Introduction to the Metal Foil Resistors.
A study of Elias Eduardo Ghershman, that compiles the work of many researchers over many years.
Metal Foil Resistors Technology in YouTube
Development of the invention and investigation of metal foil resistors.
1946, William D. Van Dyke 
1960, James E. Starr patent 
1960, Felix Zandman  ------------------------ etched
1973, Horii and Ohya 
1976, Paul Rene Simon  ------------------etching
1981, Benjamin Solow 
Historical summary of the development of Metal Foil Resistors.
The following sequences are scientific and technological developments led to the creation of the idea of metal foil resistor, it is organized temporarily.
Measurement of Current.
Although the 1820s was a time of great discoveries concerning the production of current electricity, it was also a time of widespread confusion about proper definitions for such fundamental terms as tension, intensity, and resistance
quantity. Ampere had provided an electromagnetic definition of the intensity of a current, and had clearly drawn a distinction between electrical tension and electricity, but scientists still lacked a means of relating the tension of a voltaic pile to the intensity of the current it produces and to the properties of the conductor carrying this current. A complete theory of voltaic circuits, which takes into account the driving power of the battery, was first provided in1826 by the German physicist Georg Simon Ohm (1789-1854). In 1825, Ohm resolved to dedicate himself to research in electricity. In his research was inspired by the work on heat of Joseph Fourier (1768-1830), who pointed out in 1822 that the flow of heat between any two points depends on the temperature difference and the conductivity between them. Applying this insight to the case of electricity, Ohm reasoned in a general way that the flow of current is proportional to the voltage (the electromotive force) and inversely proportional to the resistance.
Ohm first determined the lengths of wires, made from different metals, which gave the same current. He called these various lengths "equivalent lengths." Ohm then showed that the resistance was proportional to the to its length and inversely proportional cross-sectional area of the wire. Ohm performed this first series of experiments, replacing the voltaic pile with a thermocouple, recently discovered in 1821 , see in the following figure by Thomas Johann Seebeck (1770-1831). The thermocouple had the advantage over of the voltaic pile of not being prone to fluctuations in voltage. After trying the experiment with different metals and temperatures, Ohm was able to publish the law that bears his name.
In 1843 Wheatstone communicated an important paper to the Royal Society, entitled 'An Account of Several New Processes for Determining the Constants of a Voltaic Circuit.'  It contained an exposition of the well known balance for measuring the electrical resistance of a conductor, which still goes by the name of Wheatstone's Bridge or balance, although it was first devised by Mr. S. W. Christie, of the Royal Military Academy, Woolwich, who published it in the Philosophocal Transactions for 1833. The method was neglected until Wheatstone brought it into notice. His paper abounds with simple and practical formula: for the calculation of currents and resistances by the law of Ohm. He introduced a unit of resistance, namely, a foot of copper wire weighing one hundred grains (6.5 g), and showed how it might be applied to measure the length of wire by its resistance.
Although this document and does not establish the mathematical relationships of the bridge that bears his name and that an important component in measuring resistances, demonstrates the sensitivity of the system, from the page 323, “The Differential Resistance Measurer”, of such document, extract the following description : The drawing, Fig. 5 represents a board on which are placed four copper wires, Z b, Z a, C a, C b, the extremities of which are fixed to brass binding screws. The binding screws Z, C are for the purpose of receiving wires proceeding from the two poles of a rheomotor, to denote any apparatus which originates, an electric current, whether it be a voltaic element or a voltic battery, a thermo-electric element or a thermo-electric battery, in words of Wheatstone and those marked a, b are for holding the ends of the wire of a galvanometer. By this arrangement a wire from each pole of the rheomotor proceeds to each end of the galvanometer wire, and if the four wires be of equal length and thickness, and of the same material, perfect equilibrium is established, so that a rheomotor however powerful will not produce the least deviation of the needle of the galvanometer from zero, in this last paragraph and see the phenomenon of the bridge .
The circuits Z b a C Z, and Z a b C Z, are in this case precisely equal, but as both currents tend to pass in opposite directions through the galvanometer, which is a common part of both circuits, no effect is produced on the needle. Currents are however established in Z b CZ, and Z a C Z, which would exist were the galvanometer entirely removed.
But if a resistance be interposed in either of the four wires, the equilibrium of the galvanometer will be disturbed ; if the resistance be interposed in Z b or C a, the current Z a b C Z will acquire a preponderance ; if it be inserted either in Z a or C b, the opposite current, Z b a C Z, will become the most energetic.
If the resistance interposed in the wire be infinite, or which is the same thing, if the wire (which we will suppose to be C b) be removed, the energy of the current passing through the galvanometer will be that of a partial current Z b a passing through one of the wires plus the galvanometer wire.
In the following paragraph we see that Wheatstone anticipates that the phenomenon undergoing mechanical stress to the wire is a resistance change, slight differences in the lengths, and even in the tensions of the wires, are sufficient to disturb the equilibrium ; it is therefore necessary to have an adjustment, by means of which, when two exactly equal wires are placed in C a and Z a, the equilibrium may be perfectly established.
In 1833, Lenz revealed details of his research. A pair of identical spirals were built for each metal under investigation and connected in series into a single circuit whose free ends were joined by cooper lead wires to a galvanometer very similar to that invented by Nobili. By using a circuit with an electromotive force which was free of the uncertainty implied by the internal resistance of the battery, Lenz was able to find the electric conductivity of each one of the studied metals at different temperatures and found with considerable degree of accuracy the magnitude of their respective changes with this variable. determine values at between six and twelve different temperatures for, silver, copper, brass, iron and platinum , and sometime later, gold, lead and tin too. The relation he found for this specific case was, using his own notation :
The resistivity of metals increases with increased temperature, positive resistance-temperature coefficient, although there may be metals with negative resistance-temperature coefficient ; within narrow ranges of temperature where the resistance-temperature coefficient may be considered constant, the resistance of a conductor at the temperature
t is :
It was Lord Kelvin  from his investigations into the electrodynamics properties of metals who first reported in 1856 that metallic conductors subjected to mechanical strain exhibit a change in their electrical resistance, although this is not exactly true, see above Wheatstone work. He used a Wheatstone bridge circuit with a galvanometer as the indicator, adopts the system of Wheatstone to be very sensitive.
Lord Kelvin showed that metallic conductors subjected to mechanical elongation (strain) exhibited a change in resistance, compressional strains producing a decrease. The resistance of a wire is defined by
Telegraph wire signal propagation changes and time-related conductivity changes, nuisances to telegraph companies, motivated further observations of conductivity under strain. In his classic Bakerian lecture to the Royal Society of London, Kelvin reported an elegant experiment where joined, parallel lengths of copper and iron wires were stretched with a weight and the difference in their resistance change was measured with a modified Wheatstone bridge. Kelvin determined that, since the elongation was the same for both wires, “the effect observed depends truly on variations in their conductivities.” Observation of these differences was remarkable, given the precision of available instrumentation.
Furthermore, he observed that the iron wire showed a greater increase in resistance than the copper wire when they were both subjected to the same strain. Lord Kelvin also employed the Wheatstone bridge technique to measure the resistance change. In that classical experiment, he established three very important facts which helped further development of electrical resistance strain gages; 1. The resistance of the wire changes as a function of strain. 2 Different materials have different sensitivities. 3 Wheatstone bridge can be employed to accurately measure these resistance changes.
In 1905, after several years of joint experimentation, Albert L. Marsh  , a Michigan metallurgist and William Hoskins an Illinois inventor/entrepreneur patented a tough new alloy of nickel and chromium, to which they gave the trade name “Nichrome”. Containing only a small amount of iron and being carbon free, Nichrome was much stronger and more long lived than earlier thermal wire. Hoskins Manufacturing Company was former to produce high temperature electric laboratory furnaces using the wire and is credited by some with manufacturing the first commercially successful electric bread toster in 1907 derived from these furnaces.
