US3881162A

US3881162A - Film-type cylindrical resistor and method of manufacturing

Info

Publication number: US3881162A
Application number: US456474A
Authority: US
Inventors: Richard E Caddock
Original assignee: Individual
Current assignee: Individual
Priority date: 1974-04-01
Filing date: 1974-04-01
Publication date: 1975-04-29
Anticipated expiration: 1992-04-29

Abstract

A low-inductance cylindrical resistor formed of a cylindrical ceramic substrate, which is coated with a film of resistive material and overprinted with intermeshing comb termination films. End caps are mounted over the substrate ends for connection to the termination films, and the entire assembly is coated with an environmentally-protective coating. A groove is formed in the substrate in a direction parallel to the substrate axis, the groove increasing the resistance of the resistor by an amount which causes the resistance to be at the desired value, within a very small range. Because such groove is longitudinal to the substrate, it creates no substantial weakening effect relative thereto. In accordance with the method, the above-stated groove is formed by a blast of abrasive particles, the duration of the blast and the direction of relative movement being such that the resistance value is easily and accurately trimmed without weakening the substrate substantially.

Description

United States Patent [1 1 Caddock [451 Apr. 29, 1975 FILM-TYPE CYLINDRICAL RESISTOR AND METHOD OF MANUFACTURING [76] Inventor: Richard E. Caddock, 640

Sandalwood Ct., Riverside, Calif. 92507 [22] Filed: Apr. 1, I974 [2]] Appl. No.: 456,474

[52] US. Cl. 338/61; 29/593; 292/620; 338/288, 338/325; 338/332 [51] Int. Cl H0lc 3/02 [58] Field of Search 338/61, 195, 322, 262, 338/288, 332, 325, 320; 29/593, 620

[56] References Cited FOREIGN PATENTS OR APPLICATIONS 927,278 10 1943 Germany OTHER PUBLICATIONS Caddock 1973 Catalog pp. 8 & l().

Primal-y E.\'aminerE. A. Goldberg Attorney, Agent, or Firm-Richard L. Gausewitz I 57] ABSTRACT A low-inductance cylindrical resistor formed of a cylindrical ceramic substrate, which is coated with a film of resistive material and overprinted with intermeshing comb termination films. End caps are mounted over the substrate ends for connection to the termination films, and the entire assembly is coated with an environmentally-protective coating. A groove is formed in the substrate in a direction parallel to the substrate axis, the groove increasing the resistance of the resistor by an amount which causes the resistance to be at the desired value, within a very small range. Because such groove is longitudinal to the substrate, it creates no substantial weakening effect relative thereto. In accordance with the method, the abovestated groove is formed by a blast of abrasive particles, the duration of the blast and the direction of relative movement being such that the resistance value is easily and accurately trimmed without weakening the substrate substantially.

9 Claims, 10 Drawing Figures BACKGROUND OF THE INVENTION 1. Field of the Invention This invention relates to the field of cylindrical resistors formed of substrates having resistive coatings on the exterior cylindrical surfaces thereof, and further relates to a method of trimming the resistance values of such resistors.

2. Description of Prior Art It is well known that flat ceramic substrates for resistive films are impractical and/or undesirable in numerous applications. For example, where the flat substrate is thin, it has poor resistance to thermal and physical shocks. Thermal shock is an especially major consideration, since the resistor may be very rapidly heated from room temperature to several hundred degrees Fehrenheit. Where the substrate is thick, it tends to have a relatively irregular surface which is difficult to coat with the desired pattern of resistive material.

Cylindrical ceramic substrates, on the other hand, have high shock resistance, particularly when they are solid instead of hollow, and are not scored except in a certain way set forth below. They also have very smooth and regular surfaces, which are economically formed by centerless grinding. Therefore, it is very often highly desirable and important that the substrates be cylindrical instead of flat.

It is also very desirable, in many applications, that a resistive film having a high inherent resistance (for example, in excess of 50 ohms per square) be so employed that the resistive value of the resistor can be made very low. Low-value film-type resistors have long been known wherein the film is associated with intermeshing comb (or fork, or finger) termination means, whereby parallel connections are made to thus attain low resistance values.

