science 

uses

for a changing world

TREMOR\SOS 

U.S. Geological Survey

U.S. Department of the Interior 

U.S. Geological Survey

The Design and Performance of a Low-cost Strong-motion 

Sensor Using the ICS-3028® Micromachined Accelerometer

John R. Evans1

Open-file Report 98-109

This report is preliminary and has not been reviewed for conformity with U.S. Geological Survey 

editorial standards or the North American Stratigraphic Code. Use of trade, product, or firm names 

is for descriptive purposes only and does not imply endorsement by the U.S. Government.

'U.S. Geological Survey, 345 Middlefield Road, MS-977, Menlo Park, California, 94025; "evans@andreas.wr.usgs.gov".
Contents

Contents, Figures, Tables, and ftp access .................................................................. 2

Introduction .................................................................................................... 3

Design .......................................................................................................... 5

Performance ................................................................................................... 12

Operational Issues ............................................................................................ 15

Manufacturing Issues ......................................................................................... 17

Conclusions .................................................................................................... 18

Acknowledgements ........................................................................................... 19

References ...................................................................................................... 20

Appendix A (Resistor Selection) .......................................................................... 23

Appendix B (Thermistor Response) ....................................................................... 27

Appendix C (Filter Components) .......................................................................... 29

Figures

Figure la (PGA Spatial Variability) ........................................................................ 3

Figure Ib (PSV Spatial Variability) ......................................................................... 4

Figure \c (How Dense?) ...................................................................................... 5

Figure 2 (Accelerometer Schematics) ....................................................................... 6

Figure 3a (Amplifier Schematic) ............................................................................ 7

Figure 3b (Filter Schematic) ................................................................................. 8

Figure 4a (Printed Circuit) ................................................................................... 9

Figure 4b (Mounting Block) ................................................................................. 11

Figure 5 (System Noise Spectrum) .......................................................................... 12

Figure 6a (System Noise Samples) .......................................................................... 13

Figure 6b (System Noise Samples) ......................................................................... 14

Figure 7 (Amplifier Noise Spectra) ......................................................................... 15

FigureS (Tilt Test) ............................................................................................ 16

Tables

Table 1 (Component Listing and Cost) ................................................................... 21

On-line Versions

This report and related software and figures are available via anonymous ftp from "andreas.wr.usgs.gov" (130.118.49.1) in directory "~ftp/pub/outgoing/evans/OFR_98_109". Use your 

e-mail address as login password. All files are either ASCII PostScript® or binary Gerber® plot 

files originating from a PC. Use binary/#; for the Gerber® files and compressed files, asciiftp for 

uncompressed PostScript®.
Introduction

The severity of earthquake ground shaking varies tremendously over very short distances (Figures la-c). Within a distance of as little as 1 km from the nearest station, one knows little more 

than what can be obtained from an attenuation relation, given only distance from the fault rupture 

and the geology of the site. For example, if some station measures 0.5 g peak ground acceleration 

(PGA), then at a distance of 1 km from that site, under otherwise identical conditions, the shaking 

has one chance in three of being under 0.36 g or over 0.70 g, based on the curve shown in Figures 

\a,c. Similarly, pseudovelocity (PSV) response spectra have a 5% chance of differing by 2x at 1 

km distance (Figure \b). This variance can be the difference between moderate and severe damage.

(1 a) PGA Spatial Variability

(Smith et al., 1982; McCann and Boore, 1983; Hough, 1994; Boore, 1996)

CO

o

BJF93

O

Si cT

p 

o

S

. D = by definition

^ BJF93 = Boore et al. (1993) receiver sigma * sqrt(2)

 = BJF93 * (1 - exp(-sqrt(1.33 * xi)) (eyeball fit) 

D = sliding bins of 20 (o = sliding bins of 10)

012345 

Interstation Distance (median £, km)

Figure 1. The spatial variability of strong ground motion, expressed as the log-normal standard deviation 

(a) between neighboring stations separated by ^ km. These results are compiled from the literature, in some 

instances recast or evaluated by the author. Sources cited on Figures, (a) Peak ground acceleration.

Hence, there are critical needs, both in emergency response and in mitigation (prediction of 

shaking strength, building codes, structural engineering), to sample ground shaking densely enough 

to identify individual neighborhoods suffering localized, strong shaking. These needs imply a spatially dense network of strong-motion seismographs, probably numbering thousands of sites in an
urban region the size of the San Francisco Bay Area, California (Figure Ic). It has not been economically feasible to field that many instruments, since existing ones cost many thousands of dollars apiece. For example, there are currently just a few dozen digital free-field instruments in the 

Bay Area. This paper is one step toward a solution to this conundrum. I demonstrate that a recently developed class of accelerometers, those constructed from silicon by "micromachining" (a 

process similar to integrated circuit fabrication), is now capable of resolving ground motion with 

the necessary accuracy while greatly lowering both acquisition and maintenance costs.

PSV Response Spectra Spatial Variability

(standard deviations of log 10 0)*Sd ratios, averaged over 0.5 to 10 Hz)

g

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I H

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b-l

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q d

BJF93

F = Field and Hough (1996) 

A = Abrahamson and Sykora (1993) 

D = by definition

BJF93 = Boore et al. (1993) receiver sigma * sqrt(2) 

 = BJF93 * (1 - exp(-sqrt(1.33 * xi)) (eyeball fit)

01234

Interstation Distance (£, km)

Figure 1 (cont). (b) Pseudo-velocity response spectra (5% damped) averaged from 0.5 to 10 Hz.

Specifically, I describe the design and performance of a moderate-cost micromachined silicon 

accelerometer system combining the EG&G ICSensors ICS-3028® ($76 in quantity 500; ±2-g version) with a power-supply, amplifier, and filter system designed by the U.S. Geological Survey and 

one of its contractors (cf. Acknowledgements). I estimate that a completed three-component set 

including temperature sensor will cost about $550 parts plus labor in modest quantity (Table 1), 

compared to a retail cost of about $2700 for one of the commonest state-of-the-art strong-motion 

sensors used in seismology. Our sensor system is intended for use in low- to moderate-cost earthquake strong-motion seismographs in urban and suburban areas and lifeline corridors, where cultural ground noise often reaches over 50 jig peak-to-peak (FTP), and possibly along fault lines to
aid early-warning systems. (One g is the acceleration due to gravity, 980.665 cm/s2.) This sensor/amplifier system also has potential application in developing countries and other cost-sensitive 

installations, as well as general application to acceleration problems in the band above «0.1 Hz. 

We offer this design and these test results to further these aims.

(lc) How Densely Need We Sample Strong Motion?

_______Based on peak acceleration eyeball-fit curve._______

§

b

< 

O

p 

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BJF93, or what you know with only an attenuation 

relation: a factor of 1.84 (at 68% confidence).

2.5-1 

2.25-

2-

1.75-

1.5-

Uncertainty factor of 1 A (at 68% confidence)

1.05 km between stations, or 3300 sites in the 

urban Bay Area. (Uncertainty factor of 1.33 

requires 10,000 sites at 600-m intervals!).

1.25-

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Station SPACING in Network (2*£, km)

Figure 1 (cont.). (c) Recasting of the eyeball-fit curve from (a) to give PGA uncertainty examples. The 

"Equivalent Uncertainty Factor" corresponds to one standard deviation and is multiplicative.

Design

Figures 3<z and 36 show our schematics, a single-ended design. Figure 4a shows the equivalent printed-circuit board.

The sensor itself (Figure 2) is an open-loop accelerometer based on a piezoresistive Wheatstone bridge. It is not temperature compensated and is quite sensitive to temperature (for gain, 

typically -0.15% of full scale (FS) per °C, or about -0.03 g over +10 °C in the 2-g devices we 

use). Each sensor is calibrated individually by the manufacturer (EG&G ICSensors, Inc.®, 

Milpitas, California) and supplied along with calibration-resistor values and related information. 

