GB1579743A

GB1579743A - Measurment of electric currents

Info

Publication number: GB1579743A
Application number: GB353077A
Authority: GB
Original assignee: Individual
Current assignee: Individual
Priority date: 1978-01-30
Filing date: 1978-01-30
Publication date: 1980-11-26

Description

(54) MEASUREMENT OF ELECTRIC CURRENTS (71) I, BASIL LAGO, a British Subject of 35 Doxey Cresent, Doxey, Stafford, ST16 1ED, do hereby declare the invention, for which I pray that a patent may be granted to me, and the method by which it is to be performed, to be particularly described in and by the following statement: The present invention relates to measurement of electric currents, and is especially applicable to measurement of large varying or transient currents or electric current surges in high power low impedance systems such as electrical power transmission systems, for example, which are subject to heavy surge currents.

In high impedence low power systems the measurement of transient currents presents little difficulty since it is usually possible to introduce a measuring resistance of fairly high value arranged as a shunt constituting a resistive transducer providing a measurable output voltage in an associated measuring loop circuit, and the currents are small enough to make the rate of change of flux through the loop of the measuring circuit negligible except at very high frequencies. In high power low impedance systems the problem is much more severe.

Any measuring resistance element introduced into the power circuit must have a very small value and the effect of varying flux through the measuring circuit loop must be kept as small as possible by careful positioning of the measuring leads. For very heavy surge currents the mechanical design must also take account of the large forces generated, which together with a virtually instantaneous temperature rise can cause severe distortion of the resistance element.

It has been known to eliminate the problem of flux through the measuring circuit loop by using a shunt constituting a resistive transducer having a tubular measuring resistance element with measuring leads connected to the inside surface where there is no magnetic field. This arrangement is a considerable improvement on bifilar and similar constructions but the response for transient or varying currents is still not perfect due primarily to the skin effect in the conductor which affects the pattern of current density distribution and causes unacceptable errors as the frequencies involved become higher. Starting from zero, current flows initially in the outer skin of the tubular resistance element and as it builds up, it diffuses relatively slowly through the tube wall resulting in a time delay in the response represented by the measurable output voltage provided by the measuring leads, this output voltage being derived, in this arrangement, only from the electric field at the inside surface of the tube. This delay is proportional to the conductivity and permeability of the tube material and to the square of its thickness. Thus, for a good response for a rapid variation in total current using the above arrangement a very thin tube of high resistivity, non-ferrous metal is required. Such thin tubes may require large radii to achieve the necessary current-carrying capacity. They are therefore mechanically weak and often inconveniently bulky.

In order to obtain improved response characteristics with such tubular shunts, it has previously been suggested (Lago and Eatock, Proc. IEE, Vol. 114, No.9, Sept. 1967) that whilst a portion of the measuring lead should be along the inside surface of a thin-walled tubular resistance element, another portion could advantageously lie along the exterior surface thereby providing some compensation for the skin effect. It has also been suggested (R. Malewski, Rev. Sci. Instr. 39,90 (1968)) that a tubular resistance element of a shunt might be constructed of layers of foil and that an axially-extending measuring lead could advantageously be embedded at a specific intermediate level or depth within the tube wall built up by the foil layers. Neither of these proposals, however, are entirely satisfactory for overcoming the problem sufficiently to meet requirements which can arise in practice.

In one broad aspect, the present invention provides a device for measuring a variable electric current comprising a current conductor having a conductive measuring lead which provides a measuring loop adapted to yield an output voltage between output terminal ends representative of total current passing through a measuring zone of said conductor along flow paths of given configuration distributed, throughout the thickness of the conductor within said measuring zone, at successive levels or depths relative to an outer boundary surface, said measuring lead following a predetermined path such that said output voltage is derived from the electric field at a multiplicity of different levels or depths throughout the thickness of the conductor and is substantially independent of variations in the distribution pattern of current density amongst said flow paths at least throughout a given operational frequency range.

