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B�K ���� Accelerometer

and Charge Ampli�erManual

L� VicciMicroelectronic Systems LaboratoryDepartment of Computer Science

University of North Carolina at Chapel Hill��Jan���

Summary

The Br�uel�Kj�r ���� is a single axis piezoelectric accelerometersensitive along its Z axis down to nearly ���g� and conventionally use�ful over a range of � �Hz up to about ��� of its mechanical resonancefrequency of �����kHz� depending on its mounted con�guration Thecharge available on its output is proportional to acceleration sensed bythe device �including gravity� To be useful� this charge must be inte�grated by a charge ampli�er to provide a voltage proportional to accel�eration The overall low frequency performance depends on the limitingnoise �oor and frequency response of the charge ampli�er

A charge ampli�er was designed speci�cally for extending the usefullow end of the frequency range of the ���� to � ��Hz� and to provideanti�alias �ltering for adequately suppressing frequencies at the mechan�ical resonance of the accelerometer This �lter is a �fth order Cauer�lter with zeros in the stop band to cancel the mechanical resonance It provides a �at frequency response to its upper �dB cuto� frequencyat � �kHz and guarantees at least ��dB anti�alias suppression of allacceleration stimuli above ��kHz

This report comprises a user manual for the accelerometer andcharge ampli�er kit� a theory of operation section� and an appendixcontaining the design drawings Casual users need not delve furtherthan the user manual� although the theory of operation provides moredetailed technical insights which will be useful to the more serious user The design drawings along with the theory of operation are intendedto be su�ciently detailed for anyone skilled in the art to adapt andconstruct the charge ampli�er design for other accelerometers

TR������ UNC Chapel Hill� Department of Computer Science page �

L Vicci B�K ���� Accelerometer and Charge Ampli�er Manual ��Jan���

� User Manual

The accelerometer and charge ampli�er �Charge Amp� are provided as a completekit� and should always be kept together The special coaxial cable provided to connect theaccelerometer to the charge ampli�er is a calibrated component with microdot connectorswhich will not mate with any of the standard connector families To encourage keepingthe kit together� a convenient carrying case is provided A usage synopsis is posted on theinside of the case

Figure �� Kit consists of an accelerometer�a cable� a charge ampli�er �shown with bat�tery installed�� and a carrying case

Use of the kit is straightforward Allthat�s necessary is to power the Charge Amp�mount the accelerometer on the device undertest �DUT�� connect them together and toa data acquiring instrument such as a DAQcard or oscilloscope� and set the gain and lowfrequency cuto� switches

To power the Charge Amp� a ��volt bat�tery should be snapped into the front panelreceptacle To prevent damage from batteryleakage� the Charge Amp should never

be stored with the ��volt battery in�

stalled� The external battery access featureis intended to make it convenient to observethis rule Also please note the polarity of thesnap connectors and do not attempt to install the battery backwards

The accelerometer should be mounted to the device under test �DUT� using eithera ����� fastener or double backed adhesive tape Under no circumstances should

the fastener be forcibly threaded into the accelerometer� Slightly over two com�plete turns is the maximum thread depth in the ���� The manufacturer�s recommendedmounting techniques for threaded fasteners and alternatives are excerpted from B�K��and shown here as Figures �a and �b

The charge ampli�er should be set for the desired gain and low frequency cuto� Beaware that the lower frequency ranges may take a long time to settle� over a minute forthe � ��Hz range Settling can be hastened somewhat by brie�y switching to a higherfrequency range and back� but it will still take some time Even when completely settled�there is a residual DC error voltage of a few millivolts If very high accuracy is desired�this should be measured and subtracted from subsequent data

The output voltage range of the Charge Amp is nominally ����V Depending onbattery voltage� the output will clip at ����V or less If the Charge Amp is overloadedto clipping� its DC o�set will be upset and must be allowed to re�settle before meaningfulmeasurements can be made The remedy for this is either to use a less sensitive gain rangeso that overload does not occur� or to use a low cuto� range that settles acceptably quicklyafter an overload

The noise �oor of the Charge Amp is on the order of ����Vrms on all ranges Onthe most sensitive range� this corresponds to an acceleration noise �oor of approximately����g As of this writing� these measurements are very approximate� and need to be