To build one of these sensors, a square section of silicon wafer is etched nearly free of its sur-
roundings, remaining attached by four thin cantilever beams near the corners of the square. This 

proof mass is blocked from damaging overrange excursions by two more etched wafers, one fused 

to each face of the proof-mass wafer. Boron doping of the high-strain parts of the springs creates 

the bridge resistors, which are organized into a bridge circuit in a manner that cancels signals from 

rotations and cross-axis accelerations.

Resistivety sensitive supports (4) 

(with piezore sisters)

Suspended mass

Bond pads (5)

^&M^r

Double Cantilever

Figure 2. Diagrams of typical ICSensors® accelerometers (courtesy of ICSensors® Inc.). (Top) Cut-away 

perspective view of the entire device. (Center) Cross-section of the entire device. "Acceleration" is the 

negative of the acceleration vector. (Bottom) Proof-mass quad-cantilever design (sometimes called a "double" cantilever).

With a 5-V supply to the bridge, sensitivities are nominally 10 mV/g, though varying from one 

accelerometer to another by about ±20%. Resonant frequency is nominally 1 kHz, with similar 

variability, and damping is roughly 0.7, provided by viscous flow of the gas between the proof
mass and the overrange stops on either side of it. Since the natural period is well outside the seismic-signal range, its variability and that of damping will not have a significant effect on the data.

Each arm of the Wheatstone bridge is nominally 4 kQ, however slight process variability from 

one place to another across the wafer leads to imbalances between the arms. A low-valued resistor 

pair at either Rl/Rll (Rzsi) or R2/R12 (Rzs2; Figure 3d) corrects the resulting offset in the 0-g 

output. (A parallel pair aids accurate matching of very low values, typically a few Ohms.) The 

other pair is to be shorted, generally with a zero-Ohm resistor.

flnalog Poyer Supply J^h^

mDmi- N

Q}U

± 22uF 23V

-» T«n t

Either Rl or R2 is a juiper or zero Ohi "resistor". 

Either R5JR15 or R6IRIG are open. See calibretion sheets. 

Calibrate vith 50ppn letal-fili or uire-vound resistors only. 

Select resistor pairs with Evans' "pick_res_ts.c".

I LJsiaOutSensor and 

flmpl ifier

"Prox." - Keep proxiial (close) to coiponent. 

Keep all paths short, fit least one ground plane.

For tuo boards, load acceleroieter. reference, aiphfier. and filter. 

For third board, also load analog paver and thenistor. 

Distribute +¥ft. -VB. and COH to the other ti/o boards.

fill resistors 17. 50ppn letal-fili unless specified.

NOTE: Positive acceleration yields NEGATIVE voltage at SigOut+.

Organization: U.S. Geological Survey

Title:

TREHOR Sensor Board (single ended)

fluthor: Hamstra, Rogers, Evans Updated: 10 liar 97

Figure 3. Schematic of the USGS low-cost strong-motion accelerometer signal-conditioning circuit, (a) 

Main part of the circuit. A PostScript® file containing this schematic is available via anonymous ftp from 

"andreas.wr.usgs.gov" at "~ftp/pub/outgoing/evans/OFR_98_109/ampflltl.ps".

Another resistor pair at either R5/R15 (Rzici) or R6/R16 (Rzrc2) compensates the temperature 

drift of the zero level. (A series pair aids accurate matching of large values, typically on the order 

of 1 MQ.) The other pair is to be left open.

All compensating resistors, indeed all resistors in this design, must be metal-film resistors with 

low temperature coefficients. All compensating resistors must be close to the sensor to minimize 

noise pickup and prevent parasitic oscillations in U2. (Wire-wound resistors are likely to induce 

such oscillations and carbon resistors are very noisy and temperature sensitive.) We use 1-% 

metal-film resistors with 50-ppm temperature coefficients (20 each in quantity 200). Selection of
these resistors can be onerous since they are unique for each sensor. However the sensor manufacturer has indicated willingness to provide laser-trimmed compensating resistors for no additional 

cost in bulk purchases (cf. Manufacturing Issues). A simple brute-force C-language computer 

program for selecting optimal resistor pairs from standard sets is given in Appendix A.

(36)

ty-Gain 8-Pole 18.5-Hz Low-Pass Buttervortti flnti-fllias Filter

Highest-Q stage.

T--

R12315IU21 are to be selected iidividutlly btsed

upoi NERSURED (to I.5Z) C123151112). Coipute Rs

vith Evais' progrn "biquid.c*. Select »nd test resistors

to vithii I.5Z of optiial accordiig to that progrsa.

Keep all paths short, fit least one ground plane.

Organization: U.S. Geological Survey

Title:

Rnti-fllias Filter (single ended!

fluthor: Rogers and Evans Updated: 10 Har 97

Figure 3 (cont.). (b) Anti-alias filter. A PostScript® file containing this schematic is available via anonymous ftp from "andreas.wr.usgs.gov" at"~ftp/pub/outgoing/evans/OFR_98_109/aafiltl.ps".

Because analog compensation circuits for the temperature-dependence of sensitivity use one or 

more diodes or transistors, they produce too much noise in the most critical part of the circuit. (The 

ICS-3052®, equivalent to an ICS-3028® but with internal laser-trimmed compensating resistors and 

transistors, is significantly noisier than the circuit shown here. However, it may be possible to use 

a "super matched pair" of transistors in this application, since these are in fact many transistors in 

parallel and yield a significant reduction in noise.) We have elected to use digital post-acquisition 

temperature compensation. We minimize temperature variations in space and time by placement of 

all sensors and signal conditioning circuits on a small, insulated, isothermal aluminum-mounting 

block (Figure 4b). This block also ensures orthogonality of the three accelerometers.

To measure temperature near the accelerometers we include a precision negative-temperaturecoefficient (NTC) thermistor (YSI® model 44031). These low-cost sensors are accurate to ±0.2 °C 

after ten years and easily resolve to 0.001 °C. The resistance of an NTC thermistor is a highly
nonlinear function of temperature (empirically modeled by a log-cubic relation). A C-language 

program to convert the output of this circuit (at J7) from mV to °C is given in Appendix B. It is 

intended for use in post-acquisition compensation of accelerometer sensitivity.

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Bottom Right (Solder side)

Figure 4. (a) Printed circuit board for the circuit in Figure 3. Left: component-side silkscreen; top right: 

component-side copper; bottom right: solder-side copper. All views are from component side. Accelerometer outline below silkscreen is intended to be outside the board, directly attached to the aluminum block 

with leads Z-bent upward to meet the board. It can also be 90° to the board with leads bent around that corner. As drawn, positive acceleration axis is out of page toward viewer. Gerber® plot files are available on 

"andreas.wr.usgs.gov" at files "~ftp/pub/outgoing/evans/OFR_98_109/*.ger". Use "binary"^ to a PC. (£) 

Isothermal aluminum block for sensor mounting (Figure 4b is on page 11). This diagram is available as a 

PostScript® file in "~ftp/pub/outgoing/evans/OFR_98_109/TREMOR_Al_Block.ps".

A low-noise 2.5-V reference, Ul (LT1019CN8-2.5®), drives both the bridge and the thermistor 

circuit. Capacitor Cl further limits noise input to the bridge; it should be close to the sensor, with a 

very short run to the ground plane, and should be of type X7R ceramic. Half of the main gain 

stage, U2A (a bipolar PMI®/Analog Devices® OP270GP ), drives the negative input of the bridge 

to about -2.5 V, forcing the positive output of the bridge at pin 4 to ground and thereby doubling 

the range of output at pin 5. That negative output is amplified in non-inverting amplifier U2B, with 

a nominal gain of 250x. (Note that this arrangement yields negative voltage for positive accelera-
10

tion. An inverting amplifier is inappropriate because it would pull pin 5 to ground and load the 

bridge. However, rearrangement of this part of the circuit for positive-positive output is possible.) 