From another broad aspect, the invention also provides a method of measuring a variable electric current passing through a measuring zone of a current conductor along flow paths of given configuration distributed, throughout its thickness, at successive levels or depths relative to an outer boundary surface, said method comprising embedding within the measuring zone of the conductor a measuring lead which is arranged to follow a predetermined path such that it provides a measuring loop adapted to yield an output voltage, between output terminal ends, which is derived from the electric field at a multiplicity of different levels or depths throughout the thickness of the conductor and is substantially independent of variations in the distribution pattern of current density amongst said flow paths, said output voltage providing a measure of the total current passing through said measuring zone.

In preferred embodiments of the invention, the current conductor constitutes the resistance element of a shunt type resistive transducer and has a cylindrical profile. It may, for example, be a cylindrical tube or rod arranged so that all the current to be measured flows axially, and the measuring lead for providing the output voltage representative of the total current is arranged to extend through the wall of the tube or radial thickness of the rod following a predetermined path in an axial plane throughout a length of the tube which represents the measuring zone, the path being such that the output voltage is derived from the axial electric field at a multiplicity of levels thoughout the thickness of the tube wall within the measuring zone and is substantially independent of the current density distribution pattern.

The invention will be more particularly described with reference to the accompanying drawings in which: Figure I is an explanatory diagram relating to basic theoretical principles; Figure 2a and 2b are diagrams showing transverse and longitudinal sectional views respectively of an experimental co-axial shunt type resistive transducer incorporating a slotted tubular resistance element; Figures 3a, 3b and 3c are diagrams showing different possible measuring lead arrangements for a slotted tubular resistance element of the kind illustrated in Figures 2a and 2b; Figure 4 is a diagram of a double tube form of shunt type resistance element; Figure Sa is a longitudinal sectional view on line Va - Va of Figure 5b depicting the structural design of a solid rod type shunt; Figure Sb is a cross-sectional view on line Vb - Vh of Figure Sa; Figures 5c and Sd are diagrams showing different output arrangements, and Figure 6 is an exploded view showing the device of Figure Sa in a dismantled condition; Figure 7 is a sectional diagram of a basic disc shunt arrangement; Figure 8 is an explanatory diagram relating to a disc shunt; and Figures 9a and 9b are diagrammatic views of a segmented form of disc shunt in accordance with the invention.

Ideally, the measuring lead will be embedded in the material of the tube or rod and its path will follow a parabolic curve defined only by the dimensional parameters of the tube or rod and of the measuring zone. This is explained below with reference to the explanatory diagram of Figure 1 of the drawings which shows a partial axial section through a portion of a cylindrical tube 10.

Refcrring to Figure 1, u represents any path of a measuring lead extending through the thickness of the tube wall between the points I and 171 which are spaced apart axially by the distance s, the length of the measuring zone. The tube has an external radius a and an internal radius h, and points along the measuring path are given by the co-ordinates r, z.

The output voltage v between the ends of this measuring path is obtained bv evaluating the line integral

along this path. Since the electric field is entirely in the axial direction,

where J is the current density and o is the conductivity, and were the latter integral is taken along the path u.

Also, the total current is given by

Then, subject to the conditions that v a i and r = b at z = 0 ; r = a at z = s Integrating gives z= s ( r2 ~ b2) a2b2 which is the equation of the parabola.

For this measuring path, the output voltage will be v = R' or where Ro (the dc resistance of the measuring length) = s Cr rr (a2-b2) This result is independent of the way in which the current is distributed over the cross-section, provided only that the flow is parallel to the tube axis, and has the following implications: (i) If embedding of the measuring lead can be achieved, the need for thin tubes to give short response times no longer exists; (ii) The physical size of a resistive transducer shunt for a given current rating can be much reduced and its mechanical strength greatly increased enabling it to withstand the electromagnetic forces produced by heavy currents, and moreover the resistance element can be in the form of a solid rod which can be regarded as being a tube with an internal radius substantially equal to zero; and (iii) For fast current pulses, electrical connection of the measuring lead to the resistance element is unnecessary.

Feature (iii) can be appreciated by considering again the measuring path u in Figure 1 and taking the line integral round the path Imnl.

Now

the output voltage from a lead embedded along u.

Therefore v-E,,s = -dIdt.

For thick tubes and rapidly varying currents, the electric field at the inner surface E0 will be extremely small because of skin effect so that v = da/dt This means that v can be measured by a loop of wire around the path Imnl without any metallic contact with the tube. Moreover the output voltage could be increased by having a number of turns of wire round the measuring path instead of just one turn. This could be a very useful technique in some cases in view of the very small resistance which the shunt will have due to its large cross-sectional arca.

