NBSIR 73-230 (^)

Experimental Study of the Effects

of Thermal Transients on the

Performance Characteristics of

Piezoelectric Accelerometers - A Progress Report

Paul S. Lederer

Electronic Technology Division

Institute for Applied Technology

National Bureau of Standards

Washington, D. C. 20234

July 15, 1973

Progress Report covering period 9-15-72 to 4-15-73

Prepared for Lawrence Livermore Laboratory

University of California 94550

NBSIR 73-230

EXPERIMENTAL STUDY OF THE EFFECTS

OF THERMAL TRANSIENTS ON THE

PERFORMANCE CHARACTERISTICS OF

PIEZOELECTRIC ACCELEROMETERS

A PROGRESS REPORT

Paul S. Lederer

Electronic Technology Division

Institute for Applied Technology

National Bureau of Standards

Washington, D. C. 20234

July 15, 1973

Progress Report covering period 9-15-72 to 4-15-73

This is a progress report. The work is incomplete

and is continuing. Results and conclusions are not necessarily those that will be included in the

final report.

Prepared for Lawrence Livermore Laboratory

University of California 94550

U. S. DEPARTMENT OF COMMERCE. Frederick B. Dent. Secretary

IMATIOIMAL BUREAU OF STANDARDS. Richard W. Roberts, Director

Experimental Study of the Effects of

Thermal Transients on the Performance Characteristics

of Piezoelectric Acceleromoters

Progress RCj-^ort tor the Period From September 15, 1972 to April 15, 1975.

to the

University of California, Livermore Laboratory

Interagency Agreement #AT(04-3) -911

NBS Project 4253454

Prepared by

P. S. Lederer

Project Leader

1 . Introduction

The basic experimental technique used in this investigation involves subjecting two accelerometers to the same vibrational accelerations and exposing one of them simultaneously to a thermal transient.

The second accelerometer , which is shielded from the thermal stimulus,

is used as control and to monitor the acceleration amplitude to which

both instruments are subjected.

2 . Description of experimental set-up

The experimental set-up is shown in Figures 1 and 2. The electromagnetic vibration exciter rests on a large brass support plate on a work bench. A covered, aluminum, cup-like structure is fastened to

the shaker table. The reference accelerometer is mounted on the bottom of the cup, with its cable passing through a hole in the side

wall of the cup. The test accelerometer is mounted on the removable

cover plate of the cup. The surfaces on which the accelerometers are mounted are parallel with each other within 1 degree and perpendicular

to the direction of vibration within the same tolerance. The vibration

exciter is set up so that the direction of vibration is vertical. A

metal framework surrounding the vibration exciter carries shielding

material, a source of radiant heat energy and a radiation sensor.

The shielding material consists of a square plate of a nonmetallic

insulating material about 8x8 inches (20.3 x 20.3 cm) supported by

the framework about 2 inches (5.1 cm) above the cover plate on which

the test accelerometer is mounted. A circular hole in the insulating

plate 3 inches (7.6 cm) in diameter is concentric with the test accelerometer position. A sliding shutter of the same insulating material
covers the hole normally, and is pulled away to permit the radiation

to pass through the hole in performing the test.

The source of the radiant heat energy is a commercial 600 IV quartzbromine incandescent lamp with an aluminum reflector. Its energy output

is adjusted by means of a variable autotransformer fed from the laboratory ac line. The lamp is attached to an arm on the framework which

permits it to be positioned directly above the hole in the shield to

irradiate the instrument under test. The arm permits the lamp to be

swung laterally in the same horizontal plane to position it directly

above the absorption head of the radiation monitor.

The radiation monitor is a broadband power meter with a flat response

over wavelengths from 0.3 to 30 ym, and full scale power readings

of 1, 3, 10, 30, and 100 watts. The meter consists of an absorption

head and a control and read-out unit. The absorption head, which is

mounted on the tester framework, contains a coated metal disc located

at the end of the entrance cone. This disc absorbs the incident radiation over the above range of wavelengths. The periphery of the disc

is in intimate thermal contact with the finned, convection cooled, heat

sink of the absorption head, and the resultant radial heat flow

is sensed by a concentric system of thermocouples (thermopile) mounted

to the back surface of the disc. The voltage generated by the thermopile is amplified in the control unit and is displayed on the meter which

is part of the unit.