The gain resistors should be of the same type as the compensating resistors. In practice, I have selected individual gain resistors to give about the same output sensitivity (2.5 V/g) in order to optimize use of an ADC's dynamic range (cf. Manufacturing Issues). As with Cl, all op-ampdecoupling capacitors (C2, C3, and C13 through C16) must be proximal to the device served and to 

the ground plane and of type X7R ceramic.

The output of the main gain stage, U2B pin 7, goes to an 8-pole Butterworth low-pass filter for 

anti-alias filtering (Figure 36). The design used here is a bi-quad configuration. We currently use 

5% capacitors and individually tune the filters by selecting matching resistors. The C-language 

program in Appendix C aids this selection. (In mass production one would use 2% capacitors with 

standard 1% resistors to achieve adequate tuning consistency without custom part selection.) In the 

temperature circuit, R9 and C8 provide anti-alias filtering by forming a one-pole filter appropriate 

to the decimated sampling rate of that channel. All filter capacitors must be of low-impedance film 

type; we have used Panasonic® Series V to date, but similar varieties would be appropriate.

Alternatively, one might be able to use a switched-capacitor filter for anti-alias filtering, if the 

clock of that filter were synchronized with the clock of a subsequent S-A or fast multi-slope ADC 

to eliminate clock feed-through noise (R. Jarnot, personal communication, 1998). Such designs are 

likely to be simple (less expensive) and lower in power use. In another alternative, a much more 

modest anti-alias filter combined with the inherent over-sampling of S-A ADCs could significantly 

lower parts costs and manufacturing complexity. This technique has been used in other seismographs. The power supply on the left side of Figure 3a provides quiet power to the signal conditioning circuitry, nominally at ±8.2 V. It uses low-cost low-noise linear components. Input to this 

circuit is about ±12 V. Total power consumption for a three component set of accelerometers is 

very nearly 1 W, and nearly all of it goes to driving the OP270GPs®. Hence, this power level could 

be reduced by half or more by using low-noise CMOS op-amps in the Butterworth filter, however 

use of the OP270GP® in the primary gain stage (U2) is crucial to system noise performance.

Various dual-use input/output pads (J2, J4, J5, and J6) are provided to allow sharing of the 

power supply and voltage reference. The printed-circuit board in Figure 4a is used in sets of three, 

one per acceleration channel (e.g., vertical, North, East). Only one board needs to be loaded with a 

thermistor and power supply, with the other boards powered by jumpering J2, J4, and J5 between 

all boards. The voltage reference can be shared similarly, though we have not done so initially to 

avoid noise pickup in the jumpers. A redesign for a three-component surface-mount board using 

only one voltage reference would be appropriate in manufactured versions. In any case, ground 

planes must be provided in the low-level-signal parts of any board, as they are in our prototypes 

(Figure 4a). An internal, grounded aluminum box in our prototype accelerographs supplies additional shielding for this single-ended sensor block, with all digital circuits kept outside that internal 

shield box.

Lastly, avoid stressing the accelerometers during mounting. For example do not shim them for 

orientation. The manufacturer recommends mounting them flat on a machined aluminum block 

with screws tightened to 6 foot-pounds per inch of screw length (for 4-40 screws). Stressing the 

mount can stress the silicon of the accelerometer and cause large offsets in the output signal. It can 

also induce "oil canning" nonlinearity kinking of the cantilever springs causing the proof mass to 

hang up.
11

(46)

North PCB

TREMOR-Prototype 

Isothermal Block 

February, 1998 

John R. Evans 

Scale 1:1

Left-side view

Vertical PCB °

<3 Q

I:

L -

[ICS-3028 

North

<U 

GO 

T3

Top View

East PCB O

_ _ _ _«_

o W "f>

e w r* O

N)

OO

Right-side view

-l/4"-201"deep

Front-End View

All holes 4-40 threaded to 0.5" 

depth unless otherwise stated.

(Uncrossed hole on "vertical" PCB 

corresponds to an unthreaded hole 

in the block, 0.125" in diameter 

and depth. The two large base holes 

are l/4"-20 threaded to 1" deep.)

Block milled from 2" bar stock 

to get true right angles. Final 

dimensions 1.9"xl.9"x3.9".

PCBs on 1/8" nylon spacers. 

Sensors directly on block.

Base View
12

Noise Power Comparison

1000

N

oCO

100

10

1

1000

N

g: 100

bO

I IIIII I Iz

Or01 10

I I I I

0.1 1 10

Frequency (Hz)

Figure 5. Noise power spectra for the complete system (top), with an ICS-3022® accelerometer. (Bottom) 

Equivalent noise spectrum with the accelerometer replaced by a dummy bridge of 4KQ metal-film resistors. 

(Data for these two spectra were taken at the same sample rate (200 sps) but with different anti-alias filter 

corners. Each is an ensemble average of the spectra from many noise samples.) The spikes above 60 Hz 

and just below 100 Hz in the upper plot were probably caused by noise from the inverter used for power at 

our rural vault site. The lower plot was derived in the laboratory using line power.

100

Performance

Noise performance of this sensor system is shown Figures 5 to 7. Figure 5 (top) gives the 

noise power spectrum for the entire system, from the ICS-3022® accelerometer through anti-alias 

filter, taken at a quiet rock vault where ground noise is known to be far below intrinsic sensor noise 

levels. (The ICS-3022® is identical to the ICS-3028® except for packaging details like mounting 

plates and pins.) It reveals 1/f noise with two corner frequencies, at about 2 Hz and somewhere 

above the anti-alias corner frequency. Since the noise level of the same system with a dummy 

bridge replacing the sensor is about a factor of five to ten quieter (Figure 5, bottom), the principal 

limiting noise source appears to be non-Johnson noise in the resistors of the sensor's Wheatstone 

bridge. The likely source of this noise is surface imperfections in the doped resistors and intercon-
13

nects (R. Jarnot, personal communication, 1997). Manufacturing changes subsequent to the acquisition of our test samples may have improved this noise figure, but this conjecture is untested.

(6a) Prototype Noise Sample, 0.1-35 Hz (Rock Vault, 04 Mar 97)

36.9 i FTP

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E

jikiiiujl ML LIAiilLliuAllLi jitLikLUULIilJlLiiiiki klliLJiiULLuui tU.lUiUL4hLil

10 20 30 40

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C-4

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cn

C/3

u

O 

O 79.8^igPTP

0 10 20 30 40

10 20 

Time (s)

30 40

Figure 6. Noise samples for the complete system for (top) FBA-11® (limited here by noise in our test apparatus); (center) an ICS-3022®; and (bottom) a lower cost device, the ICS-3031®. Note the differing amplitude scales. FTP noise amplitude is defined as ±2a. (a) Signals in the band 0.1 to 35 Hz.

Equivalent noise samples in the time domain are shown in Figures 6a and 6b. These correspond to the desired bandwidth, 0.1 to 35 Hz, and the minimum acceptable bandwidth, 0.5 to 10 

Hz, for strong-motion seismology and structural engineering. Simultaneous noise samples are 

shown for an FBA-11® (limited by our test-system noise level) and a lower-cost silicon accelerometer, the ICS-3031®, using the same signal conditioning circuit as the ICS-3022®. For comparison, the noise level we measured in Pasadena (one block from a major freeway) was on the order of 

100 ug FTP. Noise levels measured in a quiet residential neighborhood of Palo Alto, California, 

were about 40 ug FTP on soft soil about 1 km from a freeway. (These samples were taken with a 

horizontal FBA-11® sensor. They were estimated visually possibly under estimated using an 

oscilloscope.) In the Palo Alto case, the footsteps of a worker about 20 m away were clearly visible with the ICS-3022®.