TR������ UNC Chapel Hill� Department of Computer Science page �

L Vicci B�K ���� Accelerometer and Charge Ampli�er Manual ��Jan���

Figure �a� Mounting techniques excerpted from B�K��

quanti�ed more carefully if the kit is to be used at sensitivities where this is an issue The upper cuto� frequency� or �dB rollo� point of the Charge Amp�s passband is

nominally � �kHz In the stopband� a special rejection band is provided to suppress theresonance peak of the accelerometer over the range of �����kHz in which it can occur This provides at least ��dB anti�alias �ltering for all mechanical excitation above ��kHz�

TR������ UNC Chapel Hill� Department of Computer Science page �

L Vicci B�K ���� Accelerometer and Charge Ampli�er Manual ��Jan���

Figure �b� Alternative techniques excerpted from B�K��

irrespective of the accelerometer resonance Refer to page �� of the design drawings fordetailed response curves� as simulated by SPICE

The output of the charge ampli�er will drive any single�ended instrument inputimpedance of � ��� through a conventional BNC cable It should be relatively insensi�tive to ground loops between the accelerometer and the driven instrument However careshould be taken to prevent the Charge Amp box from electrically contacting anything�as ground loops between the accelerometer and the Charge Amp itself can cause noiseproblems The Charge Amp is furnished with rubber feet to help provide the necessaryelectrical isolation

TR������ UNC Chapel Hill� Department of Computer Science page �

L Vicci B�K ���� Accelerometer and Charge Ampli�er Manual ��Jan���

� Charge Amp Theory of Operation

The Charge Amp is logically composed of �ve functional blocks and a power manage�ment block Referring to Figure �� these are the charge integrating preampli�er preamp�two stages of anti�alias �lter cauer� and cauer�� an integrating feedback circuit dcfb� anoutput driver di�out� and power management pwrgnd Also shown is an electrical modeltdcr of the accelerometer in which the acceleration stimulus is represented by voltage Va

TITLE

B&K 4370 Charge amplifierDESCRIPTION

Charge amplifier, 10[mHz] to 10[kHz]with SPICE nodes and subckts shown

DRAWN BY Leandra Vicci

DATE 30 Dec, 2002

MSLSHEET 1 OF 15SCALE 1: 1.5

DWG NO

REV 4.0

SIZE

A

Va

U2U1 U3 U4C0

Vp

Vn pwrgnd

U50

B1

dcfb

R5

R6n

R0m 5out

0

U1b

R1mR2mC2in234

U2a

R3R467

tdcr

Cp

Csain 0

qout

diffout

U2b

R1 R2

R3

R4

in 1

out

2com

0

C2

C4

preamp

U1a

C0n

sum

out

0

in

R1

cauer1

R2

R3R4

R6

R1

U3a

U3b

+

-

-+

C5

C1

1

2

3

4

in

out

0

C4 C3

cauer2

R2

R3R4

R6

R1

U4a

U4b

+

-

-+

C5

C1

1

2

3

4

in

out

0

C4 C3

Notes:1. R6 and C0 are gang switchable for three gain ranges.2. R1, R2, and R0 are gang switchable for four low cutoff points.

Figure �� Charge Amp schematic showing SPICE subcircuits

��� pwrgnd

The Charge Amp uses a single ��volt battery� and needs to have a local ground refer�ence� preferably midway between the positive and negative power rails This is generatedby U�� a TLE���� Virtual Ground Generator This local virtual ground is connected tothe instrument�s case and through the connecting cable to the body of the ���� It istherefore important not to allow a ground loop to be established between the ���� and theCharge Amp The Charge Amp has insulating rubber feet to isolate it from its supportingsurface

TR������ UNC Chapel Hill� Department of Computer Science page �

L Vicci B�K ���� Accelerometer and Charge Ampli�er Manual ��Jan���

��� di�out

Ground loop noise between the Charge Amp and the instrument it drives is howeversuppressed U�b is embedded in a di�erential ampli�er con�guration which isolates thelocal ground from the output common This prevents a ground loop from occurring betweenthe Charge Amp and the driven instrument The amount of ground noise suppressiondepends on the CMRR of the di�erential con�guration of di�out which should approach��dB