The distance of the sensing

identical to the distance of the

measurements are made.

The remainder of the test set-up consists of signal conditioning

and display devices for the accelerometer output signals and a power

amplifier and function generator to drive the electromagnetic vibration exciter.

The signal conditioning equipment consists of a commercial charge

amplifier for the reference accelerometer and another charge amplifier

of the same type or, alternately, an electrometer amplifier, for the

test accelerometer. The outputs can be displayed or recorded on an oscilloscope or oscillograph. Prior to the start of the experiments,

a patch panel had been constructed which was designed to facilitate

the work. The cables from the two accel erometers plug into connectors

on the panel, as do cables leading to-and-from the amplifiers.

Additional outlets lead to a monitoring oscilloscope and to two channels of the recorder. Finally, there is a provision for feeding the

output of either channel to a precision ac rms meter.

disk from the radiation source is

accelerometer from the source when
During the initial experiments which were designed primarily to

explore the general operation of the test set-up, one of the charge

amplifiers showed excessive instability and was returned to the manu- facturer for repair. Also, a malfunctioning potentiometer in the shaker

drive amplifier was replaced.

When the repaired charge amplifier was returned, both charge

amplifiers were calibrated over the range of possible settings and

operating conditions used with the accelerometers to be tested.

Those accelerometers (including the one used as the reference

accelerometer) fall into four ranges of sensitivity, roughly 0.03 pC/g,

0.15 pC/g, 15 pC/g, and 60 pC/g. Since most of the tests were ex- pected to be run at a level of 10 g (0 to peak), the charge amplifiers

were calibrated with those settings of sensitivity and range which

would produce a nominal 1 volt (0 to peak) output at this acceleration

level. Most tests were planned to be performed at 100 Hz, consequently

this frequency was selected as the reference frequency.

The choice of this frequency was based on two considerations: it

is a frequency above the anticipated low roll-off frequency caused by

amplifier-accelerometer time constants, and well below any frequencies at which a difference in phase or amplitude of the test and reference accelerometers might occur. Also, it was desirable for recording

purposes that the frequency be within the response capabilities of the

galvanometers of the oscillograph available. A frequency of 100 Hz met

these criteria.

3 . Charge amplifier calibrations

The reduced data from the charge amplifier calibrations are

shown in Tables I through VI. Voltage output in all cases was a nominal 1 volt (0 to peak), except for the 0.03 pC/g accelerometer

setting which produced only 0.1 volt (0 to peak). The calibrations

were performed by feeding known voltages through known capacitances

(either the built-in 100 pF ±0.5% calibration capacitor or an ex- ternal 1000 pF ±0.05% precision capacitor, depending on the range

used) into the charge amplifier and measuring the resultant output

voltages. This was done at several frequencies and for the three

time constant settings available on the charge amplifier. The data

were reduced in each case by calculating the output voltage which

should have resulted from the known input, sensitivity setting and

range setting, and dividing this value into the actual output. From

these values, frequency response ratios were calculated with reference to the 100 Hz, short time constant, voltage ratio as reference

on each range.

The ratios of the actual output to the calculated output at

100 Hz for all test conditions of the reference charge amplifier

(A) ranged from 0.961 to 1.015 (a spread of ±2.8%), for the test

charge amplifier (B) from 0.976 to 1.055 (a spread of ±4.0%).
4 . Exploratory thermal transient tests with charge amplifier

Following the calibrations of the charge amplifiers, a series of

experiments was performed to explore the effects of test condition

variations, in order to arrive at an optimum set of test conditions

for producing useful data.

For these tests an old, but satisfactorily operating, compression accelerometer with a charge sensitivity of 14.3 pC/g was used in

conjunction with the test charge amplifier. Another piezoelectric

accelerometer was used as the shielded reference. Tests were performed to explore the effects of test frequency, test acceleration level,

lamp power, lamp distance, charge amplifier time constant, and exposure

time. The test conditions for all (except for parameter variations

specified) were the following: lamp distance 7.5 inches (19.1 cm),

lamp power 1 watt, test frequency 100 Hz, acceleration level 5 g (0 to

peak), exposure time 15 seconds, amplifier range setting 100 g/volt,

time constant: short.