The prior art also incorporates teachings relative to the trimming" of film-type resistors to achieve the desired resistance value, but not (insofar as applicant is aware) in the combination or method described and claimed below. In the case of cylindrical resistors, a common way to effect trimming is by forming a cut or groove through the resistive film in a direction generally perpendicular to the axis of the substrate. Other prior-art ways of trimming cylindrical resistors include, for example, adding to or subtracting from the conductive (termination) strips, removing termination-strip portions together with the underlying resistive film, and thinning portions of the resistive film. The present invention is contrary to convention, and

achieves the combined advantages of: (a) a cylindrical substrate, (b) ability to use high-resistance films to attain a low-value low-inductance resistor, (c) ability to be manufactured economically, and without the necessity of employing gold, (d) ability to score the substrate (as part of the trimming) without substantially weakening it, (e) great stability, and a resistance value which is accurately determined within a narrow range, and (f) ability to be trimmed without wasting precious metals and without altering more than one resistor element.

SUMMARY OF THE INVENTION The above-stated (and other) advantages are achieved by employing an elongated cylindrical ceramic substrate on which is applied a film of resistive material. Intermeshing comb termination films are applied over the resistive film, with the teeth of the combs extending parallel to the substrate axis. End caps are provided at each end of the substrate, in contact with the termination films, and an environmentally protective coating is applied over the entire assembly. At least one region of the resistive film is cut through by a groove which penetrates into the ceramic substrate to score the same. Very importantly, such groove is between the teeth of the termination films, and extends longitudinally of the substrate axis, the result being that the resistance value is easily and precisely adjusted whereas the ability of the substrate to withstand physical and thermal shocks is not substantially reduced. The characteristics of the groove are such that the resistance value is as desired.

In accordance with the method, the stated longitudinal groove is formed by means of an abrasive blast, which produces little or no adverse effect relative to the stability of the resistor, and which is economical to employ.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a greatly enlarged isometric view showing a cylindrical film-type resistor embodying the present invention, but without the environmentally protective coating thereon;

FIG. 2 is a longitudinal central sectional view of the resistor, including the protective coating;

FIG. 3 is an enlarged transverse sectional view taken along line 33 of FIG. 2;

FIG. 4 is a greatly enlarged transverse sectional view along line 4-4 of FIG. 2, showing a cross-section of the longitudinal groove;

FIG. 5 is an isometric view of the cylindrical substrate;

FIG. 6 is an isometric view showing the substrate with a coating of resistive material thereon;

FIG. 7 is a similar view but showing the intermeshing comb termination films as printed over the resistive film;

FIG. 8 illustrates the end caps (and associated leads) as mounted over the end regions of the conductive films;

FIG. 9 is an isometric view showing the step of trimming the resistance value of the resistor by employing an abrasive blast to form a longitudinal groove through a region of the resistive film; and

FIG. 10 is an isometric view of the finished resistor.

DESCRIPTION OF THE PREFERRED EMBODIMENT OF THE ARTICLE AND METHOD Referring to the drawings, the present resistor comprises an elongated cylinder 10 (the substrate) formed of heat-resistant electrically-insulating material, namely a suitable heat-resistant ceramic such as aluminum oxide. To increase the strength thereof, and to minimize the possibility of moisture intrusion, cylinder 10 is preferably solid as distinguished from hcllow. It has a smooth exterior surface which is formed by centerless grinding a ceramic extrusion.

Provided exteriorly on cylinder 10, in adherent rela tionship relative to the exterior cylindrical surface thereof, is a resistive film 11. The film 11 is a continuous cylinder the ends of which terminate at regions inset substantial distances from the ends of substrate 10.

The resistive material forming film 11 preferably comprises electrically-conductive complex metal oxides in a glass matrix, and which are fired in air (for example, for 30 minutes) at temperatures above l,400 F. Another resistive material which may be employed is carbon particles, in an epoxy vehicle which also acts as an adhesive or binder.

First and second termination films 12 and 13 are printed on the substrate, in overlying relationship rela- ,,tive to resistive film 11, as best illustrated in FIG. 7.

Each film 12 and 13 may be referred to as a comb. Thus, the first film 12 has a cylindrical spine portion 14 provided in adherent relationship on one end of substrate and spaced away from the corresponding end of resistive film ll. lntegrally connected to spine portion 14 are a plurality ofteeth 15, such teeth extending longitudinally of the axis of substrate 10 to the end of film ll remote from spine 14. correspondingly, the second termination film 13 has a spine portion 16 provided in adherent relationship on the other end of substrate 10 and spaced from the resistive film. Such spine 16 is integral with teeth 17 which extend to the remote end of the resistive film.

