U.S. patent number 3,745,384 [Application Number 05/216,074] was granted by the patent office on 1973-07-10 for resonant pressure sensor.
This patent grant is currently assigned to The Bendix Corporation. Invention is credited to William Carroll Blanchard.
United States Patent |
3,745,384 |
Blanchard |
July 10, 1973 |
RESONANT PRESSURE SENSOR
Abstract
A pressure responsive diaphragm or capsule having a variable
self-resonant frequency characteristic is excited to vibrate in a
mode other than the fundamental or f.sub.01 mode, that is,
vibration occurs in a mode wherein at least first and second
portions of the diaphragm are simultaneously moving 180.degree. out
of phase with respect to one another. This is accomplished by
suitably coupling first and second electromechanical transducers to
the first and second diaphragm portions respectively. A feedback
amplifier whose output frequency is determined by the frequency at
which the first transducer is vibrating is connected to drive the
second transducer.
Inventors: |
Blanchard; William Carroll
(Baltimore, MD) |
Assignee: |
The Bendix Corporation
(Southfield, MI)
|
Family
ID: |
22805573 |
Appl.
No.: |
05/216,074 |
Filed: |
January 7, 1972 |
Current U.S.
Class: |
310/324; 73/386;
73/702; 310/338; 331/65 |
Current CPC
Class: |
G01L
9/0022 (20130101); G01L 9/0016 (20130101) |
Current International
Class: |
G01L
9/00 (20060101); H04r 017/00 () |
Field of
Search: |
;310/8.1-8.3,8.5,8.7
;340/8,10,15.5,17 ;331/65,154 ;73/67,67.2,386,398R,71.5U
;332/30 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Miller; J. D.
Assistant Examiner: Budd; Mark O.
Claims
The invention claimed is:
1. In a pressure transducer including a diaphragm having a variable
self resonant frequency wherein said frequency is correlated to
pressure differential across said diaphragm and wherein said
frequency can occur in at least one vibrational mode, characterized
in that one portion of said diaphragm moves in a first direction
while a second portion of said diaphragm moves simultaneously in a
second direction, means for maintaining vibration of said diaphragm
in said at least one vibrational mode comprising:
converting means operatively coupled to said one portion of said
diaphragm for converting mechanical oscillations into an electrical
output;
drive means operatively coupled to said second portion of said
diaphragm for exciting said diaphragm to vibrate in response to an
electrical signal; and,
electrical means responsive to said electrical output for
generating said electrical signal.
2. The pressure transducer of claim 1 wherein said electrical means
comprises means for generating said electrical signal phased to
drive the portion of said diaphragm coupled to said drive means in
an opposite direction than the direction in which the portion of
said diaphragm coupled to said converting means is simultaneously
moving.
3. The pressure transducer of claim 2 wherein said electrical means
includes filter means for generating said electrical signal only
within a predetermined frequency band.
4. The pressure transducer of claim 2 wherein said diaphragm is a
rolled metallic alloy having a rolling axis, and wherein an
imaginary straight line through said converting means and said
drive means is perpendicular to said axis.
5. The pressure transducer of claim 1 wherein said at least one
vibrational mode is characterized by at least one nodal diameter,
said one portion being to one side of said nodal diameter and said
second portion being to the other side of said nodal diameter.
6. A vibrating diaphragm pressure transducer operable in the
f.sub.11 vibrational mode having a single nodal diameter
comprising:
a diaphragm having a variable self resonant frequency
characteristic;
means for impressing fluid pressure differential across said
diaphragm;
converting means operatively coupled to a first portion of said
diaphragm to one side of said nodal diameter for converting
mechanical oscillations of said diaphragm into an electrical
output;
drive means operatively coupled to a second portion of said
diaphragm to the other side of said nodal diameter for exciting
said diaphragm to vibrate in response to an electrical signal;
and,
electrical means responsive to said electrical output for
generating said electrical signal phased with respect to said
electrical output so that said drive means drives said second
portion of said diaphragm in a direction opposite to the
simultaneous direction of movement of said first portion.
7. The vibrating diaphragm pressure transducer of claim 6 wherein
said diaphragm is a rolled metallic alloy having a rolling axis and
wherein said nodal diameter is substantially parallel with said
rolling axis.
8. The vibrating diaphragm pressure transducer of claim 6 wherein
said electrical means includes a filter whereby said electrical
signal is contained within a predetermined frequency band related
to the f.sub.11 vibrational mode frequencies.
