Compensation for spacial and temporal temperature variations in a thermal conductivity detector

A thermal conductivity detector includes a cavity wall defining a cavity for receiving a quantity of a sample fluid, the cavity wall being subject to a cavity wall temperature that is temporally and spatially variable, and a sensor located in the cavity and connected preferably in a bridge circuit configuration for providing a temperature sense signal. The sensor exhibits a resistance which is dependent on a temperature of the sensor. A first signal providing means includes reference means preferably in the form of first and second reference resistors located within first and second reference resistor cavities. The first and second reference resistors are connected to a reference voltage in a voltage divider network such that a node of the voltage divider network provides a temperature compensation signal that is representative of the average temperature of the cavity wall. Second signal providing means, connected to the balance nodes of the bridge circuit configuration, provide a temperature sense signal that is related to a change in resistance of the sensor resistor and thereby representative of the sensor temperature. The temperature compensation signal may optionally be conditioned by a voltage gain circuit and a voltage offset circuit to provide a temperature compensation signal. The temperature sense signal and the temperature compensation signal are provided to a third signal providing means wherein the temperature compensating signal is used to accurately compensate for changes in the temperature sense signal that are due to the temporal and/or spatial variations in the cavity wall temperature. In particular, the temperature compensation signal may represent an averaged value of at least two cavity wall temperatures, thus particularly compensating for the effect of a spatial temperature gradient in the cavity wall.

FIELD OF THE INVENTION 
This invention relates to thermal conductivity measurement devices, and in 
particular, to precision measurement devices for measuring the thermal 
conductivity of a fluid, such as a gas, to detect compounds within the 
fluid. 
BACKGROUND OF THE INVENTION 
Gas chromatographs are used to determine the chemical composition of a 
sample, which may be gaseous or a vaporized liquid. The term gas will 
hereinafter be used to include a vapor. In one type of gas chromatograph, 
a sample is sent through a separation column. A typical separation column 
is a long capillary tube with a coated interior. Different chemical 
compounds in the sample travel through the separation column at different 
rates and leave the separation column at different times. As compounds 
leave the separation column, they are carried by a carrier gas past a 
detector. The detector detects compounds in the carrier gas by measuring 
changes in the properties of the effluent gas. When a change in the gas 
property occurs, the timing of the change indicates the type of the 
compound passing the detector, and the magnitude of the change indicates 
the quantity of the compound. 
One type of detector used with gas chromatographs is a thermal conductivity 
detector, which detects changes in the thermal conductivity of the 
effluent gas. When a compound is mixed with the carrier gas, the thermal 
conductivity of the mixture is usually different from that of the pure 
carrier gas. A thermal conductivity detector provides a measure of the 
change in the thermal conductivity of the carrier gas and thereby provides 
a measure of the presence and amount of various compounds. 
FIG. 1 shows a typical prior art sensor circuit 10 used in a thermal 
conductivity detector of a gas chromatograph. The sensor circuit 10 
includes a metal filament 12, such as a platinum wire, placed in a cavity 
14. The effluent from a gas separation column along with a carrier gas 
fills the cavity 14 and flows along a path 16 past the filament 12. The 
filament 12 has a resistance R.sub.S which depends on its temperature and 
is heated using an electric current I.sub.1. In the case of the filament 
12 being a platinum wire, the resistance of the filament 12 is 
proportional to its temperature. 
Heat generated by the filament 12 is removed partially by the flow of the 
effluent but primarily by thermal conduction through the gas to the cavity 
wall 18 of the cavity 14, thus lowering the resistance of the filament 12. 
By effectively measuring the change in resistance of the heated filament 
12, the change in thermal conductivity of the flowing gas may be 
determined. 
In some applications, problems arise that can cause the output of the 
sensor circuit 10 to change even if the composition of the gas remains 
constant. One problem is caused by spatial and temporal variations in the 
temperature of the cavity wall 18. With the sensitivity required of a 
detector, such variations may affect the detector. Changes in the voltage 
offset of the amplifiers used to measure changes in the resistance of 
filament 12 are still another problem. 