The termination filsm l2 and 13 are preferably formed of a silver-ceramic conductive material in a glass matrix, or they may be formed of a silver-epoxy conductive plastic.

The indicated silver termination materials have the characteristic of dispersing into the resistive film 11 if they are applied to substrate 10 prior to application of film 11, that is to say in underlying (instead of overlying) relationship relative to the resistive film. Therefore, if the termination films were provided on the substrate before the resistive film was applied thereto, it would be necessary to employ gold (instead of silver), or some other extremely expensive noble metal, and this would substantially increase the cost of the resistor.

It is pointed out that when gold is thus employed, so that the film 11 overlies the termination strips, the resistance value may be trimmed by means of lapping, without decreasing the strength of the substrate 10. However, because of the expense of gold, this is not desired. In accordance with the present resistor and method, the much less expensive silver termination material may be employed, and the present trimming also employed, resulting in a product which is substantially equal in quality to that of the product containing gold yet which is produced at much reduced cost.

As best shownin FIG. 3, the spacings between the various comb teeth, and the relative orientation of the two combs, are such that the teeth mesh with each other and are substantially equally spaced about the circumference of the exterior surface of resistive coating 11. In the illustrated embodiment, there are three teeth or 17 on each comb l2 and 13, the teeth of .each comb being circumferentially spaced 120 from each other and circumferentially spaced 120 from each otherand circumferentially spaced 60 from each adjacent comb tooth. It is emphasized, however, that the number and'spacings of the teeth may be varied within a wide range.

The various comb teeth divide the resistive film 11 into a number of parallel-connected resistor elements.

Each such resistor element is wide and short. Because there are a number of parallel connected resistor ele-.

ments, and because each such resistor element is wide and short, the overall resistance value may be made very low despite the fact that the resistive material forming film ll inherently has a relatively high resistance value.

To state the above in another manner, the length of each resistor element is equal to the spacing between

adjacent teeth

15 and 17, namely in the present illustration. When the diameter of substrate 10 is small, as is often the case, this 60 may be a very short distance. The width of each resistor element is equal to the dimension of the resistive film l1 longitudinally of the substrate 10. The various (six in number, in the present example) wide and short resistor elements thus formed are all connected in parallel with each other, since one end of each such resistor element is electrically connected to spine 14 or 16. With the described relationship, the direction of current flow is circumferential to the resistive film 1 l.

The described relationship results in very low inductance, one reason being that the current paths are wide and short. Also, since the currents flow in opposite directions from (or to) each

tooth

15 or 17, the generated magnetic fields may tend to neutralize each other thus further lowering inductance.

To conduct current to and from the termination films 12 and 13, cup-shaped end caps 18 and 19 are respectively press-fit thereover. Leads 21 and 22 are mechanically and electrically connected to the centers of the respective caps.

The combination of the end caps 18-19 and the termination spines 14-16 causes the contact resistance to the resistor to be predetermined, uniform and stable. Where less accuracy and stability are permissible, the end caps may engage the

teeth

15 and 17 directly, the spines l4 and 16 then being omitted. This latter construction is now preferred.

The entire assembly is coated by means of a coating 23 (encapsulating means) formed of a suitable material having the requisite characteristics relative to environmental protection namely insulating ability, moisture resistance, heat resistance, etc. A preferred coating material is silicone conformal, which may be purchased from Midland Industrial Finishes Company, of Waukegan, Illinois.

It is extremely important that the present resistor incorporates a trimming groove 25 at one region about the circumference of the resistive film 11, that such trimming groove 25 is elongated and extends in a direction substantially parallel to the axis of substrate 10, and that such trimming groove is between two

adjacent teeth

15 and 17. The groove 25, illustrated in FIGS. 1,

cumferentially as in the case of other portions of the resistor, but instead must flow around the groove. This elongated path of flow causes the over-all resistance value of the resistor to be elevated. The length of the groove 25 is determined, as stated subsequently, in

such manner that the resistor is trimmed in a precise manner.

Since the groove 25 extends clear through the resistive film 11, it is a practical necessity that it also extends through the underlying surface of substrate 10, therefore scoring such substrate. However, since the scoring is longitudinal instead of circumferential, it does not result in substantial weakening of the substrate relative to such factors as physical and thermal shocks. The described longitudinal groove or cut is to be compared with the grooves or cuts of various priorart resistors, wherein the cutting is usually perpendicular or generally perpendicular to the substrate axis. With such resistors, the substrate is distinctly less able to withstand shock, etc.