If the tube is not too thick (e.g. b/a 0.9) the parabolic path derived above may be approximated by the straight line since (ajbj) o(abb)(iti+*bb)=a(arSb) \al - bj \a - b/ \ b+ b I \a-b/ if b a r a a and (a - b) is small.

In practicc, following the conventional construction of co-axial shunt type resistive transduccrs, the cylindrical tubular or solid resistance element will provide a terminal at one end and the other end will be connected through a metal end cap to one end of a co-axially arranged outer conducting tube of considerably greater diameter of which the opposite free end provides the second terminal of the device for connection in the external circuit, and the output terminal ends of the measuring loop provided by the measuring lead will be brought out at one end along the central axis for connection to a voltage sensitive instrument such as an oscilloscope.

In a preferred construction. using for the resistance element a thick tube, that is, a tube having a ratio of inside diameter to outside diameter less than 0.9, or a solid cylindrical rod, the measuring lead is embedded directly therein by first dividing the tube or rod into two halves along an axial plane and forming in the planar facc of one of these halves a shallow groove of the required parabolic profile into which a length of the measuring lead is inserted before accurately fitting the two halves together again.

Alternatively, especially with a tubular resistance element, the measuring lead may be embedded by being inserted into a narrow axial slot through the tube wall wherein it is fixed so as to follow at least approximately the required ideal parabolic path, and this technique may be preferred if it is particularly desired to use a thin walled tube such that the ideal parabolic path approximates to a straight line.

By way of example of this technique, a purely experimental construction for investigating the behaviour is illustrated in section in the diagrams of Figures 2a and 2b wherein a measuring lead 14 on a carricr slip 16 is placed within a longitudinal slot 18 in the wall 12' of a tubular resistance element 10' co-axially assembled within an outer return tube 20 by mcans of a welded end piece 22 and by internal collars 24, 24, of insulating material. The carricr strip 16 is mounted as indicated by a jig assembly 26 having adjustable fixing legs 28 bearing against the wall of the tubular element 10', and a series of locating holes 30 enables the carricr with the measuring lead to be positionally adjusted to provide different arrangements. The diagrams 3a, 3b and 3c of the drawings show different arrangements of the positionally adjustable measuring lead used during the investigation. Figure 3a shows the measuring lead 14 arranged parallel to the axis as for obtaining output voltage measurements from different levels in the slot ]8 in the tube wall whereas Figure 3b shows a diagonal arrangement of the measuring lead. Figure 3e is similar to Figure 3b but in this case there is no electrical connection from the measuring lead to the resistance element tube 10'. Although rather a crude device. experimental results using a ramp current input for test purposes confirmed that. for the diagonally-disposed path of the measuring lead in the slot, a very satisfactory response with a very small time delay due to skin effect could be obtained in conformity with theoretical predictions, and demonstrated that for fast current pulses (e.g. less than 801( sec) the electrically isolated measuring loop arrangement of Figure 3c was also quite satisfactory.

in a further techniquc. a tubular resistance element may be built up in layers by a number of thin tubes of successively larger diameters telescopically fitted co-axially one within another, small holes being drillcd through the walls of these tubes before assembly so as to provide aftcr assembly a path for the measuring lead between the exterior and interior surfaces which approximates sufficiently to the ideal parabolic path as to give satisfactory results within a given operational frequency range. This path, approximating to the ideal parabolic path, may have a somewhat stepped configuration, and in the simplest example of this technique, as indicated schematically in the illustrative diagram of Figure 4 of the drawings, the tubular resistance elements would comprise just two tubes, an inner tube 10a and an outer tube 10b with the measuring lead 14a following a path having a section S3 along the exterior surface of the outer tube, a section S1 along the interior surface of the inner tube, and an intermediate section S2 sandwiched between the two tubes to give a total measuring zone length S.

As mentioned above, however, the use. of a relatively thick-walled tube or solid cylindrical rod is preferred, this facilitating direct embedding therein of the measuring lead along a curved path conforming closely with the ideal parabolic path as well as providing, as compared with conventional co-axial shunts, a high mechanical strength and high current-carrying capacity within relatively compact dimensions.