Hoskins eventually sold the Nichrome patent to General Electric who had tried unsuccessfully for years to create its own thermal wire. Until the Marsh patent ran out in the mid-1920s, GE charged all other manufacturers twenty-five cents per appliance for the right to use it.
Early “Nichrome” was a major improvement over iron alloy wire in both electrical efficiency and physical strength.
America 1930, Titanium and Aluminium added to the classic heating element alloy nichrome (Ni-20Cr), resulted in significant increase in creep resistance.
Designers have long had a need for stronger, more corrosion-resistant materials for high-temperature applications. The stainless steels, developed and applied in the second and third decades of the 20th century,
served as a starting point for the satisfaction of high-temperature engineering requirements. They soon were found to be limited in their strength capabilities. The metallurgical community responded to increased needs
by making what might be termed ‘‘super-alloys’’ of stainless varieties. Of course, it was not long before the hyphen was dropped and the improved iron-base materials became known as superalloys. Concurrently, with the advent of World War II, the gas turbine became a high driver for alloy invention or adaptation. Although patents for aluminum and titanium additions to Nichrome-type alloys were issued in the 1920s, the superalloy industry emerged with the adaption of a cobalt alloy (Vitallium, also known as Haynes Stellite 31) used in dentistry to satisfy high-temperature strength requirements of aircraft en engines.
Some nickel-chromium alloys (the Inconels and Nimonics), based more or less, one might say, on toaster wire (Nichrome, a nickel-chromium alloy developed in the first decade of the 20th century) were also available.
So, the race was on to make superior metal alloys available for the insatiable thirst of the designer for more high-temperature strength capability. [ 16 ].
Alloys for electrical resistance. 
Chromium nickel alloys are characterized by having a large electrical resistance (about 58 times that of copper), a small temperature coefficient and high resistance to oxidation. Examples are Chromel A and Nichrome V, whose typical composition is 80 Ni and 20 Cr, with its melting point to 1420 ° C.
When you add a small amount of iron to nickel-chromium alloy, are becoming more ductile. The Nichrome and Chromel C are examples of an alloy containing iron. The commposicion typical of Nichrome is 60 Ni, 12 Cr, 26 Fe, 2 Mn and Chromel C, 64 Ni, 11 Cr, Fe 25. The melting temperature of these alloys are 1350 ° and 1390 ° C, respectively. In the figure are variations of resistance with temperature of these alloys.
Temperature coefficient of resistance (TCR).
If you look at this chart the variation of resistance with temperature and especially for the Nichrome V, we observed several areas in rough form, the zones A and E have an increase in resistance with temperature (TCR positive), in zones B and D it comes to points of zero or very small variation (TCR null), the C zone is characterized by a reduction in resistance with temperature(TCR Negative) .
Rugeof of M.I.T. conceived the idea of making a preassembly by mounting wire between thin pieces of paper
RESISTANCE FOIL STRAIN GAGES
In 1856 Lord Kelvin  reported that the electrical resistance of copper and iron wires increased when subjected to tensile stresses. This observation ultimately led to the development of the modern "strain gage" independently at California Institute of Technology and Massachusetts Institute of Technology in 1939. The underlying concept of the strain gage is very simple. In essence, an electrically-conductive wire or foil (i.e. the strain gage) is bonded to the structure of interest and the resistance of the wire or foil is measured before and after the structure is loaded. Since the strain gage is firmly bonded to the structure, any strain induced in the structure by the loading is also induced in the strain gage. This causes a change in the strain gage resistance thus serving as an indirect measure of the strain induced in the structure.
The material and casting technique improvements that have taken place during the last 50 years have enabled superalloys to be used first as equiaxed castings in the 1940s, then as directionally solidified (DS) materials during the 1960s, and finally as single crystals (SC) in the 1970s. Each casting technique advancement has resulted in higher use temperatures.
Metal Foil Type Strain Gauge, Metal Foil Type Strain Gauge and Method of Making Same, William D. Van Dyke 
During the 1950s the foil-type gage replaced the wire gage.
In 1954 a company Wilbur B. Drive Co. starts selling a Nickel-chromium-aluminium-copper alloy film of the order of fraction of a micron thick, called Evanohm.
The resistance-temperature coefficient of all metals depends to a large extent upon their purity and the thermal treatment. Pure metals have relatively high coefficients; the coefficients of alloys are usually smaller and can even be negative in certain ranges of temperature (manganin). Change of the physical character of the metal (annealing, recrystallization) can cause a change of the temperature coefficient which in some cases, e.g., at the curie point, can be discontinuous.  Instrumentation in Scientific Research, Kurt S. Lion, 1959.
In 1960, James E. Starr patent  a resistance made of a metal foil, as shown in the figure below,
The resistor formed of metal foil, the idea is similar to of invention of William D. Van Dyke , the ease in which the resistance value can be varied by thinning or narrowing the element of the pattern, either chemical etching or mechanical reduction of the with or thickness to increase the resistance. A resistor foil pattern or grid is formed, as by a photographic printing and chemical etching process and adhesively bonded to a thin insulating layer, epoxy or glass, .
In 1960, Felix Zandman patent the precision resistor of great stability , the invention has the following properties, controlled temperature coefficient of resistance, the idea is similar to of invention of Starr  , a thin film of a selected metal alloy upon a substrate, many times thicker than the metal film, the bulk metal film is a resistive alloy such as one of the Nichome, wherein nickel nickel and chromium are the principal metals, as indicated by John Strong , the film may be of the order of 0.04 inch, the substrate may be made of glass, the metallic film is photo-etched to pattern of the resistor, the two pictures are similar.
The structure of the system has a substrate made of glass having a temperature coefficient of expansion of the order of 3 parts per million per degree F, the thickness of the substrate is 0.04 inch and bulk metal film may be made from resistive alloy as one of the Nichrome alloy, wherein nickel and chromium are the principal metals, Ni75%Cr20%Cu2.5%Al2.5% , this film may be of the order of 0.0001 inch thick.
Zandman's contribution to the development of metal foil resistors is as follows. The resistive alloy film, etched in its predetermined pattern and bonded to the glass substrate, being of the order of one hundredth to one thousandth the thickness of the glass, exerts minimal influence upon the , dimensional responsiveness of the unit to the changes of temperature and moisture. The changes of resistance in the path ultimately determined in the patterned film between the junctions 16 and 17 is influenced by the following factors: (a) The temperature coefficient of resistivity of the alloy of which the patterned metal film is comprised; (b) The elongation and narrowing and consequent increase of resistance of the alloy film caused by the expansion of the symmetrically coated substrate with increase of temperature (and conversely, the compression and broadening of the alloy film when the symmetrically coated substrate contracts with decreasing temperature); (c) The variation of resistance as a function of the stress produced in the alloy film when the symmetrically coated substrate expands or contracts with changes of temperature.
As will be readily apparent, the factors b and c above represent the resultant effect of the forces produced in the substrate and the forces produced in the coatings thereon. By the selection of a nickel chromium alloy with such minor alloy components as to provide a desired curve of resistivity versus temperature and a desired temperature coefficient of expansion, the resistor may be made to have a reliable temperature coefficient of resistivity as low as 1 part per million per degree C. in the vicinity of a desired design temperature such as 25° C. and to have an extremely low overall temperature coefficient of resistivity throughout a range from - 55 ° C. to +175 ° C. In general, the alloy consisting primarily of nickel and chromium will have a greater temperature coefficient of expansion than the glass substrate. Hence, with increasing temperature, as the glass substrate elongates and carries with it the alloy film layer, the alloy film is subjected to compressive stress, in that paragraph shows an application of the discovery of Kelvin .