One technique for attempting to avoid some of these problems is illustrated 
in FIG. 1, wherein the filament 12 is operated in a bridge circuit 
employing a control filament 22 which is ideally identical to the filament 
12 and is located in a cavity 24 similar to the cavity 14 but containing 
only a pure carrier gas. A variable resistor R.sub.B is used to match the 
resistance of a fixed resistor R.sub.A. A differential amplifier 26 
detects an unbalance in the bridge. A DC voltage supply is used to heat 
the filaments 12, 22 to a temperature elevated above the temperature of 
the cavity walls 18, 19. If the thermal conductivity of the effluent in 
the cavity 14 is different from that of the pure carrier gas in cavity 24, 
the bridge becomes unbalanced, and a change in the amplifier's output 
voltage V.sub.A indicates the detection of a change in thermal 
conductivity of the gas in the cavity 14. Common mode temperature 
variations in the temperature of the block surrounding the cavities 14 and 
24 as well as common mode temperature variations in the temperature of the 
carrier gas are expected to change the resistances of the filaments 12 and 
22 equally, and thus not affect V.sub.A. 
However, the two different filaments 12 and 22 cannot be made exactly the 
same and therefore do not react identically to identical changes in their 
ambient environment. Even if the filaments 12 and 22 could be made to be 
initially identical, the properties of these devices may change with time, 
producing a bridge imbalance with common changes in the ambient 
environment of the filaments 12 and 22. Also, the filament 12 and the 
control filament 22 can be subject to a spatial temperature variations 
(i.e., a block temperature gradient). Thus, the filament 12 may experience 
a cavity wall temperature that is different than the cavity wall 
temperature that affects the control filament 22. As a result, the 
sensitivity and the accuracy of the detector output signal is less than 
desirable. 
In another approach (not shown), only the sensor filament 12 is employed in 
a single cell; the control filament 22 is replaced by a fixed resistor. 
The analytical flow (the carrier gas plus effluent) along path 16 is 
modulated (made to alternate) with a flow of pure carrier gas. A sensor 
signal is then extracted from the signal output (V.sub.A) by demodulation 
techniques. However, there can be loss of a sample constituent during a 
period of pure carrier gas flow. The detector output signal is therefore 
less accurate than desired, and the output signal is more susceptible to 
noise effects. 
SUMMARY OF THE INVENTION 
The present invention provides methods and structures for measuring thermal 
conductivity of a sample fluid contained in a sensor cavity. The 
measurement is made in a manner that compensates for the effects of 
spatial and/or temporal temperature variations in the cavity wall that 
defines the sensor cavity. 
In particular, a thermal conductivity detector may be constructed according 
to the present invention to include a detector block having a cavity wall 
that defines a sensor resistor cavity for receiving a quantity of the 
sample fluid, the cavity wall being subject to a cavity wall temperature, 
and the cavity wall temperature being subject to temporal and spatial 
variations. A sensor resistor is located in the sensor resistor cavity. 
The sensor resistor exhibits a sensor resistance that is dependent on the 
temperature of the sensor resistor. A first signal providing means 
includes reference means located proximate to the cavity wall so as to be 
responsive to the temporal and spatial variations in the cavity wall 
temperature for providing a temperature compensation signal representative 
of at least one of the spatial variation and temporal variations. A second 
signal providing means, connected to the sensor resistor, provides a 
temperature sense signal that is related to the sensor resistance. A third 
signal providing means receives the temperature sense signal and the 
temperature compensation signal, and, in accordance with the temperature 
compensation signal, provides a detector output signal that is 
representative of the thermal conductivity of the sample fluid, the 
detector output signal being compensated for the effect of at least one of 
the spatial variation and the temporal variation in the cavity wall 
temperature. The contemplated thermal conductivity detector thereby offers 
greater sensitivity, accuracy, and reliability in comparison to the prior 
art.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
The apparatus and methods of the present invention provide improved 
accuracy in a thermal conductivity detector suitable for use in an 
analytical instrument. The terms "analysis" and "analytical" are meant 
broadly to include both qualitative and quantitative analytical methods, 
detection, or observation of physical or chemical parameters. 