Figure 3 shows the effects of the radiant energy level on the

zero shift of the accelerometer-charge amplifier system. In this

test, power levels of 0.5, 1.0, 1.5, 2.0, and 2.5 watts were used. It can be seen that after an initial delay of about five seconds following

shutter opening after an initial small negative going shift, the zero output showed a relatively linear increase with time. The zero shift

continued for five seconds after the shutter was closed, and

then began to reverse direction. The amount of zero shift at any time

from about 5 to 20 seconds after exposure began was found to be roughly

proportioral to the radiant power level, reaching about 20 g after 15

seconds at 1.0 watt.

Tests run at frequencies of 20, 50, 100, 500, and 1000 Hz, (shown

in Figure 4) and those at acceleration levels of 2, 4, 6, and 8g(0 to

peak) , as anticipated, show that neither frequency nor acceleration

levels had any significant effect on results.

Tests performed with different time constant settings of the

charge amplifier show substantial differences as demonstrated by the

graphs in Figure 5. The short time constant test shows the same general characteristics as observed previously (see Figure 3), although

its maximum zero shift was less than that in the previous test. This

is believed due to scaling difficulties since the recorder's deflection

sensitivity was set quite low, to permit complete display of the

recordings at the other time constants. The maximum zero shift observed was about 18 g at about 21 seconds with the short time constant

(10 seconds). With the medium time constant (1000 seconds), the maxi- mum zero shift, reached after 40 seconds, was about 210 g. With the

long time constant (10^ seconds), the maximum shift was about 285 g

after 50 seconds.

4.
Medium and long time constant settings are very difficult to use

in tests with most piezoelectric accelerometers due to the large, random

drifts in charge amplifier output caused by minute accelerometer temperature changes, cable flexing, small environmental vibrations etc.

Furthermore, these time constants are rarely used in measurement, the

long time constant is recommended only for quasi-static calibrations

of transducers with low internal leakage, such as quartz crystal

pressure transducers.

In view of these limitations we feel that a useful experimental

technique should generally employ the short time constant setting on the charge amplifier unless, due to constraints imposed by a required

range setting, the resultant time constant is less than the time duration of the test stimulus. Nevertheless, it is important to realize

that thermal transient test data obtained at short time constant settings

can be highly misleading if the longer time constant settings are

used for any actual measurements with the same piezoelectric accelerometers .

The results from tests performed with different durations of thermal

energy exposure are shown in Figure 6. The data appear to indicate that

the thermal gradients set up within the accelerometer stabilize

after about 38 seconds, causing the observed zero shift to show no further increase after that time. Actually, this is probably not entirely

true since the charge amplifier time constant (10 seconds) is such

that the rate of voltage decay in the feedback circuit matches the

rate of charge build-up in the accelerometer. Thus, tests with

different time constants or at other range settings of the charge

amplifiers are expected to produce different results. This requires

further investigation.

A test performed with the radiation source at various distances

from the test accelerometer, ranging from 3 inches (7.5 cm) to 10

inches (25.4 cm), produced data which indicated that greater zero shifts occurred when the lamp was farther away. This was contrary to

expectations. It may be caused by the difference in spectral content

at the different source temperatures required to produce 1 W incident

on the accelerometer, and spectral differences in absorbtivity of the

metal shell of the accelerometer might come into play. This will also

be investigated further.

Finally, during the test at which the accelerometer was exposed

to different power levels (see Figure 3), attempts were made to

measure any changes in sensitivity in addition to zero shift. Due to

the small changes involved, the results were not wholly consistent.

It does appear, however, that a maximum sensitivity shift of 3% occurred

after about 15 seconds at 2.5 watts and somewhat smaller changes at the

lower power levels.
5 . Exploratory thermal transient tests with electrometer amplifier

One of the basic characteristics of the design of the charge

amplifier is the change in time constant with range, since the range

changing component is a capacitor in the feedback loop. This feature

would make it more difficult to make valid comparison during these

tests between accelerometers of widely differing sensitivities.

Accordingly a series of experiments was performed using a com- mercial electrometer amplifier. This instrument has a number of

voltage ranges, as well as a control for changing its input resistance

independently of the voltage range setting. The actual input resistance

values available are 10^** ohms, and from 10^^ ohms downward in decade

ranges

.