��� tdcr

The resonance of the ���� is not explicitly modeled here� but the acceleration stimulus�including gravity� is represented by Va Changes in Va cause a charge transfer through thetranscapacitance element Cs Parallel capacitance Cp comprises the parasitic capacitanceof the ���� and its connecting cable The transcapacitance gain was chosen to match themanufacturer�s sensitivity data so that Va � �V represents an acceleration of �m�s� Note that this is strictly a simulation model

��� preamp

This is the integrating ampli�er which transduces charge to voltage The transelas�tance gain is the reciprocal of capacitance C� The preamp also provides one real poleto the �fth�order anti�alias �lter The frequency of this pole is established by R� and theparallel combination of Cs and Cp Gain ranges are implemented with switch selectablecapacitances of �� ��� and ���nF for C� Operation at very low frequency requires anampli�er with a low noise �oor as well as very low bias current U� is a TLC����C duallow�noise precision op amp implemented in TI�s LinCMOS technology� with �pA typicalbias current and ��nV�

pHz at ��Hz �in the ��f noise regime� TI��a

�� cauer� and cauer�

Each of these circuits provides two complex poles and two complex zeros to the anti�alias �lter These poles along with one real preamp pole implement a �fth order lowpass Butterworth function The four complex zeros provide the desired signal suppressionover the frequency range of �� �kHz through �� �kHz to cancel out the ���� resonance Refer to pages ����� of the design drawings for a quantitative comparison �� �kHz isthe resonance of the ���� mounted on a very large DUT mass� while �� �kHz is theresonance of the unmounted device The circuits themselves are nullor realizations ofgeneralized impedance converter �GIC� derived biquadratic functions Chen��

�� dcfb

This circuit sets the low frequency cuto� of the Charge Amp In combination withthe accelerometer transfer function and the preamp transelastance� it implements a crit�ically damped second order high pass �lter function �that is� second order Butterworth� This function has two DC zeros and a pair of complex conjugate poles which set the cut�o� frequency This provides a ��dB�decade rollo� below the switch selectable cuto�frequencies of ��� �� � �� and � ��Hz �see page �� of the design drawings�

TR������ UNC Chapel Hill� Department of Computer Science page �

L Vicci B�K ���� Accelerometer and Charge Ampli�er Manual ��Jan���

The dcfb circuit itself synthesizes the equivalent of a parallel RL circuit which isconnected across C� in the preamp Accounting for the combined DC gain A of the Cauer�lter sections we have�

R �R�R�R�

AR�R�

� L �R�R�R�C�

AR�

The equivalent feedback impedance of the preamp circuit is then�

Z� ��

���ZRL � sC���

C�

s

s� � s����Q�� � ��

� where

Q� �RpL�C�

sR�R�R�C�

AR�

�R�C�

� and

�� ��pLC�

rAR�

R�R�R�C�C�

The �lter poles come from the denominator of Z�� with the cuto� frequency determinedby �� and the damping factor by Q� These parameters are highly underconstrained inthat the number of determining component values �degrees of freedom� is large Compo�nent values were chosen to implement the desired low cuto� for the various ranges whileproviding the desired Butterworth function for each range

References

B�K�� Product Data � Piezoelectric DeltaShear Accelerometers Uni�Gain� Delta�Tron and Special Types�! http�www�bksv�compdfBp����pdf�Br�uel�Kj�r� October ��� ����

Chen�� Wai�Kan Chen� Ed � The Circuits and Filters Handbook�! CRC Press� �����ISBN �������������� pp ���������

TI��a Texas Instruments Data Book� !Ampli�ers� Comparators� and Special Func�tions�! Texas Instruments� ����� SLYD���A� vol A� pp ������

TI��b Texas Instruments Data Book� !Ampli�ers� Comparators� and Special Func�tions�! Texas Instruments� ����� SLYD���A� vol B� pp ������

APPENDIX A � Design drawings

The following are the design drawings of the as�built Charge Amp

TR������ UNC Chapel Hill� Department of Computer Science page �

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IFIE

R F

OR

B&

K43

70

TIT

LE

B&

K 4

370

Cha

rge

ampl

ifier

DE

SC

RIP

TIO

N Cha

rge

ampl

ifier

, 10[

mH

z] to

10[

kHz]

Fro

nt p

anel

labe

lD

RA

WN

BY

Lean

dra

Vic

ci

DA

TE

30 D

ec, 2

002

MS

LS

HE

ET

9 O

F 1

5S

CA

LE1:

1

DW

G N

O

RE

V4.