Additionally, the apparatus and methods described herein may be applied to 
directly or indirectly effect compensation for the effects of variable 
ambient temperature on a resistive sensing element that may be present 
within a heated zone or cavity in an analytical instrument. 
Chromatographic analysis of gaseous sample is the preferred mode of 
analysis according to the practice of the present invention, and the 
following description of the invention will be directed to a thermal 
conductivity detector intended for use in a gas chromatographic analytical 
system. However, the teachings herein may be applied to a thermal 
conductivity detector suitable for use in an analytical instrument for 
effecting a chromatographic analysis of multiple component gases and 
mixtures thereof capable of regulated flow. Moreover, it should be 
understood that the teachings herein are applicable to a thermal 
conductivity detector for use in instruments that operate using other 
analytical methods or that analyze other physical parameters and 
phenomena. 
The basic mechanism underlying chromatographic analysis is the separation 
of a sample chemical mixture into individual components by transporting 
the mixture in a carrier fluid through a specially prepared separation 
column having a retentive media therein. The carrier fluid is referred to 
as the mobile phase and the retentive media is referred to as the 
stationary phase. The principal difference between liquid and gas 
chromatography is that the mobile phase is either a liquid or a gas, 
respectively. Liquid chromatography devices are capable of analyzing much 
heavier compounds than gas chromatography devices. However, gas 
chromatography detection techniques are more sensitive and therefore the 
present invention contemplates the use of a thermal conductivity detector 
in a gas chromatograph. For the purposes of clarity, only the detector 
portion of the contemplated gas chromatograph is illustrated. 
In a gas chromatographic analysis, a sample of the subject mixture is 
injected into a fluid stream and passed through the separation column. 
Separation is due primarily to differences in the partial pressures of 
each sample component in the stationary phase versus the mobile phase. As 
the basic techniques for the preparation, separation, and detection of 
sample components are known to those skilled in the art, the description 
to follow will be directed primarily to the construction and operation of 
a novel thermal conductivity detector that is sensitive, accurate, 
reliable, and inexpensive. 
As illustrated in FIG. 2, a preferred embodiment of a thermal conductivity 
detector 200 may be constructed to include a first signal providing means 
111 that includes a reference signal means 108 for providing a temperature 
compensation signal V.sub.C. The first signal providing means 111 
preferably includes a fixed reference voltage source V.sub.DC connected to 
the reference signal means 108 and a fixed resistor 104 having one leg 
connected to a ground potential. A second signal providing means 112 
includes a sensor resistor 201 in a sensor resistor cavity 234. The 
reference signal means 108 comprises at least one but preferably a 
plurality of similarly-constructed reference resistors that are embedded 
or otherwise disposed in a detector block so as to be subject to the 
temperature of the cavity wall that defines the sensor resistor cavity 
234. Accordingly, a first reference resistor 100 is provided in a first 
reference resistor cavity 101 and a second reference resistor 102 is 
provided in a second reference resistor cavity 105 within the detector 
block (embodiments of suitable detector blocks will be described in 
greater detail below with reference to FIGS. 3A-3C and 4). 
A sample fluid stream, which typically includes one or more separated 
constituents of a sample borne by, for example, a carrier gas, flows 
through the sensor cavity 234. The sample fluid exhibits a varying thermal 
conductivity that is then measurable by detecting changes in the 
resistance R.sub.S, and thus the temperature, of the sensor resistor 201. 
In the preferred embodiment, the power delivered to the sensor resistor 
201 is controlled so as to maintain a constant temperature therein. 