By way of example, therefore, the construction and testing of a solid rod shunt actually made for experimental purposes will now be described in more detail with reference to Figures 5a, b, c, d, and 6 of the drawings.

Resistance alloys are available in square bars (approximately 2" x 2") and a nickel-copper alloy was chosen. The square bar was cut into two parts 40a, 40b, and the surfaces of the cut were then ground to give a very flat and smooth finish. The two halves 40a, 40b, were then clamped together and turned to produce a split circular rod 40 with tapered ends, giving a "lead-in" for the current and ensuring virtually perfect axial current flow over the cylindrical portion. A parabolic groove 42 for the measuring lead was then milled in each of the ground surfaces. This was carried out on a milling machine controlled from punched tape so that the parabola, actually approximated by a large number of straight lines, conformed to the curve computed from the preceding equation.

Two different output arrangements were provided as shown in Figures Sc and 5d. In the first (Figure Sc) insulated wires 44a, 44b, of the measuring loop circuit were soldered to the two ends of one of the parabolic grooves 42; and in the second arrangement (Figure Sd), a complete loop of wire 44' was positioned in the other parabolic groove 42. The output wires were brought out through a groove 46 machined along the rod axis. The two output systems could be used simultaneously, enabling their output voltages to be compared on a double-beam oscilloscope.

The rod 40 was assembled within an outer coaxial return tube 48 by end caps 50 of which that at the current input end was fitted with an insulating bush 52.

The dimensions and parameters of the solid rod shunt were as follows: a = radius of resistance rod = 22.5 mm s = measuring length = 250 mm R = resistance to steady current flow of the measuring length s = 78 x 10-6ohm Cr = conductivity of resistance-rod = 2.02 > c 106s/m material = s/na2R = 2.02 x 106s/m Ii = permeability of rod material = 11O = 4 X 10-7H/m k = time scaling factor = ollOa2 = 1290 x l0-6sec T = response delay for a measuring lead embedded along the axis of the rod = o > Oa2/8= 161 x l0-6sec The alloy was approximately 56% copper, 44% nickel and was non-magnetic. The manufacturer's figure for the temperature coefficient was .00004/"C.

Upon measuring the voltage output responses to damped current discharges for a range of different frequencies, using measuring leads electrically connected to the rod resistance element, it was found that in all cases the peak values of the current substantially coincided with the instants of zero rate of change of the current indicating a near perfect response up to a frequency of 50 KHZ. Above this frequency, a slight response delay was found e.g. of the order of 0.5cm sec at 55 KHz, but this probably arose from the removal of the conductor material in excavating the grooves to accommodate the measuring lead, so that a smaller groove size should further improve the frequency response. And, using the electrically isolated measuring loop arrangement, the results for frequencies above about 25 KHz were virtually identical with those for the electrically connected measuring loop arrangement.

It will thus be appreciated that co-axial shunts of the general form hereinabove described, having an embedded measuring lead following a predetermined parabolic path through the thickness of the conductive resistance material in an axial plane, can have a highly satisfactory performance throughout a wide frequency range well suited for accurate measurement of large transient surge currents or pulses.

It may be mentioned, however, that some measuring errors are inherently liable to arise with such co-axial shunts if the current to be measured varies so rapidly with time that there is a significant differcnce in the total current flowing at opposite ends of the measuring length. Under these conditions, the displacement current between the inner and outer tubes is no longer negligible and the finite time of propagation along the co-axial transmission line formed by the two tubes becomes important. The output circuit is another transmission line enclosed by the input circuit, the resistance tube being common to both input and output circuits. The situation is further complicated by the peculiarity that the output from the outer transmission line is taken from the two ends of one of its conductors (the resistance tubc), and this voltage is applied to the two ends of a conductor belonging to the output transmission line (the resistance tube again). In effect, the tubular resistance element functions as a guiding surface in addition to its role as a transducer, and a phase difference ariscs between different points along its length i.e. the propogation direction.