9. The vibrating diaphragm pressure transducer of claim 6 with
additionally further means coupled to said first portion of said
diaphragm and responsive to said electrical signal for driving said
first portion in a direction opposite to the direction in which
said second portion is simultaneously driven by said drive means.
Description
BACKGROUND OF THE INVENTION
This invention relates to fluid pressure sensors and more
particularly to self-resonant vibrating pressure sensors generally
comprised of a diaphragm or capsule having a variable self-resonant
frequency characteristic and which thus has a generally unique
self-resonant frequency for each pressure sensed.
The use of a diaphragm or a causule having a generally unique
self-resonant frequency for each pressure as a self-resonant
pressure sensor was first suggested by J. R. Cosby in his U. S.
Pat. No. 3,019,397. This pressure sensor consists of the
aforementioned capsule, electromechanical transducers for sensing
the vibrating frequency of the capsule and for driving the capsule,
and a positive feedback oscillator or amplifier whose output
frequency is determined by the sensed frequency, which output
frequency is used to drive the capsule. The oscillator in essence
thus drives the capsule at its self-resonant frequency, which is a
measure of the sensed pressure differential across the diaphragm.
This novel use of a pressure capsule permits analog pressure to be
directly converted to frequency at the sensing element. The various
mechanical linkages associated with a pressure capsule when used to
sense pressure by static deflection of the capsule as well as the
characteristic hysteresis of the capsule are essentially eliminated
by this device.
In this prior art device the drive transducer was effective for
driving the capsule generally centrally of the diaphragm while the
pickup transducer sensed the same portion of the diaphragm. This
placement of transducers indicates that the diaphragm was excited
in the f.sub.01 vibrational mode and generally limits the diaphragm
vibration modes to those modes having no nodal diameter.
The present sensor is similar to the Cosby sensor. That is, the
sensor consists of a mechanically unloaded anerode capsule and
associated electronics. The capsule is suitably evacuated but may
optionally be filled with a standard fluid at a standardized
pressure, or may be immersed in a standardized environment and the
interior of the capsule communicated with the pressurized fluid to
be sensed. In most usages the fluid to be sensed will be
atmospheric air. At least one side of the anerode capsule is a thin
diaphragm which flexes as the pressure loading is varied. This
flexing causes the tension stresses in the diaphragm to vary. The
self-resonant frequency of the diaphragm is a function of the
tension and therefore changes as the pressure changes. Generally,
the capsule is designed so that flexing does not exceed the elastic
limit of the diaphragm material and therefore the flexing is
repeatable.
In this new pressure sensor two or more electromechanical
transducers are coupled to the surface of the diaphragm at diverse
points. These transducers are suitably any of the type which will
attract or repel the diaphragm in response to an electrical signal
of a first or second characteristic respectively. In addition, the
transducers must be capable of detecting movement of the diaphragm
and converting this movement to an electrical signal. For example,
the transducers might be of the electromagnetic type, wherein the
coupling between the transducer proper and the diaphragm is through
magnetic forces. Another type of transducer is the piezoelectric
type which is physically bonded to the surface of the diaphragm.
This type of transducer physically expands or contracts when a
positive or negative electrical potential is applied across the
transducer. Since the transducer is mechanically connected to the
surface of the diaphragm, the motion of the transducer is
transferred to the diaphragm. Conversely, the pickup transducer in
response to the flexing of the diaphragm generates an electrical
output indicative of the frequency of diaphragm vibration. Other
types of transducers are also known, such as capacitive
transducers, which are suitable for use with the invention.
Regardless of the type of transducer used, one transducer
physically excites the diaphragm by causing it to move forward or
back when a positive or negative electrical potential is applied
thereacross. The motion of the diaphragm is sensed by the other
transducer and converted into an electrical signal. The output of a
wide bandwidth electronic amplifier is used to drive the first
mentioned transducer. Initially, random excitation of the capsule
or a noise pulse from the amplifier to the transducer causes the
diaphragm to be plucked. The diaphragm then starts to vibrate at
its resonant frequency. The second transducer picks up the
mechanical motion of the diaphragm and translates that motion to an
oscillating electrical voltage. This voltage is fed to the input of
the amplifier. The electrical voltage signal is then amplified and
fed back to the drive transducer. The vibration of the diaphragm is
thus sustained.