The ICS-3022® (hence, the ICS-3028®) clearly justifies an 18-bit ADC, given its broadband 

signal-to-noise ratios. These ratios (4<r/4-g) are 15.6 bits (0.1 to 35 Hz) and 16.3 bits (0.5 to 10 

Hz). If signal-to-noise is instead defined as RMS/2-g, those values become 16.6 and 17.3 bits (100 

and 104 dB). Using a third signal-to-noise definition (RMS(noise)/RMS(4-g FTP sine wave)), the 

values become 16.1 and 16.8 bits (97 and 101 dB).

Tests of sensor linearity are partially complete. However, we can limit the nonlinearity of sensor output versus static acceleration in a tilt test (Figure 8) to the inherent accuracy of our tilt table
14

(about 0.1 %FS). Indeed, the results of our tilt tests for a research-grade accelerometer (Kinemetrics® FBA-11®) are indistinguishable from those of the ICS-3028 family our tilt table limits 

both results. We can also limit hysteresis to about 0.02% FS with the sensor axis oriented in the 

horizontal plane, which compares well with the manufacturers claim of 0.01 to 0.02% FS (G. 

Rendla, personal communication, 1996). This limit happens to be the same as the (informal) specification for the FBA-11®. More sensitive tests for this type of hysteresis are planned. Tests of 

temperature compensation for sensitivity also have not been completed. We intend to do such tests 

to verify the manufacturer's calibration. Preliminary tests suggest at least gross similarity, but are 

insufficient to test the veracity of those calibrations.

(6b) Prototype Noise Sample, 0.5-10 Hz (Rock Vault, 04 Mar 97)

o t

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e

19.0 jig FTP

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3

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10 20 30 40

51.3 jig FTP

10 20 30 40

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226.1 fig FTP

10 20 

Time (s)

30 40

Figure 6 (cont.). (6) Signals in the band 0.5 to 10 Hz.

Tests of cross-axis sensitivity also remain to be done. The manufacturer's specification is ±3% 

FS (and typically ±1% FS). Spot checks of sensor orientations agree with the manufacturer's claim 

of 2° accuracy, with all examples tested being well within that limit. The manufacturer subsequently improved orientation accuracy and now claims 1° orientation accuracy. Appropriate goals 

are ±1-% FS cross-axis sensitivity and 1° orientation accuracy.

In the process of finding an amplifier that does not contribute significantly to system noise, we 

tested many models in several configurations. We found the OP270GP® to be both quiet and stable. The noise spectra for this and two other amplifiers (installed in our Figure-3 circuit with a 

dummy bridge) are compared in Figure 7. The spectrum for the LT1007® is suspect because longer 

leads needed for these (single) op amps induced a parasitic oscillation in U2. The LT1124® and 

OP270® did not oscillate and can be compared directly. We chose the latter because its spectrum is 

slightly less red than that of the LT1124®. However, either device is adequate.
15

In short, the sensor, not the amplifier, currently limits performance. In any case, the resulting 

noise figure is quite adequate for urban strong-motion recording.

Amplifier Noise Comparison

loom i r

10

bO

0.1

100

0.1

100 I I I I + H- I 1Mb

bO

r10

0.1 i i i i i i i i i i i i i i i i i

0.1

Frequency (Hz)

10 100

Figure 7. Noise power spectra for three models of operational amplifier, with a dummy bridge in 

place of the accelerometer, as in Figure 5 (bottom). Result for the LT1007 is suspect because our 

jumpers used with that model induced a parasitic oscillation.

Operational Issues

A number of operational issues arise with this sensor. In particular, one must lower the rate of 

temperature change within the sensors and assure nearly homogeneous temperature across each 

sensor and between the accelerometers and the thermistor. These goals can be met easily by (1) 

placing all four devices in close contact with a small aluminum block, (2) making thermal contact 

between this block and the underlying concrete slab or rock of a site, and (3) insulating this block 

from the air. In practice, we insulate in two layers, one between the internal shield box of the sensors and the outer box of the instrument and the other around the whole instrument. The latter is 

made from two-inch-thick semi-rigid polyisocyanurate foam board with aluminum-foil facings, a 

common housing-construction material (e.g., Celotex Tuff-R ). It is easily sawed with bandsaw
16

or jigsaw, and assembled with adhesive caulking. Hand, arm, eye, and breathing protection should 

be worn since this material seems to contain fiberglass for strength. We attach the prototype instrument to the concrete slab and cover it with a skirted box of this foam. The box's skirt is attached to the concrete with a removable adhesive, such as DAP® Fun«Tak® or Seal 'N Peel® removable caulking. If manufactured in bulk, an equivalent enclosure could doubtless be custom 

molded to shape at very low cost.

(a) ICS-3028 (S/N 2925-056) Sensitivity

8- 

§

<O 

OO <N

2.55663 V/g 

0.08616V offset

(LI fit)

-i.o -0.5 0.0 

Input Acceleration (g)

(b) Residuals to LI fit

0.5 1.0

SO <N

g

-1.0 -0.5 0.0 0.5 1.0

Input Acceleration (g)

Figure 8. Tilt-table calibration and linearity test for an ICS-3028 . Apparent nonlineariry is 

probably due to imperfections in the tilt table. In any case, the largest apparent diversion from linear response is at -1 g, and is about 0.1% FS.

For the very large networks envisioned, maintenance costs are crucial and likely to exceed acquisition costs within a few years of operation. Keys to lowering maintenance costs are robustness 

of the instruments and sensors, non-challenging environments, and routine state-of-health (SOH) 

messaging. The latter allows one to leave an instrument untended indefinitely, visiting a site only 

when the SOH message (or lack of a message) indicates a need for repair. This messaging presupposes some low-cost telecommunications link for SOH messages, the same link required for realtime messaging in support of Emergency Services. Robustness in the partially controlled environments envisioned (mostly school closets and private garages) requires that the sensor and other 

parts of the instrument withstand occasional impacts by furniture, 2x4 studs, teenagers, dogs, etc.,
17

without damage and preferably without triggering. Similarly, washing machines, vehicles, and 

other sources of vibration must not affect the instrument significantly (preliminary field tests suggest these noise sources are tractable). Silicon accelerometers by this manufacturer are extremely 

robust, including for shock (at least 1000 g), vibration (400 g RMS), and spring sagging (none detectable in decade-old test articles). They do have some weakness to corrosion of metal interconnect parts, hence require a dry atmosphere within the instrument. This atmosphere can be maintained by desiccant and by introducing a small piece of dry ice just prior to instrument closure. The 

sublimating CC>2 displaces Oxygen and water vapor from the container (K. Young, personal communication, 1997). The trigger currently has a modest minimum-duration criterion in addition to a 

triggering threshold. The former is designed to avoid triggers caused by impacts on or near the instrument. The foam insulation also provides a significant crush zone.

The most likely component to fail is the backup batteries, which probably should be sinteredelectrode NiMH D-cells (e.g., Varta Batteries AG® or Universe Power Sources (Huan Yu US) 

Ltd.®). These were designed for the emergency-lighting industry and are rated for five years continuous float charging. In seismic applications they probably can be used for longer periods. By 

combining such non-toxic cells with careful design, one might be able to have the homeowner or 

other local representative replace the batteries when indicated by the SOH message and simply discard the old ones in their normal garbage stream.

I know of no calibration method that will work for these sensors other than tilt testing; they 

lack other means to deflect the mass. The absence of measurable spring sag and the use of diffused 

resistors in the bridge suggest that sensitivity will change only very slowly. However, this issue 

remains open.