Another possible problem at extremcly high frequencies is that the input impedance of the shunt will be high. For example, the characteristic impedance of the input co-axial system is likely to be at least 20 ohm and the input impedance may have a similar value. It is clear then that such as shunt can only be useful in high voltage, low current situations. Even in a situation involving only a relatively low fundamental frequency, it is likely that transient records will be needed, and these involve much higher frequencies. Another very important point is that any sudden change in current must be limited initially by the full charactcristic impedance of the input circuit of the shunt. and very fast current changes may be inhibited by the prcsence of the measuring device.

The obvious way to overcome these difficulties is to reduce the length of the shunt. This, however, may give rise to severe end effects and very low transfer impedance. Thus it may be desirable in some eases to consider whether other somewhat different structural forms of shunt are possible having accurately calculable responses, and which might be free from some of the problems of the tubular form. One such different form which may be advantageous can be termed a "disc shunt".

It is obvious that. if the rcsistor surface is to represent a plane of constant phase, it must, at all points, be perpendicular to the direction of propagation. Hence a resistive disc at the end of a co-axial system will not suffer from the disadvantage of phase variation in the direction of current flow which occurs with the tubular shunts hereinbefore described.

The basic arrangement of such disc shunt is shown in the diagram of Figure 7 of the drawings from which it is secn that the current i flows axially along a central conductor 60, radially through a resistive disc 62 of conductive material at one end and axially along an outer co-axial tubular return conductor 64. With this arrangement, the total current can be measured by an output voltage derived from the electric field in the disc 62 in conjunction with the D.C. resistance to radial current flow over a measuring length, extending radially between coaxial output conductors having radii a and b respectively, and there should be no distortion due to distribution of the output circuit. Thus there should be no propagation delay to cause errors, although there will still be a diffusion delay and attenuation through the thickness h of the disc 62 which must be taken into account to obtain a perfect response.

However, a compcnsation arrangement for the latter can be provided, in accordance with the invention, in a manner similar to the tubular form of shunt by arranging a measuring lead to follow a predetermined path across the thickness of the disc over a radial distance reprcsenting the length of the measuring zone, this path being such that the output voltage is derived from the electric field in different radial planes normal to the axis so as to be substantially independent of variations in the distribution pattern of current density across the thickness of the disc.

As with the tubular shunt, an "ideal" measuring path can be derived as will now be explained with reference to the explanatory diagram of Figure 8.

Consider the path S, shown in Figure 8 which extends from r = b to r = a and from z = 0 to z = h. The output voltage will be

the integral being evaluated along the curve S. Where J is the radial current density, the total current flow is

The output will be proportional to the current if dr = 2oK r dz, K being a constant; Therefore dr/r = 2xoK dz giving, log (Ar) = 2oK z, A being another constant.

At z = 9, r = b so that A = 1/b. At z = h, r = a so that K = 2oh log (a/b) = R0 (the disc resistance to steady current flow between r = b and r = a).

Therefore the equation for the ideal measuring path is log (r/b) = (z/h) log (a/b) Again, for very rapid current variations the embedded path may be used as part of a measuring loop with no electrical connections to the resistance disc. Also, in this case the output voltage may be increased by having a number of turns on the output loop.

When an embedded lead is used there will be some distortion re-introduced due to propagation delay, this time along the co-axial system formed by the measuring lead and the walls of the cavity or groove in which it is embedded, but this propagation delay is not likely to be very great unless a loop output with several turns is used.

There are, however, certain practical considerations.

Firstly, it may be difficult to achieve a high resistance value in a disc shunt as can be seen from the formula for resistance Ro= log (a/b) 1zah If a/b = 2.71828.., log (a/b) = 1. If it is desired to increase the resistance by a factor of 2, the ratio a/b must be increased to 7.389. This shows that increasing the outer radius a is very ineffective in increasing the resistance, whereas decreasing b will be more effective, but will reduce the current-carrying capacity of the shunt. This form of disc shunt is therefore likely to be more suitable for the measurement of large surge currents than for small or moderate currents.

Secondly, since the major part of the disc resistance is due to the region of high current density around the inner radius, it will be important to have a very good and uniform joint between the inner radius of the disc and the rod or tube to which it is connected. It will obviously be advisable to take the inner point of the measuring length to be at a radius greater than the inner radius of the disc to allow the current density to become uniform.