It is emphasized that, as will be appreciated by analogy to a pane of glass which is readily broken at a region where there is only a shallow scratch, the stress concentration created by even a small score in a cylindrical surface of substrate is of distinct importance. By causing the present score to extend longitudinally instead of circumferentially, applicant has so adjusted the stress concentration that the substrate 10 remains highly resistant to thermal and physical shocks.

Because of the fact that the groove 25 lies between two adjacent teeth and 17, instead of being registered with (cut through) one of such teeth and the underlying resistive film, the current flow in only one of the resistor elements (instead of in two adjacent resistor elements) is affected. If, on the other hand, the groove were registered with a tooth, that is to say if a portion of the length of the tooth (and throughout the full width of the tooth) were removed by formation of the groove, there would be a relatively large cold spot" on both sides of such removed portion since current flow on both sides would be affected. The large cold spot would tend to act as a barrier to the conduction of heat along the length of the resistor from the relatively hot central region of the resistor to the relatively cool ends thereof (it being emphasized that heat only flows in a direction from hot to cold). When, on the other hand, the cold spot is narrow, as in the present invention, it may be efficiently heated by conduction from both sides thereof, thus producing minimized effects on heat flow along the length of the resistor. It is also possible, with the present invention, to have relatively short grooves at diametrically opposite sides of the resistor, and/or at different regions along the length of the substrate, thus minimizing the sizes of the cold spots so that they are heated effectively by heat conduction from the adjacent regions. These considerations are especially important in power resistors, which these are.

DESCRIPTION OF THE METHOD Referring to FIGS. 5 through 10, as the first step in the method, the centerless-ground ceramic extrusion 10 is coated with the above-indicated resistive film 11. Such coating is preferably effected by silk-screening. To permit the complex oxides in a glass matrix to be silk-screened, they are first mixed with a pine oil (squeegee oil) vehicle. The printed cylinder 10 is then fired in air, in a furnace, at temperatures in excess of l,400 F., in order to effect melting of the glass and curing of the resistive material. Such firing step is continued for 30 minutes.

As the next step in the method, the termination films 12 and 13 are applied to substrate 10 over the resistive film 11, again by silk-screening. The cylinder is then again fired, for (for example) 5 minutes at l,l00 F.

Preferably, the silk-screening is effected by the apparatus and method disclosed in my copending patent application Ser. No. 424,810, filed Dec. 14, 1973, for Method and Apparatus for Manufacturing Cylindrical Resistors by Thick-Film Silk-Screening.

As the next step in the method, the end caps 18 and 19 are press fit over the spine portions 14 and 16 of termination films 12 and 13. The leads 21 and 22 are then electrically connected to leads 27 and 28 shown in FIG. 9. Such leads 27-28 are part of a resistance testing device comprising an ohmmeter 29 and a suitable power source 30. When power is applied from source 30, the meter 29 indicates the resistance of the resistive film pattern in the resistor being tested.

The as-formed resistive film is caused (initially) to have a resistance value slightly less than the desired final value. Therefore, the resistance value is caused to increase until the meter 29 reads the desired final value. In accordance with the present method, the resistance is increased by directing a high-velocity blast or jet 31 of abrasive particles against a region of film 11, between two adjacentterminal strips or

teeth

15, 17. The nozzle 32 from which jet 31 emanates is traversed, relative to the substrate 10 and in a direction longitudinal to the substrate, for a distance such that the ohmmeter 29 reads the desired value, following which the abrasive jet action is discontinued. The rate of traverse is sufficiently low that film 11 is penetrated and a shallow groove 25 is thus cut in the substrate.

The nozzle 32 is one which will create a very welldefined stream or jet 31, and one which may be very narrow when desired. For example, the dimension of the groove 25 in a direction circumferential to the substrate may be as low as about 6 thousandths of an inch. Such well-defined narrow grooves 25 are particularly important in film resistors formed of small-diameter substrates.

The abrasive jet 3] is highly superior to a grinding wheel, for numerous reasons, including cleanness of cut, stability of the resistor, and ability to work on small substrates and still cut longitudinally.

As the final step in the method, the coating 23 of environmentally-protective material is provided, as by spraying or dipping, to form the finished product shown isometrically in FIG. 10.

The word resistive, as employed in this specification and claims, denotes a film which (a) is not an electrical insulator, (b) is an electrical conductor, (c) is not a good electrical conductor, and (d) has a substantial amount of electrical resistance.