As aforementioned, the transducers are coupled to diverse points on
the diaphragm. It is thus now relatively simple and desirable to
excite the capsule at a resonant frequency other than the f.sub.01
mode. For example, by coupling the transducers to properly located
points on the diaphragm, as will be described, equally spaced from
a diaphragm center line and by additionally providing a proper
phase shift from one transducer to the other, it is possible to
excite the capsule to vibrate in an f.sub.11 mode. Other modes of
vibration are also possible following the teachings of this
invention.
The preferred mode of vibration of the diaphragm is the f.sub.11
mode. This mode is identified by one nodal circle, at the rim of
the diaphragm, and one nodal diameter. This vibrational mode has
the following desirable characteristics:
1. Higher mechanical Q than the fundamental or f.sub.01 mode;
hence, permitting the diaphragm to assume its resonant frequency
with greater ease despite the perturbations introduced by the
transducers and the means by which the capsu e is mounted in its
environment.
2. The f.sub.11 mode allows for symmetrical placement on a circular
diaphragm of both a driver and a pickup transducer. This technique
completely eliminates the frequency response of the diaphragm from
being dependent upon the response of the driving electronic
circuitry.
3. The range of frequency variation for a given pressure variation
is greatest because both the f.sub.01 and the f.sub.21 modes can be
discriminated against.
This ease of discrimination arises from the fact that there is a
180.degree. phase reversal of the signal at the output transducer
for these latter modes when referenced to the desired f.sub.11 mode
output.
It is thus an object of this invention to provide a vibrating
diaphragm pressure sensor which operates in a mode other than the
f.sub.01 mode.
It is a further object of this invention to provide a vibrating
diaphragm pressure sensor which has a greater range of frequency
variations versus pressure than earlier known similar devices.
It is a still further object of this invention to provide a
pressure sensor of the type described whose pressure response is
relatively predictable.
It is still a further object of this invention to provide a
vibrating diaphragm pressure sensor using an aneroid cell wherein
mechanical problems normally associated with an aneroid cell such
as mechanical linkages, hysteresis and undesirable resonances are
eliminated, and wherein further mechanical problems associated with
an aneroid cell when used as a vibrating pressure sensor, such as
structural resonances around and attached to the vibrating sensor,
are also eliminated.
These and other objects of the invention will be made obvious as
this description proceeds.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 illustrates certain of the modes of vibration of a clamped
circular plate or a stretched circular membrane.
FIG. 2 is a table showing the relationship of the various resonant
frequencies of the plates and membranes of FIG. 1.
FIG. 3 shows a preferred embodiment of the invention using
piezoelectric transducers.
FIG. 4 shows a capacitive type of transducer.
FIG. 5 shows an electromagnetic type of transducer.
FIG. 6 shows another form of the invention.
FIG. 7 shows another form of the invention wherein the capsule is
mounted at its circumference.
FIG. 8 shows an electronic feedback circuit suitable for use in the
invention.
FIG. 9 shows a bandpass filter suitable for use in the
invention.
FIGS. 10, 11 and 12 illustrate further embodiments of the
invention.
DESCRIPTION OF THE PREFERRED EMBODIMENT
Referring to the figures wherein like numbers refer to like
elements and referring first to FIG. 1, there is shown represented
the various modes of vibration of a clamped circular plate or
alternatively of a stretched circular diaphragm. In this figure,
the shaded segments are displaced in opposite phase to the unshaded
segments. For example, when a clamped circular plate or stretched
circular diaphragm is vibrated in its resonant frequency in the
f.sub.01 mode the entire surface of the structure moves alternately
towards the observer and then away from the observer at the
resonant frequency. This mode is characterized by the single nodal
circle 10 illustrated. When excited at the f.sub.02 resonant
frequency the diaphragm will vibrate in the f.sub.02 mode
characterized by concentric nodal circles 12 and 13. In this case,
a portion of the device enclosed by nodal circle 13 will be moving
in a first direction while simultaneously the portion of the device
between nodal circles 12 and 13 will be moving in the opposite
direction. Similarly, when vibrated in the f.sub.03 mode three
nodal circles 15, 16 and 17 are present. When vibrated in the
f.sub.11 mode the device exhibits a characteristic nodal circle 19,
at the rim and one nodal diameter 20, thus separating the device
into two halves 22 and 23 which move in opposite phase to one
another. The device when vibrated in the f.sub.21 mode exhibits the
single nodal circle 25 and two nodal diameters 26 and 27, thus
dividing the device into four segments. The other vibrational modes
may be derived from those already described, for example, when
vibrated in the f.sub.12 mode the device exhibits a single nodal
diameter and two nodal circles, when vibrated in the f.sub.13 mode
a single nodal diameter is noticed and three nodal circles. In the
f.sub.22 mode, two nodal diameters and two nodal circles are
present while in the f.sub.23 mode, three nodal circles and two
nodal diameters are present.