Since the current flow is radial the shunt could be constructed from a number of segments 62' as indicated in the diagram of Figures 9a and 9b. A groove to carry the embedded measuring load 64 (Figure 9b) could be machined in the edges of each of these segments 62', provided that the thickness of the disc is sufficient. (A chemical etching process could be suitable). In this way a number of loops would be obtained for the output circuit, and these could be connected in parallel to a co-axial output line. Alternatively, for an isolated output the loops could be connected in series to increase the output voltage v, as for example indicated in Figure 9a which represents a segmented disc shunt with six isolate element, the measuring lead being embedded in the wall of the latter within the selected measuring zone.

Although in many cases, it will be convenient and advantageous for the resistance element to be composed of a non-ferromagnetic metal or alloy, in other cases, particularly when using an electrically isolated measuring loop, it could be advantageous for the resistance element to be composed of a conducting ferromagnetic material such as, for example, mild steel.

The essential point of such a device is that, when using the electrically isolated output loop, the bandwidth will be extended very considerably at the lower end of the frequency range. I'here will almost certainly be some lowering of the upper frequency limit, but the result should be a useful isolating measuring device for relatively low frequency applications. There is probably no point, however, in using ferromagnetic material in a shunt which has an electrical connection between the resistance element and the output eireuit. The expected improvement at the low frequency end of the band results from a reduction of penetration depth caused by the high permeability of the ferromagnetic material. Theoretically the non-linear and irreversible characteristics of the ferromagnetic material should not affect the response if the amount of material removed, to accomodate the measuring wires, is very small.

The term conducting ferromagnetic material, as used above, is intended to exclude materials such as ferrites which have a very low conductivity and which could not therefore be used satisfactorily.

WHAT 1 CLAIM IS: 1. A device for measuring a variable electric current comprising a current conductor having a conductive measuring lead which provides a measuring loop adapted to yield an output voltage between output terminal ends representative of total current passing through a measuring zone of said conductor along flow paths of given configuration distributed, throughout the thickness of the conductor within said measuring zone, at successive levels or depths relative to an outer boundary surface, said measuring lead following a predetermined path such that said output voltage is derived from the electric field at a multiplicity of different levels or depths throughout the thickness of the conductor and is substantially independent of variations in the distribution pattern of current density amongst said flow paths at least throughout a given operational frequency range.

2. A device, as claimed in Claim 1. wherein the current conductor forms the measuring resistance element of a shunt constituting a resistive transducer for connection in the circuit which carries the variable electric current which is to be measured and has a cylindrical profile.

3. A device, as claimed in Claim 2. wherein said current conductor comprises an elongate cylindrical tube or rod arranged so that all the current to be measured therein flows parallel to the axis, and the measuring load for providing the output voltage representative of the total current is arranged to extend through the wall of said tube or radial thickness of said rod, the path of said measuring lead lying in an axial plane throughout a length of the tube or rod which constitutes the measuring zone.

4. A device, as claimed in Claim 3, wherein the measuring lead is embedded in the tube or rod and its path follows at least substantially a parabolic curve defined only by the dimensional parameters of the tube or rod and of the measuring zone.

5. A device, as claimed in Claim 4, wherein said parabolic path is defined by the formula z= 5 b2 z= s a2 - b2 where r and z are the co-ordinates of points along said measuring path, s, is the axial length of the measuring zone, and a and b are the external and internal radii respectively of the tube or rod.

6. A device, as claimed in any of Claims 3 to 5, wherein the ratio of the internal radius to the external radius of said tube or rod is less than 0.9.

7. A device, as claimed in any of Claims 3 to 5, in which the current conductor comprises an elongate substantially solid cylindrical rod having a central narrow bore or groove sufficient to accommodate a portion of the measuring lead.

