U.S. patent number 3,922,388 [Application Number 05/525,587] was granted by the patent office on 1975-11-25 for method of making an encapsulated thick film resistor and associated encapsulated conductors for use in an electrical circuit.
This patent grant is currently assigned to Honeywell Inc.. Invention is credited to Sergei Schebalin.
United States Patent |
3,922,388 |
Schebalin |
November 25, 1975 |
Method of making an encapsulated thick film resistor and associated
encapsulated conductors for use in an electrical circuit
Abstract
A method of making an encapsulated thick film resistor and an
associated encapsulated conductor so that the stability of the
resistor will be maintained at a precise level over an abnormally
long period of time by first firing selected mixtures of positive
and negative thick film resistor ink materials on a
non-electrically conductive substrate at a selected high
temperature, jointly firing the resistor and conductor ink
materials associated with this resistor at a temperature that is
lower than the first mentioned temperature and which is at a level
that will not allow any detrimental diffusion to occur between the
conductor and the resistor materials, applying a resilient buffer
material formed of a silicone polymer filled with magnesium oxide
over the fired resistor and the fired conductor and then applying a
hard outer glyptal coating over the resilient buffer.
Inventors: |
Schebalin; Sergei (Ambler,
PA) |
Assignee: |
Honeywell Inc. (Minneapolis,
MN)
|
Family
ID: |
32397873 |
Appl.
No.: |
05/525,587 |
Filed: |
November 20, 1974 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
|
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334956 |
Mar 22, 1973 |
|
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|
|
120199 |
Mar 2, 1971 |
3788891 |
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Current U.S.
Class: |
427/103; 427/102;
338/308 |
Current CPC
Class: |
H01C
17/02 (20130101); H05K 3/28 (20130101); H05K
1/167 (20130101) |
Current International
Class: |
H01C
17/00 (20060101); H01C 17/02 (20060101); H05K
3/28 (20060101); H05K 1/16 (20060101); H01H
037/36 (); H01B 001/02 () |
Field of
Search: |
;117/212,215,217,227,218
;338/309 ;252/514,518,521 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Esposito; Michael F.
Attorney, Agent or Firm: Swanson; Arthur H. Burton; Lockwood
D. Stevenson; J. Shaw
Parent Case Text
This application is a continuation of my prior application bearing
Ser. No. 334,956, filed Mar. 22, 1973, now abandoned, which is a
division of U.S. patent application Ser. No. 120,199, filed Mar. 2,
1971, now U.S. Pat. No. 3,788,891.
Claims
The embodiments of the invention in which an exclusive property or
privilege is claimed is defined as follows:
1. A method of making an encapsulated thick film resistor having
conductive portions associated with opposite ends thereof that form
portions of an electrically conductive circuit, comprising the
first step of selecting an ink from a mixture of positive and
negative resistor inks, the second step of firing the resistor ink
mix in amorphic form at 1000.degree.C into a sintered state onto an
electrically non-conductive substrate, the third step of selecting
a conductive ink material that has a sintering temperature
substantially lower than the sintering temperature of the resistor,
the fourth step of firing said conductive ink at a sintering
temperature of about 550.degree.C in overlapping relationship with
said opposite ends of said resistor on the substrate whereby the
tendency to diffusion between the conductive and resistive
materials is minimized and whereby a resulting temperature
coefficient of resistivity value of the resistor that is produced
is within plus or minus 20 parts per million per degree centigrade
from zero, the fifth step of applying a coating of resilient buffer
material formed of a silicone polymer filled with magnesium oxide
to cover said resistor and the said fired conductive ink and the
sixth step of applying a layer of iron oxide with magnesium
silicate suspended in xylene to cover the outer surface of said
resilient material.
Description
BACKGROUND OF THE INVENTION
Field of Invention
The invention relates to a method of making an encapsulated thick
film resistor having encapsulated conductive end portions.
DESCRIPTION OF THE PRIOR ART
Prior to the present invention, coatings of glass, vinyl paint,
acrylic paints, varnishes and different types of epoxy materials
have been employed as hard coatings to cover thick film resistors.
Such hard coatings are necessary to protect these resistors from
scratches and from exposure to moisture and undesired corrosive
gases in the atmosphere, such as chrloine gas, which have a
tendency to corrode the resistor and alter its resistivity.
In the prior art, attempts to select a hard coating to cover thick
film resistors that have exactly the same thermal expansion as the
resistor that it covers so that stresses would not be introduced
into the resistor and the coating during a change in ambient
temperature have not been able to be achieved. Stresses were
introduced into the resistor and its associated hard coating and
transferred between the resistor and coating because slight
differences were always present between the thermal expansion of
the resistor and the thermal expansion of any one of the
aforementioned hard coatings. Furthermore, as the magnitude of the
ambient temperature change increases, the magnitude of the
aforementioned stresses that are introduced into the resistor and
coating also simultaneously increased. This change in stress of the
resistor is also simultaneously accompanied by an undesired change
in the resistance of the thick film resistor.
The value of a resistor must be maintained within plus or minus
0.1% in order to be classified as a precision thick film resistor.
Since none of the aforementioned prior art encapsulated thick film
resistors can be maintained within this .+-. 0.1% resistor value,
none of these prior art hard coated encapsulated resistors have
been found to be satisfactory for use as precision thick film
resistors.
Another reason why a thick film resistor that is coated by any one
of the aforementioned coatings is not satisfactory is that when the
aforementioned stresses are introduced into these parts, due to
their differences in thermal expansion, cracks formed in their
coatings and this allowed the thick film resistor to become exposed
to harmful atmospheric gases, such as previously mentioned chlorine
gas.
Heretofore, it was a common practice, after the selection of the
size and the aspect ratio of a resistor which would fall within a
prescribed resistance range, to consult a table or a graph filled
geometry correcting tables that predicts the resistivity and the
T.C.R. as a function of the resistors geometry. This procedure is
slow, tedious, and has circuit design limitations in that the
resistor could only be made of a certain geometric shape and size.
It is also well known that these resistors will have undesired
different T.C.R. and resistivity values.
SUMMARY OF THE INVENTION
It is a major object of the present invention to disclose a unique
method for making an encapsulated thick film resistor having
encapsulated conductive end portions, which resistor is known in
the art as a cermet resistor.
It is another object of the present invention to provide a method
for manufacturing an encapsulated resistor of the aforementioned
type that possesses electrical resistance characteristics, that are
precise and whose performance is unaffected by the time it remains
on the shelf, the time period over which it is employed in an
electrical circuit or changes in ambient temperature.