Two accelerometers supplied by the Lawrence Radiation Laboratory were used in these tests. Accelerometer (A) a "general purpose charge

accelerometer" (compression type) with top connector and electrical

isolation has a nominal charge sensitivity of 13 pC/g, a capacitance

of 2700 pF and a range of ±1000 g. Accelerometer (B) , a "shock

accelerometer" (shear type), with top connector, has a nominal charge

sensitivity of 0.03 pC/g, a capacitance of 115 pF and a range of

-20,000 g, + 100,000 g. The nominal voltage sensitivities of the two

instruments with 300 pF external capacitance (representing about 10

ft (3 m) of the standard connecting cable) is 4 mV/g for accelerometer

(A), and 0.06 mV/g for accelerometer (B)

.

The test conditions for these tests (except for the parameter

variation specified) were the following: lamp distance 7.5 inches

(19.1 cm) , lamp power 5 watts, test frequency 100 Hz, acceleration level

15 g (0 to peak), exposure time 15 seconds, input resistance 10^ ohms.

In all of these tests, the electrometer output was displayed on

an oscilloscope and photographic records taken of the resulting traces.

The output of the monitoring accelerometer system was measured with

the aid of the ac voltmeter. Data from the photographs were reduced

with knowledge of the displayed acceleration level and the 'scope

preamplifier attenuator settings.

The effect of input resistance on zero shift was investigated

first. Results, shown in Figures 7 and 8, indicate, as expected,

that the apparent zero shift is greater for large values of input re- sistance. As before, a time constant short compared to the duration

of the thermal transient tended to mask the effects of the transient.

The effect of radiation power level on zero shift is shown in Figure

9 for both accelerometers. As with the charge amplifier tests described earlier, the effect increased with increased power level. And

again, as in the earlier tests, there is no significant effect on the

6.
magnitude or shape of the zero output characteristics caused by testing

at acceleration levels of 5 g or 15 g (0 to peak) . This can be seen in Figure lOA, which shows test data for accelerometer (A).

Figure lOB confirms that different voltage range settings of the

electrometer amplifier also have no effect on the apparent zero shift

observed

.

6. Further tests with charge amplifier

The two test accelerometers were tested again, but with the charge

amplifier instead of the electrometer as in section (5). The results

obtained are shown in Figures 11 and 12. Tests were performed at

100 Hz, 5 g (0 to peak), and power levels of 5 watts and 10 watts at a variety of range settings. The shapes of the curves obtained from

these tests are quite similar to those obtained with the electrometer,

and are shown in Figure 9.

Considering accelerometer (A) at a charge amplifier range setting,

of 200 (described by the amplifier manufacturer as resulting in a time

constant of 2 seconds), the zero shift after 15 seconds at 5 watts

was found to be -60 g (Figure 12). Using the electrometer with an

input resistance of 10^ ohms, which teamed with a combined accelerometer

and cable capacitance of 3000 pF results in a time constant of 3 seconds,

the zero shift observed after 15 seconds at 5 watts was -110 g (Figures

7 and 9).

In the case of accelerometer (B) , at a charge amplifier setting

of 10 (time constant 0.1 second), zero shift after 15 seconds at 5 watts

was +80 g (Figure 11). Using the electrometer, the time constant (10^

ohms X 400 pF) was 0.4 seconds, and the observed zero shift after 5 seconds at 5 watts was +80 g.

7 . Preliminary conclusions

From the work done so far it appears that comparisons of the effects

of thermal transients on piezoelectric accelerometers should probably be done

with the aid of the electrometer so as to be unhampered by gain-time

constant constraints. To get an idea of the actual accelerometer measurement performance, which will most likely involve the use of a charge

amplifier, the latter should be used in testing. Accordingly we feel

it desirable that all accelerometers be tested using both methods. The

test data also indicate that operation at 100 Hz and 5 g(0 to peak) appears

optimum from the point of view of shaker capability, output signal

magnitude, and ability to calibrate the system.

The time constants used in both methods are of the order of, or shorter,

than the 15 second radiant heat exposure used in these tests. Longer

time constant settings on the charge amplifier (or high values of

electrometer input resistance) tend to result in considerable amounts

of output signal instability, large enough to mask the effects of the

thermal transients.