We intend to operate most of these instruments at "free field" sites, relatively unaffected by 

soil-structure interactions. As a practical matter, truly open sites are rare in urban areas and even 

less often secure from weather and vandals. In practice, we will compromise by using one- and 

two-story buildings, where possible of light construction (e.g., wood-frame). These are commonly 

regarded as having little effect on earthquake signals (W. Joyner, personal communication, 1997). 

Initial feedback from likely hosts suggests that siting on grade-level slabs in the garages of private 

homes is the most viable solution, with janitors' closets in schools a likely alternative.

Manufacturing Issues

Issues of manufacturability have been mentioned at various points throughout this report. Here 

we collect and elaborate on these issues.

Individual selection of sensor-calibration resistors is the most serious issue to be solved before 

low-cost mass-production could begin. The selection process is labor intensive and vulnerable to 

human error. Luckily, the manufacturer has indicated willingness (at least at 10,000-quantity purchases) to make certain custom modifications to the design and testing of these devices. In particular, they already offer a similar device, the ICS-3052®, which has laser-trimmed Ruthenium 

calibration resistors integrated with the accelerometer package. This device also contains a transistor pair, used in temperature-compensating sensitivity. Our design would simply leave out this 

transistor pair call the result an "ICS-305*". The manufacturer has indicated willingness to offer 

such a device at the same price. If, in addition, one more pin could be added to the design, then a 

calibrating resistor now used in conjunction with these transistors could be used instead to provide
18

R3 of Figure 3<z, the gain-setting resistor. This change would allow easy correction for gross sensitivity differences between individual sensors. The addition of this sixth pin is problematic, however, requiring more significant retooling and redesign. It is not clear whether the manufacturer 

would undertake it without a price change. Changing from an 18- to a 19-bit ADC would obviate 

the need for this sixth pin and could well prove less expensive. Sensitivity corrections would then 

be made in the same post-acquisition process as are temperature corrections.

The manufacturer has also indicated willingness to customize their testing procedure to suit the 

needs of a large purchase. I suggest in-circuit testing using the final amplifier design. This change 

would minimize the degree of inference required for subsequent digital compensation. Furthermore, it may be desirable to get testing in three orientations, -1 g, 0 g, +1 g, and at more temperature points than is standard (perhaps at -10°, 5°, 20°, and 40° C).

Filter components would not be custom-selected in any final design. With more lead-time, 2% 

capacitors can be ordered, which when combined with 1% resistors would provide adequate tuning 

precision. The alternative design suggestions in Design could lower power, cost, and complexity 

still further.

Orientation of the accelerometer's active axis should be adequate without shimming or other 

corrections. Those we have checked were well within the ±2° tolerance then specified by the 

manufacturer. That specification is now ±1°, which is adequate for seismology. Furthermore, 

shimming stresses the accelerometer and causes large offsets in its output and may also induce 

nonlinear behaviors. Simply attach the sensors flat on the faces of a rectilinear aluminum block.

The thermistor used to sense this block's temperature should be of high quality. YSI® Inc. has 

very tight closed-loop quality control allowing it to guarantee ±0.1 °C accuracy when purchased 

across all examples of certain models (e.g., model 44031) and ±0.2 °C after ten years deployment. 

Their price depends very strongly on quantity; at the large quantities envisioned here they would 

cost a few dollars apiece for the raw, epoxy encapsulated version. This version is difficult to handle since it is small and has very fine leads. However, numerous packaging options are available, 

including surface-mounting and threaded-insert versions. The latter (e.g., YSI 093) probably is the 

most cost-effective solutions.

In any production version one would probably use surface-mount techniques and redesign the 

board of Figure 4a into a three-component version with better I/O connectors. This change would 

reduce the parts count, for example by sharing one voltage reference (Ul) among all sensors. It 

probably is not appropriate to use connectors to attach the accelerometers to this board because the 

signal levels are so low in that part of the circuit and because the bimetal-junction count probably 

would increase, causing larger temperature-induced signal offsets. The isothermal mounting block 

and shield box probably would be integrated into a single unit of cast aluminum or conductive 

polymer. Indeed, a complete two-chamber box with mounts may be appropriate. All envisioned 

digital circuitry for a low-cost instrument would fit on a single board as well so the completed instrument should be very compact.

Conclusions

As shown by Evans and Rogers (1995), even far noisier sensors are adequate for attenuation 

relation studies; certainly the noisier sensors are also adequate for Emergency Services needs. We
19

have shown that the ICS-3028® is capable of much more, of reaching below urban background 

noise levels. In other words, it is capable of measuring all the seismic signal there is to record in 

such environments, with the possible exception of long period signals (Figure 5). It opens the door 

to serious research in seismology and structural engineering, research with direct impacts on life 

safety.

Manufacturing issues can be overcome in large purchases by inclusion of laser-trimmed compensating resistors inside the sensor package. Sensor robustness promises long field life even in 

imperfectly controlled environments, such as schools and the garages of private homes.

In short, micromachined silicon accelerometers admit a new paradigm in strong-motion seismology. We can look forward to a day where the necessarily few high-grade research instruments 

are augmented by spatially dense networks of robust, low-cost instruments. With these, we could 

produce the equivalent of Doppler weather radar, showing earthquake-shaking "storms" and the 

badly shaken "squall lines" within them. Emergency Services can then both estimate overall needs 

and direct scarce resources optimally to those most in need. Seismologists could finally make and 

test detailed shaking models for predictive purposes. And structural engineers and seismologists 

could finally unravel the effects of shaking, design, construction, and maintenance upon structural 

vulnerability. The need for such arrays and their usefulness in response and mitigation are incontrovertible.

Acknowledgements

This work is part of the TREMOR/SOS Project, funded by the USGS Earthquake Hazards Reduction Program. We are grateful for their support even in times of very lean budgets.

John Rogers, with minor help from the author, performed the initial design and operationalamplifier selection. This effort led to the selection of the OP270GP® dual amplifier for its superior 

noise performance, which is both low and fairly white. The design of the voltage reference, powersupply, and amplifier now used is that of Robert H. Hamstra Jr., a private consultant specializing in 

low-noise instrumentation, while he was under contract to the USGS. He went far beyond the call 

of duty and taught this author many essentials of good instrumentation design. Dr. Robert Jarnot of 

JPL provided critical reviews of the design and of this paper and gave important insights into crucial design issues. The anti-alias filter is a joint effort of John Rogers, Gray Jensen, and the author, 

all of the USGS. Testing was performed at various stages by the author, John Rogers, Bill Robinson, and John Coakley, all of the USGS. We are grateful for the contribution of Bill Robinson's 

time and expertise by the USGS Marine Facility. ICSensors® Inc. kindly supplied the diagrams 

comprising Figure 2. Sensor-in-circuit noise tests were done at a USGS seismometer vault on the 

Gerber-Wells Ranch with the kind permission of Helen Gerber and her family. Willie Lee provided insights, comments, facilities, and an occasional kick in the pants I limp gratefully. 

Throughout it all, Paul Spudich provided essential insight, guidance, support, and tactical skill.
20

References

Abrahamson, N. A., and D. Sykora, Variations of ground motions across individual sites, in: Proc. 

DOE Natural Phenomena Hazards Mitigation Conf, Atlanta, October, 1993, I, 192-198, 

1993.

Boore, D. M., Estimates of average spectral amplitudes at FOAKE sites, in: An evaluation of 

methodology for seismic qualification of equipment, cable trays and ducts in ALWR plants by 

use of experience data, K. K. Bandyopadhyay, D. D. Kana, R. P. Kennedy, and A. J. Schiff, 

NUREG/CR-6464 and BNL-NUREG-52500, C-l-C-69,1997.