Conversely, as the glass substrate contracts with decreasing temperature and the alloy layer tends to undergo greater contraction, the resistive metallic film which is bonded to the glass and constrained to duplicate the contraction of the glass is subjected to tensile stress. Provided that the net sum effect of the resistance change component due to changing stress in the alloy film and the resistance change component due to expansion or con- traction of the film is substantially equal to the temperature coefficient of resistivity of the alloy under stress free conditions, and of opposite sign, the overall temperature coefficient of resistivity of the device is substantially zero. Since the last named factor is not linear, the device will have a predictable variation of its temperature coefficient of resistivity throughout the design temperature range.
In 1976, Paul Rene Simon, patent a process for etching a thin film or foil of an electrically conductive resistive material, preferably an alloy predominantly comprising nickel and chromium, by electrolytic etching under conditions of electrochemical machining above Jacquet's plateau on the I.V. characteristic curve, process called electropolishing. The process is particularly suitable for manufacturing a planar electrical resistor having a high stability, a low temperature coefficient, and a high ohmic value despite the relatively low resistivity of the film or foil. The anode surface polarization is maintained substantially constant over the surface of the foil or film by removing the by-products of the etching process, i.e., gases, viscous layers and other impurities, by mechanical effects such as an electrolytic flow or mechanical vibration, or both together. These mechanical effects are carefully balanced against the applied potential values such that the rate of formation of the layers and gases at the anode is equal to their rate of removal. Moreover, the anode electrical resistance is kept at a negligible value independent of the progress of the attack, by securing the film or foil to a thick layer of a conductor such as copper, whereby the evolution of potential drop across the foil, due to the electrical current flow, is kept at a negligibly small level. Under these conditions, a quasi-uniform etching is obtained all over the foil or film surface. The operating parameters of the process are also described as well as the advantages of the resistor produced according to the process of the invention.
Between 1980 and 1990, Mark Robinson presents a publication Strain Gage Materials and Processing, Metallurgy and Manufacture, using evanohm alloy, among other. 
These resistors comprise an insulating substrate, usually ceramic material, of thickness about 0.5 mm, a thin metallic foil bonded to the substrate, the foil having a circuit path formed by photographic techniques denominated etched-pattern resistor layer of bulk metal film ,the foil is a resistive Ni-Cr,or similar alloy like Karma o Evanohm , with a thikness of 2-8 mm (78.74 min-314.96 min) , the foil initially is heat treated to adjust its temperature coefficient of resistance (TCR) .
A photosensitive resin is then deposited on the foil using microelectronic processes, similar to integrated circuit process technology. The photosensitive resin is exposed (photolithography) through a photographic mask representing the design of resistance circuit, which resembles a series of looping filaments. The nonexposed areas are washed off, leaving the exposed areas intact, forming a meander pattern (photoresist mask) on top of the foil. The foil areas not protected by the photoresist mask are then etched by means of electrolytic or chemical processes, reproducing the design of the mask. This step creates hundreds of resistive filaments in series or parallel such that the resistance of the circuit reaches the desired value. Such resistance elements are usually produced in an array of several hundred on a wafer. The next process step is to singulate resistor chips from the wafer. Resistor Theory and Technology. Felix Zandman, Paul Rene Simon, Joseph Szwarc. Pag. 156 .
The following step is to cut the ceramic formed by many resistors to obtain them individually, next connector leads attached to the thin foil at each end of the circuit path and a protective coating surrounding the entire structure.
The Karma is compound one of alloy of Ni 74%, Cr 20%, Al 3%, Fe 3% and used to make grids of electrical resistance strain gages for applications at both cryogenic and elevated temperatures. It also possesses good fatigue characteristics. Karma alloy has similar overall properties to Constantan.
A high-precision resistor is constructed by supporting a metal film of Evanohm (Ni75%Cr20%Cu2.5%Al2.5%) alloy , for example, upon a substrate having know physical properties , the substrate being many times thicker than the metallic film, in the order of 100 to 1,000 times thicker. The metallic film is caused to have a predetermined pattern, including a great number of parallel narrow linear path portions in a planar array.
A low temperature coefficient of resistance (TCR), is generally accomplished by making use of a foil resistive element wherein the foil's resistivity changes with temperature are capable of compensating for the strain induced resistance changes which are developed as a result of mismatch of the coefficients of thermal expansion of the resistive foil and of the substrate to which it is applied.
Strain (e) is capable of being expressed as a function of temperature and as a function of resistance, in accordance with the following equations: (the following analysis was studied from a document of doctor Zandman, Swarc  )
e = ( as - af ) D T (differential thermal expansion) (1)
This phenomenon is denominated differential thermal expansion in layered materials, the shear stresses induced by two
layers undergoing differential expansion induces a curvature in the structure.
e = (1/ K) (DR/R) (strain gauge effect) (2)
as is the coefficient of thermal expansion of the substrate material
af is the coefficient of thermal expansion of the foil material
K a constant dependent upon the foil material
R is the resistance at temperature T,
Ro is the resistance at the base temperature
DR = R- Ro
DT is the temperature interval (T-25°C).
Accordingly, in defining changes in resistance as a function of temperature:
DR/R = K (as - af ) D T (3)
With reference to FIG. 7 of the drawings, this graph shows qualitatively the superposition of two effects, the change in resistance DR/R, due to change in resistivity with temperature, as a function nonlinear and other due strain, with a negative sign, it will be noted that by appropriate selection of the materials used, the characteristic defined in accordance with equation (3) is capable of being compensated by the foil's resistivity change with temperature r(T) (4).
As illustrated in FIG. 8 at (E), such compensation is operational over a range of temperatures. However, such compensation is not perfect because r(T) is non-linear while K (as - af ) D T is essentially linear. Nevertheless, the resulting temperature coefficient of resistance is very low and very useful for precision applications and this is the contribution of Zandman to the development metal foil resistor.
In 1973 Horii and Ohya , work with the idea of Zandman and present the results quantitatively experimentally determined.
Measurement of Electrical and Magnetic Quantities.
Study of Precision Alloys for the Production of Foil Resistors. 
Foi1 resistors are notable for their high stability (+/- 0.005%) and low temperature coefficient of resistance , TCR (+/- 5.10^-6 K^-1) . In the achievement of these parameters the resistive material and also the fabrication technology of the resistors are of decisive importance. For the manufacture of foil resistors the domestic industry has developed and put into production different types alloys based on nickel in the form of a foil, which have similar electrical characteristics (see Table 1). These alloys differ from manganin, which was developed and put into production previously, in having higher resistivity, a thinner toil in a cold-worked state, and a wider working temperature range.
Operating experience with the new alloys indicates that in resistors they display different properties. This can probably be explained by the fact that the mechanical properties of these alloys in a foil have not been studied enough, for among other things it is not clear whether the new alloys are brittle or plastic. There has also been no investigation of heat-treatment conditions with respect to foil thickness. It is known that with an increase in the amount of strain the initial temperature of recrystallization is lowered but with an increase of annealing time for a highly strained metal or alloy the initial temperature of its recrystallization is reduced exponentially. The explanation of this is that with increased strain, the density of dislocations and the energy accumulated with the strain are both increased. This temperature threshold for the recrystallization must be established for particular foil thickness that are used in the manufacture of foil resistors.
The existence of internal stresses in the resistance can cause instabilities and problems in controlling the TCR, temperature coefficient of resistance, in the engineering design of the metal foil resistor is desirable to control the stress in the foil and the substrate are joined by an adhesive, and should not approach their respective yield points, which can be defined as the point where a tensile test piece begins to extend permanently, if the load is reduced to zero, the test piece will not return to its original length. 
