Wide range vacuum gauge

A device for determining a pressure of gas in an evacuated chamber including a cylinder positioned in fluid communication with the evacuated chamber with the cylinder forming a compressed gas chamber, a reciprocating piston received within the cylinder and mounted for reciprocal movement therein, a port or valve for providing selective fluid communication between the compressed gas chamber and the evacuated chamber is disclosed. A drive mechanism is provided for reciprocating the piston between a retracted position, where the compressed gas chamber communicates with the evacuated chamber, and an extended position where communication between the compressed gas chamber and the evacuated chamber is interrupted, the position being a position where a pressure transducer determines that a predetermined pressure differential between the chambers has been reached. In the preferred embodiment, a stepper motor is used to measure a distance travelled by the piston at the point where the predetermined pressure differential is reached. Utilizing these parameters, a processor then determines the pressure of the gas within the evacuated chamber.

TECHNICAL FIELD OF THE INVENTION 
The present invention relates to a vacuum gauge for measuring pressure in a 
vacuum system over a wide pressure range. More particularly, the present 
invention relates to a vacuum gauge and method for measuring pressure in a 
vacuum system wherein gas leakage in the measuring means is taken into 
account when determining the pressure in the vacuum system. 
BACKGROUND OF THE INVENTION 
It has long been known that a liquid manometer can be used to measure the 
pressure of gases that obey Boyles Law by compressing the gas a known 
amount prior to making the measurement. The McLeod gauge, once widely used 
for measuring low pressures, utilizes this principle, as discussed in, J. 
H. Leck, Pressure Measurement in Vacuum Systems, Second Edition (Chapman 
and Hall, London 1964) pp. 3-7. A mercury piston is used to compress gas 
trapped in a known volume by a measurable amount thereby permitting the 
unknown pressure to be calculated. In one mode of operation, both the 
compression ratio and pressure differential created by compression of the 
gas are variables. In the second mode, the compression ratio is fixed but 
the pressure differential is a variable. At best, a McLeod gauge is a 
fragile, large, cumbersome gauge which requires considerable operator 
skill to manually make a measurement of pressure. A single pressure 
measurement is carried out over an extended period of time in that the 
mercury must be transferred slowly to avoid disastrous results. Also, 
mercury vapor is a health hazard if inhaled, ingested, or absorbed through 
the skin, and mercury vapor is anathema in modern day vacuum systems. 
However, mercury or other liquid which does not wet the inner surfaces is 
required to prevent leakage of the compressed gas in a McLeod gauge. 
McLeod gauges have been largely replaced by modern capacitance manometers. 
As is known, diaphragm vacuum gauges measure absolute pressure independent 
of gas species. Such gauges which measure force per unit area are 
typically used for measuring low pressures of gas mixtures where 
measurement of ionization currents in an ionization gauge or heat lost 
from a hot wire are ineffective: where high accuracy is required; or of 
corrosive or hostile gases. At low pressure, the force per unit area 
exerted by the gas molecules on a surface is extremely small so very thin 
diaphragms must be used to achieve the required sensitivity. Producers of 
such gauges are now providing 1 and 0.1 Torr full scale sensors with 4 to 
5 decades of dynamic range in an attempt to satisfy user requirements. 
However, the force per unit area exerted on a surface by a gas at, for 
example, 1.times.10.sup.-4 Torr is only about 2.times.10.sup.-6 psi. It is 
apparent that a gauge capable of measuring such a small force per unit 
area will be extremely sensitive to mechanical and thermally induced 
stresses. Even a slight overpressure will cause a significant zero shift 
in such instruments incorporating these sensitive diaphragms. 
U.S. Pat. No. 4,413,526 to Delajoud issued Nov. 5, 1983, discloses a device 
for measurement of fluid pressures including a vertical cylinder, a piston 
adapted to slide in the cylinder with viscous friction with the pressure 
to be measured being applied to the upper face of the piston which rotates 
the piston inside the cylinder. An electromagnetic precision weighing 
machine including a shaft and piston arrangement to which the pressure to 
be measured is applied is used to measure the force on the piston. The gas 
pressure which is to be measured acts on the piston, the force of which 
corresponds to the product of the affected area of the piston and the 
pressure difference across the piston. Devices such as this are not useful 
in most vacuum measurement applications because of gas leakage. 
