yet simple and readily understandable. They are drawn up for the reader who wishes to secure a scientific knowledge of radio.

HH three questions which usually exercise the mind of one who essays to design a coil are as follows: (1)’ What inductance will be required? (2) How many turns on:a former of given diameter will be necessary to provide this inductance? (3) What gauge of wire will produce the most efficient coil? In addition, definite information regarding the high-frequency resistance of different coils will be useful, not only as a basis of comparison, but also at a later stage when the problem of designing a primary winding to complete ‘an intervalve coupling transformer ‘ comes up for solution. It will be seen that all these matters, together with certain pertinent incidentals, are treated in some detail. Firstly, what inductance is required? It is well known that a "coil" with its associated tuning condenser and incidental capacities is a resonant circuit; that is to say, it will respond more readily, or present a greater impedence (according as it is a. series or parallel circuit) to an alternating or high-frequency currént having a particular frequency to which it is said to be -tuned. The phenomenon of resonance is utilised in a radio receiver to differentiate between, signals of the desired frequency (or wavelength) to which the system is "tuned’ to resonance and therefore responsive, and the host of signals or other frequencies which have —

but a small, in most cases a negligible, effect on the tuned system. It will be clear that the frequency or wavelength to which the system will respond may be varied by alteration of either the inductance or the capacity of the system. The variometer which was popular for tuning some years ugo. and is still sometimes used in crystal sets is an example of a variable inductance; the modern tendency, however, is towards the use of a fixed inductance and a variable capacity or condenser, and the mechanical conattained a high standard of precision. The -frequency or wavelength to which a combination of inductance and capacity is resonant may be calculated from the equation W = 1884.96 VY LO where W is the wavelength in metres, L.the inductance in microhenries, and C the capacity in microfarads. Normally, however, the designer is already

aware of the wavelength to which the system is desired to respond and of the approximate value of the capacity in circuit; the unknowr quantity is the inductance. The equation must therefore be restated in the form | w2 3,553,225 &* © the symbols having the same signifieance as before. The determination of the required inductance now presents little difficulty. Assume that it is desired to

tune: over the broadcast band. (say, 250 metres to 550 metres) using a variable condenser of maximum capacity .00035 mfd. Then, solving for the minimum inductance which will, in combination with the maximum capacity of the condenser, tune to 550 meties, the following result is arrived at: WwW L= 8,553,225 kK O 5502 3,553,225 x .00035 802500 . = == 243 microh. 1248.62875 Solving next for the muximum inductance which will permit tuning

down to 250 metres (it is unsafe to assume that the residual capacity will be less than about .00005 mfd., while it may easily be more) with the variable condenser "all out" the following is the result: , 2502 L= 3,553,225 .00005 | 62500 as == 852 microh, 177.66 It is evident that a variable condenser of maximum capacity .00035 mfd, will cover the required range of wavelengths in combination with a fixed inductance having a salue anywhere between 248 microhenries and 552 microhenries; a value of about 280 microhenries would be very suitable. It is equally evident that if a variable condenser having. too small a maximum capacity were chosen, it would be impossible to cover the required band. At first sight there might seem to be no temptation | to’ use a condenser of small maxi .um capacity and the high inductance necessitated thereby. When

it is remembered, however, that the maximum amplification obtainable from a high-frequency stage depends on the magnitude of the factor . CR (where. R is the effective series high-frequency resistance of the coil in ohms), it will be seen that, as regards amplification, there is every reason for increasing the inductance-L (and reducing the capacity C correspondizg« ly), provided the. resistance is pot unduly increased as a result. ‘ Thus the real limit to increasing the ratio of inductance to capacity is imposed by the necessity of covering a given. band, although some designers do not go as far in the direction of in-

creasing this.ratio as they readily could, preferring, rather foolishly, in the writer's opinion, to secure the Slightly enhanced selectivity to be gained from 4 preponderance of capacity. However, it will be séén that in the charts provided for simplifying design, everyone has been ¢ateréd for; the high-capacity enthusiast can use his beloved .0005 mfd. condenser with an inductance of 200 microhenries, at the other extreme, design data is provided for 340-mh. coils for usé with .00025 condensers, while a compromise may be effected with either a 280 mh. coil and 00085 condenser, or a 820 mh. coil and 0003 mfd, condenser. , How Many Turns? AVING answered thé first of the three questions propounded ay an introduction to this paper, it is now nedbssary to face the second-"How

. many turns?’ ‘The~inductance of a single layer solenoid (which is the only type of coil proposed to be dealt with) may be calculated from Nagaoka’s formula, usually expressed in the forni 987 X LX D2 xX N2xX EK Lex .; — microhenries ~ 1000 , where L is the length of the winding in ce etres, D the diameter of the coil*in centimetres, N the number of turns per centimetre, and K a_ constant depending on the ratio of diameter to winding letigth; this constaiit is obtained from a series of tables. Mathematicians will appreciate that this formula lends itself to simplification, and it may, in fact, be expressed in the form 7 $ N2D Le +~--_-_ microhenries 1900 whére 8 is a shape factor depending 6n thé ratio existing between the "‘Yength of the winding (ie. the length ot the portion of the eoil former covered by the winding), and its diameter; knowing this ratio, the shape factor S may be read off from Chart 1. For example, take a coil which covers 2 inches on an ebonite tube of 4 inches

diameter; the ratio length to diameter is then 0.5, and reference to the chart: shows the value of S corresponding to this:ratio to be 10.2. D is the diameter in centimetres, arid N the total number of turns, Since our aim is to find the number of turns to arrive at a given inductance, this formula also requires restating, If it is put in the form ‘10001 N=y SD it. will answer our requirements. It is recognised thdt not everyone is prepared to make even these humble a

Chart 1. excursions into the realm of mathetnatics. Consequently, while for the gake of completeness, the formulae have been quoted anid -explained, the | data required for winding coils to the four inductances previously quoted as being suitable for covering the broadcast band with various values. of, variablé condensefs has -been collated in the form of charts which are almost self-explanatory. ° Thtis, suppose it is désired to wind a 200 mierohenry coil ona 3-inch. diameter former, the winding to cover 2 inchés of the length of thé former, reference is made to the: appropriate chart, which is in this casé No, 2. Along the bottom line of the chart various winding lengths are marked off. A vertical line is drawn upwards from the point marked "2in." until the curve labelled "diameter 3 inches" is encountered. From the point of intersection between the vertical line and the ctirve, a horizontal line is drawn to the left until it reachés the vertical line miarked "turtis," which is appropriately subdivided into tens, ‘The number of turns to reach the required inductance is then simply read off. In the instance in question, somie 54 turns would: be the réquisite number. The point to notice is that the number of turns required to reach a given inductance depends not only on the diameter of the coil, but on the winding length, also; the charts eliminate all calculation if only these two things aré ‘known. As a final word, it may be well to point out that, if the coll is to be

close-wound, the gatige of wire (and_ the covering) must be so chosén that the number of turns which can be accommodated in an inch is such that the total turns will approximately fill the allotted space. ‘Thus, in the example quoted, a type of wire which would wind approximately 27 turns to the inch would be necessary, a wire table disclosing that 22 S.W.G. doulfe cotton-covered fills this requirement, The next article in this series will deal with the diameter or gauge of wire necessary to produce the most efficient coil of any given dimensions.