More specifically, it is another object of the invention to provide
a method of manufacturing a precision encapsulated resistor of the
aforementioned type whose resistance will remain within an
acceptable .+-. 0.1% level over long periods of use that extend
beyond a two year period of time.
It is another object of the invention to provide a method of
manufacturing an encapsulated cermet resistor for use in measuring
circuits whose accuracy and overall stability is as good and
reliable as those possessed by present day commercially available
wire wound resistors.
One of the terms that is used to define a critical characteristic
of a thick film resistor is its "sheet resistivity". This term
sheet resistivity relates to the electrical resistance which a 1
milli-inch thick square of any size of resistive material offers to
a steady current passing between any two opposite faces of this
resistive material along which, for example, a conductive film is
attached. This sheet resistivity is known to vary with ambient
temperature between, e.g., +300 PPM/.degree.C to -300 PPM/.degree.C
depending on the sheet resistivity of resistor material being
used.
Another term that is used to define the characteristic of a thick
film resistor is T.C.R. or temperature coefficient of resistivity
whicch is the change in resistivity expressed in ohms per degree
centigrade.
In achieving the aforementioned objectives, it has been discovered
that an adverse change in resistivity and T.C.R. of a thick film
cermet resistor is caused by diffusion of the conductive material
in the conductor, which has an extremely low resistivity value,
into resistive material of the resistor which has a much greater
resistivity when the resistor and conductor are fired on a ceramic
substrate. Heretofore it was a common belief that this adverse
change was based upon the geometry, or the so-called aspect ratio
factor which is a ratio of the length to width of the resistor.
It is another object of the invention to recognize for the first
time that the aforementioned detrimental effect of diffusion is
much greater between the ends of a rectangular strip of resistor
and a conductor that extends away from the resistor when the
longest opposite sides of the rectangular resistor strip are
selected for connection to the conductor for jointly firing onto a
substrate rather than the shorter opposite sides of the rectangular
resistor strip.
Furthermore, experimentation has shown that firing temperature
changes adversely affects T.C.R. and the resulting resistivity of
thick film resistors because of the high degree of the
aforementioned diffusion that takes place between the resistor and
the associated conductors to which it is attached when they are
jointly fired.
It is, therefore, another object of the invention to provide a
unique method of firing resistor and conductor inks onto substrates
so that no undesired diffusion will take place between the
resistive and conductive materials that will adversely affect the
T.C.R. and resistivity; and, therefore, the precise resistance
offered by the resistor.
To accomplish the aforementioned feat it is another object of the
invention to provide a means whereby the dried resistor ink is
first fired for a preferred preselected period of time, e.g., 15
minutes at a high temperature of, e.g., 1000.degree.C on a
substrate to form an amorphic mass and thereafter the conductor
extending from either side of the resistor is printed, dried and
then fired for a similar period of time at a substantially lower
temperature in the neighborhood of 550.degree.C, onto the already
fired resistor to eliminate substantially all of the undesired
diffusion of the conductive material that would otherwise diffuse
into or from the resistor material.
It is another object of the invention to provide a method of the
aforementioned type which will allow an ink, such as a resistor ink
having a high firing temperature, to be fired at a high temperature
onto a substrate, and a conductor ink having a lower firing
temperature than the resistor ink to be then fired jointly with
portions of the already fired resistor ink onto the substrate so
that undesired diffusion of the conductor ink material into the
fired resistor ink will be negligible and an acceptable cermet
resistor having a low T.C.R. to be produced.
It is, also, another object of the invention to eliminate the need
for the previously mentioned geometry correcting tables.
It is also another object to provide a method of manufacturing a
cermet resistor whose shape can be of any one of a number of
different forms or configurations, and need not, therefore, be
limited to a restricted shape as has heretofore been required.
It is another object of the invention to provide a method of
blending one or more positive T.C.R. resistor inks with one or more
negative T.C.R. resistor inks so that the resulting temperature
coefficient of resistivity T.C.R. and the resistivity of the
resulting resistor can be precisely predicted by changing the
blending proportions of the negative T.C.R. resistor ink and the
positive T.C.R. resistor ink before firing in the aforementioned
unique manner so that a number of different shaped resistors can be
formed which individually possess different precisely fixed
resistance values.
It is another object to provide resistors of the aforementioned
type that extend over a wide range and which will result in each of
the resistors having a temperature coefficient of resistivity
value, T.C.R., that is within a few parts per million per degrees
centigrade from zero.
Since it is not possible to obtain a precise resistance value for
the resistor from the aforementioned unique firing process nor from
any other firing process, it is, therefore, another object of the
present invention to provide a means of trimming such a resistor
after it has been fired so that a more exact value of the
resistance can be achieved for these resistors.
It is another object of the invention to provide a method of making
an encapsulated cermet resistor and associated encapsulated
conductor so that no undesired stresses will be introduced into the
resistor and the resistance of the resistor to be altered
thereby.
More specifically, it is a major object of the present invention to
provide a method of the aforementioned type in which the resistor
and associated conductors are first coated with a resilient buffer
material, formed of silicone polymer filled with magnesium oxide,
and then coated with a hard outer glyptal coating.
It is another object of the present invention to provide a method
of the aforementioned type wherein the buffer coating is employed
to eliminate any thermally induced stresses in the resistor and
hard outer coating as thermal expansion of the resistor and thermal
expansion of the hard outer coating takes place, thereby
eliminating the possibility of cracks in the hard outer glyptal
coating.
It is still another object of the present invention to employ the
aforementioned encapsulating method as a way of preventing the
resistivity and the T.C.R. value of the resistor produced by this
method from being changed by exposure to the destructive oxidation
of air, moisture, hydrogen sulfide or other similar ambient
atmospheres.
It is another object of the invention to provide a method of
blending one or more positive T.C.R. resistor inks with one or more
negative T.C.R. resistor inks so that the resulting temperature
coefficient of resistivity, T.C.R., and the resistivity of the
resulting resistor can be precisely predicted by changing the
blending proportions of the negative T.C.R. resistor ink and the
positive T.C.R. resistor ink before firing in the aforementioned
unique manner so that a number of different shaped resistors can be
formed which individually possess different precisely fixed
resistance values.
It is another object to provide encapsulated resistors of the
aforementioned type that extend over a wide range and which will
result in each of the resistors having a temperature coefficient of
resistivity value, T.C.R., that is within a few parts per million
per degrees centigrade from zero.
