US2246293A - Resistance element - Google Patents

Description

June 17, 1941. COLLAR]: 2,246,293 RESISTANCE ELEMENT Filed May 6, 1939 I NV EN TOR. JOHN C'OLLARD ATTORNEY.

Patented June 17, 1941 2,246,293 RESISTANCE ELEMENT John Collard, Hammersmith, London, England,

assignor to Electric & Musical Industries Limited, Hayes, Middlesex, England, a company of Great Britain Application May 6, 1939, Serial No. 272,189v

In Great Britain May 12, 1938 7 Claims. (Cl. 17844) This invention relates broadly to impedance elements that are required in impedance networks to appear substantially as constant resistances over a range of frequencies from zeroto quite high frequencies, or are such as to -have duced, wherein for the purpose of substantially in an impedance network and for a given purpose the same effect as constant resistances. More particularly, though not exclusively, this invention relates to the use .of such impedances in an attenuator network for use at high frequencies. 2 In the specification of British Patent No.

362,472 an attenuator in the form of an artificial line constructed of vr-type sections isv described suitable for transmitting with modified amplitude a potential from a source to a ,load. As described, the attenuator is suitable for use only at frequencies for which the resistances that form its structure remain pure resistances, and at which the effect of stray capacities and inductances in the attenuator are of negligibly small effect. At frequencies of the order of 1 megacycle per second it is difiicult to obtain res stances suitable for use in such an attenuator, which are both stable and non-inductive. Also at such frequencies the effect of stray capacities in the attenuator is liable to cause the attnua} tion to depart from the intended value.

It is one object of the invention to overcome or reduce these difiiculties and defects in such an attenuator when it is operated at high frequencies.

According to one feature of the invention there is provided an electrical network for use over a wide range of frequencies comprising impedance e ements required to appear resistive over said 5 range to a high degree of accuracy, but possessing inductance and capacity to a degree such that at least at the higher frequencies of said range appreciable inductive and capacitative reactances are introduced, wherein for the purpose eliminating the effect of these reactances the inductance capacity and resistance, L, C and R respectively of said impedance element are so chosen as to satisfy substantially the condition L/C= /2R and a reactive element possessing properties chosen in nature and magnitude with regard to those of said impedance element is so associated with said impedance element that said impedance element appears as a substantially constant resistance throughout said range.

In order that the said invention may be better understood and more readily carried into effect, the same will now be described by way of ex ample with reference to the accompanying drawing, in which:

Figure 1 illustrates a single section of an attenuator such as has been referred to above;

, Figure 2 illustrates-the character of a resistive element in such .an attenuator at high frequencies; Y

Figure 3 shows a circuit in theoretical form that may be applied to overcome the effect of small variations with frequency of the image impedance of an attenuator due to small variations of the impedance ofits resistive elements;

Figure 4 shows a practical elaboration of the circuit illustrated in Figure 3;

Figures 5, 6 and '1 illustrate ways in which by suitably associatin'g'reactive impedances with a resistive element the capacitative and inductive of substantially eliminating the effect of these reactances the inductance and capacity of said elements are so related to the respective resistance of said elements and the inductance and resistance of each element is so proportioned with respect to the same properties in the remainder of said elements that said effect is substantially eliminated.

According to another feature of the invention, there is provided an electrical network for use over a wide range of frequencies comprising an impedance element possessing inductance and capacity to a degree such that at least at the higher frequencies of said range appreciable inductive and capacitative reactances are introproperties'of-the element may be rendered of substantially inappreciable effect;

Figure -8 shows an arrangement by which the stray capacity of leads to a resistive element may be effectively removed, and

Figures 9 and 10 show the equivalent electrical circuits when a source and load respectively are connected to an apparatus such as an attenuator.

In order that the description with respect to the above mentioned drawing may be the better appreciated, the more important features of the type of attenuator described in the aforementioned British patent specification will be first briefly referred to. Such an attenuator may be regarded as a semi-infinite line provided, of course, that the far end of the attenuator is correctly terminated. In use a source (or a load impedance) is connected to the near end and a load impedance (or a source) is connected across the line at some tapping point along its length. By altering the position of this point the attenuation between the source and the load may be changed. ihe tapping point is shifted in finite steps corresponding to whole sections in the attenuator, so that if the attenuation of the separate sections is known changes in attenuation may be measured. The attenuation may, however, only be measured in this way provided either the impedance connected across the near end of theline is equal to the characteristic impedance of the line, or the impedance connected across the line at the tapping point is very high compared with the characteristic impedance of the line; both these conditions, of course, may be satisfied simultaneously. In the following it will be assumed that the attenuator is used in accordance with the foregoing conditions.