The diaphragm of the pressure sensor appears as a clamped edge
uniformly loaded diaphragm. The loading of the diaphragm is the
pressure differential created by the evacuation of the aneroid
cell. The diaphragm acts over the transition range where its
resonance frequency performance can be simplified from that of a
clamped plate to that of a stretched membrane as the resonant
frequency increases in response to pressure increase. The
theoretical analysis and general equations in a differential form
can be found in "Theory of Plates and Shell" by Timoshenko and will
not be further discussed here.
The simplified relations of a plate and membrane are described in
"Acoustical Engineering" by Olson and relates the appropriate
configuration to the fundamental frequency, f.sub.01. The modes of
vibration are defined and the frequency of vibration for each
calculation is referenced to the fundamental mode vibrational
frequency. In brief, the fundamental frequency f.sub.01 of a
clamped unloaded plate is given by:
f.sub.01 = (0.467t/R.sup.2) (Q/.rho.(1 - .sigma.2)) .sup.1/2
where
t = thickness of plate in cm
R = radius of plate in cm
.rho. = density of plate in gm/cm.sup.3
.sigma. = Poissons ratio
Q = Young's Modulus in dym/cm.sup.2
The modes are identified by the resonant frequency subscripts
f.sub.xy where x identifies the number of nodal diameters and y
identifies the number of nodal circles in the vibrational patterns.
These are the modes shown in FIG. 1 and already described.
The fundamental frequency of a stretched membrane is given by:
f.sub.01 = (0.382/R) (T/M).sup. 1/2
t = tension in dym/cm.sup.2
M = mass in gm/cm.sup.2
R = radius of membrane in cm
For a uniformly pressure-loaded circular membrane the radial stress
is not uniform but varies from:
.delta..sub.1 (EP.sup.2 R.sup.2 /t.sup.2) .sup.1/3 at the center
to:
.delta..sub.2 (EP.sup.2 R.sup.2 /t.sup.2) .sup.1/3 at the edge,
where:
.delta..sub.1 .apprxeq. 0.423
.delta..sub.2 .apprxeq. 0.0328
P = pressure across the membrane and
E = modulus of elasticity.
For modes with diagonal nodal lines (for example the f.sub.11 mode)
there is, in addition to radial stress, a tangential component of
stress which is generally small in comparison to the radial
component of stress. If the tangential component of stress is
neglected and T is taken as uniform and as the average of these two
radial component values of the stresses, the equation above
becomes:
f.sub.01 = AP.sup.1/3
where A is a constant.
In the intermediate pressure range, the restoring forces in a
sensor diaphragm are expected to include both (a) the diaphragm
rigidity effects and (b) the stresses caused by stretching the
diaphragm as a result of pressure loading. Since the square of the
resonant frequency is proportional to the restoring forces and
these forces are additive, a simplified relationship is:
f.sub.01.sup.2 = f.sub.0.sup.2 + f.sup.2 (p)
where:
f.sub.0.sup.2 is the f.sub.01 contribution due to the unloaded
sensor and f.sup.2 (p) is the contribution due to pressure
loading.
The frequency of oscillation expressed in terms of the modes for
both the plate and membrane case are given in FIG. 2.
Before referring to that figure it should first be mentioned that
generally a diaphragm of the type used in the preferred embodiment
of the invention acts as a plate when relatively less stressed
corresponding to the sensing of low pressure differential, and acts
as a membrane when relatively highly stressed, corresponding to the
sensing of high pressure differential.
In any event, FIGS. 1 and 2 clearly illustrate the desirability of
exciting the device in the f.sub.11 mode whether the environment in
which the device is operating causes it to act as a circular plate
or a membrane. Refer to these two figures now and particularly to
the portion of FIG. 1 that illustrates the f.sub.11 vibrational
mode. It has previously been mentioned that this is the optimum
mode for exciting the vibrating diaphragm of the pressure sensor.