0

SIZ

E A

TIT

LE

B&

K 4

370

Cha

rge

ampl

ifier

DE

SC

RIP

TIO

N Cha

rge

ampl

ifier

, 10[

mH

z] to

10[

kHz]

Car

ryin

g ca

se a

nd w

arni

ng l

abel

sD

RA

WN

BY

Lean

dra

Vic

ci

DA

TE

30 D

ec, 2

002

MS

LS

HE

ET

10 O

F 1

5S

CA

LE1:

1

DW

G N

O

RE

V4.

0

SIZ

E A

B&

K43

70 A

CC

EL

ER

OM

ET

ER

AN

D C

HA

RG

E A

MP

LIF

IER

KIT

Mic

roel

ectr

on

ic S

yste

ms

Lab

ora

tory

, Dep

artm

ent

of

Co

mp

ute

r S

cien

ce, U

NC

CH

INS

TR

UC

TIO

N S

UM

MA

RY

• In

stal

l 9-v

olt

bat

tery

.•

Mo

un

t ac

cele

rom

eter

an

dco

nn

ect

to c

har

ge

amp

lifie

r.•

Co

nn

ect

BN

C c

on

nec

tor

to a

sco

pe

or

oth

er in

stru

men

t.•

Up

per

cu

toff

fre

qu

ency

is6.

8[kH

z]. P

LE

AS

E D

O•

Sto

re a

ll p

arts

of

kit

tog

eth

er.

DO

NO

T•

Sto

re w

ith

bat

tery

inst

alle

d.

• In

sert

fas

ten

er m

ore

th

an 2

turn

s in

to a

ccel

ero

met

er.

Larg

est d

iago

nal 1

.175

Larg

est h

t 0.6

68la

rges

t wd

1.03

8

+

-0.

668

(0.6

5)

1.03

8 (1

.025

)

1.81

3 (1

.70)

0.12

5

TIT

LE

B&

K 4

370

Cha

rge

ampl

ifier

DE

SC

RIP

TIO

N Cha

rge

ampl

ifier

, 10[

mH

z] to

10[

kHz]

9-vo

lt ba

ttery

DR

AW

N B

YLe

andr

a V

icci

DA

TE

31 D

ec, 2

002

MS

LS

HE

ET

11 O

F 1

5S

CA

LE2:

1

DW

G N

O

RE

V4.

0

SIZ

E A

TIT

LE

B&

K 4

370

Cha

rge

ampl

ifier

DE

SC

RIP

TIO

N Cha

rge

ampl

ifier

, 10[

mH

z] to

10[

kHz]

Circ

uit p

hoto

s, to

p an

d bo

ttom

DR

AW

N B

YLe

andr

a V

icci

DA

TE

16 J

an, 2

003

MS

LS

HE

ET

12 O

F 1

5S

CA

LE1:

1

DW

G N

O

RE

V4.

0

SIZ

E A

No

te: C

42 a

nd C

44 w

ere

adde

daf

ter

thes

e ph

otos

wer

e ta

ken.

-180

-160

-140

-120

-100-80

-60

-40

-200

1[m

Hz]

10[m

Hz]

100

[mH

z]1

[Hz]

10 [Hz]

100

[Hz]

1[k

Hz]

10[k

Hz]

100

[kH

z]1

[MH

z]F

requ

ency

SP

ICE

sim

ulat

ion

of C

harg

e A

mpl

ifier

res

pons

e cu

rves

for

G1k

= 1

00 [m

V/m

/s2 ]

Gain [db(V/m/s2)]

flo = 10 [Hz]

flo = 1 [H

z]

flo = 100 [mHz]

flo = 10 [mHz]

TIT

LE

B&

K 4

370

Cha

rge

ampl

ifier

DE

SC

RIP

TIO

N Cha

rge

ampl

ifier

, 10[

mH

z] to

10[

kHz]

SP

ICE

sim

ulat

ions

of a

s de

sign

ed c

ircui

tD

RA

WN

BY

Lean

dra

Vic

ci

DA

TE

17 J

an, 2

003

MS

LS

HE

ET

13 O

F 1

5S

CA

LE1:

1

DW

G N

O

RE

V4.