The materials used in production of foil resistors have the following characteristics:
Moduli of elasticity:
Foil Ef = 22 000 kg/mm^2
Substrate Es = 30 000 kg/mm^2
Yield point of foil = 85kg/mm2
Poisson ratio for both materials:
μ = 0.3 (approx.)
Coefficients of thermal expansion:
Foil αf =13 ppm/°C
(ppm = parts per million)
Substrate αs =6 ppm/°C
Both materials behave like Hookian elastic
Mathematical basis of the metal foil resistors and design guidelines.
Resistors are electrical devices used to direct current flow through a circuit thus producing a drop in voltage between two points. A vital component of most electrical networks and electronic circuits, resistors operate according to Ohm’s law. The law states that the current between two points of a conductor is directly proportional to the potential difference through the two points.
The level of resistance determines the functionality of a particular resistor. During resistor design, several factors must be considered. The necessary precision of the resistance is set by the manufacturing tolerance of the selected resistor, in accordance with unique application requirements.
A maximum power rating of a particular resistor must be higher than the predicted power dissipation in a particular circuit. Plus, the temperature coefficient of resistance (TCR) may be another important factor if the
application calls for high precision. The TCR is the relative change of resistors’ value when the temperature changes. For applications subject to large temperature changes, the TCR should be as low as possible.
coefficient of resistance, TCR as defined by
TCR = (R-R0)/R0. ΔT
where TCR is the temperature coefficient of resistance, R is the resistance at temperature T, R0 is the resistance at the base temperature, typically 25°C, ΔT is the temperature interval (T-25°C).
Heat treatment of metals. 
Most of the engineering properties of metals and alloys are related to their structure. Equilibrium structure can be predicted for an alloy with the help of an equilibrium diagram. Mechanical properties can be changed by varying the relative proportions of microconstituents. In practice, change in mechanical properties is achieved by a process known as heat treatment. This process consists of heating a metal or alloy to a specific predetermined temperature, holding at this temperature for required time, and finally cooling, holding at this temperature for required time. All these operations are carried out in solid state. Sometimes, it becomes necessary to repeat these operations to impart some characteristics. Therefore, heat treatment may be defined as heating and cooling operation(s) applied to metals and alloys in solid state so as to obtain the desired properties.
Heat treatment of metals is an important operation in the final fabrication process of many engineering components. The object of this process is to make the metal better suited, structurally and physically, for some specific applications. All metals can be subjected to thermal cycling. But the effect of thermal cycling may differ from one metal to another. For example, het treatment has significant impact on steels, and its properties may be changed considerably by definite heating and cooling cycles. In contrast, there is hardly any effect of thermal cycling on properties of hot rolled copper. Heat treatment may be undertaken for the following purposes:
(1) Improvement in ductility
(2) Relieving internal stresses
(3) Refinement of grain size
(5) Increasing hardness or tensile strength and achieving changes in chemical composition of metal surface as in the use of case-hardening.
Other beneficial effects of heat treatment include improvement is machinability, alteration in magnetic properties, modification of electrical conductivity, improvement in toughness and development of recrystallized structure is cold-worked metal
There are a number of factors of paramount importance which are to be considered when heat treating a metal or alloy. Some of them are the temperature up to which the metal/alloy is heated, the length of time that the metal/alloy is he1d at the elevated temperature. the rate of cooling, and the atmosphere surrounding the metal/alloy when it is heated. Any heat treatment process can be represented graphically with temperature and time as coordinates. Figure 1.1 describe a simple heat treatment cycle, whereas Figs. 1.2 and 1.3 represent some complex heat treatment cycles.
Graphical representation of a simple heat treatment cycle, rate of heating = XY/X’Y’ = AB’’/AB’ = constant.
Experiences made with different alloy and substrate materials. 
In 1973 Horii and Ohya , work with the idea of Zandman and present the results quantitatively experimentally determined, although Zandman ideas are the basis of metal foil resistors, an intensive experimental work was done by Horii and Ohya and is set out below.
An Ni-Cr alloy is rolled to be of a thickness of about 1 to 10 m by a known process. The Ni-Cr alloy is of Ni/Cr = 90/10 to 70/30 at the weight ratio. As additives thereto, Cu, Al, Si and Mn, here you see a change in the composition of the material, are used to adjust the temperature coefficient and linear expansion coefficient of the alloy. The amounts of the addition of these additives by weight percent are:
Cu 2 to 5 %
Al 0.5 to 3 %
Si 0.5 to 2 %
Mn 0.5 to 4 %
A desired linear expansion coefficient of about 136 x 10^-7 /grad. C is thus obtained. The metal foil of the alloy thus made and rolled as above is then heat-treated in a vacuum or inert gas, the latter idea will be taken by Mark Robinson in his work on the alloys . For the heat-treatment, it is desirable to keep the foil at about 600 grad.C for 3 hours with the rates of the temperature rise and fall as shown in Fig. 3
Such insulating base having a linear expansion coefficient in the range of 40 x 10^-7 /grad.C to 125 x 10^-7 /grad.C wich is lower that of the Ni-Cr metal foil as, for example, of borosilicate glass, sintered alumina, soda glass or the like is used, the authors used for the first time, the sintered alumina in experiments. The relation between the thickness of the base and the thickness of the metal foil is selected to be of such a ratio that
the thickness of the base / the thickness of the metal foil = 100 to 1000
The metal foil is then adhered to a surface of such an insulating base as above. An adhesive is thinly applied onto said base. At this time, the thickness of the adhesive should be preferably about 10 m, and it is also preferable to use an adhesive made of a thermosetting resin.
The difference in the linear expansion coefficient b between the base and metal foil is to be utilized in this procedure, for this purpose it is desirable that the difference in the coefficient b between the base and metal foil is in the range of 26 to 66 x 10^-7 /grad.C .
If the diffence in the coefficient b is made to be large than 66 x 10^-7 /grad.C, only resistance temperature coefficient as low as in the conventional thechnique will be obtained. Even if it is made smaller than 26 x 10^-7 /grad.C, only a large value of the resistance temperature coefficient will be obtained.
The metal foil bonded to the base as above is then etching-processed depending on desired resistance patern of each kind, then the insulating base including the foil of desired insulating pattern cut,lead wires (for example, tin-plated copper wires of a diameter of 0.16 mm.) are welded to it to form terminals.
Then the system is adjusted to be a desired resistance value by trimming. After the adjustment, the thus obtained resistance element is molded with a phenol resin or epoxy resin so as to be enclosed in the molded resin.
An experimental example shall be explained in the following :
A metal foil of a thickness of 3 m was made of an Ni-Cr alloy of Ni/Cr of 85/15 and additives of 4 percent by weight Cu, 2 percent by weight Al, 1 percent by weight Si and 1 percent by weight Mn, and was heat-treated as shown in Fig. 3. A base was of sintired alumina of 48 mm. long, 48 mm. wide and 0.6 mm. thick . This base was thinly painted with a bis-phenol type denatured epoxy resin and the above mentioned metal foil was bonded to it. It was etched in squares of 6 mm. x 6 mm. to form a resistance pattern, the lead wires are spot-welded to the terminal parts of the resistance body, the lead wire should be preferably a tin plated copper wire of a diameter of 0.16 mm. ,the resistance-temperature characteristics in this case were as shown in Fig. 4, in which the abscissa represents the temperature and the ordinate represents the resistance variation. The results when the ratio was varied and the material of the base was varied were as in Table 1,
In the above table, the temperature coefficient was calculate by measuring the resistance values at temperatures of -55 grad.C, +25 grad.C and 125 grad.C and making 25 grad.C to be a base. As evident from Table 1, the temperature coefficient can be made remarkably low in the case where the difference in the linear expansion coefficient between the metal foil and insulating base is of a certain value , the Fig. 5 ,
Materials used in the manufacture of metal foil resistors.