Boore, D. M., W. B. Joyner, and T. E. Fumal, Estimation of response spectra and peak accelerations from western North American earthquakes: an interim report, U.S. Geol. Surv. Open File 

fo/?., 93-509, 72pp., 1993.

Evans, J. R., and J. A. Rogers, Relative performance of several inexpensive accelerometers, U.S. 

Geol. Surv. Open File Rep., 95-555, 38 pp., 1995.

Field, E. H., and S. E. Hough, The variability of PSV response spectra across a dense array deployed during the Northridge aftershock sequence, Earthquake Spectra, 13, 243-258, 1997.

Hough, S. E., Southern surface rupture associated with the M7.3 1992 Landers, California, earthquake, Bull. Seismol. Soc. Am., 84, 817-825, 1994.

McCann, M. W. Jr., and D. M. Boore, Variability in ground motions: root mean square acceleration and peak acceleration for the 1971 San Fernando, California, earthquake, Bull. Seismol. 

Soc. Am., 73, 615-632, 1983.

Smith, S. W., J. Ehrenberg, and E. Hernandez, Analysis of the El Centro differential array for the 

1979 Imperial Valley earthquake, Bull. Seismol. Soc. Am., 72, 237-258, 1982.
21

Table 1 Parts Listing and costs

Parts Cost for TREMOR Accelerometer Three-component Sets

For 10 Units

UseQty

3

1

3

3

3

24

9

3

Reference

U3

Al mounting block

U2

R3

R4

Rl,2,5,6,ll, 12,15,16

Cl,2,3

J8

Value

ICS-3028

Block

OP270GP

24.9 K

100

Calibration

0.1 uF

Filtln

Unit Price

$90.00

$71.00

$3.37

$0.02

$0.02

$0.02

$0.2128

$0.00

Accelerometer Section Parts

6

12

3

3

3

3

3

3

3

3

12

3

3

3

3

3

3

U8,U9

C13,14,15,16

R21

R22

R31

R32

R41

R42

R51

R52

C21,31,41,51

C22

C32

C42

C52

J9

no

OP270GP

0.1 uF

28.1 K

67.5 K

24.1 K

29.4 K

107 K

120 K

16.7 K

34.4 K

0.39 uF

0.1 uF

0.267 uF

0.01 48 uF

0.33 uF

SigOut+

SigOut-

$3.37

$0.2128

$0.02

$0.02

$0.02

$0.02

$0.02

$0.02

$0.02

$0.02

$0.265

$0.174

$0.252

$0.135

$0.285

$0.00

$0.00

Filter Section Parts

1

l

0

i

i

i

i

Ul

RIO

RIO, alternate

R9

C8

J6

J7

Temperature and

LT1019CN8-2.5

Threaded 44031

BareYSI-44031

49.9 K

0.39 uF

Vref

Temperature

Vref Parts

$4.58

$35.46

$12.00

$0.02

$0.265

$0.00

$0.00

BuyQty

25

7

100

200

200

200

100

N/A

76.1%

100

100

200

200

200

200

200

200

200

200

100

10

10

10

10

N/A

N/A

6.2%

25

10

1

200

100

N/A

N/A

8.7%

Total

$270.00

$71.00

$10.11

$0.06

$0.06

$0.48

$1.92

$0.00

$353.63

$20.22

$2.55

$0.06

$0.06

$0.06

$0.06

$0.06

$0.06

$0.06

$0.06

$3.18

$0.52

$0.76

$0.41

$0.86

$0.00

$0.00

$28.97

$4.58

$35.46

$0.00

$0.02

$0.27

$0.00

$0.00

$40.33

For 1000 Units

Unit Price

$66.00

$13.00

$2.13

$0.012

$0.012

$0.012

$0.127

$0.00

$2.13

$0.127

$0.012

$0.012

$0.012

$0.012

$0.012

$0.012

$0.012

$0.012

$0.138

$0.087

$0.125

$0.067

$0.142

$0.00

$0.00

$3.70002

$16.80

$6.30

$0.012

$0.138

$0.00

$0.00

BuyQty

3,000

1,000

10,000

1,000

1,000

1,000

1,000

N/A

80.5%

10,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

10,000

1,000

1,000

1,000

1,000

N/A

N/A

6.4%

1,000

1,000

1,000

1,000

10,000

N/A

N/A

7.6%

Total

$198.00

$13.00

$6.39

$0.04

$0.04

$0.29

$1.14

$0.00

$218.89

$12.78

$1.52

$0.04

$0.04

$0.04

$0.04

$0.04

$0.04

$0.04

$0.04

$1.66

$0.26

$0.38

$0.20

$0.43

$0.00

$0.00

$17.51

$3.70

$16.80

$0.00

$0.01

$0.14

$0.00

$0.00

$20.65
22

Table 1 (cont.)

1 U4

2 U5,U6

1 U7

2 C4,C6

2 C5,C7

2 R7,R8

LM317LZ

LM329DZ

LM337LZ

22uF 16V Tant

22uF 25V Tant

1.2K

1 Printed-circuit board PCB

1 Al shield box

3 J2

3 Jl

3 J3

3 J4

3 J5

Power and

Parts Total

Box

COM

+ 12V

-12V

+VA

-VB

Miscellaneous Parts

1 Assembly Labor (a wild guess)

$0.45

$0.75

$1.30

$0.735

$1.488

$0.02

$12.12

$22.00

$0.00

$0.00

$0.00

$0.00

$0.00

$100.00

25

25

25

10

10

200

51

1

N/A

N/A

N/A

N/A

N/A

9.0%

10

Grand Total

3 U3

Parts Total

Parts Cost

ICS-3031

Using ICS-3031

with Alternative

$58.00 25

$0.45

$1.50

$1.30

$1.47

$2.98

$0.04

$12.12

$22.00

$0.00

$0.00

$0.00

$0.00

$0.00

$41.86

$464.78

$100.00

$564.78

Sensor

$174.00

$368.78

$0.2394

$0.399

$0.691

$0.366

$0.74

$0.012

$4.00

$7.06

$0.00

$0.00

$0.00

$0.00

$0.00

$50.00

$26.00

250

250

250

,000

,000

,000

,000

,000

N/A

N/A

N/A

N/A

N/A

5.5%

1,000

3,000

$0.24

$0.80

$0.69

$0.73

$1.48

$0.02

$4.00

$7.06

$0.00

$0.00

$0.00

$0.00

$0.00

$15.02

$272.08

$50.00

$322.08

$78.00

$152.08
23

Appendix A C Program for Selecting Compensating Resistor Pairs

The following software is available via anonymous/ijp at "andreas.wr.usgs.gov" in file 

~ftp/pub/outgoing/evans/OFR_98_109/pick_resistors_ts.c.

PICK_RESISTORS_TS()

Given a target resistance, pick resistors for a network of either 

one parallel pair ("-p", the default) or one series pair ("-s") 

from the 1% metal-film resistors IN THE TREMOR/SOS STOCK to match 

the desired value as closely as possible. Schematic:

 * Rl *__________

| | == R (DEFAULT) 

* R2 *

* OR

 * Rl * R2 * == R 

Simply searches ALL available permutations for the best match, 

ignoring issues of precision. First searches single-resistor 

solution, then two-resistor solutions, returning whichever is 

better (i.e., a more precise match).

USAGE: pick_res_ts [-p | -s] < R_in_0hms . . . > result_file 

AUTHOR: JREvans, USGS, January 14, 1997. 

