Proceedings of ASME Turbo Expo 2015: Turbine Technical Conference and Exposition
GT2015
June 15 – 19, 2015, Montréal, Canada
GT2015-42895
Real-Time, Advanced Electrical Filtering for Pressure Transducer Frequency
Response Correction
Adam M. Hurst1
Steve Carter1
Doug Firth2
Alan Szary2
Joe VanDeWeert1
1
Kulite® Semiconductor Products Inc.
One Willow Tree Road
Leonia, New Jersey, USA
Contact Author Email: adamh@kulite.com
2
Precision Filters Inc.
240 Cherry Street
Ithaca, New York, USA
response in applications such as shock and blast testing. A
theoretical model of the frequency response correction
methodology is presented. We additionally present temperature
dependent experimental results that compare the frequency
response with and without the correction scheme. These results
demonstrate that the usable bandwidth of pressure transducers
can be increased when real time, analog frequency response
correction is applied. This work shows that if the frequency
response of a transducer is well characterized, advanced signal
conditioning can be implemented to substantially extend the
flat bandwidth of the transducer without changes to the sensor,
packaging or mounting.
ABSTRACT
The frequency response of a pressure transducer is
influenced by the natural resonance of the sensor structure, the
spatial resolution of the sensor due to its diaphragm size, the
sensor packaging, signal conditioning and mounting at the
measurement location. The resonance of the sensor and
aerodynamically-driven resonances related to the sensor
packaging and/or mounting, specifically, can distort dynamic
pressure measurements within the range of greatest interest
(10Hz-20kHz), typically resulting in erroneous amplification.
Historically, correcting for such errors within the frequency
response of a pressure transducer or measurement system has
been challenging, because such errors are hard to quantify with
unknown resonant frequencies and damping factors (quality
factors). However, with the ability to fully characterize
resonant frequencies that lie within 10Hz - 50kHz using a
previously demonstrated dynamic pressure characterization
methodology, it is possible to apply electrical filtering to
substantially extend the flat (0±2dB) frequency response of a
transducer before any digital signal conversion. In this work,
we present a real-time frequency response compensation
scheme that uses electrical filtering to correct for
aerodynamically driven packaging or mounting related
resonances while at the same time preventing signal distortion
caused by the sensor resonances. The compensation extends the
useable, flat amplitude bandwidth of the transducer while also
correcting the phase response to maintain constant time delay
over the extended bandwidth. This real-time frequency
response correction scheme can be similarly used to
compensate for chip resonances, which can limit the frequency
INTRODUCTION
The measurement of unsteady or dynamic pressures is
critical for gas turbine health monitoring, design validation,
research and active control.
Unsteady pressures exist
throughout rotating machinery that can lead to phenomena such
as rotating stall and surge in the compressor, flow instabilities
in the combustor, low and high cycle fatigue, accelerated
component wear and noise pollution. Through accurate
measurement and characterization of wideband pressure levels
within gas turbines, engineers can redesign turbines to reduce
the presence of undesirable dynamic pressures. Accurate, realtime dynamic pressure measurements on production engines
can be used for engine health monitoring as well as active
control to prevent potentially catastrophic events such as
compressor surge and stall [1, 2].
Dynamic pressure
measurements are also critical to understanding and mitigating
screech and rumble in gas turbine augmentors [3]. Since these
1
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time delay errors in the measurement. This problem has
historically been addressed by modifying the packaging of the
sensor to achieve the highest measurement bandwidth. This
results in a sensor design having no protective screen and all
cavities around the sensing element filled with an epoxy or a
room temperature vulcanizing silicone (referred to herein as
RTV) [4, 5]. These package modifications are often at the cost
of sensor protection, as high speed, small particles in a wind
tunnel or gas turbine can impact the diaphragm of the sensor,
catastrophically destroying it. The tradeoff between robust,
protective packaging and frequency response, specifically for
MEMS sensors (pressure, acoustics, acceleration, etc.) has been
a significant challenge.
measurements provide such a vital role in both the design and
operation of gas turbines, it is important for instrumentation
engineers to understand and quantify the accuracy of unsteady
pressure measurements.
The frequency response of the pressure sensors employed
in such measurements along with the mounting within the
turbine determines the measurement accuracy. Unfortunately,
there are limited published standards for dynamic pressure
measurement in gas turbines and sensor calibration as well as
no known commercially available, in-situ dynamic pressure
calibration tools [2, 4, 5]. Therefore, instrumentation engineers
often attempt to characterize the response of a pressure sensor
mounted in a test apparatus using the same mounting
configuration employed within the turbine [2, 6]. Due to sensor
temperature limitations, dynamic pressure sensors are often
recessed away from the high temperatures within gas turbines
at the cost of frequency response. Historically, the loss of
frequency response has been compensated through data postprocessing [7]. This work presents a real-time, analog solution
to extend the flat bandwidth of a dynamic pressure sensor and
its mounting configuration.