Referring to Figure l, the resistance A is the series element and the resistances B, B are the shunt elements of a single 1r section of the attenuator. The impedances connected across the ends of the section indicate that the section is correctly terminated at either end in its characteristic impedance Z0. When this is so a potential difference V1 applied across one end of the section will give rise at the other end to a potential difference BZ AB+ AZ,,+BZ,,

In order that the attenuator should function correctly it is necessary, as is clear from the above equation, that the resistances A and B should behave as pure and constant resistances.

It is possible to achieve this condition even at quite high frequencies by using resistances of the so-called chemical-type in which a thin conducting filmis deposited on a small rod of glass or otherinsulating material, as these have very small inductances' and capacity, but such resistances are subject to random variations which make them unsuitable for use in accurate apparatus. Accordingly it is preferable to employ resistances of the non-inductive wire wound type and provide compensating means to correct for their residual inductance and stray capacity. Such resistances have besides their stability the further advantage overthe chemical type, that they possess a comparatively small temperature coefiicient.

Figure 2 indicates diagrammatically how such a non-inductive wire wound resistance must be regarded at high frequencies of the order of 1 megacycle per second. In series with the resistance R there is the residual inductance L and across these there is the effective stray capacity C. The impedance of this combination is given by the expression If it is arranged that then for frequencies at which w LC is negligibly small compared with unity the expression reduces simply to R. However, the range of values of resistance required in an attenuator of the kind here considered is such as to render it impossible that for every resistance the magnitude of w LC should be small compared with unity.

One manner in which according to the invention this difiiculty is overcome is as follows: If #0 110 is not negligible compared with unity then the above expression reduces not to R, but to the expression and is of theorder of 0.1. To the order of accuracy that is required in measurement, since k =w LC it follows that k is not a negligibly small quantity. However, k will be of the order of 0.001 which may be taken as negligible and so the above expression in k may be written more simply as is, according to the invention, made the same for all resistances in the attenuator. With this arrangement the value of k is identical for all resistances at all frequencies. Even if, therefore, the magnitude of comparatively highpowers of k: is not negligible compared with unity, the attenuator will give the same attenuation as it does at low frequencies where .no complications due to I residual inductance and stray capacity arise. Thus if and -tan 0=lc the impedance of any of the resistance elements in the attenuator can be expressed in the form: RM1 0 so that in terms of V1 the potential difference V2 is given according to the equation:

In this way it will be seen the attenuation is rendered independent offrequency by the fulfilling of two conditions, namely:

(a) That shall have identical values for all resistances;

(b) That with all resistances the value of amazes manner across the resistance until the-correct ratio of I is obtained.

If the method just described is carried into effect it will be appeciated that the characteristic impedance of the attenuator will no longer be simply Z at high frequencies but will be given by Z=ZOM L 0. If therefore the attenuator is being used in the condition where the source connected to the near end of they a tenuator should be substantially matched to the input impedance of the attenuator the potential difference applied across the input ofthe attenuator will be dependent upon the frequency. Thus if a source of internal impedance Z0 and electromotive force e is employed thepotential difference applied to the attenuator-will"begiven by the expression and if the ratio is designated by k then the: impedance of: the device is expressible as which, provided k is negligibly small compared with unity, reduces to It will be seen, therefore, that theiimpedance of the attenuator and the shunting device may be written respectively as:

provided the cubes of the terms in t are neg ligible compared with unity, and accordingly the impedance of the combination ZZ Z Z may be written RZ R+Zn+kZoki By making hy li k Z the impedance of the combination, therefore, becomes to a highdegree of accuracy simply but by making R sufficiently large the apparent impedance of the attenuator may be made to approach as nearly to Z0 as desired. Alternatively, of course, the source impedance may be reduced from Z0 to or the attenuator may be designed in the first place to have a rather higher impedance, so that when shunted by the device the resultant impedance is substantially that of the source.