In an effort to overcome some of the above-noted shortcomings, a 
capacitance manometer was developed and disclosed in U.S. Pat. No. 
4,823,603 to Ferran et al. issued Apr. 25, 1989. Therein, a capacitance 
manometer having stress relief for a fixed electrode including a thin 
electrically conductive diaphragm fixedly mounted to a housing comprising 
an electrode of a variable capacitor is disclosed. While the manometer set 
forth therein solves the problem associated with capacitance changes 
caused by temperature and a stray capacitance caused by leakage currents 
through a dielectric ceramic material, the disclosed manometer is still 
very sensitive to mechanical disturbances and requires a reference 
pressure for absolute pressure measurement. 
In yet another attempt to overcome the above noted shortcomings, U.S. Pat. 
No. 5,022,207 to Rud Jr. issued Jun. 11, 1991, discloses a transmitter 
having a pressure sensor for sensing pressure and an overpressure 
protection means for limiting the pressure applied to the pressure sensor 
when the applied pressures exceeds a preselected limit. 
Clearly, there is a need for a gauge which can measure low pressures 
without being sensitive to mechanical or thermal stresses or to 
overpressure. Further, it is desirable to measure even lower pressures 
than can be measured today with typical sensitive diaphragm gauges. It 
would also be desirable to be able to utilize a single diaphragm thickness 
over a wide pressure range rather than resort to installing a separate 
gauge for each pressure range, and to utilize a differential diaphragm 
manometer rather than an absolute manometer to measure absolute pressure. 
These needs and advantages can be achieved in accordance with the present 
invention and will become apparent from the following description. 
SUMMARY OF THE INVENTION 
A primary object of the present invention is to provide a vacuum gauge 
which overcomes the above noted shortcomings associated with the prior art 
devices. 
A further object of the present invention is to provide a diaphragm gauge 
which can accurately measure low pressures utilizing a thicker diaphragm 
than in prior art devices intended for the same pressure range. 
Another object of the present invention is to provide a diaphragm gauge 
which is relatively immune to mechanical and thermal disturbances by 
rapidly and periodically trapping and compressing a volume of trapped gas 
to a higher pressure before measuring the pressure differential across the 
diaphragm. 
Another object of the present invention is to provide a diaphragm gauge to 
measure absolute vacuum pressures without the necessity of providing the 
customary absolute reference pressure on one side of the diaphragm. 
Yet another object of the present invention is to provide a diaphragm gauge 
with a useful pressure range from above atmospheric pressure to very low 
pressures with a single diaphragm thickness. 
A further object of the present invention is to provide a diaphragm gauge 
with continuous and precise automatic rezero. 
Another object of the present invention is to provide a method for 
dynamically measuring the gas leakage past the piston used to compress the 
gas and for dynamically correcting the pressure indication for leakage. 
A further object of the present invention is to provide a method for using 
a diaphragm gauge for measuring absolute vacuum pressures which provides 
automatic immunity from overpressure effects. 
These as well as additional advantages of the present invention are 
achieved by providing a diaphragm vacuum gauge for determining the 
pressure within an evacuated chamber including a cylinder positioned in 
fluid communication with the evacuated chamber with the cylinder forming a 
compressed gas chamber, a reciprocating piston received within the 
cylinder and mounted for reciprocal movement therein and a port or valve 
for providing selective fluid communication between the compressed gas 
chamber and the evacuated chamber. A drive mechanism is provided for 
reciprocating the piston between a retracted position, where the 
compressed gas chamber communicates with the evacuated chamber, and an 
extended position where communication between the compressed gas chamber 
and the evacuated chamber is interrupted, the extended position being a 
position where a pressure transducer determines that a predetermined 
pressure differential between the chambers has been reached. In the 
preferred embodiment, a stepper motor is used to measure a distance 
travelled by the piston at the point where the predetermined pressure 
differential is reached. Utilizing these parameters, a processor then 
determines the pressure of the gas within the evacuated chamber. 