Historically, to achieve the widest bandwidth, pressure
transducers are mounted flush with the flow field at the desired
measurement location [8, 9]. Even with an ideal flush
mounting configuration, the natural resonance or size of the
pressure sensing diaphragm as well as the packaging have been
demonstrated to limit the frequency response [5, 8, 10]. All
pressure transducers have a force collecting diaphragm or
suspended membrane that deflects under pressure. Diaphragm
deflection changes the strain in the diaphragm, which, for Si
MEMS piezoresistive pressure transducers, is measured by
integrated resistors on or diffused within the surface of the
sensor’s Si diaphragm. The Si diaphragm of a typical MEMS
pressure sensor is ~500-1000μm with a thickness of several
microns to hundreds of microns [11, 12]. This micro-scale
geometry and the high stiffness of Si results in a typically
natural diaphragm resonance of 100+kHz to several MHz,
depending on pressure range. The high natural resonance of the
diaphragm and small size of MEMS piezoresistive pressure
sensors results in the capability of accurate dynamic pressure
measurements over the range of greatest interest 10Hz to
20kHz at the chip level [5].
When the sensing element is packaged into a full
transducer housing, there is some volume surrounding the chip
and often a protective screen covering the chip, as illustrated in
Figure 1.
This volume cavity and screen results in
aerodynamically-driven resonances, modeled with the modified
Helmholtz equation, Eq. 1 [5, 10].
n, Holes of Diameter, a
r
Protective B-Screen
Volume Cavity, VCavity
MEMS Pressure Sensing Element
Pressure
Transducer T
Housing
Figure 1: Common packaging methodology for MEMS
pressure transducers.
Similar to packaging, there is again a tradeoff between
mounting of sensors at the location of measurement and the
achievable frequency response. In practice, close coupling the
pressure transducer to the flow is not always possible due to the
transducer limited operating temperature range, sensor size,
acceleration at the measurement location or other constraints. In
such instances, engineers install the transducer at the
termination of a recess tube. As illustrated in Figure 2, a
transducer at the end of a recess tube results in the well-known
organ pipe resonance, Eq. 2 [13]. The organ pipe resonance will
amplify dynamic pressure signals by factors as high as ~10+X
at the organ pipe resonant frequency depending on tube length,
diameter, surface roughness, etc. [14, 15]. As a general rule, the
frequency response of a recessed diaphragm system will be
useable from static conditions to approximately 30% of the 1st
harmonic of the organ pipe resonant frequency where a signal
increase of approximately 10% (1 dB) is present.
(1)
These aerodynamically-driven resonances can be on the order
of 25-100+kHz for air which overlaps with the range of
measured pressure signals. The resonances cause amplification
and/or attenuation of the pressure signal as well as phase or
2
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substantially improve the accuracy of high-frequency dynamic
pressure measurements. The resulting hardware solution will be
of significant benefit to instrumentation engineers interested in
high frequency measurements and will ultimately result in
lower overall program costs. All data reported herein is with
air as the media.
(2)
THEORETICAL BACKGROUND
While the resonant frequencies of these packaging and
recess mounting aerodynamic resonances have been
successfully modeled and are now easily predicted, the quality
factor, Q, is not easily predicted. The quality factor is also
referred to as the damping factor, ξ, for under-damped second
order systems and can be equated using Figure 2: Pressure transducer recessed length, L, from flow
field.
A 2.54cm (1in) long recess tube terminated with a pressure
transducer for example, will exhibit an organ pipe resonance at
~3.36kHz for air at room temperature, yielding a potentially
useable flat bandwidth to ~1kHz (± 1dB), (damping or quality
factor dependent). This large resonant peak located so close to
the desired alias free pressure data bandwidth creates the
possibility for clipping on pressure signals located at the
resonance as well as an aliasing problem for a data acquisition
system. Advanced signal conditioning and filtering techniques
are required to address these problems [14].