It will be noted that this mode allows for symmetrical placement of
the transducers. That is, the transducers may be placed
respectively in portions 22 and 23 on either side of the nodal
diameter 20. In this description the word located is used in the
sense of coupled to. The transducers are optimally located at the
center of the maximum motion perpendicular to the plane of the
diaphragm. For a membrane this occurs when J.sub.1 (X) is a maximum
where J.sub.1 is the Bessel function of the first kind and of the
first order. The argument of X is 1.8, and 0.58 is the value of the
function. The location of the maximum motion is therefore 0.58r
from the center of the diaphragm where r is the effective radius of
the membrane. The actual configuration of the pressure sensor to be
described does not allow the diaphragm to act as a membrane over
the entire pressure range. This is because the diaphragm has
thickness and is welded to a backup cup to form a sensor cell. The
rim or periphery of of the diaphragm therefore remains rigid or
clamped and not simply supported. The value of r is thus also a
function of the pressure loading. The physical size of the
transducers, however, is large compared to the variation of the
effective radius of the diaphragm and therefore the variation in r
is ignored.
With the transducers located at diverse portions of the diaphragm
the feedback circuit must be correctly phased in order to apply
positive feedback from one transducer to the other transducer.
Since for the f.sub.11 mode the motion of the transducers is
oppositely phased one to the other the feedback circuit must take
account of this phasing to produce the positive feedback, as will
be fully described below.
FIG. 2 shows the resonant frequency of the diaphragm when vibrated
in the various vibrational modes with respect to the resonant
frequency of the f.sub.01 mode. For example, if the device is
acting as a plate in the f.sub.02 mode its resonant frequency will
be 3.91 times the resonant frequency of the device in the f.sub.01
mode. In the same manner if the device is acting as a membrane its
resonant frequency in the f.sub.02 mode will be 2.3 times the
resonant frequency when in the f.sub.01 mode. Three vibrational
modes are of particular interest at this time, the f.sub.11, the
f.sub.12 and the f.sub.13 modes. It can be seen that the resonant
frequency of the device in the f.sub.12 mode when acting as a
membrane is almost twice the resonant frequency of the device in
the f.sub.11 mode when acting as a membrane. The resonant frequency
of the f.sub.13 mode as well as the device when acting as a plate
is even further removed from the resonant frequency of the device
in the f.sub.11 mode. A filter is provided in series with the
feedback oscillator to prevent feedback of the higher resonant
frequencies associated with the f.sub.12 and f.sub.13 modes as well
as the other listed modes to thus ensure that the device is
vibrated only at the f.sub.11 mode. The characteristics of the
feedback oscillator will be disclosed below.
FIG. 3 shows a cross-section of a capsule 29 taken along line 3--3
of FIG. 1. Reference should now be made to this figure. Transducers
of the type which are bonded to the diaphragm, such as
piezoelectric transducers 30 and 31 are shown coupled to the
diaphragm 33. In a device actually built the sensor diaphragm was
constructed of Ni Span-C alloy. The diaphragm was 0.004 inch thick
and had an effective diameter of 11/4 inches. A backup cavity 35
was constructed of the same material but was 0.016 inch thick in a
cup shape as shown. The two members were welded together at the
disk circumference. The welding operation was performed in an
evacuated chamber so that the gas pressure inside the capsule was
at a very low predetermined pressure. Of course, a pump-out tube
may be provided in backup cavity 35 for evacuating the capsule
after welding.
The transducers of the constructed model consist of two lead
zirconate titanate piezoelectric ceramic devices. The electrodes on
the polarized ceramic disks are made of silver fused to the faces
of the ceramic. The ceramic disks used are 0.25 inch in diameter by
0.010 inch thick. Soft copper wire (not shown) is soldered to the
top of the transducers for electrical connection therewith in the
sensor of FIG. 3.
Other forms of transducers can be used as previously discussed. For
example, in FIG. 4 there is shown the capacitor type of transducer
wherein plate 37, together with diaphragm 33, form a capacitor
which receives an electrical signal on electrical lead 36. FIG. 5
shows an electromagnetic type of transducer wherein winding 40
cooperates with armature 39 and diaphragm 33.
A further form of the invention is shown in FIG. 6 wherein the
vibrating diaphragm 42 has a generally hat-shaped form and the
backup cavity 44 has a similar form. In this embodiment a stud 46
supports the backup cavity and provides means for mounting the
capsule. A further means of mounting a capsule such as that shown
in FIG. 6 is shown in FIG. 7 where the capsule is mounted about its
circumference.