DEBUG:

dbxtool -I . sun4/pick_res_ts

stop in main

*

* RUNS:

*

/bin/rm -f Rz*.out

pick_res_ts -s < Rztcl.in > Rztcl.out 

pick_res_ts -s < Rztc2.in > Rztc2.out 

pick_res_ts -p < Rzbl.in > Rzbl.out

pick_res_ts -p < Rzb2.in > Rzb2.out

*

*/

#include <stdio.h>

#include <string.h>

#include <math.h>

#define streq Istrcmp

ttdefine TRUE 1

ttdefine FALSE 0

ttdefine PARALLEL 0

ttdefine SERIES 1

ttdefine PAR_VAL(R1, R2) ( (double) 1.0 / (( (double) 1.0 / ( (double) Rl) ) + ( (double) 1.0 / ((double)R2) )) )

ttdefine SERVAL(R1, R2) ( ((double)Rl) + ((double)R2) )
#define

#define

/*

24

FRAC_ERR(R1, R2) ( fabs( (double)1.0 - ((double)R1 / (double)R2) ) ) 

TOLERANCE ((double)0.005) /* Acceptable Fractional error */

* The TREMOR/SOS stock of 1% (50 ppm temperature sensitivity) metal-film

* resistors (mainly at 2% intervals). This stock is in Room 8B03. A

* few higher values available only from the CalNet (200 ppm) stash.

*/

/* In Ohms */

#define NJTABLE (312)

static double r_table[NJTABLE] = {

/* TREMOR/SOS special buys: */

0.0, 1.00, 1.47,

/* TREMOR/SOS dense stash (mainly for Rzb[12]): */ 

4.02, 4.75, 10, 10.2, 10.5, 10.7, 11, 11.3, 11.5, 11.8, 12, 12.1, 

12.4, 12.7, 13, 13.3, 13.7, 14, 14.3, 14.7, 15, 15.4, 15.8, 16, 

16.2, 16.5, 16.9, 17.4, 17.8, 18, 18.2, 18.7, 19.1, 19.6, 20, 20.5, 

21, 21.5, 22, 22.1, 22.6, 23.2, 23.7, 24, 24.3, 24.7, 24.9, 25.5, 

26.1, 26.7, 27, 27.4, 28, 28.7, 29.4, 30, 30.1, 30.9, 31.6, 32.4,

/* TREMOR/SOS light stash: */

33, 33.2, 34, 36, 39, 43, 47, 51, 56, 59, 62, 68, 75, 82, 88.7, 

100, 110, 120, 130, 140, 150, 165, 180, 200, 220, 240, 270, 300, 

330, 350, 390, 430, 470, 510, 560, 590, 620, 680, 750, 820, 910, 

1000, 1100, 1200, 1300, 1400, 1500, 1600, 1800, 2000, 2200, 2400, 

2700, 3000, 3300, 3600, 3900, 4320, 4700, 5100, 5600, 5900, 6200, 

6800, 7500, 8200,

/* TREMOR/SOS dense stash (mainly for anti-alias filters): */ 

8800, 8870, 9090, 9100, 9310, 9530, 9760, 10000, 10200, 10500, 

10700, 11000, 11300, 11500, 11800, 12000, 12100, 12400, 12700, 

13000, 13300, 13700, 14000, 14300, 14700, 15000, 15400, 15800, 

16000, 16200, 16500, 16900, 17400, 17800, 18000, 18200, 18700, 

19100, 19600, 20000, 20500, 21000, 21500, 22000, 22100, 22600, 

23200, 23700, 24000, 24300, 24900, 25500, 26100, 26700, 27000, 

27400, 28000, 28700, 29400, 30000, 30100, 30900, 31600, 32400, 

33000, 33200, 33600, 34000, 34800, 35700, 36000, 36500, 37400, 

38300, 39000, 39200, 40200, 41200, 42200, 43000, 43200, 44200, 

45300, 46400, 47000, 47500, 48700, 49900, 51000, 51100, 52300, 

53600, 54900, 56000, 56200, 57600, 59000, 60400, 61900, 62000, 

63400, 64900, 66500, 68000, 68100, 69800, 71500, 73200, 75000, 

76800, 78700, 80600, 82000, 82500, 84500, 86600, 88700, 90900, 

91000, 93100, 95300, 97600, 100000, 102000, 105000, 107000, 

110000, 113000, 115000, 118000, 120000, 121000, 124000, 127000, 

130000, 133000, 137000, 140000, 143000,

/* TREMOR/SOS light stash: */

150000, 160000, 180000, 200000, 220000, 240000, 270000, 300000,

330000, 340000, 360000, 390000, 430000, 470000, 511000, 560000,

590000, 620000, 680000, 750000, 820000, 909000,

1000000, 1500000, 2200000,

/* CalNet stash: */

1100000, 1300000, 1430000, 1580000, 1700000, 1760000, 1900000, 

1910000, 2150000, 2430000, 2610000, 2870000, 4750000, 5230000, 

5900000, 8060000, 8250000, 10500000, 21000000

void stash(); 

main(argc, argv)

/* Defined below */
25

int argc; 

char **argv;

int ii, jj, geometry;

double R, Rnow, Rbest;

double Rl, R2, Rlbest, R2best;

(void) printf ("\nMainly from TREMOR/SOS stashes of 1%% resistors in Room 8B03.\n"); 

( void) print f (" (Some higher values are only in the CalNet stash in Room 7B25.)\n");

if (argc >= 2 ) {

if (streq(argv[l] , "-s"))

geometry = SERIES; 

else if (streq(argv[l] , "-p"))

geometry = PARALLEL; 

else

geometry = PARALLEL;

/* Reproduce schematic */

if (geometry == PARALLEL) {

(void) printf ("\nParallel pair: \n") ;

( void) printf (" * Rl * \n") ;

( void) printf (" | l\n");

( void) printf (" * R2 *\n\n") ; 

} else {

(void) printf ( "\nSeries pair: \n") ;

(void) printf (" * Rl * R2 * \n\n") ;

/* Solve */

while (scanf ("%lf", &R) != EOF) {

(void) printf ("For %.21f Ohms:\n", R) ; 

( void) printf (" \n") ;

/* ***************************************** */ 

/* First find best SINGLE-resistor match ... */

Rbest = r_table[0];

Rlbest = r_table[0];

R2best = (double) 0.0; /* flag as "null" */

for (ii = 1 ; ii < NJTABLE ; ii++) { 

/* Test fractional error */ 

if (FRAC_ERR(r_table[ii] , R) < FRAC_ERR (Rbest, R) ) {

Rbest = r_table[ii];

Rlbest = r_table[ii];

/* ****** ************************************ */

/* ... then permute over all available PAIRS. */ 

for (ii = 0 ; ii < N_TABLE ; ii++) { 

for (jj = ii ; jj < N_TABLE ; jj

if (geometry == PARALLEL)

Rnow = PAR_VAL (r_table [ii] , r_table [ j j ] ) ; 

else

Rnow = SER VAL(r table [ii], r tablet jj]);
26

/* Test fractional error */

if (FRAC_ERR(Rnow, R) < FRAC_ERR(Rbest, R)) {

Rbest = Rnow;

Rlbest = r_tabletjj];

R2best = r_table[ii] ;

/* Return result */

(void) printf ("Rl = %.21f Ohms", Rlbest); 

(void) stash (Rlbest) ;

if (R2best == (double)O.O)

if (geometry == PARALLEL)

( void) print f("R2 = Open (Inf Ohms)\n"); 

else

( void) printf ("R2 = Short (0 Ohms)\n"); 

else {

( void) print f("R2 = %.21f Ohms", R2best) ; 

(void) stash (R2best) ;

if (geometry == PARALLEL)

( void) printf (" PARALLEL \n") ; 

else

(void) printf (" SERIES \n") ;

(void) printf ("Yields % . 21f Ohms . \n", Rbest);

(void) printf ("Error = %.21f Ohms (%.21f%%)",

Rbest - R, (double)lOO. * FRAC_ERR( Rbest, R) ) ;

if (FRAC_ERR (Rbest, R) > TOLERANCE)

(void) printf (" \t***ERROR OVER % . llf %%***\n\n\n", 

TOLERANCE * (double) 100 .);

else

(void) printf ( " . \n\n\n" ) ;

exit (0) ;

void 

stash (RR)

double RR; 

{

if ( (RR <= (double) 32. 4)

|| (RR >= (double)8800. && RR <= (double) 143000 .) 