Since it is not possible to obtain a precise resistance value for
the resistor from the aforementioned unique firing process nor from
any other firing process, it is, therefore, another object of the
present invention to provide a means of trimming such a resistor
after it has been fired so that a more exact value of the
resistance can be achieved for these resistors.
In accomplishing these and other objects, there has been provided
in accordance with the present invention a method of making an
encapsulated thick film resistor having conductive portions
associated with opposite ends thereof that form portions of an
electrically conductive circuit, comprising the first step of
selecting an ink made from a mixture of positive and negative
resistor inks, the second step of firing the resistor ink mix in
amorphic form at 1000.degree.C into a sintered state onto an
electrically non-conductive substrate, the third step of selecting
a conductive ink material that has a sintering temperature
substantially lower than the sintering temperature of the resistor,
the fourth step of firing said conductive ink at a sintering
temperature of about 550.degree.C in overlapping relationship with
said opposite ends of said resistor on the substrate whereby the
tendency to diffusion between the conductive and resistive
materials is minimized and whereby a resulting temperature
coefficient of resistivity value of the resistor that is produced
is within plus or minus twenty parts per million per degree
centigrade from zero, the fifth step of applying a coating of
resilient buffer material formed of a silicone polymer filled with
magnesium oxide to cover said resistor and the said fired
conductive ink and the sixth step of applying a layer of iron oxide
with magnesium silicate suspended in xylene to cover the outer
surface of said resilient material.
BRIEF DESCRIPTION OF THE DRAWING
A better understanding of the present invention may be had from the
following detailed description when read in connection with the
accompanying drawings in which:
FIG. 1 shows a nomograph having a uniquely constructed semi-log
scale for graphically determining the amount of additional positive
or negative ink that should be added to an ink mixture of positive
and negative inks to provide a thick film resistor ink of a desired
zero T.C.R.;
FIG. 2 shows the steps required in a first method of trimming the
aforementioned thick film resistor;
FIG. 3 shows the first step required in a second method of trimming
the aforementioned thick film resistor;
FIG. 4 shows the second step required in the second method of
trimming a thick film resistor;
FIG. 5 shows the third step required in the second method of
trimming the aforementioned thick film resistor;
FIG. 6 shows how the aforementioned trimmed thick film resistor can
be encapsulated to prevent the destructive oxidating effect of the
ambient atmosphere from affecting its resistivity and T.C.R. value;
and
FIG. 7 shows a chart having a solid line thereon to indicate the
wide resistivity range of values over which a zero T.C.R. prevails
for many different positive and negative cermet resistor ink blends
when they are produced by the unique method to be hereinafter
described in which no diffusion is allowed to occur between the
conductor and the resistor as contrasted by the line shown in dash
line thereon which indicates that zero T.C.R. can be achieved for
only a single resistivity value of many psoitive and negative
cermet resistor inks when they are produced by the well known
profile firing method as a result of undesired diffusion occurring
between the conductor and its associated resistor.
FIG. 8 is a graph to vividly illustrate the desirable independent
relationship that can be achieved, as shown by curve B, between the
temperature coefficient of resistivity and the aspect ratio
(geometry) values of thick film resistors by firing them in the
previously referred to unique non-diffused manner with their
associated conductors onto a substrate. FIG. 8 also shows a curve A
which represents the undesired dependent, restricted, temperature
coefficient of resistivity versus aspect ratio (geometry)
relationship that must be adhered to when thick film resistors and
their associated conductors are fired jointly at a high temperature
which causes diffusion to occur between the last mentioned
conductors and their associated resistors.
FIG. 9 is a graph to vividly illustrate the desirable independent
relationship that can be achieved as shown by curve B between the
resistivity and the aspect ratio (geometry) values of thick film
resistors by firing them in the previously referred to unique
non-diffused manner with their associated conductors onto a
substrate. FIG. 9 also shows a curve A which represents the
undesirable dependent restricted resistivity versus aspect ratio
(geometry) relationship that must be adhered to when thick film
resistors and the associated conductors are fired jointly at a high
temperature which causes diffusion to occur between the last
mentioned conductors and their associated resistors.
DESCRIPTION OF THE PREFERRED EMBODIMENT
Method of Blending Cermet Inks to Fabricate Encapsulated Thick Film
Resistors Having Encapsulated End Portions Which Are Not Sensitive
to Temperature Charges
The temperature coefficient of resistivity, T.C.R., for thick film
cermet resistors has heretofore been changed by altering the firing
temperature profile and/or by changing the geometry, or in other
words, the previously referred to aspect ratio of these
resistors.
Since the changes in T.C.R. obtained by these methods are several
parts per million per degree centigrade, PPM/.degree.C, usually in
the vicinity of 1 to 10 PPM/.degree.C for 1.degree. C change in
firing temperature, they are, therefore, not sufficiently exact to
obtain the desired T.C.R. value.
A unique method of ink blending to obtain a desired T.C.R. value
which does not have to rely on the selection of a desired firing
temperature profile will now be described.
The magnitude of change of T.C.R. obtained by this unique method is
at least 10 times larger than the previously mentioned method which
was based upon a change in firing profile and a change in the
geometry of the resistor.
Experimentation has shown that an addition of a metal in powder
form such as a gold powder with the particle size of three to
twenty microns or a metal powder mixed with lead-boro-silicate
glass powder of the same particle size when mixed with a liquid
agent such as "decanol" provide a suspension that will decrease the
sheet resisitivity of a resistor and cause a change in its T.C.R.
in a positive direction. The addition of metal oxide powder, for
example, ruthenium oxide powder, or a metal oxide powder mixed with
boro-lead-silicate glass powder and a liquid agent such as
"decanol" causes a change in T.C.R. in a negative direction. It
can, therefore, be concluded that by adding metal or metal oxide to
a cermet ink the T.C.R. is changed in either a desired positive or
a negative direction; and, therefore, if two or more resistor inks
are available and if one of them has a positive T.C.R. and the
other a negative T.C.R. or vice versa, they may be blended to
obtain a desired T.C.R., and the blending proportion can be
calculated by the method to be hereinafter described:
Measure the T.C.R. of resistors made from the ink which is to be
modified to obtain a zero T.C.R. resistor. This measurement of
T.C.R. is accomplished by firing the resistor ink on an
electrically non-conductive substrate and then taking measurements
of its electrical resistance at room temperature such as
73.degree.F and at a higher temperature such as 173.degree.F and
calculating the T.C.R. from these values of the following formula:
##EQU1## where .DELTA. R equals the resistance of the resistor at
the aforementioned high temperature minus its resistance at the
aforementioned room temperature.