The precision cold rolling process.
Conventional cold rolling and foil, wich has been carried out for over 100 years is practiced in many manufacturing locations around the world. Conventional cold rolling is usually carried out on 2-high or 4-high rolling mills, where coils of metal thousands of feet long are rolled at speeds up to 5,000 feet per minute and widths up to 6 feet. Steel, stainless steel, aluminium alloys, brass another copper alloys in strip and foil form are made in the millions of tons every year by cognitional cold rolling.
In many applications, the components are forced to endure constant loads during long periods, such as turbine rotor blades, pipes and valves filament, steel wires, etc. In such circumstances the material can continue to deform until its usefulness is seriously impaired. Such types of time-dependent deformations may be almost imperceptible but grow throughout the life of the part and lead to breakage, even without the load has increased.
With loads applied for a short time, as in a static tensile test, there is a simultaneously initial deformation increases with load. If, under any circumstances, the while continuing deformation load remains constant, this additional deformation is the known as creep.
The phenomenon known as "creep", is defined as: "the time-dependent part of the deformations from tension " . Because of their close connection to high temperatures in important applications, usually
associated with problems related to creep at high temperatures.
This is true only if elevated temperatures are defined relative to the melting point Tm d, lead displays a creep significant at room temperature and asphalt, for example, at lower temperatures. in some materials such as concrete and wood, the temperature is not an important factor. Recent developments in analysis are linked creep resistant heat alloys as used in gas turbines and steam power plants. As the trend in current designs is continuously increasing temperature, the situation becomes increasingly critical.
The following figure shows a creep curve. The same is obtained by applying a load constant and measuring the deformations that occur with time, keeping the temperature constant.
EVANOHM® alloy S is a nickel-chromium resistance alloy developed to fill a specific need in ultra-precision resistance wire. It offers optimum stability and flexibility with regard to both size and required temperature coefficient of resistance (TCR).
The alloy's high resistivity and extremely low electro-motive force (EMF) versus copper are highly desired properties in precision resistance wire. It also possesses high tensile strength, high resistance to corrosion and is non-magnetic.
The temperature coefficient of resistance of this material is very closely controlled by the addition of aluminum, manganese and silicon combined with critical processing controls.
EVANOHM alloy S is supplied in the annealed and heat treated condition to ± 5 ppm in the temperature range of -67°F to 221°F (-55°C to 105°C). This results in very stable resistance.
Although EVANOHM alloy R is the only high-resistance, low-TCR alloy on which extensive stability tests have been conducted, EVANOHM alloy S is heat treated in the same manner and is believed to have equal stability because its properties are produced by the same short range ordering as EVANOHM alloy R.
Mechanical stresses, such as cold working, decrease resistivity and increase TCR in a positive direction. The magnitude of these changes is similar to EVANOHM alloy R, so that the same stress relieving procedures used in processing EVANOHM alloy R can and should be used. 
Evanohm® R is a unique resistance alloy with high electrical resistivity and very low temperature coefficient of resistivity (TCR). The alloy is produced by melting and conditioning practices which result in a low level of pinholes at ultra-thin thicknesses. This combination of attributes with inherent corrosion resistance makes it suitable for a variety of strain gauge and foil resistor applications. 
The alloy is supplied with 90% cold reduction which has a positive TCR of about 70 PPM/ºC. A stabilizing heat treatment, approximately475ºC during manufacture of finished parts adjusts the TCR to a desired value, in this case if we look at the graph drawn heat treatment above this temperature is approximately the value used for TCR of 0 ppm/Deg C . The heat treatment virtually eliminates any drift tendency of the resistivity. A heat-treat curve for each melt is developed at Hamilton and is made available as a guide in regulating TCR.
Long- and short-range order.
A solid is crystalline if it has long-range order. The fundamental difference between single crystal , polycrystalline and amorphous solids is the length scale over which the atoms are related to one another by translational symmetry (‘periodicity’ or ‘long-range order’). Single crystals have infinite periodicity, polycrystals have local periodicity, and amorphous solids (and liquids) have no long-range order.
An ideal single crystal has an atomic structure that repeats periodically across its whole volume. Even at infinite length scales, each atom is related to every other equivalent atom in the structure by translational symmetry.
A polycrystalline solid or polycrystal is comprised of many individual grains or crystallites. Each grain can be thought of as a single crystal, within which the atomic structure has long-range order. In an isotropic polycrystalline solid, there is no relationship between neighbouring grains. Therefore, on a large enough length scale, there is no periodicity across a polycrystalline sample.
Amorphous materials, like window glass, have short-range order at all, so they have no translational symmetry.
Once the positions of an atom and its neighbours are known at one point, the place of each atom is known precisely throughout the crystal. Most liquids lack long-range order, although many have short-range order. Short range is defined as the first- or second-nearest neighbours of an atom. In many liquids the first-neighbour atoms are arranged in the same structure as in the corresponding solid phase. At distances that are many atoms away, however, the positions of the atoms become uncorrelated. These fluids, such as water, have short-range order but lack long-range order. Certain liquids may have short-range order in one direction and long-range order in another direction; these special substances are called liquid crystals. Solid crystals have both short-range order and long-range order.
Solids that have short-range order but lack long-range order are called amorphous. Almost any material can be made amorphous by rapid solidification from the melt (molten state). This condition is unstable, and the solid will crystallize in time. If the timescale for crystallization is years, then the amorphous state appears stable. Glasses are an example of amorphous solids. In crystalline silicon (Si) each atom is tetrahedrally bonded to four neighbours. In amorphous silicon (a-Si) the same short-range order exists, but the bond directions become changed at distances farther away from any atom. Amorphous silicon is a type of glass. Quasicrystals are another type of solid that lack long-range order.
Most solid materials found in nature exist in polycrystalline form rather than as a single crystal. They are actually composed of millions of grains (small crystals) packed together to fill all space. Each individual grain has a different orientation than its neighbours. Although long-range order exists within one grain, at the boundary between grains, the ordering changes direction. A typical piece of iron or copper (Cu) is polycrystalline. Single crystals of metals are soft and malleable, while polycrystalline metals are harder and stronger and are more useful industrially. Most polycrystalline materials can be made into large single crystals after extended heat treatment. In the past blacksmiths would heat a piece of metal to make it malleable: heat makes a few grains grow large by incorporating smaller ones. The smiths would bend the softened metal into shape and then pound it awhile; the pounding would make it polycrystalline again, increasing its strength.
Wire Strain Gauges. 
This strain gauge, consists essentially of a fine wire, usually of about 0.001 in. diameter. When exposed to strain within the elastic limit, two physical mechanisms will cause a change of its resistance. First, its geometrical form will vary, i.e., the wire will show an increase of length and a decrease of cross-sectional area. Second, a change of electrical resistivity will occur, which can result in an increase or decrease of resistance,
depending upon the material of the wire.
The strain coefficient of resistance is,
where R is the resistance of the wire, dR is the resistance variation due to the variation of strain de, m is the Poisson ratio, and r the resistivity. Of the two terms of the right side of Eq. (w1), the first denotes the geometric effect, the second the physical effect of resistivity variation. Apparently, the change of resistivity has its origin in a variation of the number of free electrons and of their mobility.
In the strain-gauge engineering literature, the behavior of the strain gauge is commonly expressed by
where L is the length and R the resistance of the unstrained wire, DL its change of length, and DR its change of resistance caused by external stress. The dimensionless magnitude S ,sensitivity factor of the wire, can be positive or negative and varies for different metals between — 12.1 and +3.6. The following table shows some representative values of S.