These as well as additional advantages of the present invention will become 
apparent from the following detailed description of the preferred 
embodiments when read in light of the several figures.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Referring now to the several figures and particularly FIG. 1, there is 
shown a diaphragm vacuum gauge 10 comprising a cylinder 12, a moveable 
close fitting piston 14, a flexible diaphragm 16 which separates a trapped 
volume of gas 18 to be compressed from the gas in the evacuated chamber 20 
of the vacuum system 22 whose pressure is to be measured. A port or 
opening 24 is provided in the cylinder wall 26 which permits gas to flow 
freely in or out of the cylinder 12 from or to the vacuum system 22 when 
the piston 14 is in its fully retracted position. A pressure transducing 
device 27 for transducing the amount of deflection of the diaphragm into a 
pressure indication and a bellows motion seal 28 for transmitting piston 
motion from the piston rod 29 through the wall 30 of the vacuum system 22 
are provided. 
The cylinder 12 is preferably a circular cylinder with a smooth hard 
interior wall 26. The piston 14 also has a smooth hard outer surface on 
skirt 32 which closely fits in the cylinder 12 so that the gap 34 between 
the piston 14 and cylinder 12 is minimal but not so tight that the piston 
14 does not move freely within the cylinder 12. Piston rings (not shown) 
or similar known seals may be used to minimize leakage past the piston 14. 
The skirt 32 of the piston 14 is preferably made relatively long so that 
the leakage path between the piston 14 and cylinder 12 is long. The port 
24 is preferably a relatively narrow rectangular slot with the long side 
extending in a direction of piston travel as exemplified by arrow 36. A 
narrow rectangle is preferred so that when the piston 14 covers the port 
24 on the down stroke a minimum amount of circumference of the cylinder 12 
is exposed as a leakage path for gas out of the cylinder 12. 
Alternatively, a valve (not shown) may be used to open and close the port 
rather than relying on the piston 14 to seal the port 24. 
The pressure transducing device 27 can be a small commercially available 
piezoresistive or capacitance pressure sensor, or the like fabricated 
using silicon processing techniques common in the semiconductor industry. 
The device 27 may be hermetically sealed to a bottom 38 of the cylinder 12 
with an o-ring or other sealing means (not shown). If required, the end of 
the piston 14 can be suitably shaped to occupy any dead space in the end 
of the cylinder 12 when the piston 14 is fully extended. Alternatively the 
pressure transducing device 27 can be a diaphragm capacitance manometer as 
illustrated in FIG. 1 with the flexible diaphragm 16 forming the closed 
end of the cylinder 12 and having an electrical feed thru 39 in the vacuum 
system wall 30. The remainder of the capacitance manometer can be of a 
conventional design. It should be noted, however, that the pressure sensor 
may be any device capable of sensing a differential pressure and having a 
geometry compatible with achieving a relatively high compression ratio. 
The bellows motion seal 28 is preferably made of metal and with a length 
selected to provide long life. Means for mounting the cylinder 12 in the 
vacuum system 22 are not shown. 
Referring now to FIG. 2, there is shown a mechanical drive mechanism 
assembly 40 for providing a precisely controlled variable compression 
ratio. The drive mechanism 40 includes a stepper motor 42, a drive screw 
44 and nut 46, a mounting bracket 48, a nut 50 for attaching the drive 
screw 44 to the piston rod 29, and a flange 51 for securing the assembly 
40 to the vacuum system 22. A typical stepper motor can produce extremely 
rapid motor step angles, typically 1.8.degree., but which can be as small 
as 0.0144.degree.. Stepping accuracy is typically noncumulative so that 
the final rotation position is never more than approximately 5% of one 
full step regardless of the number of steps from the intended position. 
The step angle and pitch of the drive screw 44 are selected to give the 
desired resolution in piston position while still providing the desired 
speed of piston travel. 
FIG. 3 illustrates an alternative mechanical drive mechanism 60 for 
providing a precisely controlled variable compression ratio including a 
stepper motor 62, support bracket 64, drive drum 66, a taut band 68, and a 
spring 70 to provide compression. The spring 70 is confined by a nut 72 
for attachment to the piston rod 29 and the support bracket 64 and places 
the band 68 in tension such that the piston rod 29 moves in response to 
rotation of the stepper motor 62. The support bracket 64 also includes a 
flange 73 for securing the support bracket 64 in the proper position 
adjacent the cylinder 12 of FIG. 1. While two alternative drive mechanisms 
are set forth in FIGS. 2 and 3, these mechanisms are set forth by way of 
example, and any mechanism which can precisely position the piston 14 and 
measure the position of the piston 14 may be used. While the mechanism 60 
illustrated in FIG. 3 is not exposed to the inherent wear of the screw 
illustrated in FIG. 2, the mechanism 40 of FIG. 2 will be discussed in 
detail with respect to the operation of the preferred embodiment of the 
invention in order to simplify the discussion. 