We present an electronic filtering algorithm and signal
conditioning solution (referred to as KSC-2) that solves this
historic problem of aerodynamic resonances from packaging
and/or recess mounting. The filtering algorithm presented in
this work corrects the frequency response in the analog domain,
enabling for example the use of robust packaging methods,
such as the B-screen illustrated in Figure 1 without a significant
loss in frequency response. For example, a Kulite XCS-062 Bscreen configuration without any RTV around the chip exhibits
a bandwidth of DC-16kHz (± 2dB), but with the signal
conditioning algorithm presented herein the same configuration
exhibits a flat frequency response of DC-~45kHz (± 2dB), a
~280% improvement.
This solution reduces the tradeoff between robust
protective packaging or constraints on recess mounting and the
achievable frequency response. We demonstrate that this realtime frequency response correction scheme typically extends
the flat frequency response (defined as 0dB ±2dB or less) [16,
17] of a pressure transducer from ~30% of the mounting or
packaging resonance to 100% of the resonance value (a 200300% improvement in the flat, useable bandwidth). We further
present frequency response data over a range of temperatures
and the coefficients to correct the frequency response over
temperature.
This electrical filter frequency response correction (also
referred to as FRC) scheme has been designed and built into a
signal conditioning unit that enables easy modification of both
the signal conditioning employed (excitation, gain, pre and post
amplification, filtering) and frequency response correction
parameters for any measurement. The application of the
adjustable electronic filter with various pressure transducer
packaging schemes and recessed installations will be shown to
[18]. Experimental advancements have made these resonances
and Q factors easier to accurately measure. A theoretical
example of this capability is shown in Figure 3, and an
experimental example is shown with the magnitude and phase
plot of the Kulite P/N: XCQ-062 B-screen without RTV
transducer in Figure 8. The experimental data exhibit a clear
resonance peak at ~37kHz with a Q of ~6, which can either be
extracted visually or by curve fitting the data to the secondorder system transfer function equation below [19].
(3)
Knowing the packaging resonance and its Q, we take the
reciprocal of the transfer function, G(s), to create an equal and
opposite transfer function which can be used to correct for the
resonance of the packaging, extending the useable frequency
range.
The complementary transfer function to correct a sensor
having a cavity resonance as modeled by a second order system
is given by:
(4)
where ωr is the resonant frequency of the cavity in units of
rad/sec and Q is the resonance quality factor. The sensor Q and
ωr may be estimated or determined experimentally and will
vary for different sensor types and packages. It is therefore
highly desirable to implement such a frequency response
correction approach where Q and ωr are programmable values.
By combining Equations 3 and 4, a characterized, unwanted
resonant frequency, ωr, can be removed, providing an improved
frequency response. As Figure 3 demonstrates, the resulting
combined transfer function now exhibits a flat frequency
response (0dB). The amplitude response is flattened to the
extent that the ωr and Q are known for a particular sensor. The
overall phase of the sensor is compensated as well.
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20
15
second order transfer function, the frequency response
correction algorithm utilizes a double integrator with
appropriate feedback to realize the denominator of the transfer
function. The numerator is realized by weighting of the second
order high-pass, band-pass and low-pass outputs, each
multiplied by their respective constants, KHP, KBP and KLP.
The three outputs are then summed to form the final transfer
function.
Sensor Response
(Uncompensated)
10
Gain (dB)
5
0
Compensated
Response
–5
–10
KSC-2 Compensator
–5.0
–20
3k
5k
Figure 3:
algorithm.
7k
10k
20k 30k
50k 70k 100k
Frequency (Hz)
Example
frequency
200k 300k
response
correction
The effectiveness of the correction relies on the sensor
adhering to a second order response model and the accurate
characterization of a particular sensor’s Q and ωr. For sensor Q
>> 1, the overall correction of the transfer function is less
sensitive to the Q setting of the frequency response correction
algorithm. Referring to Figure 4, a sensor with packaging
resonances characterized by a Q of 10 shows excellent
amplitude response correction with the Q set between 8 and
12.5 (-20%/+25% error). The sensitivity of the frequency
response correction algorithm to ωr is much more dramatic,
particularly if the compensator ωr is adjusted too low. When the
correction frequency is set to 0.8 ωr, the amplitude response is
over compensated so that instead of response error due to
peaking, there is dip in the frequency response. If the correction
frequency is set too high at 1.25ωr the amplitude response,
while not optimally corrected, shows significant improvement.
Figure 5: Block diagram of sensor frequency response
correction algorithm.
Having defined the frequency response correction
methodology, a signal conditioner may be implemented in
hardware to include appropriate excitation to the sensor,
amplification and low-pass filtering. Figure 6 shows the block
diagram of the KSC-2 Signal Conditioner as pictured in Figure
7. The KSC-2 is a compact, dual-channel high precision
amplifier/filter with programmable constant voltage excitation
optimized for conditioning pressure sensors, accelerometers
and microphones.