Metal Foil Resistance Strain Gages. 
PRINCIPLE OF OPERATION.
The operative principle of the electrical resistance strain gage has been known for more than a century. In 1856, Lord Kelvin reported that certain metal wires exhibited a "change of electrical resistance with change in strain." The total electrical resistance of a rectangular uniform cross section conductor is given by the equation
R= (r . L )/( a . b)
where R, r, L, a, and b are the resistance, specific resistance, length, and lateral dimensions of the rectangular cross section of the conductor, respectively. Taking logarithms and differentiating Eq. 2.1 leads to
Wheatstone Bridges and Strain Gages.
Strain gages are devices which are aligned and glued (bonded) to a structural member. When the structural member is then loaded, the strain gage undergoes the same elongation ,in the direction of its alignment as the fibers of the structural member to which it is immediately bonded. The elongation of the strain gage causes changes in the electrical resistance of the gage. A Wheatstone bridge is extremely important to the manipulation of the strain gage’s resistance change, hence, it is the instrument of choice in the research and production of metal foil resistors . A voltage is applied to the bridge and changes in resistance of the strain gage cause changes in the output voltage of the bridge.
The law of electric flow is based upon experimental results appertaining to a property of matter. It implies that the potential difference between any two fixed points on a given homogeneous conductor, when flow of electricity between those points is steady, is a direct measure of the current in the conductor,
between those points. The ratio of that potential difference to that current, in these circumstances, is a characteristic of the portion of the conductor in question, and is called the "resistance." So long as Ohm's law applied, "resistance" thus defined is constant for all values of the potential difference between the two points.
The magnitude of the current in a galvanic circuit is directly proportional to the sum of all the electromotive forces, and inversely proportional to the whole of the reduced length of the circuit, and it must be remembered that by reduced length is to be understood the sum of all the quotients which can be formed corresponding to all the actual lengths of the homogeneous parts and the products of the corresponding conductivities and cross-sections.
The law is most easily demonstrated to hold in the case of homogeneous metallic conductors at constant temperature. Ohm's law thus defined is applicable to all conducting systems and is free front ambiguify;
its usefulness has carried it into the wider field of electrical research and engineering, where its interpretation has occasionally been stretched to the very limits of its validity.
From metallic conductors it has been extended to electrolytes, from electrolytes to dielectrics, from dielectrics to electric arcs, and from arcs to thermionic valves. Moreover, by mathematical devices, inductance, capacity, and leakance have all been operated upon to convert them. into terms capable of being interpreted as "resistance."
Pioneer work in electrical communication, from the middle to the end of the nineteenth century, was in great measure carried on by electricians whose equipment of theory was limited to applications of Ohm's law in the somewhat ambiguous form :
Current = C = E/R= Electromotive force of battery/Resistance
He started from the fact that when two dissimilar metals, or certain other substances, touch one another, they maintain at the point of contact a difference of potential. He recognised that chemical changes in fluid portions of a circuit introduce complexities that occasionally lead to apparent exceptions. These, until inter- preted, amount almost to contradictions. He therefore deferred consideration of the parts of circuits that are subject to chemical change, and he dealt first with a circuit of homogeneous material of the same cross-section throughout. For such a circuit he found by experiment that the slope representing potential, coordinated
against electrical resistance, is a straight line. This line he plotted, and he proceeded in like manner to obtain zig-zag representations of the fall of potential for composite circuits built up of conductors of various lengths, sections, and materials. Then he showed how to calculate the fall between any two given points along such a composite circuit. He demonstrated that for the steady state, for a circuit the cur- rent is of equal strength at all points along the conducting system, and that a change of current at any one point corresponds to similar change of current throughout. He stated his law, in terms not of "resistance " but of "reduced length." By "reduced length" he meant the length of a wire of given material, such as standard copper, and of given sectional area having a resistance equal to the sum of the resistances of the circuit in question.
His argument was next directed to proving that interchange of the parts of a composite line of conductors has no effect upon the total resistance. He proved that for all points along the conductor, provided that the ratio of potential difference to resistance is constant, the current is constant. The trouble in his experiments arose because the resistance of his battery was large and unsteady. He explained why results of greater consistency were obtained with a thermocouple, where the resistance is small. Then he dealt with problems relating to cells in series and in parallel, the effect of putting a galvanometer into the circuit, and general expressions for the resistance of conductors in parallel.
All structural materials possess to a certain extent, the property of elasticity, i.e., if external forces, producing deformation of a structure, do not exceed a certain limit, the deformation disappears with the removal of the forces, we assumed that the bodies undergoing the action of external forces are perfectly elastic, i.e., that they resume their initial form completely after removal of forces.
The molecular structure of elastic bodies will not be considered here. It will be assumed that the matter of an elastic body is homogeneous and continuously distributed over its volume so that the smallest element cut from the body possesses the same specific physical properties as the body. To simplify the discussion it will also be assumed that the body is isotropic, i.e., that the elastic properties are the same in all directions.
Structural materials usually do not satisfy the above assumptions. Such an important material as nickel-chromium, for instance, when studied with a scanning electron microscope, is seen to consist of crystals of various kinds and various orientations. The material is very far from being homogeneous; but experience shows that solutions of the theory of elasticity based on the assumptions of homogeneity and isotropy can be applied to nickel-chromium structures with very great accuracy.
The explanation of this is that the crystals are very small; usually there are millions of them in one cubic inch of nickel-chromium. While the elastic properties of a single crystal may be very different in different directions, the crystals are ordinarily distributed at random and the elastic properties of larger pieces of metal represent averages of properties of the crystals. So long as the geometrical dimensions defining the form of a body are large in comparison with the dimensions of a single crystal the assumption of homogeneity can be used with great accuracy, and if the crystals are orientated at random the material can be treated as isotropic.
When, due to certain technological processes such as rolling, a certain orientation of the crystals in a metal prevails, the elastic properties of the metal become different in different directions and the condition of anisotropy must be considered. We have such a condition, for instance, in the case of cold-rolled copper.
2- Stress. 
Let Fig, 1 represent a body in equilibrium. Under the action of external f orces P1, ... , P7, internal forces will be produced between the parts of the body. To study the magnitude of these forces at any point O, let us imagine the body divided into two parts A and B by a cross section mm through this point.
Considering one of these parts, for instance, A, it can be stated that it is in equilibrium under the action of external forces Pl, ... , P7 and the inner forces distributed over the cross section mm and representing the actions of the material of the part B on the material of the part A. It will be assumed that these forces are continuously distributed over the area mm in the same way that hydrostatic pressure or wind pressure is continuously distributed over the surface on which it acts. The magnitudes of such forces are usually defined by their intensity, i.e., by the amount of force per unit area of the surface on which they act. In discussing internal forces this intensity is called stress. In the simplest case of a prismatical bar submitted to tension by forces uniformly distributed over the ends (Fig. 2), the internal forces are also uniformly distributed over any cross section mm. Hence the intensity of this distribution, i.e., the stress, can be obtained by dividing the total tensile
Electric currents are flows of electric charge. Suppose a collection of charges is moving perpendicular to a surface of area A, as shown in the following figure,
The electric current is defined to be the rate at which charges flow across any crosssectional area. If an amount of charge ΔQ passes through a surface in a time interval Δt, then the average current Iavg is given by
Iavg= DQ/Dt (6.1.1)
In the limit Dt→0, the instantaneous current I may be defined as,
Because flow has a direction, we have implicitly introduced a convention that the direction of current corresponds to the direction in which positive charges are flowing. The flowing charges inside wires are negatively charged electrons that move in the opposite direction of the current. Electric currents flow in conductors: solids (metals, semiconductors), liquids (electrolytes, ionized) and gases (ionized), but the flow is impeded in non-conductors or insulators.