The method of measuring an unknown pressure P.sub.x in the vacuum system 
using the wide range vacuum gauge assembled using the diaphragm vacuum 
gauge 10 illustrated in FIG. 1 combined with the drive mechanism 40 
illustrated in FIG. 2 will now be discussed in detail. 
Initially, the following assumptions need be made. It should be noted that 
these assumed values may be readily varied in order to provide a wide 
range vacuum gauge which reliably and accurately measures the unknown 
pressure P.sub.x in the vacuum system. The assumptions and system 
parameters are as follows: 
1. The diaphragm 16 is rated for a maximum differential operating pressure 
.DELTA.P.sub.m of, for example, 1 PSI. 
2. The piston 14 is fully retracted and the port 24 in the cylinder 12 is 
open to the evacuated chamber 20. 
3. Let P.sub.x =the unknown pressure in the evacuated chamber 20 and in the 
cylinder 12 when the piston 14 is in the retracted position. 
4. Let L=the maximum length of the cylinder 12 of trapped gas, that is, the 
length of the cylinder when the port 24 is just closed as illustrated in 
FIG. 1. 
5. Let L.sub.x =the length of the cylinder 12 of compressed gas that was 
initially at unknown pressure P.sub.x, but is now at a pressure sufficient 
to create a pressure difference across the diaphragm 16 of .DELTA.P.sub.m. 
6. Let A=the cross sectional area of the cylinder 12. 
7. Thus, the initial volume of trapped gas in the cylinder 12 satisfies the 
formula: 
EQU V.sub.initial =LA (1) 
The piston 14 is then caused to rapidly advance downward such that the 
compression time ranges from 0.1 second to 10 seconds, thus compressing 
the gas in the cylinder 12 initially at a pressure P.sub.x until the 
differential pressure across the diaphragm 16 is .DELTA.P.sub.m. 
Accordingly, by using a variable compression ratio, the maximum 
differential pressure across the diaphragm 16 is automatically limited to 
the rated value .DELTA.P.sub.m for the diaphragm 16 regardless of the 
pressure in the evacuated chamber 20. In doing so, the objective of 
providing automatic immunity to overpressure of the diaphragm 16 is 
achieved. Inadvertent overpressuring is a serious problem with known 
diaphragm gauges as discussed hereinabove. By only moving the piston 14 
the distance required to achieve a predetermined .DELTA.P.sub.m, the 
diaphragm will never be overpressured regardless of the pressure in the 
evacuated chamber 20. 
The distance the piston 14 advances is a distance .DELTA.L.sub.x, where 
EQU .DELTA.L.sub.x =L-L.sub.x (2) 
This distance .DELTA.L.sub.x is determined from the piston 14 position 
where the port 24 is just sealed, that being the position illustrated in 
FIG. 1, to the end of its compression stroke when the pressure 
differential equals .DELTA.P.sub.m. As P.sub.x changes, the value of these 
parameters will change. The subscript x is used to uniquely identify 
parameters with the unknown pressure P.sub.x. .DELTA.L.sub.x can readily 
be determined by circuitry well known in the art for counting the number 
of stepper motor steps N, and by a one time measurement of the lead of the 
drive screw 44. 
Accordingly, the compression ratio defined as the initial volume of gas 
divided by the final volume of compressed gas satisfies the formula: 
##EQU1## 
It should be noted that the above calculation ignores the slight deflection 
of the diaphragm 16 which may be accounted for if determined to be 
significant by means well known in the art. 
8. Let P.sub.1x =The maximum pressure of trapped gas at the completion of 
the compression stroke when the differential pressure across the diaphragm 
is .DELTA.P.sub.m. 