Bipolar \ Unipolar Excitation Supply
Reg
Power
20.0
Uncompensated Sensor
Q = 10
f/Fr = 1
15.0
10.0
Gain (dB)
Post-Filter Gain
Compensated Response
fcomp = Fr
Qcomp = 8
5.0
Input
2-6 Wire
w/Shield
Amp
Resonance
Compensator
Cal
–5.0 Compensated Response
fcomp = 0.8 Fr
–10.0 Qcomp = 10
–20.0
0.1
Compensator
In
Pre-Filter
Gain
0.0
–15.0
Output
Overload
Input
Overload
Compensated Response
fcomp = Fr
Qcomp = 12.5
0.2
0.3
Input
Compensated Response
fcomp = 1.25 Fr
Qcomp = 10
0.5 0.7 1
2
Normalized Frequency (f/Fr)
3
5
7
Auto Balance/
Zero Suppress
Compensator
Out
LP6F or
LP6P
Programmable
6-Pole
Filter In
Prog.
Buffered
Amp
Filter Out
Auto Calibrate
Gain & Offset
Input
Short
Figure 6: Block diagram of amplification and filtering in
KSC-2.
10
Figure 4: Sensitivity of frequency response correction to Q
and ωr , (Fr ).
The block diagram for the implementation of the frequency
response correction is shown in Figure 5. To implement a
4
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Output
Front
(a)
ï
Back
ï
(b)
Figure 7: KSC-2 Signal conditioner (a) Front, (b) Back.
The KSC-2 contains an analog, hardware implementation
of the frequency response correction technology presented in
this work that extends the useable frequency response of
sensors with packaging (cavity), recessed pressure sensors or
seismic resonances in real-time with no need for data postprocessing. Based on user entry of sensor ωr and Q, the
frequency response correction tool extends the usable sensor
bandwidth. As the block diagram in Figure 6 illustrates, a
programmable pre-filter gain is first applied to the input signal
in order to preserve signal-to-noise ratio of the in-band sensor
signal while allowing for headroom for out-of-band signals.
Next the frequency response correction, FRC, filter is applied
to remove unwanted resonant frequencies of the sensor or
mounting configuration. A programmable 6-pole low-pass
precision filter is then applied to the signal to eliminate outband energy and prevent aliasing. Finally, the signal is passed
through a post gain stage to ensure use of the full range of the
A/D after removal of the resonance characteristics [20].
Overload detectors alert the user to pre-filter overload
conditions that could otherwise be masked by the filter. In
addition, output overload detectors are provided with
programmable threshold voltages.
Alternative to this frequency response correction method, it
is possible to correct for undesired resonant frequencies by
post-processing test results [7]. However, post-processing data
after digitization can result in poor signal-to-noise ratios
because the A/D input must accommodate both the in-band
signal of interest and the sensor resonance. Allowing for
transducer packaging or mounting resonance headroom results
in the user not maximizing the amplification for the small inband signal above the self-noise of the signal conditioner and
A/D. This results in less than ideal signal-to-noise ratios
regardless of the resolution of the A/D [20]. With this in mind,
this real-time, analog frequency response correction approach
provides superior performance by maximizing signal-to-noise
ratios. With the frequency response correction applied to the
output of a transducer using the KSC-2, a flat frequency
response beyond the original resonance (~45kHz) is easily
achieved, as shown in Figure 8.
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Figure 8: Overview of frequency response correction.
This advanced amplification and higher-order filtering scheme
is carefully designed to have a linear phase response and thus
constant time delay. Figure 9 illustrates the phase shift plotted
with a linear frequency scale, making the linear phase
properties more apparent.
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0 Figure 9: Phase of frequency response correction system,
KSC-2.
A linear phase shift corresponds with a constant time delay at
all frequencies [21]. This can be quantitatively understood by
using Equation 5, below.
5
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(5)
Copyright © 2015 by ASME
Applying Equation 5, the time delay of the frequency response
correction algorithm is quantified over frequency and displayed
in Figure 10. The time delay is 4±0.5μs from 1kHz-10kHz
with a gradual increase in the delay to 7μs at 50kHz. Figure 10
displays the phase shift as a time delay associated with the
non-frequency response corrected XCQ-062 B-screen
transducer without RTV around the chip. As the data show, the
delay is approximately 0s until the resonance (33.5kHz) is
approached at which point the time delay grows rapidly to
~10μs.
preamplifier adding a gain of 128X, the 6-pole, flat anti-alias
filter set at 75 kHz (-3dB) to remove out-of-band energy and
the post-filter amplifier gain set to 16X. Signals were
additionally AC coupled to remove any DC content. These
filter parameters were experimentally characterized using a HP
3562A Dynamic Signal Analyzer the results of which are
displayed in Figure 11.