In carrying the above method for correcting for the impedance variation of the attenuator into effect, it is preferable to adopt a slight modification, on account of the fact that the resistance R in the shunting device shown in Figure 3, requires to be a pure resistance and to be independent of frequency. This modification is indicated in the arrangement of Figure 4 which is identical with that of Figure 3, except that the pure resistance R is replaced by the equivalent circuit, namely, a resistance R. in series with a residual inductance L, these being shunted by a capacity C, by which a typical non-inductive resistance must be represented at high frequencies. The analysis for this case is similar to that already given except that R must be replaced by the expression:

1 k3 where and provided that The impedance of the whole device is thereby modified to but this may be written with suflicient accuracy i 1+ r he modification, therefore, amounts to replacthere is now obtained the relation and from this kz'may be determined since k1,

k3,Rand Z are known quantities. V

This device is used to give the attenuator a constant impedance Z0 at-the point at which it is tapped across, into which the source of impedance Z is to work; if, therefore, the point at which the source is tapped across the attenuator is varied, the point at which the'correcting device is tapped across must be correspondingly altered so that the device is always across the attenuator at the same point as the source.

Another method in accordance with the invention by which measurements with the attenuator may be rendered independent offrequency at high frequencies and thereby reliable at 'such frequencies, will now be described. Broadly speaking, this method comprises adding reactive impedances to the resistance elements in the attenuator in such a way that these elements are made to appear substantially pure constant resistances.

- R i asbefore, but in deriving whichequation it has been supposed that 1 1 3 I q The impedance Z2 of;theremaining portion is expressible simply according to Z2=R(1+7'k) and it will be clear if k and k are very small compared with unity, then the total impedance Z1+Zz is equal merely to 2R. It will be appreciated that this method is an improvement on the simple method of connecting a capacity 0 across the whole resistance R and arranging that t- V since with this procedure the impedance depends mostly on k through a square term, but in the improved method the impedance depends on k mostly through a cubic term. and is therefore, less susceptible to changes in frequency.

An even better method can be obtained by means of the arrangement shown in Figure 6. In this case as in the previous case there is a resistance R in series with a residual inductance L, across both of these in series there being connected a capacity C, but instead of a further resistance R and inductance L being connected in series, there is connected a parallel combination of an inductance L and a capacity 0. As before it is arranged that I and with this restriction and writing the impedance of the whole arrangement can be expressed as Here be seen that the least power of k involvedis as high as the fourth power, whereasin the previous case the least power was onlythe third power V. L

It may e pointed out that the device shown in Figure 3' and described above, may also be used in renderingindividual resistance elements substantially independent of frequency. a v

This may be done by connecting it in" shunt with any given resistance.

To. any of the compensating arrangements that have been described above it will be realized that there are of course, equivalents of an inverse character. Thus it is well known that two networks may be constructed having impedances Z1 and'Zz'which satisfy such a relation as Z1Z2 =Zo Where Z0 is a constant, provided the individual elements of the networks are arranged and related in certain definite ways. Such networks are said to be inverse to each other withrespect to Z and. as an example there is shown in Figure '7 an arrangement which is such an inverse of that illustrated in-Figure 6. -In this arrangement the series portion in Figure 6 comprising the inductance L and the capacity C in parallel has been transformed to a parallel branch in Figure 7, comprising the capacity in parallel. Thus each group of elements in one arrangement has its inverse in the other, the inverses being taken with respect to R, so that the impedances'of such mutually inverse groups satisfy conditions of-the form Z11 Z21=R and in particular if Z1, Z2 signify the impedances of the whole networks of Figures 6 and '7 respectively, these will satisfy Z1Z2=R2. Since, however, Z1 is a very close approximation to the constant value R it follows that Z2 is an equally close approximation to the same value. In the same kind of way the inverses to the other arrangements described may beconstructed.

It wi1l','of course; be appreciated in all the above cases, wherever'a capacity is shown across an element, that this capacity may be partly or wholly constituted by the self capacity of the element.

When the method of rendering each element in the attenuator substantially a constant resistance is adopted,'it is necessary to take precautions vagainst the efiect of the stray capacity of leads connected to the elements. A way of eliminating the effect of such stray capacity is indicated in the arrangement shown in Figure 8.

B1 and R2 in this figure are two identical resistances of magnitude R which have been made substantially independent of frequency by any of the methods described above. C1 and C2 represent stray capacities, and these by the suitable addition of capacity are adjusted to the same value C. R1 and R2 are joined together directly at one end and indirectly through the inductance L at the other end. The method then consists in so choosing the magnitude of the inductance L that the efiects of the capacities C1 and C2 are eliminated to a substantial which if k may be regarded as a negligibly small quantity, becomes simply R.