) 

( void) printf (" \t(T/S dense collection) \n") ;

else if ( (RR >= (double) 33. && RR <= (double) 8200 .)

M (RR >= (double) 150000. &.& RR <= (double) 1000000 .) 

| | (RR == 1500000) 

I | (RR == 2200000) 

) 

( void) printf (" \t(T/S sparse collection) \n") ;

else

( void) printf (" \t(CalNet main collection) \n") ;
27

Appendix B C Program for Computing Temperature from NTC Thermistor

The following software is available via anonymous/#i at "andreas.wr.usgs.gov" in file 

~ftp/pub/outgoing/evans/OFR_98_l 09 /Thermistors.c.

/*

* YSI 44031 thermistor using their test points at 0, 25, and 40 C from

* "Temperature Sensors and Probes, 1993, p. 11 and their algorithm on p.

* 74 (their BASIC program, but done on HP calculator).

*

* MAKE: make -f Makefile.Thermistors install

*

* USAGE: Thermistors [-v | -mv] [-RO non_default_RO_in_Ohms]

* < file_of_measurements > file_of_temperatures

*

* Argument interpreter is stupid the order of the arguments is

* NOT flexible.

*

* If "-v" option, file_of_resistances contains VOLTAGES measured by

* final-design (17 Jan 97) circuit with 49.8K RO and 2.50 Vref. If

* "-mv", assumes millivolts rather than volts, and makes a terse output

* of only the equivalent Celsius temperature. Hence, "-mv" makes a

* simple filter to change Lawson data to temperature. If neither "-mv"

* nor "-v", assumes values are resistances in Ohms.

*

* If "-RO" (note zero, not letter 0) then the reference resistance

* is changed from 49.8K to what is given in the next argument.

*

* J.R.Evans, USGS, Menlo Park. Last modified 21 May 97.

*/

#include <stdio.h> 

tfinclude <math.h>

tfdefine R0_dflt ((double)49800.0) /* in series with thermistor */

#define Vref ((double)2.50) /* across series pair */

main(argc, argv)

int argc;

char *argv[]; 

{

double temperature, resistance, voltage, Ir, degF, RO;

double aa = 1.034034113e-03; 

double bb = 2.383800240e-04; 

double cc = 1.592455177e-07;

RO = R0_dflt;

while (scanf("%lf", &resistance) == 1) {

/* If reference resistance is not the default */ 

if (argc >= 3 && !strcmp("-RO", argv[l]))

RO = atof(argv[2]); 

if (argc >= 4 && !strcmp("-RO", argv[2]))

RO = atof(argv[3]);

/* If really a voltage, compute resistance */ 

if (argc >= 2 && !strcmp("-v", argv[l])) { 

voltage = resistance;
28

resistance = voltage * RO / (Vref - voltage) ; 

printf ("V = %.llf mV > ",

(double) 1000. * voltage);

/* If really an mV voltage, compute resistance */ 

if (argc >= 2 && ! strcmp ( "-mv", argvfl])) {

voltage = resistance / (double) 1000. ;

resistance = voltage * RO / (Vref - voltage) ;

/* Now digest a resistance */

Ir = log (resistance) ; 

temperature = (double) 1.0 /

( aa + bb * Ir + cc * Ir * Ir * Ir ) ; 

temperature = temperature - (double) 273 . 15; 

degF = 32.0 + (temperature * 9.0 / 5.0);

if (argc >= 2 && ! strcmp ( "-mv" , argv[l]))

printf ( "% . 3 If \n", temperature) ; 

else

printf ("R = %.01f ohms > T = %.21f C, %.21f F\n", 

resistance, temperature, degF) ;

exit (0) ;
29

Appendix C C Program for Computing Filter Component Values

The following software is available via anonymous ftp at "andreas.wr.usgs.gov" in file 

~ftp/pub/outgoing/evans/OFR_98_l 09 /biquad.c.

Use the method of Johnson, Johnson, and Moore, A Handbook of 

Active Filters, Prentice-Hall, 1980, to tune an 8th-order (gain=l) 

Butterworth low-pass filter, given imperfect (5%) capacitors 

near their ideal values. (Reverse their naming of Cl and C2. 

Than is, "Cl" < > "C2". Also move their stage 1 (A) to my 

stage C since it is high-Q and can clip.)

USAGE: biquad > out_file (and answer questions) 

AUTHOR: JREvans, USGS, Menlo Park, 12Dec96.

#include <stdio.h>

#include <math.h>

#define BstageA

#define BstageB

#define BstageC

#define BstageD

#define CstageA

#define CstageB

#define CstageC

#define CstageD

({double)!.111140) 

((double)1.662939) 

((double)0.390181) 

((double)1.961571)

((double)1.000000) 

((double)1.000000) 

((double)1.000000) 

((double)!.000000)

ttdefine MICRO ((double)0.000001) 

tfdefine KILO ((double)1000.0)

main() 

{

double BB[4]; 

double CC[4];

double fcorner, wcorner; 

double Cl, C2, Rl, R2;

char sn[128];

int ii;

char stage[4];

int aka[4]; /* decade portion of new part name

while(1) {

BB[0] = BstageA;

BB[1] = BstageB;

BB[2] = BstageC;

BB[3] = BstageD;

CC[0] = CstageA;

CC[1] = CstageB;

CC[2] = CstageC;

CC[3] = CstageD;

stage [0] = 'A 1 ; aka[0] = 2;

stage[1] = 'B 1 ; aka[l] = 3;
30

stage [2] = 'C f ; aka[2] = 4; 

stage [3] = 'D f ; aka[3] = 5;

fprintf (stderr, "Give serial number: ") ; 

if (gets(sn) == NULL)

break; 

printf("\n \nSerial number: \"%s\".\n", sn) ;

fprintf (stderr, "Give corner frequency (Hz): ");

scanf("%lf", Sfcorner) ;

wcorner = (double) 6. 283185308 * f corner; /* 2*pi */

printf("Gain 1 eight-pole Butterworth lowpass, corner at %.21f Hz:\n", 

fcorner) ;

for(ii = 0 ; ii < 4 ; ii++) {

fprintf (stderr, "Give Cl (preferably near %.31f uF) : ",

10. 0 / fcorner) ; 

scanf("%lf", &C1); 

Cl = Cl * MICRO;

fprintf (stderr,

"Give C2 (MUST be <= %.51f uF, preferably the largest): ", 

(BB[ii] * BB[ii] * Cl) / (double) 4.0 / MICRO); 

scanf("%lf", &C2); 

C2 = C2 * MICRO;

Rl = (double) 2.0 / ( 

wcorner * (

BB[ii] * Cl + 

sqrt (

BB[ii] * BB[ii] * Cl * Cl - 

(double) 4.0 * CC[ii] * Cl * C2

R2 = (double) 1.0 / (

CC[ii] * Cl * C2 * Rl * wcorner * wcorner

printf ("\nCl%c (C%ldl) = %.51f uF, ",

stage [ii], aka[ii], Cl / MICRO); 

printf ("\tRl%c (R%ldl) = %.31f K0hms.\n",

stage[ii], aka[ii], Rl / KILO); 

printf ("C2%c (C%ld2) = %.51f uF, ",

stage [ii], aka[ii], C2 / MICRO); 

printf ("\tR2%c (R%ld2) = %.31f K0hms.\n\n",

stage[ii], aka[ii], R2 / KILO);

/* Clear input buffer to NEWLINE */ 

(void) gets (sn) ;