Thus, .DELTA.P.sub.m satisfies the following: 
EQU .DELTA.P.sub.m =P.sub.ix -P.sub.x, and (4) 
EQU P.sub.1x =R.sub.x P.sub.x (5) 
Substituting equation (5) into equation (4) results in: 
##EQU2## 
And substituting equation (3) into equation (6) yields: 
##EQU3## 
Accordingly, from the foregoing, the unknown pressure P.sub.x can be 
calculated by first compressing the trapped gas until the differential 
pressure across the diaphragm 16 is .DELTA.P.sub.m and then measuring the 
piston travel .DELTA.L.sub.x required to provide a differential pressure 
.DELTA.P.sub.m and subsequently processing these values by a processor. 
This process may be repeated periodically, for example, every 2 seconds to 
follow a continuously changing vacuum system pressure. Thus, the objective 
of measuring the absolute pressure in the vacuum system without requiring 
an absolute reference pressure has been achieved. It should be noted that 
if the pressure P.sub.x changes significantly during the compression 
stroke, the calculated value of P.sub.x will be in error. However, when 
P.sub.x is changing rapidly an accurate measurement of P.sub.x is 
typically not required. 
An important step in this process is assuring that the port 24 is open a 
sufficiently long time to assure that the pressure difference across the 
diaphragm 16 is zero before the next compression stroke is initiated. A 
very important benefit is achieved by providing for automatic rezeroing of 
the pressure sensing means during the time when the pressure difference 
across the diaphragm 16 is zero between compression strokes. Thus, zero 
shifts due to creep in the diaphragm or other parts and temperature 
induced changes of the zero reading are greatly reduced. Such zero shifts 
are some of the most significant causes of error in diaphragm manometers 
presently used. Correcting for zero shift in a conventional capacitance 
manometer is a time consuming process involving pumping the vacuum system 
to a pressure significantly lower than the lowest pressure to be measured 
and then resetting the zero. The system in accordance with the present 
invention eliminates this problem. 
Even though piston rings or similar seals are used to reduce leakage, gas 
leakage past the piston may still be unacceptably high and the calculated 
value of P.sub.x may be in error due to these leakage effects. Gas leakage 
may be corrected for in the following manner. 
Referring to FIG. 4, circuitry is shown for determining the rate of change 
of pressure of compressed gas (dp/dt). This circuitry may be used to 
measure (dp/dt) on a continuous basis. At the end of the compression 
stroke (dp/dt)=0 and as gas leakage past the piston 14 occurs, the 
pressure of trapped gas will fall and (dp/dt) will become negative. The 
appearance of a negative (dp/dt) can be used as a start signal to the 
correction algorithm block shown in FIG. 4 to calculate a correction 
factor and correct the pressure indication as a function of the leakage of 
gas past the piston 14. Alternatively, a start signal may be generated 
utilizing a stepper motor signal. Gas leakage will occur during the 
compression stroke. Initially the gas leakage will be negligible when the 
differential pressure is negligible, and the gas leakage will be at a 
maximum at the end of the compression stroke. The amount of leakage will 
depend on how far the piston 14 extends beyond the port 24 and on the 
pressure differential as well as on the gap between the piston 14 and 
cylinder 12 which may change with temperature fluctuations and with use. 
Assuming the maximum rate of pressure decrease (dp/dt).sub.mx in the 
compressed volume of gas is measured at the end of the compression stroke 
when the unknown gas pressure in the vacuum system is P.sub.x as 
calculated by the precessor, the rate of gas leakage out of the compressed 
volume will be: 
##EQU4## 
Equation 8 represents the leak rate at a maximum pressure difference across 
the piston 14. A good approximation of the average leak rate during the 
compression stroke will be 1/2 of this maximum rate or: 
##EQU5## 
Leakage occurs during the travel time of the piston .DELTA.t.sub.x during 
the compression stroke where: 
EQU .DELTA.t.sub.x 32 .DELTA.L.sub.x /y seconds (10) 
where y is the average speed of the piston during the compression stroke. 