To relate current, a macroscopic quantity, to the microscopic motion of the charges, let’s examine a conductor of cross-sectional area A, as shown in Figure 6.1.2.
One of the most outstanding and important characteristics of a metal is its ready ability to conduct electricity. Shortly after J.J. Thomson's discovery of the electron in 1897 it was appreciated by Drude (1900) and
Lorentz (1904) that this property of a metal was due to the presence of large numbers of non-localized valence electrons, which were free to move through the metallic lattice under the action of an applied electric field.
Nickel Chromium (Ni80Cr20) .
Alloying one metal with other metals or non-metals often enhances its properties. The physical properties of an alloy may not differ greatly from those of its elements, but engineering properties may be substantially different from those of the constituent materials. Whether in the form of element or alloy with other metals, nickel materials have made significant contributions to present-day society. The favorable physical
and mechanical properties as well as corrosion resistance characteristics of nickel and its alloys provide aids to the solution of many industrial problems(Teeple 1954). Alloying with nickel increases the impact strength and ductility of sintered materials without adversely affecting their strength (Enríquez and Mathew2003). Nickel alloys have good corrosion resistance and heat resistance, the standard alloy being used for electrical-resistance for heaters and electrical appliances is Nickel–Chromium (Murray 1997). Chromium–nickel steel alloys have good mechanical properties (Radomysel’’skii and Kholodnyi 1975).
Benjamin Solow. 
A thin film foil resistor is disclosed wherein a thin metallic foil is bonded to an insulating substrate and a circuit path is formed on the foil by photographic art work-etching techniques. After the circuit is formed, the structure is subjected to another etching process to reduce the thickness of the foil circuit thereby adjusting the value of the resistor. Terminal lands of the circuit are electroplated and the connecting leads are soldered to the lands. The value of the resistor is finally adjusted by use of a laser beam, and the resistor is encapsulated.
These resistors comprise an insulating substrate (usually of glass or ceramic material); a thin metallic foil bonded to the substrate, the foil having a circuit path thereon usually formed by photographic acid etch techniques; connector leads attached to the thin foil at each end of the circuit path; and a protective coating surrounding the entire structure.
Typically the photographic-acid etch technique of forming the circuit path comprises the steps of photographing the desired circuit path and reducing the art work in size to correspond to the desired size of the final resistor; coating the thin metal foil with a photosensitive masking medium; exposing the coated side of the foil to the photographed circuit; and, subjecting the exposed foil to an etching process wherein all foil not corresponding to the desired circuit is removed. The etching process may be undertaken either before or after the foil has been bonded to the substrate.
Despite the general acceptance of this basic method by the electronics industry, the resistors formed thereby have exhibited several deficiencies. Among the more prominent problems has been the use of a welding process to attach the connector leads to the terminals of the foil circuit path. Due to the small size of the terminals and the thinness of the circuit foil (on the order of0.000l") the welds attaching the relatively thick connector leads to the circuit terminals have exhibited very poor strength. Normal usage often causes a breakage in the welds and, consequently, a catastrophic failure in the resistor due to the open circuit.
A typical foil circuit has a serpentine current path defined by a series of closely spaced foil “legs." The value of the resistance may be adjusted, to overcome inaccuracies inherent in the manufacturing process, by
cutting through specifically designated portions of the circuit to alter the path of current travel. This method of adjustment requires a number of circuit portions for fine adjustment, since the adjustment must be made in discrete steps.
In the prior art resistors, the required adjustment causes serious deficiencies, notably the extremely fine lines used to adjust circuit patterns by the scratch and break method are often much finer than the basic pat tern and are, therefore, sensitive to the tiniest defects during manufacture. Obviously, this decreases the reliability of the resistor.
The methods of adjusting by cutting through the foil to alter the current path, it is necessary to carry out the adjustment manually, usually by an operator with the aid of a microscope. The manual adjustment necessitates a large amount of time in the production process and results in a higher priced product which is subject to human error.
The technology resistors devote a portion of the foil area to a trimmer circuit pattern i.e. a pattern used solely in the adjusting operation to adjust the value of the resistor. This portion serves no other purpose than
adjustment, and results in a resistor somewhat larger in size than is absolutely necessary. The standard adjustment technique of cutting the foil to the current flow path also contributes to unnecessary size since, usually, a number of conductor lines do not carry any current. In this age of miniaturization, it is a serious product deficiency to have unused or partially used space which results in a resistor larger than necessary.
The method of manufacturing the resistor, comprises the steps of bonding an annealed thin metallic foil to an insulating substrate using an epoxy glue; coating the foil surface of the laminate with a photosensitive masking medium; exposing the coated surface to photographic artwork of the desired circuit pattern or patterns; etching away the metallic foil not required for the circuit; removing the masking medium; etching the thickness of the circuit pattern to roughly adjust the value of the resistor; recoating the circuit with a masking medium except for the terminal lands to which the connecting leads are to be attached; electroplating the terminal lands; removing the masking medium; soldering the connecting leads to the terminal lands; coating the resistor with varnish; laser adjusting the resistor to its final value; coating the resistor with rubber for strain relief; and encapsulating the completed resistor structure.
By etching the thickness of the circuit pattern to achieve the rough adjustment of the resistance value, the present invention does not require a resistor to have a separate portion of the circuit used only for value adjustment. Thus, a resistor formed by this method allows the maximum amount of the substrate area to be
utilized for the .actual resistor circuit. This allows a given value resistor to be smaller in size or, conversely, a larger circuit path to be incorporated onto a given substrate area.
FIG. 1 is a perspective view of a resistor,
A resistor made by the preferred embodiment of this invention is illustrated in FIG. 1 generally as 10 and comprises a substrate 12 of insulative material, such as glass or ceramic, a thin metallic foil resistor circuit
pattern 14 with integral terminal lands 16, and connecting leads 18 having flattened portions 20 attached to the terminal lands 16 by soldering. The resistor as just described may be encapsulated by molding an insulating
material around the entire structure after first coating with varnish (such as Dow Corning G P 77 NP) and rubber or by potting in a case, as is well known in the art. The encapsulation and coatings are omitted from FIG. 1 for purposes of clarity.
Benjamin Solow did not explain in his invention, how to attach the terminal of the resistor to the metal foil and in the drawing does not see any effect of that union, in a publication the company Wilbrecht Ledco, explains the effects of this critical union , and unlike solow gives a drawing with an elaborate process to avoid the effects given by NASA,
The individual resistor 10 is cut from a series of resistor patterns 14 applied to a substrate as shown in FIG. 2. These resistor patterns are formed by a thin metallic foil which has been bonded to the substrate by a laminating process to be described hereinafter, and subsequently subjected to a photographic artwork-etching process which removes all of the foil except that which forms the circuit patterns. Prior to bonding to the substrate, the thin metallic foil is first annealed. The metal foil may be made from any resistive alloy, such as Evanohm alloy made by Wilbur B. Driver Co. and is on the order of 0.0001" thick. The foil is annealed by heating it in an inert atmosphere at1000◦F. for a sufficient time to provide a temperature coefficient of resistance of the completed resistor in combination with the particular substrate of approximately zero. The requisite time will, of course, vary with the particular alloy metal foil being used, but for Evanohm metal foil, it has been found that heating the foil at I000◦ F. for a period of approximately 15 minutes will produce the desired temperature coefficient of resistance when laminated to a Soda Lime glass substrate.
Ceramic compounds. 
Defining a ceramic compound as anon-metallic inorganic compound is a paradoxical* choice, because it supposes that the concept of metal is sufficiently unambiguous ** to serve as basis for clarifying its antonym. However, confusions are frequent here, and are aggravated by the fact that ceramic compounds are metallic- non-metallic compounds, which we shall now study in detail.