7.
8. Future Efforts

We plan to investigate in more detail operation with longer time

constants. We will also, however, attempt to shorten the exposure time

of the accelerometer , to enable adequate testing using the shorter time

constants. This will probably necessitate construction of a mechanical

shutter arrangement to control the radiation energy beam. Operation with

short exposure times will probably also require a higher beam power level,

as to produce a reasonably large output signal. As indicated

earlier, we plan to conduct these tests on all accelerometers with the

charge amplifier as well as the electrometer. The question of possible

spectral effects will also be resolved.

8.
TABLE I

CALIBRATION OF REFERENCE CHARGE AMPLIFIER (A)

AT INPUT EQUIVALENT TO lOg 0 TO PEAK

Accelerometer Charge Amplifier Settings Frequency

Hz

Output Ratio

Measured

Calculated

*Frequency Response

0 Sensitivity

pc/g Range

g/v

Sensitivity

PC

Time

Constant

0.03 1 3.0 Short 10

50

100

500

1000

lOkHz

0.588

0.946

0.974

0.986

0.989

1.002

60.4

97.

1

100.0 * 101.2

101.5

102.9

0.03 1 3.0 Medium 10

50

100

500

1000

lOkHz

0.933

0.947

0.961

0.985

0.988

1.000

95.8

97.2

98. 7 101.

1

101.4

102.7

0.03 1 3.0 Long 10

50

100

500

1000

lOkHz

1.006

1.011

1.015

1.022

1.024

1.033

103.3

103.8

104.2

104.9

105.

1

106.

1

60 100 6.0 Short 10

50

100

500

lOOO

lOkHz

0.987

0.987

0.987

0.988

0.988

0.988

100.0

100.0

100.0 * 100.

1

100.

100.

60 100 6.0 Medium 10

50

100

500

1000

lOkHz

0.987

0.987

0.987

0.987

0.987

0.988

100.0

100.0

100.0

100.0

100.0

100.

1

60 100 6.0 Long 10

50

100

500

1000

lOkHz

0.987

0.988

0.988

0.988

0.988

0.988

100.0

100.

1

100.

1

100.

100.

1

100.

*Note: Frequency Response Referred to 100 Hz - Short Time Constant

9.
TABLE II

CALIBRATION OF REFERENCE CHARGE AMPLIFIER (A)

AT INPUT EQUIVALENT TO lOg 0 TO PEAK

Accelerometer

Sensitivity

pC/g

Charge; Amplifier Settings

- Frequency

Hz

Output Ratio

Measured

Calculated

*Frequency Response

0.

'0 Range

g/V

Sensitivity

pC

Time

Constant

0. 15 1 1.5 Short 10 57 8 59 4 50 94 6 97 2 100 97 3 100 0

* 500 98 6 101 3 1000 98 8 101 5 10000 99 4 102. 2 15 190 1.5 Short 10 100 0 100. 1 50 99 9 100. 0 100 99. 9 100. 0

* 500 99. 9 100 0 1000 99. 8 99. 9 10000 97 8 97. 9

*Note: Frequency Response Referred to 100 Hz - Short Time Constant

10.
TABLE III

CALIBRATION OF REFERENCE CHARGE AMPLIFIER (A)

AT VARIOUS ACCELERATION LEVELS

Accelerometer

Sensitivity

pc/g

Charge .Ajnplifier Settings Frequency

Hz

Output Ratio

Measured

Calculated

Equivalent

Acceleration

Level g Range

a' * Sensitivity

pC

Time

Constant

0.03 1 1.5 Short 100 97.4

97.4

97.6

510

20

0.15 1 1.5 Short 100 97. 3 97.3

97.6

5 10

20

15 100 1.5 Short 100 98.7

99. 9 99.0

5 10

20

60 100 6.0 Short 100 98.8

98.7

98.7

5 10

20

11.
TABLE IV

CALIBRATION OF TEST CHARGE AMPLIFIER (B)

AT INPUT EQUIVALENT TO lOg 0 TO PEAK

Acceleration

pc/g

Charge

Range

g/v

Amplifier S Sensitivity

pC

sttings

Time

Constant

Frequency

Hz

Output Ratio

Measured

Calculated

rrec[uency Kebpuiibc

q.