8. A device, as claimed in Claim 6 or 7, wherein the tube or rod is divided along an axial plane into two half sections of which the planar faces are fitted together in abutting engagement, and the measuring lead is accommodated in a shallow groove formation which is formed in at least one of said planar faces and which defines the required predetermined

**WARNING** end of DESC field may overlap start of CLMS **.

Claims

**WARNING** start of CLMS field may overlap end of DESC **. element, the measuring lead being embedded in the wall of the latter within the selected measuring zone. Although in many cases, it will be convenient and advantageous for the resistance element to be composed of a non-ferromagnetic metal or alloy, in other cases, particularly when using an electrically isolated measuring loop, it could be advantageous for the resistance element to be composed of a conducting ferromagnetic material such as, for example, mild steel. The essential point of such a device is that, when using the electrically isolated output loop, the bandwidth will be extended very considerably at the lower end of the frequency range. I'here will almost certainly be some lowering of the upper frequency limit, but the result should be a useful isolating measuring device for relatively low frequency applications. There is probably no point, however, in using ferromagnetic material in a shunt which has an electrical connection between the resistance element and the output eireuit. The expected improvement at the low frequency end of the band results from a reduction of penetration depth caused by the high permeability of the ferromagnetic material. Theoretically the non-linear and irreversible characteristics of the ferromagnetic material should not affect the response if the amount of material removed, to accomodate the measuring wires, is very small. The term conducting ferromagnetic material, as used above, is intended to exclude materials such as ferrites which have a very low conductivity and which could not therefore be used satisfactorily. WHAT 1 CLAIM IS:

1. A device for measuring a variable electric current comprising a current conductor having a conductive measuring lead which provides a measuring loop adapted to yield an output voltage between output terminal ends representative of total current passing through a measuring zone of said conductor along flow paths of given configuration distributed, throughout the thickness of the conductor within said measuring zone, at successive levels or depths relative to an outer boundary surface, said measuring lead following a predetermined path such that said output voltage is derived from the electric field at a multiplicity of different levels or depths throughout the thickness of the conductor and is substantially independent of variations in the distribution pattern of current density amongst said flow paths at least throughout a given operational frequency range.

path of the measuring lead.

9. A device, as claimed in Claim 3 or 4, wherein the current conductor comprises an elongate cylindrical tube having a narrow axial slot formed through the tube wall and said measuring lead is fixed in said slot so as to follow said predetermined path.

10. A device, as claimed in Claim 9, wherein the ratio of the inside diameter to the outside diameter of said tube is greater than 0.9, and the path of the measuring lead within said slot approximates to a straight line.

11. A device, as claimed in any of Claims 3 to 6, in which said current conductor tube or rod is built up in layers by a number of relatively thin tubes of successively larger diameters telescopically fitted co-axially one within another, small holes being drilled through the walls of these tubes before assembly so as to provide after assembly a path for the measuring lead between the exterior and interior surfaces which approximates to the required predetermined path.

12. A device, as claimed in any of Claims 3 to 11, wherein said current conductor tube or rod provides a terminal of the shunt at one end and the opposite end is connected through a conductive end cap to a co-axially arranged outer conducting tube of considerably greater diameter having a free end which provides a second terminal for connection of the device in the current carrying external circuit, and the output terminal ends of the measuring loop provided by the measuring lead are brought out at one end along the central axis for connection to a voltage sensitive instrument.

13. A device, as claimed in Claim 1 or 2, wherein the current conductor is in the form of a resistive disc of conductive material interconnecting one end of a central cylindrical conductor element with an outer co-axial tubular conductor element so that the current passed through the device flows radially through said disc, and the predetermined path of the measuring lead extends across the thickness of the disc over a radial distance constituting the length of the measuring zone such that the output voltage is derived from the electric field in different radial planes normal to the axis throughout the thickness of the disc, being substantially independent of variations in the distribution pattern of current density across said thickness of the disc.

14. A device, as claimed in Claim 13, wherein the path of the measuring lead follows at least substantially a logarithmic curve defined only by the dimensional parameters of the disc and of the measuring zone.

15. A device, as claimed in Claim 14, wherein said logarithmic path is defined by the formula log (r/b) = (z/h) log (a/b) where h is the thickness of the disc, a, and b are the radial dimensions of the radially outermost and innermost limits respectively of the measuring zone, and r and z are the co-ordinates of points along said measuring path as shown in Figure 4 of the accompanying drawings.

16. A device, as claimed in any of Claims 13 to 15, wherein the disc is constructed from a number of separate segments.

17. A device, as claimed in any of the preceding claims, wherein the loop of the measuring lead is insulated from direct electrical contact with the current conductor.

18. A device, as claimed in Claim 17, wherein the measuring lead comprises a plurality of turns of insulating wire extending around the measuring path.