Changes in the resistance R.sub.S are then discerned by monitoring changes 
in the power delivered to the sensor resistor 201. It should be noted that 
in a departure from the prior art, the sample fluid flow need not be 
subject to the modulation techniques as described hereinabove, nor is 
there any need for the use of a control filament in a cavity that receives 
a flow of carrier gas only. 
The detector block is subject to a controlled temperature by temperature 
control apparatus (not shown) as known in the art. However, one may expect 
that the detector block, and in particular the cavity wall, are subject to 
two types of temperature variations: one that is distributed over time 
(temporal variation) and one that is distributed according to location 
within the detector block (spatial variation). The first signal providing 
means 111 may therefore be operated for providing a temperature 
compensation signal representative of at least one (and preferably both) 
of the spatial and temporal variations such that the effects of the 
temperature variation(s) on a detector output signal may be compensated. 
As will be described below, the contemplated temperature compensation 
signal is used in particular for compensating for the influence of such 
spatial and/or temporal variations on a temperature sense signal derived 
from the operation of the sensor resistor 201. 
In a particular feature of the present invention, the first and second 
reference resistors 100, 102 are located with respect to sensor resistor 
cavity 234 such that the temperature of the cavity wall is predominant in 
influencing the temperatures of the first and second reference resistors 
100, 102. That is, the detector block is intentionally constructed such 
that the temperature of the cavity wall is a substantial influence on the 
temperatures of the first and second reference resistors 100, 102 in 
comparison to the temperatures of other portions or regions of the 
detector block. To achieve this end, the detector block may be constructed 
such that the thermal impedance between the sensor resistor cavity 234 and 
the first and second reference resistors 100, 102 is substantially less 
than the thermal impedances between the first and second reference 
resistors 100, 102 and the remainder of the detector block. In some 
embodiments, the desired influence of the temperature of the cavity wall 
on the operation of the first and second reference resistors 100, 102 may 
be achieved by placement of the first and second reference resistor 
cavities 101, 105 such that they are located immediately adjacent the 
sensor resistor cavity 234 and are separated from the sensor resistor 
cavity 234 by a thin cavity wall. Thus, sufficient thermal impedances are 
effected between the first and second reference resistors 100, 102 and the 
remainder of the detector block so that such thermal impedances are each 
several times greater than, or an order of magnitude greater than, the 
thermal impedances that exist between the first and second reference 
resistors 100, 102 and the respectively nearest portions of the sensor 
resistor cavity 234. For example, the thermal impedances between the first 
and second reference resistors 100, 102 and the remainder of the detector 
block may be considered a thermal break, whereas the thermal impedances 
provided between the first and second reference resistors 100, 102 and the 
sensor resistor cavity 234 may be so low as to allow the temperatures of 
the first and second reference resistors 100, 102 to "track" (follow), 
without any significant delay, the temperatures of the respectively 
nearest portions of the cavity wall. 
The reference resistors 100, 102 are selected to have particular 
temperature coefficients such that a change in the temperature of either 
of the two reference resistors 100, 102 causes a proportionate change in 
the resistance of the respective resistor. A spatial temperature gradient 
causes differing resistances that are exhibited by each of the first and 
second reference resistors 100, 102. The spatial temperature gradient in 
the portion of the detector block between the positions of the first and 
second reference resistors 100, 102 is thereby represented by a voltage 
derived from the operation of the reference signal means 108. The voltage 
represents an average of the differing resistances; a resulting 
temperature compensation signal from the first signal providing means 111 
that represents an averaged value of the detector block temperature. 
In the illustrated embodiment, either one of the first and second reference 
resistors 100, 102 is believed to be adequate to effect a compensation 
signal that is suitable for compensating for the effects of temporal 
temperature variation in the cavity wall. The combination of the first 
reference resistor 100 and the second reference resistor 102 is believed 
to be adequate to derive a compensation signal that is also suitable for 
compensating for the effects of a spatial temperature variation. 