"6

0.03 1 3.0 Short 10

50

100

500

1000

10000

0.635

0.988

1.017

1.034

i.042

1.068

62.4

97.1

100.0 * 101.7

102.5

105.0

0.03 1 3.0 Medium 10

50

100

500

1000

10000

0.964

0.983

0.996

1.027

1.038

1.066

94.8

96.7

97.9

101.0

102.1

104.8

0.03 1 3.0 Long 10

50

100

500

1000

10000

1.044

1.048

1.055

1.065

1.070

1.065

102.7

103.0

103.7

104.7

105.2

104.7

60 100 6.0 Short 10

50

100

500

1000

10000

0.985

0.986

0.986

0.986

0.986

0.986

99.9

100.0

100.0 * 100.0

100.0

100.0

60 100 6.0 Medium 10

50

100

500

1000

10000

0.985

0.985

0.985

0.985

0. 985

0.986

99.9

99.9

99.9

99.9

99. 0

100.0

60 100 6.0 Long 10

50

100

500

1000

10000

0.977

0.986

0.977

0.986

0.986

0.986

99.

1

100.0

99.

1

100.0

100.0

100.0

*Note: Frequency Response Referred to 10 Hz - Short Time Constant

12.
TABLE V

CALIBRATION OF TEST CHARGE AMPLIFIER (B)

AT INPUT EQUIVALENT TO lOg 0 TO PEAK

Accelerometer

Sensitivity

pc/g

Charge Amplifier Settings

Frequency

Hz

Output Ratio

Measured

Calculated

''Frequency Response

0,0 Ranee

g/v

Sensitivity

pC

Time

Constant

0.15 1 1.5 Short 10 61.8 61.3

50 98.0 97.2

100 100.8 100.0 * 500 102.5 101.7

1000 103.3 102.5

10000 105.3 104.5

15 100 1.5 Short 10 97.6 100.0

50 97.7 100.

1

100 97.6 100.0 * 500 97. 7 100.1

1000 97.7 100.

1

10000 97.6 100.0

*Note: Frequency Response Referred to 100 Hz - Short Time Constant

13.
TABLE VI

CALIBRATION OF TEST CHARGE AMPLIFIER

AT VARIOUS ACCELERATION LEVELS

Acceleration

Sensitivity

pc/g

Charge? Amplifier Settings

Frequency

Hz

Output Ratio

Measured

Calculated

Equivalent

Acceleration

Level g Range

g/v

Sensitivity

pC

Time

Constant

0.03 1 1.5 Short 100 101 8 5 101 7 10

102 0 20

0. 15 1 1.5 Short 100 100 8 5 100 8 10

101 0 20

15 100 1.5 Short 100 98 1 5 97 6 10

98 0 20

60 100 6.0 Short 100 98 4 5 98 6 10

98 6 20

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FORM NBS-114A (1-71) U.S. DEPT. OF COMM. 1 . PU B LIC AT ION OR RE PORT NO. 2. Gov't Accession

BIBLIOGRAPHIC DATA ^^3^^ No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Experimental Study of the Effects of Thermal Transients on the

Performance Characteristics of Piezoelectric Accel erometers - A Progress Report.

5. Publication Date

u u 1 y 10) 1 y /

0

6. Performing Organization Code

7. AUTHOR(S)

Paul S. Lederer

8. Performing Organization

NBSIR 73-230

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 4253454

11. Contract/Grant No.

AT - (04-3) - 911

12. Sponsoring Organization Name and Address Lawrence Livermore Laboratory

lini vprs i tv nf rfllifnrnifl

Livermore, California 94550

13. Type of Report & Period Covered

Progress Report

q-lS-7? to 4-T^-73

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

This progress report describes the development of an experimental technique for

subjecting piezoelectric accel erometers to controlled thermal transients. It

involves the exposure of a vibrating test accelerometer to radiation from a high

power incandescent lamp. A second accelerometer, shielded from the radiation,

monitors the vibration amplitude. Considerations pertaining to the characteristics

of the electronic readout equipment, and their effects on the measurements, are

discussed.

7. KEY WORDS (Alphabetical order, separated by semicolons)

Accelerometer; Charge Ampl if ier; Electrometer; Piezoelectric; Pyroel ectric

;

Thermal Transient

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