2
0
Delay [μs]
-2
-4
-6
-8
XCQ-062 B-Screen, No RTV
w/o Freq. Resp. Correction
With Freq. Resp. Correction
-10
-12
10
3
10
4
Frequency [Hz]
Figure 10: Time delay of frequency response correction,
KSC-2.
EXPERIMENTAL SETUP
The periodic dynamic pressure calibration tool employed
to quantify the resonant frequencies of various sensor packages
as well as recess mounted transducer configurations has
previously been reported [5]; however a brief description is
provided for clarity. The dynamic calibration system uses a
speaker and waveguide. The speaker generates large amplitude
acoustic waves with peak-to-peak pressures ranging from 10Pa1300Pa over the frequency range of 1-50kHz. A flush mounted
Kulite XCQ-062 with no screen and an RTV filled volume
cavity is used as a reference sensor. This sensor configuration
was previously demonstrated to have a flat frequency response
of DC to >50kHz [5].
Test transducer configurations are mounted directly across
from this reference sensor. Sensors are evaluated by sweeping
the dynamic pressure frequency from 1kHz to 50kHz over a
time period of 25s. The output voltages from each sensor are
conditioned using the KSC-2 and presented herein with the
Figure 11: KSC-2 signal conditioner filter characterization
with a 6 pole, flat anti-aliasing 75kHz (-3dB) low-pass filter.
*Signals were AC coupled at 0.25Hz for all measurements
herein.
When employed, the frequency response correction
algorithm provides the desired attenuation at the resonant
frequency. Post signal conditioning and frequency response
correction, all dynamic pressure data presented herein were
collected using a 16-bit NI USB-6366 X-Series DAQ with data
sampled at a rate of 250kHz.
SENSOR PACKAGING RESULTS AND DISCUSSION:
As discussed in the Theoretical Background section, the
resonant frequency, ωr, and quality factor, Q, of the package or
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The experimental results in Figure 12 confirm theoretical
predictions, showing an increase in ωr with temperature for the
XCQ-062-35kPa with a B-screen and without RTV around the
chip. Figure 13a shows good agreement between the observed
increase in ωr with temperature to that predicted theoretically
using the change in the speed of sound with temperature (Eq. 6)
and the modified Helmholtz equation (Eq. 1). In addition, the
inverse relationship of Q with temperature is anticipated as the
viscosity of air increases with temperature which contributes to
higher damping [22]. Figure 13b provides a plot of Q versus
temperature.
recess related resonance of a transducer needs to be accurately
quantified in order to implement the active frequency response
correction in the KSC-2 signal conditioner. Using the dynamic
pressure calibration tool, the frequency response was
characterized for the following MEMS piezoresistive sensor
packaging configurations:
1)
2)
3)
4)
5)
6)
XCQ-062-35kPa with B screen
XCQ-062-35kPa with A screen
XCQ-062-35kPa without a screen
XTEL-190-35kPa with B screen
XTEL-190-35kPa with M screen
XTEL-190-35kPa without a screen
To determine the package related resonance and Q, data
were taken without the KSC-2 frequency response hardware
correction algorithm. The data were fit to Equation 3 to
determine ωr and Q. These values were then input into the
freqeucny response correction (FRC) stage of the KSC-2 and
the frequency response was retested using the periodic dynamic
pressure calibration tool.
Aside from quantifying ωr and Q for each MEMS package
configuration, there are two additional critical areas of study
required:
a.) Change in ωr and Q over temperature
b.) Variation in ωr and Q for a batch of transducers with
identical packaging or mounting.
Beginning with the impact of temperature, theory predicts
that ωr will increase with temperature, as the speed of sound in
air is directly dependent on temperature [22].
46
(a)
Model XCQ−062 B−Screen, No RTV
44
Exp. Results
Resonant Frequency,fr [kHz]
Linear Fit to Exp. Results
42
fr(T)=0.0506*T+34.742
40
38
36
34
0
50
100
Temperature [deg. C]
150
200
(6)
(b)
20
Q(T)=−0.0022*T+5.9054
5.9
5.8
10
5
Quality Factor, Q
Gain [dB]
15
0
-5
3
10
10
4
5.6
5.5
0
Phase [Degrees]
5.7
-50
Exp. Results
5.4
Linear Fit
-100
T = 24°C
T = 100°C
T = 150°C
T = 200°C
-150
-200
3
10
5.3
10
0
50
100
Temperature [deg. C]
150
200
Figure 13: Plots of XCQ-062-35kPa B-Screen, No RTV fr
and Q coefficients over temperature.