R is the resistance value at room temperature and .DELTA. t.degree.
equals the difference between the aforementioned high temperature
and room temperature.
If the T.C.R. value of the resistor is zero, no further
modification of the ink is needed. If it is not zero and it is
negative, then a metal such as gold is added to the ink. It is then
blended and a measurement of its T.C.R. value is again made in a
manner similar to that already described.
The amount of metal added to the ink, such as gold must be large
enough to provide a positive T.C.R. value of not less than 20 parts
per million per degrees centigrade. If the T.C.R. of the ink under
modification is found to be positive then metal oxide, e.g., powder
325 mesh, ruthenium oxide, is added until the ink provides a
negative T.C.R. resistor material of 20 parts per million per
degrees centigrade of a higher negative number. The purpose of the
above modification of the available commercial inks is to make a
pair of inks so that one of the pair will have a negative T.C.R.
resistor value and the other of the same pair will have positive
T.C.R. value. These two inks are then blended by mixing them
together in a proportion that will provide a blend of zero T.C.R.
ink.
The amount of positive T.C.R. ink and the negative T.C.R. ink
forming the blended proportion is calculated from the following
equation and is done as explained below: ##EQU2## Where: P = % of
positive T.C.R. ink in blend for manufacture of zero T.C.R.
resistors
Exp = base of natural log
A = 1n .sub..epsilon. (100+s)
B = 1n .sub..epsilon. S
s = a constant, based on statistical data derived from
experimentation for ruthenium system inks which is equal to 3
T.sub.100 = T.C.R. of positive T.C.R. ink
T.sub.0 = T.C.R. of negative T.C.R. ink
Both T.sub.0 and T.sub.100 are in PPM/.degree.C. S is
dimensionless.
The percentage of positive ink in a blend which will provide zero
T.C.R. resistors is found through the use of the aforementioned
equation. This same percentage can also be found graphically by
first plotting the T.C.R. of the positive ink on the semi-log paper
chart as shown in FIG. 1. The point T.sub.100 plotted on the
semi-log chart shown in FIG. 1 is the T.C.R. of a positive ink or
in other words is the T.C.R. of a blend which consists of 100%
positive ink. The abscissa of this point does not correspond with
the 100% point on the abscissa axis but instead purposefully
corresponds with the 103% point. This offset of 3% is the variable
S in the aforementioned equation. In this particular example where
ruthenium system ink is used it has been found by experimentation
that the value of S = 3.
The T.C.R. of a negative T.C.R. ink is then plotted as an ordinate
on a linear scale on the semi-log chart of FIG. 1 as the point To.
This represents the value of a blend which has zero percent of
positive ink in it. The abscissa, or log scale value, of this point
does not correspond with the zero percent point on the abscissa
axis, but rather corresponds with the 3% point selected as a result
of statistical data derived from experimentation. This offset of 3%
is variable S in the equation. After the positive and negative
T.C.R's of a pair of inks are plotted as described above the
percentage of positive ink P which should be in the blend to
provide zero T.C.R. resistors is found as follows:
A straight line is drawn between T.sub.100 and T.sub.0. This line
represents a change in T.C.R. of resistors versus percentage of
positive T.C.R. ink in the blend and crosses the zero T.C.R. line.
Looking at the base of the graph immediately below the point at
which the aforementioned line crosses the zero T.C.R. line we find
that its value as read on the abscissa is the percentage of
positive ink in the blend which will provide desired zero T.C.R.
resistor value. It should be noted that the value of this point
along the abscissa is the value of the P shown in the previously
mentioned equation.
Knowing the percentage P of the positive ink in the blend the zero
T.C.R. blend can then be prepared. However, the T.C.R. of the
resistors made from this blend will not necessarily be zero; it may
not even be within the zero plus or minus 20 parts per million per
degree centigrade limits. This is so because the previously
mentioned equation represents the best fit or linearized condition
that can be derived from the T.C.R. versus log percentage of blend
that exists for several different blending proportions. The degree
of misfit depends on the number of test blends and on the ink
composition. If the T.C.R. of resistors prepared from this blend is
not zero as claculated from the previously mentioned equation
##EQU3## or is not within the desired limits, the blend must be
corrected. It is evident that the process parameters relating to
the preparation of resistors must be constant. For example, the
firing profile, absolute humidity in the furnace, atmosphere in the
furnace, and the dried thickness of the resistors must be kept
constant.
The following blending proportion correction is performed in order
to bring T.C.R. of the resistor closer to a zero value.
The actual value of the T.C.R. of the resistor, T.C.R..sub.1, as
derived from the equations ##EQU4## is determined from
representative samples of the blend and is plotted in FIG. 1. If
this T.C.R..sub.1 is positive as indicated by its plotted position
in FIG. 1, this point T.C.R..sub.1 is connected with the already
plotted point T.sub.0 or in other words, the point which is the
T.C.R. value of the negative T.C.R. ink. This line between the
points T.C.R..sub.1 and T.sub.0 represents a corrected change in
T.C.R. of resistors versus percentage of positive T.C.R. ink in the
blend or, in other words, the change T.C.R. of resistors versus
percentage of positive T.C.R. ink in the blend which was previously
determined in FIG. 1 was incorrect due to imperfect linearization
when parameters were chosen as previously described for the first
previously mentioned equation that was used to figure out the value
of P.
If this TCR.sub.1 were negative, e.g., TCR.sub.1 ' this TCR.sub.1 '
point would be connected by a straight line to the point T.sub.100.
The line connecting point TCR.sub.1 with point T.sub.0 or TCR.sub.
1 ' with point T.sub.100 must in each instance cross the zero
T.C.R. line. In one example, the T.C.R. of the resistors made from
a blend prepared by the previously mentioned graphical method is
positive and plotted at its point TCR.sub.1 in FIG. 1. The abscissa
of the point of intersection or point I.sub.1 on FIG. 1 between the
TCR.sub.1 -T.sub.0 line and the zero T.C.R. line is a corrected
percentage of positive ink in the blend which shall provide zero
T.C.R. resistors and is marked on FIG. 1 as P.sub.1.
Knowing P.sub.1 which is the corrected and more accurate percentage
of positive T.C.R. ink in the blend, the blend can be either
corrected by adding corresponding amounts of negative T.C.R. ink to
the blend or a new second blend can be prepared based the
information derived in the aformentioned manner.