Throughout this specification and claims, the word cylinder" is used in its conventional sense (a surface traced by a straight line moving parallel to a fixed straight axis and intersecting a fixed circle, the circle lying in a plane perpendicular to the axis, the circle having the axis as its center).

The foregoing detailed description is to be clearly understood as given by way of illustration and example only, the spirit and scope of this invention being limited solely by the appended claims.

I claim:

1. A film-type resistor, which comprises:

a. an elongated cylindrical substrate formed of ceramic, b. a resistive film provided adherently on the exterior cylindrical surface of said substrate, c. a plurality of termination film strips or lines formed of highly-conductive material, said termination film strips being superimposed adherently over said resistive film,

said termination film strips being elongated and extending in directions substantially parallel to the axis of said substrate,

said termination film strips being circumferentially spaced about said substrate,

said termination film strips dividing said resistive film into a plurality of resistor elements through which current flows in directions generally circumferential to said substrate, d. means to connect one set of alternate ones of said termination film strips to one lead extending from one end of the resistor, and to connect the other set of alternate ones of said termination film strips to another lead extending from the other end of said resistor, and e. a groove formed through said resistive film at one region thereof in order to increase the current path length and thus raise the resistance value of the resistor, said groove extending substantially parallel to the axis of said substrate,

said groove being formed in only one of said resistor elements,

said groove scoring said substrate but, because of said substantial parallelism to the axis of said substrate, having minimal effect upon the physical and thermal shock resistance thereof,

said groove not being formed through any part of any of said termination film strips or lines.

2. The invention as claimed in claim 1, in which said means recited in clause (d) comprises metal end caps respectively mounted over opposite ends of said substrate, one of said end caps being electrically connected to said one set and said one lead, the other of said end caps being electrically connected to said other set and said other lead, and in which said groove is formed by particle-blast abrasion and not by grinding.

3. The invention as claimed in claim 2, in which said resistive film is not present on the end portions of said substrate beneath said end caps, and in which said means recited in clause (d) comprises two additional termination films formed of highly-conductive material, one of said additional termination films being provided adherently on said substrate beneath said one end cap and being connected integrally to said one set, the other of said additional termination films being provided adherently on said substrate beneath said other end cap and being connected integrally to said other set.

4. The invention as claimed in claim 3, in which an environmentally-protective coating is provided over said entire substrate, films and end caps.

5. The invention as claimed in claim 1, in which said groove is one formed by a high-velocity jet of abrasive particles.

6. The invention as claimed in claim 1, in which said substrate is solid, not hollow.

7. A method of mass-manufacturing a high-strength high-stability cylindrical film-type resistor having a prea. providing an elongated cylindrical ceramic substrate,

b. applying adherently to the central region of the exterior cylindrical surface of said substrate a film of resistive material, while leaving the end regions of said cylindrical surface bare,

c. applying first and second comb-shaped termination films of conductive material to said cylindrical surface, the spine portions of said termination films being respectively applied adherently to said bare end regions of said cylindrical surface, the teeth portions of said termination films being connected to said spine portions and being applied adherently in superimposed relationship over said resistive film and in longitudinal relationship to the axis of said substrate, said teeth portions of one of said termination films being applied in intermeshing, alternating and circumferentially-spaced relationship to said teeth portions of the other said termination films, whereby said teeth portions divide said resistive film into a plurality of resistor elements through which current flows circumferentially of said substrate,

d. forming a groove through a portion of said resistive film in a direction generally longitudinal to said substrate axis, thereby increasing the lengths of the current paths adjacent said groove and consequently increasing the resistance value of the resistor, said groove being formed in such manner as not to reduce the length or width or thickness of any of said teeth portions,

e. causing the length of said groove to be such that the resistance value of the resistor is within a predetermined narrow range, and

f. making electrical connections to said spine portions.

8. The invention as claimed in claim 7, in which said method further comprises effecting said step (d) by generating a narrow jet of abrasive particles, directing said jet against a region of said resistive film spaced from said teeth portions and effecting relative movement between said jet and said resistive film in a direction longitudinal to said substrate and at a rate sufficiently slow that said jet abrades away substantially all of said resistive film where said film is engaged by said jet.