4
Frequency [Hz]
Figure 12: Frequency response of XCQ-062-35kPa with Bscreen, no RTV at four temperatures.
In Figure 13, the equations for the linear fit to the experimental
data are included which can be extrapolated to provide ωr and
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Q for this frequency response correction algorithm outside the
test temperature range or at a higher resolution within the
range. These equations can further be combined with Equation
4 to create a frequency response correction transfer function
(Eq. 7) as a function of temperature and frequency with only
the quality factor being estimated from experimental data,
which is shown below:
B-screen or an XCQ-062 with a B-screen. If the same
coefficients can be used then it is not necessary to measure each
transducer. However differences in sizing due to normal
manufacturing variability creates slightly different resonant
frequencies for each transducer. Figure 15 shows three
different XCQ-062-35kPa differential transducers with Bscreens, Figure 16 shows the same transducers each corrected
with individual coefficients of ωr and Q as listed in Table 1.
The variance in Q is small for these transducers but there is a 5
kHz variance in the resonant frequency.
(7)
!" Equation 7 can be used to develop an active adjustment of the
frequency response correction algorithm if temperature is
measured, which can be achieved via the change in overall
bridge resistance [23].
The equations for ω r and Q were then used to calculate
the required coefficients, and experimental tests were then
conducted at each temperature point applying the calculated
coefficients of ωr and Q. The resulting experimental frequency
response corrected transfer functions are illustrated in Figure
14. This XCQ-062 transducer packaged with a B-screen and
without RTV now exhibits an achievable flat bandwidth from
DC to approximately 40kHz; a 200-300% improvement
depending on temperature.
All transducer packaging
configurations and multiple types of transducers were
characterized in this manner over temperature with the goal of
producing a set of linear equations that provide ωr and Q
coefficients that can be used universally.
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Figure 15: Three XCQ-062 B-screen, no RTV sensors with
no frequency response correction.
0
Gain [dB]
5
-5
103
104
ï
0
-50
-100
-150
-200
103
T = 24°C
T = 100°C
T = 150°C
T = 200°C
ï
Phase [Degrees]
104
Frequency [Hz]
ï
ï
Figure 14: Frequency response of XCQ-062-35kPa with Bscreen, no RTV at four temperatures with frequency
response correction.
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Figure 16: Three XCQ-062 B-screen, no RTV sensors with
individual frequency response correction coefficients.
It would be advantageous to be able to use the same
correction coefficients for an entire family of transducers with
identical packaging, such as a Kulite series XTEL-190 with a
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The average resonance and Q were then used to correct all three
transducers as shown in Figure 17. Using the averaged
correction values, a 150% improvement in the flat (+/- 2dB)
frequency response was obtained. As shown in Figure 16, the
application of individual correction values for transducers can
result in as much as a 300% improvement in frequency
response (DC to ~40 kHz). Therefore, individual or average
correction coefficients should be used depending upon the
frequency response needs of the application.
In many
instances, a 150% improvement in frequency response is
sufficient and average correction coefficients can be applied
without the need to calibrate and correct each transducer
individually.
frequency response correction technique will work at any
temperature.
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ï
&%(#) *
!' &'
Figure 18: Frequency response corrected output for various
transducer series and packaging configurations.
ï
ï ï&#& $ & ï
ï
&%(#) *
Figure 17: Three XCQ-062 B-screen, no RTV with average
correction coefficients applied to all sensors.