Accordingly, the quantity of gas leaking past the piston during the 
compression stroke satisfies the following: 
##EQU6## 
It should be noted that the initial quantity of gas in the cylinder at the 
start of the compression stroke is LA P.sub.x but a smaller amount was 
actually compressed due to leakage. This smaller amount is the original 
amount less leakage and satisfies the following: 
##EQU7## 
The measured compression ratio R.sub.x will be too large by the ratio of 
the initial quantity of gas V.sub.i to the final quantity of compressed 
gas V.sub.f or: 
##EQU8## 
Thus, the corrected compression ratio R.sub.xc is obtained by multiplying 
the measured compression ratio R.sub.x by the reciprocal of equation (13) 
or by K, such that: 
EQU R.sub.xc =K R.sub.x (14) 
Accordingly, by substitution of equations, to account for leakage, the 
unknown pressure P.sub.x satisfies: 
##EQU9## 
By substituting equation (13) into equation (15), the unknown pressure 
P.sub.x becomes: 
##EQU10## 
Accordingly, equation (16) can be readily solved for P.sub.x as follows: 
##EQU11## 
Equation (17) being the value of P.sub.x corrected for gas leakage during 
the compression stroke. It should be noted that for zero leakage 
(dp/dt).sub.mx =0 and the above expression for P.sub.x then becomes: 
##EQU12## 
which is the same as equation (7) where zero leakage was assumed. 
Each of the above-noted parameters of equation (17) for P.sub.x can readily 
be measured and the calculations of P.sub.x made by known techniques. That 
is, the pressure difference across the diaphragm .DELTA.P.sub.m is 
determined by the diaphragm capacitance manometer illustrated in FIG. 1, 
the lengths, L, L.sub.x and .DELTA.L.sub.x are determined by the position 
of the stepper motor 42, (dp/dt).sub.mx being determined by the diaphragm 
capacitance manometer and the speed y by the stepper motor 42 as well. 
Thus, gas leakage past the piston 14 can be dynamically corrected for 
after a compression stroke. In this way, the errors due to leakage may be 
reduced to negligible values. It should be noted that this method of 
correcting for leakage depends on the value of P.sub.x remaining 
relatively fixed during the short time while (dp/dt).sub.mx is being 
measured. However, if P.sub.x is changing rapidly, then an accurate 
leakage correction is of little value. 
The pressure range which can be measured utilizing the arrangement shown in 
FIG. 1 is limited by the minimum incremental motion of the piston 14 which 
can be resolved. At low unknown pressures P.sub.x, when a high compression 
ratio must be utilized to achieve a given .DELTA.P.sub.m, only a small 
increment in .DELTA.L is required to compress the gas by, say, 1% of 
reading. At high unknown pressures P.sub.x when a small compression ratio 
is required to achieve a given .DELTA.P.sub.m, only a small increment in 
.DELTA.L is required to compress the gas by 1% of reading. If the minimum 
change in .DELTA.L which can be reliably measured is, for example, 0.00005 
in., the maximum and minimum pressures which can be resolved to 1% are 
shown in Table I for different .DELTA.P.sub.m 's. 
TABLE I 
______________________________________ 
.DELTA.P.sub.m P.sub.x max P.sub.x min 
(Torr) (Torr) (Torr) 
______________________________________ 
51 10,000 0.25 
(1 PSI) 
1 200 5 .times. 10.sup.-3 
1 .times. 10.sup.-1 
20 5 .times. 10.sup.-4 
1 .times. 10.sup.-2 
2 5 .times. 10.sup.-5 
______________________________________ 
Maximum and minimum pressures which can be resolved to 1% for various 
.DELTA.P.sub.m using the device shown in FIG. 1 for L = 1 in. and a 
minimum measured increment in piston travel of 0.00005 in. 
FIG. 5 illustrates an alternative embodiment for compressing the trapped 
gas to higher compression ratios and with greater resolution of the 
distance travelled by the piston. The system 100 includes a large cylinder 
112, a large piston 114, a port 124 in the large cylinder wall connecting 
the large cylinder 112 to an evacuated chamber 120, a pressure difference 
sensing means in the form of a capacitance manometer diaphragm and plate 
127 having an electrical feed thru 121 in the wall 117 of evacuated 
chamber 120, a small cylinder 119 in the end of the large piston 114 
forming a small compression chamber 123, a small piston 125, a small 
piston flange 131, a back stop 133, a spring 137 and flexible bellows 128. 