In the case of an attenuator in which an arm moves over a series of studs in order to make contact with any required point on the attenuator, the capacity of this arm to earth must be taken into account since otherwise it will cause the attenuation to vary with frequency. The problem is different from that of other stray capacitors in the attenuator in that the stray capacity of the arm moves from point to point along the attenuator according to the position of the arm. Furthermore, the cable, lead or conductor used to connect the attenuator to the source will have a certain inductance and capacity and it is possible at some frequencies that the inductance of the cable may resonate with the capacity of the attenuator and so cause errors. This may be avoided in the manner indicated in Figure 9.

In this figure there is shown a source of electromotive force 6 of internal impedance Zu which is equal to the impedance of the attenuator, and this source is connected to the attenuator through a cable of inductance L. The capacity C shown in the figure represents the capacity of the cable together with that of the moving arm of the attenuator. If the effects of the inductance L and capacity C were absent the potential difference V developed across the attenuator would be /26. In actual fact V is given by It may, however, be reduced in value to /28, provided a term in a may be neglected, if the length of the cable is so arranged that In this way errors due to the stray capacity of the moving arm and to the inductance of the cable may be subtantially removed. v

A similar difliculty arises in connecting to the attenuator the load impedance, which may be a valve voltmeter. In this case the circuit appears as shown in Figure 10. Z0 represents the output impedance of the attenuator and this is in series with the effective generator of electromotive force e. C represents the stray capacity of the attenuator arm and the capacity of the valve voltmeter whose input impedance is mainly capacitative, while L is in the inductance of the cable connecting the valve voltmeter to the attenuator. The capacity of the moving arm and of the voltmeter are regarded as being located at one point as the length of the cable is short.

Owing to the effect of the inductance L and the capacity C the potential difference across the valve voltmeter is not equal to e, but given y (It-(c +jZwC By arranging, however, that L 1 c i and neglecting as before the term in at, V reduces to e, so that by choosing the correct length of cable to satisfy this equation the effects of the inductance of the cable and of the capacity of the valve voltmeter may be made to cancel out.

It will be appreciated that although the methods described in this specification have been with special reference to an attenuator for high frequencies particularly to an attenuator as described in the specification of British Patent No. 362,472, they are not of such limited application, and may clearly be applied to other pieces of apparatus, for example, a resistance box, which require resistances that are non-inductive to a high degree at high frequencies.

I claim:

1. An electrical network comprising a plurality of resistances, each having distributed capacity and distributed inductance, and means to make the ratio of inductance to resistance of each resistance equal to a single predetermined value and for making the ratio of inductance to capacity proportional to the second power of a corresponding resistance, the proportionality factor being identical for all resistances.

2. An electrical network comprising a plurality of resistances, each having distributed capacity and distributed inductance, and means to make the ratio of inductance to resistance of each resistance equal to a single predetermined value and for making the ratio of inductance to capacity equal to the second power of the corresponding resistance.

3. An electrical network comprising a plurality of resistances, each having distributed capacity and distributed inductance, and means to make the ratio of inductance to resistance of each resistance equal to a single predetermined value and for making the ratio of inductance to capacity equal to one-half of the second power of the corresponding resistance.

4. An electrical attenuating network comprising a plurality of resistances associated with capacity and inductance, in which the ratio of in ductance to its associated resistance for all resistances is substantially identical and in which the ratio of the inductance to capacity associated with each resistance is equal to the square of the associated resistance.

5. An electrical attenuating network comprising a plurality of resistances associated with capacity and inductance, in which the ratio of inductance to its associated resistance for all resistances is substantially identical and in which the ratio of the inductance to capacity associ--' ated with each resistance is proportional to the second power of a corresponding resistance, the proportionality factor being substantially identical for all resistances. v V

6. An electrical attenuating network comprising a plurality of resistances associated with capacity and inductance, in which the ratio of inductance to its associated resistance for all resistances is substantially identical and .in which the ratio of the inductance to capacity associated with each resistance is equal to ,onei half of the square of the associated resistance..-

7. In an attenuator having a plurality of resistances, each resistance having associated therewith capacity and inductance, the method of providing a substantially pure resistive eat-H proportionality factor being identical for all re-.

sistances. :V

JOHN COLLARD.

Images