Similar tests were conducted on several identical
transducers for multiple packaging configurations. Figure 18
shows various transducer packaging configurations with
frequency correction applied. Table 1 provides a complete set
of experimentally determined ωr and Q coefficients for each
transducer over temperature (24, 100, 150, 200°C) and the
achieved flat frequency response with and without the
correction algorithm applied. The 200°C upper bound was
chosen due to the temperature limitation of the test setup. This
9
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Table 1: Correction Coefficients and Frequency Response Improvement:
No Frequency Response
Correction
Type
XCQ-062
Screen
B
Serial
Number:
651
XCQ-062
B
650
XCQ-062
B
133
XCQ-062
A
598
XCQ-062
None
598
XTEL-190
B
114
XTEL-190
XTEL-190
M
None
114
114
Temp
[°C]
24
100
150
200
24
100
150
200
24
100
150
200
24
100
150
200
24
100
150
200
24
100
150
200
24
24
100
150
200
fr
[kHz]
36.6
40
43.5
45.4
33
37.6
39
41.7
38.2
41.5
45.3
47
>50
>50
>50
>50
>50
>50
>50
>50
37.7
42.3
45.1
>50
47.6
>50
>50
>50
>50
±2 dB [kHz]
16
15
14.3
13.6
14.1
17.4
19
20.5
17.6
19.2
20.3
21.3
22.7
27
29.5
31.6
29.7
33.65
37.54
40.9
18.63
18.9
19.3
19.7
26.2
36.9
40.5
42
47
With Frequency Response Correction
Bandwidth
fr
Improvement
[kHz]
Q
± 2 dB [kHz]
[%]
36.5
6
41
256
40
6
44
293
43.5
6
44.5
311
45.5
6
44
324
33
5.5
42.3
300
37.5
5.5
43.5
250
39
5
48
253
41.5
5
46.9
229
38
6
48.9
278
41.5
5.8
48.2
251
45.5
5.5
45
222
47
5.5
45
211
50
10
1.0 dB*
>220
57
10
1.6 dB*
>185
61
10
1.7 dB*
>169
65
10
1.6 dB*
>158
61
10
1.1 dB*
>168
69
10
1.0 dB*
>149
77
10
1.4 dB*
>133
84
9.5
1.5 dB*
>122
38
10
36
193
42
8
41
217
45
6
44
228
47
6
45
228
50
5
48.5
185
75
10
1.0 dB
>136
83
9.5
0.8 dB
>123
86
9.5
< 1.0 dB
>119
95
9
< 1.0 dB
>106
*2 dB point beyond measurement range. Error at 50 kHz presented. Bandwidth approximation based on 50 kHz.
**All test results apply to air or gaseous media with equivalent properties only.
the termination of the pipe. These configurations were
examined to simulate a possible mounting in a hightemperature location on a gas turbine where flush mounting the
transducer is not possible due to the operating temperature
limitations of the sensor and some dynamic pressure content up
to the highest achievable flat bandwidth is desired [7].
Typically such applications are for static and low-frequency
dynamic pressure applications because the low, organ pipe
resonance of the standoff tube distorts any frequency above
1kHz (2.54cm standoff tube).
Figure 19 shows the
uncompensated frequency response of a 2.54cm (1in) standoff
SENSOR MOUNTING RESULTS AND DISCUSSION:
Sensor mounting typically has the greatest impact on the
achievable flat frequency response of dynamic pressure
measurements. We experimentally evaluated the frequency
response correction algorithm (KSC-2) presented herein on two
recess mounting configurations.
The recess mounting
configurations included a 2.54cm (1in) and a 7.62cm (3in)
standoff pipe with an XCS-190 dynamic pressure transducer at
10
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tube. After the coefficients are determined for the organ pipe
resonance, the frequency response correction algorithm is
applied to extend the frequency response by 220% to a flat
(±2dB) bandwidth of DC-2.83kHz, which is a significant
extension of the useable frequency response again while
retaining a linear phase response.
The current frequency response correction algorithm built
into the test KSC-2 signal conditioning system limits the
resolution of fr, (ωr), to 500Hz increments. At the lower
resonant frequencies of such longer standoff pipes, this
resolution limits the effectiveness of the correction algorithm.
With greater resolution of fr, (ωr), better frequency response
correction can be achieved. To demonstrate the potential
improvement of the system with better resolution, we applied
the model frequency response correction transfer function using
the exact value of fr, (ωr), which is indicated as the best-fit
correction curve in the plots below.
Gain [dB]
30
20
also address varying length to diameter ratios as well as an
array of different lengths of tubing for various applications.
40
7.62cm (3in) Recess Tube, No FRC
Gain [dB]
10
102
Phase [Degrees]
2.54cm (1in) Recess Tube, No FRC
Recess Tube w/ Exp. FRC
Recess Tube w/ Best-Fit FRC
0
-100
2
3
10
10
10
4
Frequency [Hz]
Figure 20: Plot of XCS-190 at the termination of a 7.62cm
(3in) standoff tube (3.81mm diameter) without and with
frequency response correction.
103
104
Table 2: Standoff Tube Correction Coefficients and
Frequency Response Improvement at 24°C
100
0
-100
102
104
100
-200
200
-200
103
200
0
Phase [Degrees]
Recess Tube w/ Best-Fit FRC
20
0
10
102
Recess Tube w/ Exp. FRC
30
103
104
Frequency [Hz]
Figure 19: Plot of XCS-190 at the termination of a 2.54cm
(1in) standoff tube (3.81mm diameter) without and with
frequency response correction.