During the manufacture of the Ni Span-C alloy from which the
diaphragm is fabricated the material undergoes a work hardening due
to the rolling operation. This causes an additional stiffness on
the rolling axis. It is desirable that a nodal diameter coincide
with this rolling axis. For example, when the diaphragm is excited
to resonate in the f.sub.11 mode the nodal diameter is optimally
parallel with the roll marks on the diaphragm. Thus, the proper
location for the transducers to excite and sustain the f.sub.11
mode should be on a diameter line perpendicular to the roll
marks.
In order to ensure a continuous pressure-frequency transfer
function for the sensor all undesirable resonant structures in the
desired sensor frequency range should be removed. If this is not
done, the vibrating diaphragm will impart energy to the undesired
resonating structure. As this occurs, the frequency of vibration of
the sensor will be altered. This change of sensor frequency is a
function of the Q of the diaphragm and of the undesired resonating
structure, of the coupling coefficient between the structures and
of the separation of the center frequencies of the resonating
structure. These undesired resonances might be introduced by the
transducer leads, the sensor backup cavity, mounting structure and
adjacent structures. The undesired resonance frequency of the
backup cavity 35 of the device of FIG. 3 is far removed from the
resonant frequency of the sensor and is thus less objectionable
than the undesired resonances introduced by the backup cavities of
the devices of FIG. 6 or FIG. 7 where the resonant frequency of the
backup cavity is closer to the resonant frequency of the sensor due
to similar configuration of the backup cavity with the diaphragm.
For this reason, the device of FIG. 3 is preferred. Of course,
radiators of energy with a spectral content near the desired
frequency of the sensor should also be avoided since in this case
the sensor will absorb energy from the radiator with resultant
frequency shift.
FIG. 8, reference to which should now be made, shows the entire
sensor including the capsule 29 connected in an electronic circuit
for detecting and sustaining the resonant frequency of the sensor
diaphragm. The sensor backup cavity 35 is rigidly attached (through
means not shown) to a relatively massive structure 58. The pickup
transducer 31 is connected to terminal B and hence through filter
51 to the negative input port of operational amplifier 50. In
addition, terminal B is connected through resistor 52 to ground.
The positive input port of the operational amplifier is connected
through resistor 53 to ground. The output of the operational
amplifier is grounded through resistor 55 and is additionally used
to drive transducer 30 through resistor 56. In order to ensure the
proper phase shift relationship in the feedback circuit, one
transducer is mounted with the positive side to the diaphragm while
the other transducer is mounted with the negative side to the
diaphragm. This yields a -90.degree. phase shift through the
transducers. Of course, if both transducers are mounted with the
positively polarized side up or down, the voltage phase shift
through the transducers would be +90.degree.. The gain of the
feedback circuit must be sufficient to overcome the transducer or
mechanical losses associated with the sensor. It will also be
remembered that the gain through the feedback circuit should be
reduced as frequency is reduced to minimize exciting higher order
modes on the diaphragm.
The gain variation versus frequency and the phase shift
requirements are satisfied by using the operational amplifier
beyond its cutoff frequency. Beyond the cutoff frequency the
voltage gain of the amplifier is reduced by 20 DB per decade. Also
beyond the cutoff frequency the phase shift through the amplifier
is .+-.90.degree. depending on the inversion resulting from the
connections at the amplifier input. These connections should be
made such that the phase shift through the operational amplifier is
+90.degree. so that the total phase shift is zero degrees resulting
in positive feedback.
The resistance network comprised of resistors 55 and 56 reduce the
amplified gain thus improving the feedback stability and aiding in
the elimination of higher frequency oscillation.
As previously discussed the gain at higher frequencies should be
low enough to prevent the diaphragm from oscillating at undesirable
frequency modes. This can be accomplished by placing a filter in
series with the amplifier input such as filter 51. The requirements
of this filter are rather severe. The phase error introduced by the
filter over the desired frequency range causes an error which is a
function of the loaded Q of the mechanical resonating sensor. The
more phase error the greater the pulling and therefore the greater
pressure reading error. This filter is shown as item 51 in FIG. 8
and is shown in greater detail in FIG. 9, reference to which should
now be made. The filter of FIG. 9 is a Chebishev 0.1 DB ripple,
four section impedance transforming type described by Matthaei in
IEEE Transactions on Microwave Theory and Techniques, Volume
MTT-14, Number 8, August 1966 at Page 372. The filter is connected
in FIG. 8 between terminal B and the negative input terminal of
operational amplifier 50. The filter is comprised of a resistor 60
shunted between terminal B and ground and a resistor 70 shunted
across the filter output terminal and ground. A capacitor 68 shunts
resistor 70. Inductors 62 and 66 are serially connected between
terminal B and the negative input terminal of the operational
amplifier 50. A further capacitor 64 is connected between the
common junction of inductors 62 and 66 and ground. The circuit
values illustrated provide for a reduction in feedback gain above 8
KHz.