The spring force of spring 137 is sufficient to hold the small piston 
flange 131 firmly against the backstop 133 as the piston assembly is 
advanced by a drive mechanism connected to piston rod 129 such as that 
shown in FIG. 2. The piston rod 129 is reciprocated in a direction shown 
by arrow 136 such that the small diameter piston 125 moves with the larger 
piston 114 until the larger piston encounters a mechanical stop at the 
limit of its downward travel. The stop may take any form so long as it 
stops the forward movement of the large piston 114. When the larger piston 
114 stops, the smaller piston 125 is designed to continue advancing 
downward, compressing the spring 137 and further compressing the trapped 
gas until the predetermined pressure difference .DELTA.P.sub.m across the 
diaphragm 127 is realized. While FIG. 5 illustrates a two piston 
arrangement, three or more piston arrangements may also be used depending 
upon the particular application of the device. Each subsequent piston 
would be received in a cylinder formed in a previous piston. Further, 
while the piston arrangement of FIG. 5 illustrates the pistons as being 
concentrically positioned relative to one another, this need not be the 
case so long as each assembly communicates with the trapped volume of gas. 
The method for measuring an unknown pressure P.sub.x in an evacuated 
chamber using the elements of FIG. 5 will now be explained in detail for 
two conditions. In condition 1, the maximum pressure difference across the 
diaphragm .DELTA.P.sub.m is assumed to be achieved before the large piston 
114 bottoms out, that is, before the large piston 114 reaches the 
mechanical stop. 
As with the previous embodiment, the following assumptions will be made: 
1. The diaphragm 127 is rated for a maximum differential operating pressure 
.DELTA.P.sub.m, for example, 1 PSI. 
2. The two pistons 114 and 125 are fully retracted and the port 124 in the 
large cylinder 112 is open to the evacuated chamber 120. The zero setting 
of the diaphragm gauge may be reset at this point to minimize zero shift 
errors. 
3. Let P.sub.x =The unknown pressure in the evacuated chamber and in the 
large and small cylinders. 
Accordingly, in Condition 1, the large piston 114 is not bottomed out and 
the compression ratio, which is equal to the ratio of the initial volume 
of compressed gas to the final volume satisfies the following equation: 
##EQU13## 
where: A.sub.1 =The cross-sectional area of the large cylinder. 
A.sub.2 =The cross-sectional area of the small cylinder. 
.rho.=A.sub.2 /A.sub.1 
L.sub.1 =The maximum length of the large cylinder of trapped gas when the 
port is just closed. 
L.sub.1x =The length of the large cylinder when the pressure difference 
across the diaphragm is .DELTA.P.sub.m and the small piston flange is 
still held firmly against the back stop. 
L.sub.1x min=The length of the large cylinder when the large cylinder is 
bottomed out at the lower limit of its travel. 
L.sub.2 =The maximum length of the small cylinder with the small piston 
fully retracted. 
L.sub.2x =The length of the small cylinder when the pressure difference 
across the diaphragm is .DELTA.P.sub.m and the large piston is at the 
lower limit of its travel. 
Assuming P.sub.1x equals the maximum pressure in the large and small 
cylinders at the end of the compression stroke for Condition 1 when the 
pressure difference across the diaphragm is .DELTA.P.sub.m, .DELTA.P.sub.m 
satisfies the equation: 
EQU .DELTA.P.sub.m =P.sub.1x -P.sub.x and, (20) 
EQU P.sub.1x =R.sub.x P.sub.x (21) 
Substituting equation (21) into equation (20) yields: 
##EQU14## 
and substituting equation (19) into equation (22) results in: 
##EQU15## 
Utilizing the relations .DELTA.L.sub.x =L.sub.1 -L.sub.1x Condition 1 is 
represented by equation (24) as follows: 
##EQU16## 
It should be noted that when L.sub.2 =0, this expression for P.sub.x 
becomes the same as was previously obtained utilizing the system of FIG. 1 
without a second piston. 