Even now, the second corrected blend may still not provide zero
T.C.R. resistors. If this is the case, a second correction is
needed and the T.C.R. of the resistors made from No. 2 blend as
determined from the equation ##EQU5##
in FIG. 1 as point TCR.sub.2 is then determined. In this example,
TCR.sub.2 turned out to be negative. This is accomplished by
drawing a line through this point TCR.sub.2 and the previously
obtained point TCR.sub.1. This line represents the second corrected
change of T.C.R. versus percentage of positive ink in the blend.
The abscissa of the point of intersection between the line
TCR.sub.1 -TCR.sub.2 and the zero T.C.R. line is a corrected
percentage of positive inks in the blend which will provide zero
T.C.R. resistors and is marked P.sub.2 in FIG. 1.
Knowing P.sub.2 which is the second corrected percentage of
positive T.C.R. ink in the blend, this blend can then be either
corrected by adding corresponding amounts of positive T.C.R. ink,
for example, ink with TCR = T.sub.100 or a new third blend can be
prepared based on the aforementioned information.
In the above example, the T.C.R. of the second blend TCR.sub.2 was
negative. If it were positive then the TCR.sub.2 point would be
connected by a straight line with point T.sub.0 and the abscissa of
the point of intersection between line TCR.sub.2 -T.sub.0 and the
zero T.C.R. line would be the percentage of positive T.C.R. ink in
the third blend. When an additional correction of the blend is
needed, such as in the case where the T.C.R. of the resistors made
from the blend are outside of the desired limits, the last obtained
and plotted T.C.R. point, e.g., TCR.sub.2 is then connected with
the nearest T.C.R. point of opposite sign as measured along the
abscissa. The abscissa of the intersection point of this last
mentioned line which connects the two nearest T.C.R. points of
opposite signs with the zero T.C.R. line represents the percentage
P.sub.2 of positive T.C.R. ink which should be in the corrected
blend.
Experimentation has shown that in the majority of blending
operations only two such corrections are sufficient to bring the
T.C.R. within the .+-. 20 parts per million per degree C
limits.
It should also be further understood that a method has been
described that can be used for obtaining any desired T.C.R. for
resistors other than zero by observing where the interconnecting
line between T.sub.0 and T.sub.100 passes a horizontal line on the
chart that passes through the desired positive or negative value of
the blend that is desired rather than through the zero T.C.R. line.
This T.C.R. of the blend cannot, of course, be made more negative
or more positive than the T.C.R. value of the two basic inks that
were used to make this blend.
The change in T.C.R. resistors causes the change in the sheet
resistivity of the resistors and the more negative that the T.C.R.
is the higher will be the sheet resistivity. This is so because the
addition of metallic oxide to the ink causes the T.C.R. to change
in the negative direction and increases the sheet resistivity.
Knowing the sheet resistivity of the two inks which are used for
blending and knowing their percentage in the final blend the sheet
resistivity of resistors made from this blend can be easily
predicted by using known methods of calculation.
METHODS OF TRIMMING OF HIGH ACCURACY RESISTORS (CERMET) WITH LOW
ACCURACY TRIMMING MACHINE
Present day accuracy of cermet resistors after they are printed and
fired is about .+-. 20% of the value desired. Therefore, if a
better accuracy is desired, they must be corrected. Usually, the
correction consists of removing a portion of the resistor until the
resistance reaches the desired value. A partial removal of resistor
material causes an increase in the resistance. In other words, the
value of resistance can be corrected only in the direction of
increase of the resistance.
Usually the resistance of the resistor under trimming is constantly
measured by using a high precision resistance measuring bridge, for
example, a Kelvin bridge.
The accuracy of resistance measuring bridges is usually of .+-.
0.05%. However, the accuracy of trimmed resistors is seldom better
than .+-. 1%. This is caused by the unpredictable time lag between
the electrical signal from the bridge, indicating that the resistor
has reached its desired value and the execution of the signal
(i.e., stopping the trimming) by conventional electromechanical and
pneumatic links between the bridge and the cutting device. The
degree of overtrim or, in other words, overcuts, depends on the
speed of the cutting device which is usually a nozzle which directs
the stream of abrasive particles on the resistor and also on the
resistivity of the resistor's material. The higher the nozzle speed
and the resistivity, the larger will be overtrim or error. Usually,
the degree of overtrim does not exceed 1% of nominal desired
resistance. In other words, even if the trimming machine, which
includes resistance measuring bridge and the cutting devices, has a
high precision bridge, its total accuracy, i.e., the accuracy of
trim, usually is in a low precision range.
Described below are two methods of trimming a high precision
resistor 10 with low precision trimming machines, which have a high
precision resistance measuring bridge. The first method is as
follows:
The resistor 10 is laid out so that it consists of two parts 12 and
14 as shown in FIG. 2. Part 12 measured between points a and b of
conductive parts 16, 18 must be of sufficient size and length to
provide at least 98% of the nominal desired total resistance after
trimming along trimming path 20. Part 14 resistor measured between
the points b and c of conductors 18, 22 must have not more than 1%
of the nominal total resistance before it is trimmed along the
trimming path 24.
Measuring across the entire resistor, i.e., between the points a
and c of conductors 16, 22, the resistor part 12 is trimmed to 98%
of the total nominal resistance because the accuracy of trimming
machine is .+-. 1%. The resistance of the entire resistor measured
between a and c will be 98% .+-. 1% of the total nominal resistance
and the resistance of just trimmed resistor alone measured between
a and b of conductors 16 and 22 can be 98% of nominal .+-. 1% of
nominal - R.sub.bc, where R.sub.bc is the resistance of the
untrimmed part 14 measured between 18 and 22.
As it was mentioned before, the maximum resistance of untrimmed
R.sub.bc resistor 14 does not exceed 1% of total nominal
resistance, therefore, in the worst case, the minimum resistance of
just trimmed R.sub.ab resistor is 98% - 1% = 97% of the total
nominal resistance.
To correct the error after the first trim along trim path 20 the
actual value of the trimmed R.sub.ab resistor part 12 must be
measured. Since the resistance measuring bridge only is involved in
this measurement, the measured value of R.sub.ab resistor 12 will
be within the accuracy of the bridge, i.e., usually within .+-.
0.05%. This uncertainty in the trimmed R.sub.ab value can obviously
not be corrected, and it depends on the accuracy of measuring
bridge alone.