The invention can be practiced under some circumstances by using a
plurality of transducers. For example, if the f.sub.21 mode is to
be excited, the system designer can use four transducers, one
coupled to each of the quadrants illustrated in FIG. 10 for the
f.sub.21 mode. Reference to FIG. 10 should now be made. In this
figure, piezoelectric transducers 72 to 75 are seen. Transducers 72
and 74 are located on diametrically opposite quadrants as are
transducers 73 and 75. In addition, transducers 72 and 74 are
coupled to the diaphragm with a common polarity, for example, with
the negative side to the diaphragm while transducers 73 and 75 are
coupled with an opposite polarity, for example, with the positive
side to the diaphragm. The output leads from transducers 72 and 73
are connected together and through bandpass filter 76 to the
negative terminal of operational amplifier 78. Filter 76 permits
those frequencies expected when the diaphragm is excited in the
f.sub.21 mode to pass therethrough. Resistor 79 is connected
between the operational amplifier positive terminal and ground. The
output from the operational amplifier is supplied in common to
drive transducers 74 and 75 through resistor 80. A resistor 82 is
connected between the amplifier output and ground. It will be noted
that except for the multiplicity of transducers the circuit of FIG.
10 is very similar to the circuit of FIG. 8 and like principles of
operation apply. In the case of the device of FIG. 10 the f.sub.11
mode is absolutely suppressed due to the constraint on the
transducers where transducers 72 and 74 are constrained to move in
one direction while transducers 73 and 75 are moving in the
opposite direction.
Reference should now be made to FIG. 11 wherein the invention is
further illustrated to produce the f.sub.11 mode of vibration. The
device of FIG. 11 is also very similar to the device of FIG. 8
having transducers 85 and 91 located on opposite sides of the nodal
diameter 83 and oppositely poled with respect to one another.
Transducer 85 is connected through a suitable filter 86 for
allowing f.sub.11 frequencies to pass therethrough to the negative
terminal of operational amplifier 87. As before, the amplifier has
a resistor 88 connected between ground and the amplifier positive
terminal and a resistor 89 connected between ground and the
amplifier output terminal. The amplifier output is also connected
through resistor 90 to not only drive transducer 91 in a direction
opposite from the direction of transducer 85 motion but also to
drive transducer 92, located on the same side of nodal diameter 83
as transducer 85, in the same direction as transducer 85. The
location and connection of transducer 92 absolutely suppresses the
f.sub.21 mode for example.
Referring to FIG. 12 a further means of using multiple transducers
is seen. Here the f.sub.21 mode is to be excited, however, as will
become clear, other modes are not absolutely suppressed by this
means and filtering alone provides the suppression of certain
modes. In this figure transducers 92 and 95 are coupled to
diametrically opposite quadrants of the diaphragm as are
transducers 93 and 94. In addition, transducer 92 is oppositely
poled from transducer 93 while transducer 94 is oppositely poled
from transducer 95. The feedback circuit between transducers 92 and
93 is essentially identical to the feedback circuit of FIG. 8. That
is, the feedback circuit includes filter 95 between transducer 92
and one input to operation amplifier 97, a resistor 96 connected
between ground and the other input terminal, the amplifier output
being connected to drive transducer 93 through resistor 98 and the
amplifier output being also connected through resistor 99 to
ground. In like manner, transducer 94 is connected through the
feedback circuit comprised of filter 101, operational amplifier 102
and resistors 103, 104 and 105 to drive transducer 95. If filters
95 and 101 are designed to pass the frequencies of the f.sub.21
mode, that mode will generally be excited. However, if filters 95
and 101 are designed to pass the f.sub.11 mode, that mode will be
excited. Thus, there is a possibility that some ambiguity will
exist when using the means illustrated at FIG. 12 and the
constrains imposed by the filters are thus more critical.
* * * * *