The 7.62cm (3in) standoff tube exhibits a significantly
lower first resonance of ~1kHz, as Figure 20 shows. This
standoff tube’s harmonics, occurring at odd integers of the first
resonance, are also accurately measured. Again applying
frequency response correction, we demonstrate a substantial
improvement in the achievable flat bandwidth of 235% from
400Hz to 1kHz for this mounting configuration.
While such a standoff is still inappropriate for higher
frequency dynamic pressure measurements, this correction
methodology improves the flat frequency response of a recessmounted transducer by 200%. Table 2 provides values for both
the experimental and best-fit frequency response correction for
the 2.54cm and 7.62cm standoff tubes. Further experiments are
required to determine the effects of temperature and thermal
gradients within standoff tubing. Additional experiments will
Standoff Pipe
Length
Uncorrected
±2
ftube
dB
[kHz]
[kHz]
ftube
[kHz]
Corrected
±2
dB
Q
[kHz]
Improv
ement
[%]
2.54cm, Exp.
3.164
1.278
3
15
2.83
220
2.54cm,Best-Fit
3.164
1.278
3.021
10.8
3.08
240
7.62cm, Exp.
1.076
0.4
1
9.4
0.94
235
7.62cm,Best-Fit
1.076
0.4
1.006
7.6
1.04
260
CONCLUSION
This work presents a real-time, analog frequency response
correction algorithm that extends the bandwidth of dynamic
pressure measurements by 150-300%. A theoretical and
experimental characterization of this frequency response
correction algorithm, as implemented in the KSC-2 signal
conditioning system, has been undertaken. We demonstrate the
performance of the algorithm by utilizing the filtering and
amplification features of the KSC-2 signal conditioner to
correct the frequency response of pressure transducers
manufactured in several different configurations.
This
frequency response correction should be implemented
whenever the transducer, sensing element and/or package, or
mounting configuration limit the bandwidth of the
11
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ωr
measurement by generating predictable resonances. This
correction enables the use of transducers with a screen or recess
mount when making wide bandwidth measurements, which
historically would require a less protected, flush mounted
sensor. This system can specifically be used to extend the
useable bandwidth of transducers that are recess mounted on
gas turbines such that the temperature seen by the transducer is
within its operating range. With better unsteady pressure
measurement accuracy, engineers can make informed design
changes, ensure safe system operation and reduce system down
time through longer component life and predictive
maintenance.
This frequency response correction system has been
developed into a commercially available analog signal
conditioner such that the frequency response limitations of a
transducer or mounting configuration can easily be overcome in
real time without the need for post-processing data. In the
future, we plan to perform in-situ testing of this frequency
response correction algorithm in an operational gas turbine. In
such a test, a recessed transducer utilizing the frequency
response correction algorithm will be compared to a flush
mounted transducer, a recessed transducer without correction
and a transducer utilizing a semi-infinite tube configuration.
s
R
M
γ
Δt
T
dB
REFERENCES
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ACKNOWLEDGEMENTS
We would like to acknowledge and thank Andrew Bemis
and Lou DeRosa for their oversight, guidance and support of
this work. We would also to thank John P. Hilton and Andrew
Bemis for their technical feedback and careful review of this
work. Finally, we would like to thank Mrs. Nora Kurtz for
funding and supporting this effort.
NOMENCLATURE
i
G(s)
f
Tc(s), Tc(s,T)
d
fScreen-Vol.
n
a
VCavity
fTube.
L
c
m
Q
Q(T)
fr.
Resonant frequency, package or recess
mounting configuration, rad/sec
Complex number
Molar gas constant, 8.3145 J/(mol*K)
Molar mass, kg/mol
Ratio of specific heats
Time delay, sec
Temperature, K
Decibel, Complex number
Transfer function
Frequency, Hz
Frequency response correction transfer
function
Diameter of pressure transducer, m
Modified Helmholtz resonance, Hz
Effective diameter, m
Number of holes in screen
Diameter of holes in screen, m
Volume cavity around the chip, m3
Organ pipe, recess tube resonance (closedend), Hz
Length of recess tube, m
Speed of sound in air, 343m/s at 20°C
Harmonics of organ pip resonance (closedend)
Quality factor
Quality factor as a function of temperature
Resonant frequency, package or recess
mounting configuration, fr=2πωr, Hz
12
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13
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