In Condition 2, where the maximum pressure difference across the diaphragm 
.DELTA.P.sub.m is achieved after the large piston 114 bottoms out, the 
compression ratio is described as: 
##EQU17## 
Assuming P.sub.2x equals the maximum pressure in the small cylinder 119 at 
the end of the compression stroke of the large cylinder 112 when the 
pressure difference across the diaphragm is .DELTA.P.sub.m, .DELTA.P.sub.m 
satisfies the equation 
EQU .DELTA.P.sub.m =P.sub.2x -P.sub.x and, (26) 
EQU P.sub.2x =R.sub.x P.sub.x (27) 
Substituting equation (27) into equation (26) yields: 
##EQU18## 
Substituting equation (25) into equation (28) gives 
##EQU19## 
Utilizing the relationship L.sub.2x =L.sub.2 -.DELTA.L.sub.2x Condition 2 
is represented by equation (30) as follows: 
##EQU20## 
Accordingly, utilizing the arrangement shown in FIG. 5, P.sub.x can be 
readily determined for Conditions 1 and 2 by measuring several parameters 
utilizing known methods and calculating P.sub.x utilizing known 
instrumentation techniques. As mentioned previously, the pressure 
difference across the diaphragm .DELTA.P.sub.m is determined by the 
diaphragm capacitance manometer illustrated in FIG. 5 and the lengths 
L.sub.1, L.sub.1xmin, L.sub.2, L.sub.2x and .DELTA.L.sub.2x are determined 
by the position of the stepper motor of FIG. 2. 
In Table II there is shown the maximum and minimum pressures which can be 
resolved with the dual piston system illustrated in FIG. 5. 
TABLE II 
______________________________________ 
.DELTA.P.sub.m P.sub.x max P.sub.x min 
(Torr) (Torr) (Torr) 
______________________________________ 
51 10,000 0.030 
(1 PSI) 
1 200 6 .times. 10.sup.-4 
0.1 20 6 .times. 10.sup.-5 
______________________________________ 
Maximum and minimum pressures which can be resolved to 1% for various 
.DELTA.P.sub.m using the device shown in FIG. 5 for L.sub.1 = 1 in., 
L.sub.2 = 0.5 in., .rho. = 0.1, L.sub.1x min = 0.0005 in. and a minimum 
measured increment in piston travel of 0.00005 in. 
The maximum compression ratio which can be achieved with the arrangement of 
FIG. 5 is limited by the dead volume in the large cylinder when the large 
piston 114 bottoms out. Gas in this dead volume must also be compressed by 
advancing the small piston, thus limiting the maximum compression ratio 
which can be achieved. If the diaphragm sensor has a repeatability of, 
say, 0.5% of full scale, that is of .DELTA.P.sub.m, the repeatability at 
one tenth of full scale will typically only be 5%. However, the 
repeatability of the measurement of P.sub.x utilizing the devices in FIGS. 
1 and 5 will be 0.5% of reading. It is this improvement in repeatability 
which constitutes a major benefit of the present invention. If the 
repeatability of a given diaphragm pressure sensor is sufficiently good 
at, say, one tenth of full scale, the lower pressure range of the present 
invention may be extended by selecting a pressure difference of 
approximately 0.1 .DELTA.P.sub.m as the fixed pressure difference. 
Therefore, in accordance with the present invention, compressing gas in a 
known volume with a solid piston (as opposed, for example, to the liquid 
mercury piston employed in a McLeod gauge) until the pressure difference 
across a diaphragm is a known amount and calculating the initial pressure 
in the known volume from measurements of the geometry after compression is 
achieved. Additionally, in accordance with a preferred embodiment of the 
invention the present invention, a measured, variable compression ratio 
and a known (or predetermined) fixed pressure difference across a 
diaphragm can be used to extend the pressure range which can be measured 
with a single diaphragm thickness. Further, as can be appreciated from 
Equation (7), a measured, variable compression ratio and a measured, 
variable pressure difference across a diaphragm may also be utilized in 
order to extend the pressure range which can be measured with a single 
diaphragm thickness. Alternatively, a known (or predetermined) fixed 
compression ratio and a measured, variable pressure difference may be also 
utilized to extend the pressure range which can be measured with a single 
diaphragm thickness. Further, multiple known fixed pressure differences 
and multiple known fixed compression ratios may be utilized in extending 
the pressure range which can be measured with a single diaphragm 
thickness. In utilizing the diaphragm vacuum gauge in accordance with the 
present invention, a full scale repeatability is achieved such that the 
unknown pressure may be reliably and repeatably read. 
While the present invention has been described with reference to a 
preferred embodiment, it should be appreciated by those skilled in the art 
that the invention may be practiced otherwise than as specifically 
described herein without departing from the spirit and scope of the 
invention. It is, therefore, to be understood that the spirit and scope of 
the invention be limited only by the appended claims.