Accordingly, one of the features of the present invention is the provision 
of a temperature compensation signal that is derived from operation of one 
or both of the first and second reference resistors 100, 102 in the 
reference signal means 108. Therefore, the illustrated embodiment employs 
compensation for the temporal and/or spatial temperature variations that 
would otherwise degrade the sensitivity and accuracy of the detector 200. 
Further, it should be recognized that the teachings of the present 
invention contemplate the use of third, fourth, etc. reference resistors 
(not shown), as may be located in certain embodiments at other positions 
relative to the sensor resistor 201 within the detector block. 
Accordingly, FIG. 2 illustrates a variable voltage signal V.sub.T that 
represents the average temperature of the cavity wall in the immediate 
vicinity of the sensor resistor cavity 234. The voltage V.sub.T is 
provided on a signal line 116 for conditioning, when necessary, by a 
voltage gain circuit 120 and a voltage offset circuit 122. The output of 
the voltage offset circuit 122 then constitutes a temperature compensation 
signal V.sub.C that represents the average temperature of the wall of the 
sensor cavity 234. 
In a particularly preferred embodiment, the sensor resistor 201 and the 
first and second reference resistor 100, 102 are located in spaced, 
co-planar arrangement within the detector block. 
In still another embodiment, the temperature coefficients of the sensor 
resistor 201 and the reference resistors 100, 102 are matched. 
A preferred embodiment of the second signal providing means 112 includes 
resistors 202, 203, and 204 connected to the sensor resistor 201 in a 
bridge circuit 208. The resistors 202-204 can be located remote from the 
sensor resistor 201 on (for example) a circuit board assembly; none of the 
resistors 202-204 need to be embedded or otherwise integrated with the 
detector block. In the embodiment shown in FIG. 2, the resistances 
R.sub.2, R.sub.3, and R.sub.4 of the resistors 202, 203, and 204, 
respectively, determine the resistance R.sub.S of the sensor resistor 201 
necessary to balance the bridge circuit 208. For example, if R.sub.3 and 
R.sub.4 are equal then R.sub.S must equal R.sub.2 to balance the bridge. 
The second signal providing means 1 12 includes a first differential 
amplifier 205 having input terminals that are connected to balance nodes 
206 and 207 of the bridge circuit 208. The output of the first 
differential amplifier 205 is connected to the common node of resistors 
203 and 204 such that the amplifier 205 acts as a variable power supply 
for dynamically balancing the bridge 208. 
The output of the first differential amplifier 205, representing the bridge 
voltage V.sub.A of the bridge circuit 208, is also connected to a a third 
signal providing means 113 that includes a non-inverting input in a second 
differential amplifier 210. The inverting input of the second differential 
amplifier 210 also receives the temperature compensation signal V.sub.C 
from the voltage offset circuit 122. The second differential amplifier 210 
measures the amount of power dissipation in the bridge 208 based upon the 
value of the bridge voltage V.sub.A at various times. The measured change 
in power dissipation is then compensated according to the value of the 
temperature compensation signal V.sub.C so as to provide a detector output 
signal V.sub.O that is representative of the thermal conductivity of a 
detected sample constituent. The presence or concentration of one or more 
analytes in the sample fluid may then be indicated by providing the 
detector output signal V.sub.O to an information output device (not 
shown); of course, the detector output signal V.sub.O is also useful for 
other applications as known in the art. Suitable information output 
devices are known in the art and may include a strip chart recorder, a 
segmented or alphanumeric character display, a video display, or audio 
frequency transducer. 