Assuming that R.sub.ab resistance of resistor part 12 after trim
was 97% of total nominal resistance, the untrimmed resistor 14 must
be trimmed along trimming path 24 until it reaches 100% - 97% = 3%
of the total nominal value.
Because of .+-. 1% accuracy of the trimming machine, the resulting
value of trimmed resistor 14, measured between points b and c
during the trimming, and trimmed along trim path 24 will be 3% of
total nominal resistance .+-. 1% of 3% of nominal or 3% .+-. 0.03%
of total nominal value versus desired 3% of nominal. Assuming one
of the worst possible cases, the resistance of trimmed resistor
part 14 can be 3% - 0.03% = 2.97% of the total nominal value; and
the total value will be R.sub.ab (part 12) + R.sub.bc (part 14) =
97% + 2.97% = 99.97% of the total nominal value, i.e., the error
after two trims will be - 0.03%. Adding the uncertainty or the
resistance measuring bridge (.+-. 0.05%) the maximum error after
two trims will be (in this example) .+-. 0.05 - 0.02 = - 0.08%.
The above example shows that, dividing the resistor 10 into two
parts 12, 14 and performing two trims 20, 24, the final accuracy
obtained is more than ten times better thann the accuracy of
conventional trimming machine and that it approached the accuracy
of a precision resistance measuring bridge.
The accuracy obtainable by this two trim method is determined as
follows: R.sub.T R = Nominal (desired) value of R.sub.T (Ohms) o o
o a R.sub.1 b R.sub.2 c C = Accuracy of resistance measuring bridge
(%) A = Accuracy of trimming machine (including % bridge accuracy)
B = Value of R.sub.2 untrimmed (in % of nominal) R.sub.1 = Part 1
of total resistor R.sub.T (or R.sub.ab resistor) (.OMEGA.) R.sub.2
= Part 2 of total resistor R.sub.T (or R.sub.bc resistor) (.OMEGA.)
E =.+-. (2A.sup.2 + AB + A.sup.3 + C) R.sub.T = Total resistance
(R.sub.T = R.sub.1 + R.sub.2) (.OMEGA.) E = Total maximum error in
R.sub.T after trimming (in % of nominal) After first trim described
above: R.sub.T = (1-A) R .+-. (1-A) RA NOTE: The resistor is
trimmed to (1-A) % of nominal value. A is expressed in
decimals.
R.sub.1 trimmed = R.sub.T - R.sub.2 untrimmed = (1-A) R .+-. (1-A)
RA - BR = R [1 - (A+B) .+-. A (1-A)]
Note: B is expressed in decimals
Error in R.sub.1 trimmed - R = R - (A+B) .+-. A (1-A) = -R (A+B)
.+-. A (1-A) .+-. CR
Note: C is expressed in decimals. The error in R.sub.1 trimmed is
measured with res. bridge of .+-. C % accuracy.
After the second trim, i.e., after R.sub.2 is trimmed to [R.sub.1
trimmed - R] value:
R.sub.2 trimmed = R [(A+B) .-+.A (1-A)] .+-. CR .+-. AR [(A+B)
.-+.A (1-A)] = R {(A+B) .-+.A (1-A) .+-. CR .+-. A [(A+B) .-+. A
(1-A) ]} = R {(A+B) .-+.A (1-A) .+-. C .+-. [A.sup.2 + AB .+-.
A.sup.2 (1-A)]}
r.sub.t = r.sub.1 trimmed + R.sub.2 trimmed = R {[1 - (A+B) .+-. A
(1-A)] + [(A+B) .-+. A (1-A)] .+-. C .+-. [A.sup.2 + AB .+-.
A.sup.2 (1-A)] } = R {1 - (A+B) .+-. A (1-A) + (A+B) + A (1-A) .+-.
C .+-. [A.sup.2 + AB .+-. A.sup.2 (1-A)]}
Error in R.sub.T = R.sub.T - R = R {- (A+B) .+-. A (1-A) + (A+B)
.-+. A (1-A) .+-. C .+-. [A.sup.2 + AB .+-. A.sup.2 (1-A)]} =
r {.+-. c .+-. [a.sup.2 + ab .+-. a.sup.2 (1-a)]} = .+-. r {a.sup.2
+ ab .+-. a.sup.2 .-+. a.sup.3 .+-. c}
max error in R.sub.T = .+-. R {2A.sup.2 + AB + A.sup.3 + C}
##EQU6## Note: A, B, C, expressed in % A numerical example where A
= .+-. 1%, B = 1%, C = .05%, as it was described before will yield
the following accuracy in the resistor trimmed by described
method:
Max. error = .+-. (2 (0.01%) + 0.01% + 0.0001% + 0.05%) = .+-.
0.0801%. A second method of trimming high precision resistors with
low precision trimming machine which employs a high precision
bridge is described below, and shown on FIGS. 2, 3 and 4.
The resistor 10 is trimmed along a trimming path as shown at 26 to
98% of its desired value. The maximum error after this trim is
usually .+-. 1%.
Without changing the resistor position in the trimming machine, the
resistor 10 is trimmed again to 99.5% of the desired value along
trimming path 28. In other words, the cutting device (which usually
is a nozzle which provides a jet of abrasive particles suspended in
air) repeats the same cutting pattern. Experiments have shown that
the amount of resistor's material removed by this second trimming
is about 0.5% of that removed in the first trimming. This is
equivalent to slowing down the trimming speed by the factor of
1/200.
The same trimming pattern is repeated for a third time along
trimming path 30 and the resistor is trimmed to its desired value.
The amount of resistor material removed by this third trim is about
0.05% of that removed by the first trim, which is equivalent to
slowing down the trimming speed by the factor of 1/2000 as compared
with the first trimming period.
The accuracy of the trimmed resistors (assuming the accuracy of
resistance measuring bridge as .+-. 0.05%) is usually in the order
of 0.08-0.09%, which is comparable with the first described
method.
The accuracy of trimmed resistors can be improved further if four
trims are used instead of three, approaching the accuracy of the
resistance measuring bridge.
Both of the methods described herein allow a single thick film
resistor to be trimmed to any one of a number of desired
values.
The aforementioned precise trimming method enables a reduction to
be made in the cost of manufacturing resistors having different
resistor values because the same common blend of positive and
negative resistor ink having a zero T.C.R. can be fired onto each
one of a number of substrates before different individual selective
trimming of each of these resistors occurs.