* A paradox is an argument that produces an inconsistency, typically within logic or common sense. ** unambiguous :Not open to more than one interpretation. *** antonym: A word opposite in meaning to another.
Chemistry of ceramics.
Metallic elements form a majority among the elements of the periodic table. We know that these elements are located on the left of this table, and are therefore electropositive elements , which tend to lose electrons to yield positively charged cations. Non-metallic elements, sometimes denoted by their old name metalloids, are located on the right of the table: they are electronegative and tend to capture electrons. The ionic bond is illustrated by the attractions that develop between a metal, sodium, and anon-metal, chlorine, to create sodium chloride NaCI , also written as Na(+)CI(-).
Electropolishing is an electrochemical process similar to, but the reverse of, electroplating. The electropolishing process smooths and streamlines the microscopic surface of a metal object such as 304, 316, and the 400 series stainless steel. As a result, the surface of the metal is microscopically featureless, with not even the smallest speck of a torn surface remaining.
In electropolishing, the metal is removed ion by ion from the surface of the metal object being polished. Electrochemistry and the fundamental principles of electrolysis (Faraday's Law) replace traditional mechanical finishing techniques, including grinding, milling, blasting and buffing as the final finish. In basic terms, the metal object to be electropolished is immersed in an electrolyte and subjected to a direct electrical current. The object is maintained anodic, with the cathodic connection being made to a nearby metal conductor.
During electropolishing, the polarized surface film is subjected to the combined effects of gassing (oxygen), which occurs with electrochemical metal removal, saturation of the surface with dissolved metal and the agitation and temperature of the electrolyte.
The Electropolishing Characteristics Fig. 1 reports a typical I-V characteristic for the electropolishing of Copper in orthophosphoric (prefix designating more hydrated acid) acid solution in the case of planar and parallel faced electrodes, when edge effects are negligible [Jacquet, P.A., Metal Finishing, 48, 1, 2 (1950)],
Phosphoric acid. 
Phosphoric acid is not a particularly strong acid as indicated by its first dissociation constant. It is a stronger
acid than acetic acid, but weaker than sulfuric acid and hydrochloric acid. Each successive dissociation step
occurs with decreasing ease. Thus, the ion H2 PO4(-) is a very weak acid, and HPO4 (-)is an extremely weak
The NASA qualification standard for metal foil resistors requires both a100G-shock test and a 20G (peak value) vibration test. To meet this standard, NASA has recognized the importance of wire terminations in metal foil resistors. Thus, in their Specification S-311-P-813—developed for the procurement of Space Level precision resistors—NASA specifically calls out(§3.3 Design and Construction) “resistor constructions using a thin metal foil element shall include a flexible intermediate conductor between the terminal lead and the foil (ex., a metal ribbon or thin wire).”
 METAL FOIL TYPE STRAIN GAUGE AND METHOD OF MAKING SAME William D. Van Dyke, Patent number: 2457616
 ADJUSTABLE RESISTORS AND METHOD OF MAKING THE SAME James E. Starr, Patent number: 3071749
 Precision Resistor of Great Stability, Felix Zandman, Patent number: 3517436
 ELECTRIC RESISTANCE ELEMENT ALBEET L. MARSH, Patent number: 811859
 Instrumentation in Scientific Research, Kurt S. Lion, 1959, page 156.
 Zero TCR Foil Resistor Ten Fold Improvement in Temperature Coefficient. Reuven Goldstein .
 Resistor Theory and Technology. Felix Zandman, Paul Rene Simon, Joseph Szwarc. Pag. 158
 Experimental study of Evanohm thin film resistors at subkelvin temperatures. A F Satrapinski, A M Savin, S Novikov and O Hahtela, Measurement Science and Technology, Volume 19 Number 5.
Thin film resistors, based on the Evanohm (Ni75%Cr20%Cu2.5%Al2.5%) alloy, have been investigated at cryogenic temperatures. The objective of the study is the development of the high value resistor for precision electrical measurements at low temperature and particularly for metrological triangle experiments. Thin film resistors of different configurations have been designed and fabricated by the thermal evaporation process. The resistivity of investigated resistors is 110 × 10−8 Ω m; the resistance exhibits a Kondo minimum at a temperature near 30 K and increases with further reduction of temperature. In the temperature range 50–65 mK, the temperature coefficient reaches −20 × 10−3 K−1. Power dependence measurements at subkelvin temperatures demonstrate that noticeable electron overheating takes place only at the power level above 10 pW for a 500 kΩ resistor. The electron–phonon coupling constant for the fabricated Evanohm thin films has been derived from experimental results.
 Felix Zandman, Joseph Swarc ( USP 4,677,413), 1987, Patent number: 4677413
 Kazuo Horii, Kazuo Horii, An improved thin-film resistor, Patent number: 3824521
An improved thin-film resistor low in the resistance temperature coefficient is provided. A metal film or foil is bonded with a thermosetting resin onto an insulating base plate having a lower linear expansion coefficient than the metal and is etching-processed so as to be of a desired resistance pattern. The difference in the linear expansion coefficient between the metal and the insulating base is selected to be 26 to 66 .times. 10.sup.-.sup.7 /.degree.C. The metal and base are covered with a resin so as to be a molded assembly, together with lead wires connected to both ends of the metal.
 Strain Gage Materials Processing, Metallurgy and Manufacture, Mark Robinson, Hamilton Precision Metals.
TCR Manipulation in Gage Materials.
Adjustment of the TCR to compensate for thermal effects is carried out by heat treating the cold rolled gage resistor foil. Both Constantan and Evanohm can be adjusted over the range of interest, but the heat treating response of the two alloy is different.
Cold rolled Evanohm foil can have its TCR adjusted over the range of about + 10 to – 40 ppm/°C by heat treating in the 400°C to 600°C(750°F to 1100°F) temperature range. A curve showing the TCR resulting from a 4 hour heat treatment is shown in Figure 8. The TCR response is parabolic in shape, going through a minimum of about – 40 ppm/°C near 500°C(925°F) and crossing the zero TCR axis twice.
Different heats of Evanohm, which exhib slight differences in composition, all show similar behavior. The parabolic curve shifts slightly from heat to heat, but remains generally the same.
The mechanism responsible for this change in TCR is not fully understood. The TCR response for Evanohm was empirically determined and has been used in both strain gage and precision resistor manufacturing for some time. The most likely cause of the TCR shift is a phenomenon called short range ordering which is known to occur in many nickel-chromium alloys heated into this temperature range. When short range ordering occurs in a metal crystal, the random first-neighbor arrangement of alloying atoms on the crystal lattice is replaced by a specific arrangement over a few atomic distances. Short range ordering is difficult to observe directly, so its presence is usually detected indirectly by observation of properties affected by ordering, such as electrical resistivity.
 Heat Treatment: Principles and Techniques By T. V. Rajan, C. P. Sharma, Ashok Sharma
 EVANOHM® Alloy , Carpenter
 Wheatstone bridge
 Metal Foil Reasistance Strain Gage, Nanjing University of Aeronautics and Astronautics,
 Metal and Alloy Bonding: An Experimental Analysis, R. Saravanan , M. Prema Rani
 Deviations from Matthiessen’s Rule for the Electrical Resistivity of Imperfect Metals, Robert J. Berry, 1972
 Benjamin Solow, Metal foil resistor, 4,297,670
 Method for etching thin foils by electrochemical machining to produce electrical resistance elements , Paul Rene Simon, 1976, 4,053,977
 Method for producing electrical resistance strain gages by electropolishing, Post Daniel, 1961, 3,174,920
 AUTOMATED ELECTROPOLISHING, V. Palmieri, V. Rampazzo