0

SIZ

E A

G1k

= 1

00 [m

V/m

/s^2

]

-100-9

0

-80

-70

-60

-50

-40

-30

-20

-10

Fre

quen

cy

-140

-130

-120

-110

1m

Hz

10 mH

z10

0m

Hz

1 Hz

10 Hz

100

Hz

1kH

z10 kH

z10

0kH

z1

MH

z

G1k

= 1

0 [m

V/m

/s^2

]

G1k

= 1

[mV

/m/s

^2]

Gain [db(V/m/s2)]S

PIC

E s

imul

atio

n of

Cha

rge

Am

plifi

er r

espo

nse

curv

es fo

r F

lo =

10

[mH

z]

TIT

LE

B&

K 4

370

Cha

rge

ampl

ifier

DE

SC

RIP

TIO

N Cha

rge

ampl

ifier

, 10[

mH

z] to

10[

kHz]

SP

ICE

sim

ulat

ions

of a

s de

sign

ed c

ircui

tD

RA

WN

BY

Lean

dra

Vic

ci

DA

TE

17 J

an, 2

003

MS

LS

HE

ET

14 O

F 1

5S

CA

LE1:

1

DW

G N

O

RE

V4.

0

SIZ

E A

+ 40

dB

+ 30

+ 20

+10

0

-10

Calibration Chart for Accelerom..., Type 4370

j Serial no .... BZ.l R .Q.Q ....... . --A......_ '-ltMty at ...... S.Q .... Hut ... .:1.~ ...... °C

Cllllle c.ecltance ~f .....•.... ..1./.0 ....................... pF

c ..... leneivitv••

......... }t,/Ua .... pC/ms-2.or ........... <-t.l,k .... pC/g"

V .... leMitivity••

............ ~.2. ... mV/ms-2,or .......... R.f,.fi ..... mV/g

~ .... _(including cablel ............. U.'-8. . ...... pF

Maximum Tranaveraa Sanaitivity at 30Hz ... .'!I,D ... %

Weltht ............... 5.'-f,.O ....... grams

Unc~Mnped natural frequency ........... 2.1, ........... kHz For mountacl Reaonant Frequency and for Frequency Reapoi'IH relative to Reference Sensitivity .... at­tachacl individual Frequency R81P0fl88 Curve

Polerity is poeitive =center of the c:qn_nector for an acceleration dir from lhe mounting surface into the body of the terom«er.

Realatence minimum 20000Mn~ room temperature.

Date .2:-.J.a.~.-u ... Signa._. ......... ::r;; ................ . • 1 g • 8,B07 ms-'-2

•• This calibration is traceable to the National Bureau of Standards Washington D.C.

IIC 01!10

pate: Potentiometer:

)0 500 1 kHz 2 5

Typical Temperatura Seneltivity Error in dB rei. the Reference Values Individual deviation max. ± 1 dB

-d•'o1----s~o--~1+oo~~150~---2oo~--~250~--~3oo~•c 32 122 212 302 312 482 572°F

Phy8ical: 79o39l

!:~ Material: Stainless Steel W-, IIi'­

I Mounting Thread: 10-32 UNF-2B

Electrical Connector: Coaxial 10-32 UNF-2A thread

Environmental: Humidity: Seaied Max. Temperature: 250"C or 4B2°F Max. Continuous Sinuaoidal Ace. (peakl:

20000ms-2or 2000g Max. Shock Acceleration: 50000 ms-2 or 5000 g Typical Magnetic Sensitivity (50 Hzl: f.2 m$-2/T or

0,012 g/kgauss Typical Temperature Transient Sensitivity:

(Low. Lim. Freq.: 3 Hzl O.OB ms-2;oc or O.OOB g/°C Typical Baee Strain Sensitivity:

0.003 ms-2/pstrafn or 0,0003 g/pstrain

For further information see B & K "Piezoelectric Accel­erometer and Preamplifier" Handbook.

Zero Level: D A 8 C Lin.

I

\

10 20 '- 50 100 n. Fr~.: ____ Hz Writing. Speed: ____ mm/~c. Paper Speed: ____ mm/sec.

{

·--

j I

:

-

-