It should be noted that trimming of the cermet resistor by either
of the aforementioned methods is done after the previously
described selected zero T.C.R. blend of positive and negative
cermet resistor ink that was used to form resistor 10 has been
fired onto the aluminum oxide substrate 32.
When a thick film cermet resistor 10 of the aforementioned type is
left exposed to its surrounding atmosphere its precisely
manufactured resistance and T.C.R. value will be altered with time
because of the destructive oxidation and other similar detrimental
effects which air, moisture, hydrogen sulfide or other similar
destructive delequescent materials have on the resistor 10.
More particularly, the stability of cermet resistors that are not
protected from the ambient atmosphere, whether under a load or no
load condition, is usually in the order of 0.3-0.5% per year. In
other words, the resistance of these resistors have heretofore
changed by 0.3-0.5% a year after they are manufactured.
Such a poor stability precludes the possibility of the manufacture
of high precision resistors which have a tolerance of .+-. 0.1% or
better.
Manufacturing a thick film resistor in the manner to be hereinafter
described provides a resistor which will retain a stability of 0.1%
for at least 2 years.
In other words, the resistance of these resistors will change no
more than 0.1% of their nominal value after two years of active use
in a circuit or during the period in which they are stored on the
shelf for this length of time.
Experimental tests showed that the main reason for the instability
of thick film resistors or, in other words, drift in resistivity
with time was caused by oxidation of the metals in the resistor and
by absorption of water, contained in the atmosphere.
Therefore, the resistors must be insulated from the ambient
atmosphere.
To solve this problem, an insulator layer must be provided which
has the same temperature coefficient of expansion as the ceramic
substrate 32 and the resistor 10 and conductor 16 and 22.
Otherwise, thermal stresses will develop with an accompanying
change in resistance. Another way is to make the insulating layer
flexible enough to prevent stresses from occurring in the resistor
which would change its resistance by more than .+-. 0.05% for the
desired specified temperature range, e.g., a 100.degree. change in
ambient temperature. Also, the layer which physically contacts the
resistor must be chemically inert with respect to resistor
material, for example, it should not cause oxidation or reduction
of the resistor material to occur and at the same time it must be
able to adhere to the resistor 10. Another factor that had to be
considered was that since the flexible insulation layer must
possess a soft flexible characteristic it needs additional
protection from mechanical damage such as scratches, etc. The
encapsulating structure on the substrate as described below
provides a system of layers to protect the cermet resistor from
ambient air, water vapors, water, and hydrogen sulfide (H.sub.2 S).
Furthermore, the layers to be described have been found
satisfactory in protecting the resistor from being affected when
continuous changes in ambient temperature that may vary from the
standard reference level of 25.degree.C .+-. 50.degree.C so that no
more than .+-. 0.1% change in value of the resistor can occur.
The ceramic substrate 32 which is preferably at least 96% pure
aluminum oxide material is exposed to 1000.degree.C for 15 to 20
minutes. It is assumed that the substrate 32 is clean prior to this
operation; if it is not, it is cleaned ultrasonically in ethyl or
methyl alcohol for 3 minutes. Next, the previously mentioned
resistor 10 and conductor inks 16, 22 are printed, dried and fired
in the manner previously described as shown in FIG. 6 of the
drawing.
A silicone polymer filled with magnesium oxide 34 such as
dimethylpolyxilaxane which is commercially available from the EMCA
Company as plastic coat 1139B is then printed or brushed over the
resistor 10 and conductor areas 16, 22 except for the conductor
areas that are reserved for the terminals 38 and 40. The substrate
32 is then heat cured at 108.degree.C for 24 hours to provide
polymerization and the resistor 10 is trimmed through the plastic
coat 34 to 99 .+-. 1% of its desired value as previously described
and the terminals 38, 40 are then soldered with suitable soldering
material 42, 44 as shown in FIG. 6.
Next, the substrate 32 is heat cycled twice between 25.degree.C to
125.degree.C at the temperature-time slope of 20.degree.C per
minute and kept for 2 hours at 125.degree.C then cooled down on the
same rate to 25.degree.C. The same heat cycle is repeated for a
second time, and then for a third time for a period of 15 hours
instead of 2 hours and at the same temperatures.
The resistor is then finally trimmed as previously described under
the description of FIGS. 2-5 to minus 0.03% of the desired value.
The resistor is then cleaned with a jet spray of nitrogen. A
mixture of iron oxide with magnesium silicate suspended in xylene
36 such as glyptal 1201B paint that is commercially available is
sprayed over the entire substrate including the resistor conductors
and portions which form the solder joint and terminals. The
substrate is then exposed to 100.degree.C for 4 hours.
The thickness of the flexible silicone polymer layer 34 that is
selected is never less than 12 microns and the thickness of the
hard glyptal layer 36 is not less than 50 microns. A
cross-sectional view of the projected resistor 10 is as shown in
FIG. 6.
Experimentation has also shown that cermet resistors that are
prepared in the above-described manner will remain stable within
.+-. 0.1% for at least two years or more.
The plotted dotted line shown in FIG. 7 indicates that it is
possible through the use of a conventional diffusion introducing
profile firing method to obtain only a single resistor blend of ink
that has a zero T.C.R. value from a series of different blends of
inks which possess different sheet resistivity values.
FIG. 7 also shows a second plotted solid line to indicate that a
series of resistors having different resistivity values over a wide
resistivity range can be obtained which each has a zero T.C.R.
value when the resistor is first fired by the unique non-diffusing
method previously described in which the resistor is first fired to
the substrate at one temperature and the conductor and resistor are
thereafter jointly fired at a second temperature that is
approximately 500.degree.C lower than the first mentioned
temperature.
The unique steps employed in the preparation of a zero T.C.R. thick
film resistor are:
1. Ultrasonically clean substrate 32 in methanol for 30
seconds.
2. Prefire substrate 32 at 1000.degree.C.
3. clean substrate 32 with N.sub.2, print resistor.
4. Dry resistor at 107.degree.C for 45 minutes.
5. Ascertain the correct firing temperature of the furnace.
6. Fire resistor at a plateau temperature of 1000.degree.C on a
2-inch per minute moving belt.
7. Clean substrate 32 with N.sub.2 and print conductors 16, 22.
8. Dry conductors 16, 22 at 107.degree.C for 45 minutes.
9. Ascertain the correct firing temperature of the furnace.
10. Fire the conductors 16, 22 at a plateau temperature of
550.degree.C on a two-inch per minute moving belt.