9. A method of mass-manufacturing a high-strength high-stability cylindrical film-type resistor having a precisely predetermined resistance value, which comprises:

a. providing an elongated cylindrical substrate,

b. applying adherently to the exterior cylindrical surface of said substrate a film of resistive material,

c. applying first and second sets of elongated termination film strips of conductive material,

longitudinal relationship to the axis of said substrate,

said film strips being applied in circumferentiallyspaced relationship,

relative movement between said jet and said resistive film in a direction longitudinal to said substrate and at a rate sufficiently slow that said jet abrades away substantially all of said resistive film where film is engaged by said jet, causing the length of said groove to be such that the resistance value of the resistor is within a predetermined narrow range, and f. making one set of electrical connections to alternate ones of said film strips, and another set of electrical connections to the remaining alternate ones of said film strips.

Claims

1. A film-type resistor, which comprises: a. an elongated cylindrical substrate formed of ceramic, b. a resistive film provided adherently on the exterior cylindrical surface of said substrate, c. a plurality of termination film strips or lines formed of highly-conductive material, said termination film strips being superimposed adherently over said resistive film, said termination film strips being elongated and extending in directions substantially parallel to the axis of said substrate, said termination film strips being circumferentially spaced about said substrate, said termination film strips dividing said resistive film into a plurality of resistor elements through which current flows in directions generally circumferential to said substrate, d. means to connect one set of alternate ones of said termination film strips to one lead extending from one end of the resistor, and to connect the other set of alternate ones of said termination film strips to another lead extending from the other end of said resistor, and e. a groove formed through said resistive film at one region thereof in order to increase the current path length and thus raise the resistance value of the resistor, said groove extending substantially parallel to the axis of said substrate, said groove being formed in only one of said resistor elements, said groove scoring said substrate but, because of said substantial parallelism to the axis of said substrate, having minimal effect upon the physical and thermal shock resistance thereof, said groove not being formed through any part of any of said termination film strips or lines.

7. A method of mass-manufacturing a high-strength high-stability cylindrical film-type resistor having a precisely predetermined resistance value, which comprises: a. providing an elongated cylindrical ceramic substrate, b. applying adherently to the central region of the exterior cylindrical surface of said substrate a film of resistive material, while leaving the end regions of said cylindrical surface bare, c. applying first and second comb-shaped termination films of conductive material to said cylindrical surface, the spine portions of said termination films being respectively applied adherently to said bare end regions of said cylindrical surface, the teeth portions of said termination films being connected to said spine portions and being applied adherently in superimposed relationship over said resistive film and in longitudinal relationship to the axis of said substrate, said teeth portions of one of said termination films being applied in intermeshing, alternating and circumferentially-spaced relationship to said teeth portions of the other said termination films, whereby said teeth portions divide said resistive film into a plurality of resistor elements through which current flows circumferentially of said substrate, d. forming a groove through a portion of said resistive film in a direction generally longitudinal to said substrate axis, thereby increasing the lengths of the current paths adjacent said groove and consequently increasing the resistance value of the resistor, said groove being formed in such manner as not to reduce the length or width or thickness of any of said teeth portions, e. causing the length of said groove to be such that the resistance value of the resistor is within a predetermined narrow range, and f. making electrical connections to said spine portions.

9. A method of mass-manufacturing a high-strength high-stability cylindrical film-type resistor having a precisely predetermined resistance value, which comprises: a. providing an elongated cylindrical substrate, b. applying adherently to the exterior cylindrical surface of said substrate a film of resistive material, c. applying first and second sets of elongated termination film strips of conductive material, said film strips being applied adherently in superimposed relationship over resistive film and in longitudinal relationship to the axis of said substrate, said film strips being applied in circumferentially-spaced relationship, whereby said film strips divide said resistive film into a plurality of resistor elements through which current flows circumferentially of said substrate, d. forming a groove through a portion of said resistive film in a direction generally longitudinal to said substrate axis, thereby increasing the lengths of the current paths adjacent said groove and consequently increasing the resistance value of the resistor, said groove being formed by generating a narrow jet of abrasive particles, directing said jet against a region of said resistive film and not against said film strips of conductive material, and effecting relative movement between said jet and said resistive film in a direction longitudinal to said substrate and at a rate sufficiently slow that said jet abrades away substantially all of said resistive film where film is engaged by said jet, causing the length of said groove to be such that the resistance value of the resistor is within a predetermined narrow range, and f. making one set of electrical connections to alternate ones of said film strips, and another set of electrical connections to the remaining alternate ones of said film strips.