It will be recognized that although the functions provided by the first and 
second differential amplifiers 205, 210, the gain circuit 120, and the 
offset circuit 122 are each illustrated as a respective circuit element 
functional block, these functions may in alternative embodiments be 
subsumed into a single circuit element, or into other circuit elements 
that provide additional functions. Such circuit elements may be integrated 
within a data processor or other electronic systems for performing 
control, processing, and communication functions in addition to those 
described herein. Such circuit elements may be constructed from discrete 
and/or integrated circuit devices amenable to the practice of this 
invention and may include, e.g., one or more active devices such as 
microprocessors, microcontrollers, interface circuits, switches, logic 
gates, or equivalent logic devices capable of performing the functions 
described herein. The relevant processors may include random access 
memories and read-only memories in which information and programming can 
be stored and retrieved by known methods. Such memory may be used for 
storage and retrieval of operating condition parameters (such as voltage 
gain and voltage offset values, spatial temperature gradient thresholds, 
and so on). 
FIGS. 3A-3C respectively illustrate three alternative embodiments 308A, 
308B, 308C of a preferred detector block. Each of the detector blocks 
308B, 308C includes a sensor resistor cavity 334, a first reference 
resistor cavity 301A-C, and a second reference resistor cavity 305A-C. An 
embodiment of the sensor resistor 201 (FIG. 2) may be provided in the form 
of a resistive filament 321 that is centrally supported within the sensor 
resistor cavity 324. The resistive filament may be fabricated to include a 
filament of material such as tungsten or platinum having a resistance that 
is proportional to its temperature. Embodiments of the first reference 
resistor 100 may be provided in the form of electrically-insulated, 
resistive strip elements 300A, 300B, or resistive filament 300C; 
embodiments of the second reference resistor 102 may be provided in the 
form of electrically-insulated, resistive strip elements 302A, 302B, or 
resistive filament 302C. The embodiment illustrated in FIG. 3C (which 
employs resistive filaments 321, 300C, 302C) offers a manufacturing 
advantage in that each of such filaments may be similar or identical in 
construction, and the electronic circuitry required to monitor the signals 
provided by each filament is simplified. 
The sensor resistor cavity 334 is preferably designed as a conduit for a 
controlled flow of a sample fluid containing one or more analytes to be 
detected, as described above. In contrast, the first reference resistor 
cavity 301A-301C and second reference resistor cavity 305A-305C are 
preferably sealed (self-contained). The first reference resistor cavity 
301A-301C and second reference resistor cavity 305A-305C are respectively 
separated from the sensor resistor cavity 334 by cavity walls 334A, 334B. 
The first and second reference resistors 300A, 302A are embedded within 
the detector block 308A at respective locations proximate to the cavity 
walls 334A, 334B. Thus, the first and second reference resistors 300A, 
302A fill respective first and second reference resistor cavities 301A, 
305A such that each reference resistor and its cavity are one in the same. 
The first reference resistor cavities 301B, 301C and second reference 
resistor cavities 305B, 305C are larger in volume than the respective 
first and second reference resistors 300B, 300C, 302B, 302C. The first 
reference resistor cavities 301B, 301C and second reference resistor 
cavities 305B, 305C are preferably gas-filled. Alternatively, the first 
reference resistor cavity 301B and second reference resistor cavity 305B 
in FIG. 3B may be evacuated and sealed. Suitable techniques for 
construction of filaments and cavities in a detector block may be found in 
U.S. Pat. No. 4,170,126, the disclosure of which is incorporated herein by 
reference. 
The resistive strip elements 300A, 302A are preferably embedded so as to be 
aligned with, and proximate to, the sensor resistor 321. The resistive 
strip elements 300B, 302B are similarly positioned but attached or 
embedded onto the surface of the first and second reference resistor 
cavities 301B, 305B so as to be aligned with, and positioned proximate to 
the sensor resistor 321. The filaments 300C, 302C are preferably supported 
on posts so as to be aligned with, and proximate to, the sensor resistor 
321; filaments 300C, 302C are also electrically insulated with respect to 
the interior surfaces of the first and second reference resistor cavities 
301C, 305C. 