11. Anneal by heat cycling at 177.degree.C for 15 hours.
12. Clean resistor 10 and conductors 16, 22 with N.sub.2 and screen
on flexible layer 34.
13. Dry flexible layer 34 at 126.degree.C for 12 hours.
14. Stake pins 38 and 40 and solder at 42, 44.
15. Trim resistor 10-98% of its normal resistance value and clean
with N.sub.2.
16. heat cycle at 121.degree.C two times for 2 hours and then
overnight to eliminate stresses induced by trimming.
17. Trim to desired value and clean with N.sub.2.
18. spray on hard layer 36.
19. Dry hard layer 36 at 93.degree.C for 4 hours.
The significance of eliminating the harmful effects the diffusion
has on T.C.R. and resistivity which has heretofore been brought
about by firing the resistor and conductor at substantially the
same high temperature is clearly illustrated in FIGS. 8 and 9.
FIGS. 8 and 9 show, for example, how T.C.R. and the resistivity of
thick film resistors are dependent on the previously referred to
geometry, or aspect ratio of the resistor when they are fired with
associated conductors at the same high temperature and how this
dependence was practically eliminated when the unique process
heretofore described was employed.
Curve A in FIG. 8 shows the dependence of T.C.R. on the aspect
ratio when a thick film precision resistor is manufactured by using
conventional methods in which the resistor and conductor is fired
at the same high temperature. It can be seen in this conventional
method that the T.C.R. value changed from +74 PPM/.degree.C at the
aspect ratio of 0.1 to -56 PPM/.degree.C at the aspect ratio of 10.
In other words, curve A shows that a total change in T.C.R. of 130
PPM/.degree.C occurred when the previously mentioned ruthenium
system ink is used as the resistor material, platinum gold ink is
used as the conductor material and after the resistor ink and
conductor were fired at the high temperature of 1000.degree.C.
FIG. 8 curve B shows how the dependence of T.C.R. on the aspect
ratio is for all practical purposes eliminated when the thick film
resistor is manufactured by the previously described unique method
of manufacturing.
The dependence of T.C.R. on the aspect ratio decreases from 130
PPM/.degree.C for conventional methods that have heretofore been
used as shown in FIG. 8 curve A to 28 PPM/.degree.C for the unique
method of manufacturing that has for the first time been disclosed
herein.
Furthermore, in addition to the decrease in the T.C.R. dependence
on the aspect ratio it can be seen that the T.C.R. versus aspect
ratio curve shifts in a negative direction after the unique
manufacturing method was used.
More specifically, both curves A and B represented the relationship
between the T.C.R. and the aspect ratio for the same ruthenium
system ink resistor material. The only difference in the
manufacturing process depicted in the curves A and B shown in FIG.
8 is that in curve A the resistors and their associated conductors
were fired at approximately the same temperature such as about
1000.degree.C and for curve B the resistors were first fired at
1000.degree.C and thereafter the resistors and their associated
conductors were jointly fired at about 550.degree.C.
It should also be noted that the conductor which is connected to
the resistor represented by curve B contains silver combined with
glass instead of the conventional platinum-gold (PtAu) combined
with glass type conductor as represented by curve A. The only
reason for the change in conductor material from PtAu to silver was
that it was not possible to fire a PtAu type conductor at
550.degree.C whereas a silver type conductor can be fired at this
temperature.
A shift of curve B in a negative direction shows that the degree of
diffusion of conductor material into the resistor material has
decreased and that the true T.C.R. of the resistor ink is in
reality that shown on curve B rather than the generally heretofore
assumed value that is shown on curve A.
Curve C, FIG. 8, depicts the dependence of T.C.R. on the aspect
ratio after the resistive ink was blended with ink having positive
T.C.R., such as PtAu type conductor ink or pure gold powder. After
blending, the resulting ink lies approximately between +13
PPM/.degree.C and -8 PPM/.degree.C T.C.R. and its dependence on the
geometry (aspect ratio) for all practical purposes is nil.
FIG. 9, curve A shows the dependence of resistivity on the aspect
ratio when the thick film resistors are manufactured by
conventional methods.
2150 ohm per square per mil was the change in resistivity that
occurred when a change in aspect ratio went from 0.1 to 10.
Curve B of FIG. 9 provides a way of showing the independence of
resistivity on the aspect ratio when the resistor is manufactured
by the unique method previously described for FIG. 8, curve B.
The dependence of resistivity on the aspect ratio (geometry)
decreases from 2150 ohm per square per mil on curve A to 1100 ohm
per square per mil on curve B.
FIG. 9, curve C shows the resistivity versus aspect ratio after
blending as previously described under FIG. 8.
It has been determined by experimentation that substantially 20% by
weight of RuO.sub.2, 40% by weight of Ru and 40% by weight of glass
frit is one type of positive temperature coefficient of resistivity
resistor ink that can be employed to advantage in the
aforementioned described ink mixtures that are formed from positive
and negative temperature coefficient of resistors ink. It has also
been determined by experiment that substantially 40% by weight of
RuO.sub.2, 20% by weight of Ru and 40% by weight of glass frit is
one type of negative temperature coefficient resistivity resistor
ink that can be advantageously used in the aforementioned ink
mixture to make the resistor 10.
It can, therefore, be seen that the unique apparatus and method of
first firing the resistor 10 onto a substrate 32 at 1000.degree.C
and the later joint firing of the resistor 10 and its associated
conductors 16, 22 onto the substrate 32 at a lower temperature,
namely 550.degree.C, will substantially eliminate diffusion that
has heretofore occurred between the conductor material and the
resistor material.
By procuring a resistor and its associated conductors after firing
in the substantially same undiffused state that they were in before
firing, it is for the first time possible to eliminate the T.C.R.
and resistivity dependency on the geometry of the resistor commonly
referred to as aspect ratio that has heretofore existed when other
firing means have been employed for this purpose.
Because of the aforementioned advantages derived from the unique
firing technique, it is now possible for the first time to
manufacture precision thick film resistors without concerning
oneself with the heretofore existing problem of:
1. Selecting the right aspect ratio or, in other words, the
length-width ratio, or the geometry, of the resistor that is to be
fired onto a substrate,
2. Spending time in consulting geometry correcting tables to
predict resistivity and the T.C.R. of the resistor as a function of
the resistors geometry, and
3. Requiring the creative ability of the designer who is designing
an electrical, thick film circuit from being able to present the
most desired economical compact circuit because the resistors that
have heretofore been used were required to be of a prescribed
geometric shape and size.
* * * * *