The present invention contemplates the use of a minimal cavity wall 
thickness in the cavity walls 334A, 334B in the vicinity of the resistive 
strip elements 300A, 300B, 302A, 302B and filaments 321, 300C, 302C so as 
to facilitate heat transfer for effecting the above-described compensation 
for temperature variations. Suitable electrical connections (not shown) to 
the resistive strip elements 300A, 300B, 302A, 302B or filaments 321, 
300C, 302C may be provided through the body of detector blocks 308A, 308B, 
308C in accordance with the circuit schematic presented in FIG. 2 using 
electrically-insulated, high-temperature connectors as known in the art. 
FIG. 4 illustrates a fourth alternative embodiment of a preferred thermal 
conductivity detector block fabricated as a microminiature planar thermal 
conductivity detector by use of techniques known in the arts of integrated 
circuit fabrication, micromachining, and microfabrication. 
With reference to FIG. 4, a microminiature detector block 420 may include 
upper and lower substrates 408, 409 each constructed in the form of 
silicon chips which have been fabricated from one or more silicon wafers 
using batch processing steps. After fabrication, the upper and lower 
substrates 408, 409 may be superimposed, bonded together, and packaged by 
known techniques to form the microminiature detector block 420. 
The construction of the detector block 420 may be generally understood as 
follows. An insulating layer 410 of electrical insulation, such as silicon 
dioxide, may be provided on the lower substrate 409. A flow channel in the 
form of a flow channel upper portion 434 (formed on the underside of the 
upper substrate 408) and a flow channel lower portion 435 (formed atop the 
lower substrate 409) may be provided by known etching techniques in the 
respective substrates. Individual resistive traces 400, 402, 421 of 
resistive material may be provided atop the insulating layer 410. The 
upper substrate 408 may be etched in certain areas such that resistive 
trace cavities 401, 405 are provided. The insulating layer 410 may be 
fully under etched in certain areas such that the portion of the 
insulating layer 410 that supports the resistive trace 421 is suspended 
within the flow channel. The insulating layer 410 may also be fully under 
etched in certain areas such that the the flow channel upper portion 434 
and the flow channel lower portion 435 experience substantial fluid 
communication therebetween. Preferably, the resistive traces 400, 402, 421 
and the upper and lower portions of the flow channel 434, 435 have similar 
lengths and are formed in parallel to the direction of the flow of the 
sample fluid in the flow channel. 
The upper substrate 408 may be superimposed upon the lower substrate 409 
such that the perimeters of the resistive trace cavities 401, 405 are 
aligned over the resistive traces 400, 402 and sealed on the insulating 
layer 410, and the perimeters of the flow channel upper portion 434 and 
flow channel lower portion 435 are sealed onto the insulating layer 410 to 
form the fluid-tight conduit necessary for the flow channel. (Ports (not 
shown) for directing a sample fluid into and through the flow channel may 
be formed in one or both of the upper and lower substrates 408, 409. For 
example, a sample fluid may be introduced through a port that communicates 
with one end of the combined upper and lower flow channel portions 434, 
435 and allowed to exit the flow channel at a port that communicates with 
the opposing end of the flow channel.) The resistive trace 421 then may be 
employed as an embodiment of the sensor resistor 201 of FIG. 2, and the 
resistive traces 400, 402 may be employed as respective embodiments of the 
first and second reference resistors 100, 102 of FIG. 2. 
While the embodiment illustrated in FIG. 4 has been described as being 
fabricated from silicon, other materials may be used. For example, other 
crystalline substrates such as gallium arsenide may be used, and 
modifications in the structure of the disclosed embodiments may be 
effected by use of differing patterns of etch-resistant coatings. In 
addition, specialized coatings such as silicon dioxide may be deposited or 
grown on one or more surfaces of the completed structure. 
Those skilled in the art will appreciate that numerous changes and 
modifications may be made to the preferred embodiments of the invention 
and that such changes and modifications may be made without departing from 
the spirit of the invention. It is therefore intended that the appended 
claims cover all such equivalent variations as fall within the true spirit 
and scope of the invention.