52
PTB-Mi eilungen 125 (2015), No. 2Dynamic Measu emen o Mechanical Quan i ies
measu emen esul and an associa ed measu e-
men unce ain y has o be assigned o each
componen .
While such p ocedu es a e well es ablished o
s a ic measu emen s, he e a e no s anda dized
p ocedu es ye in he ield o dynamic measu e-
men s. The equi emen s o he dynamic calib a-
ion o b idge ampli ie s a e al eady included in
in e na ional s anda ds [4], al hough he e a e no
comme cially a ailable calib a ion de ices ye .
Cu en ly, s anda ds desc ibing he p ocedu es o
a dynamic calib a ion o condi ioning ampli ie s
a e unde de elopmen in na ional and in e na-
ional s anda diza ion wo king g oups, namely
he Ge man DKD Fachausschuss “K a und
Beschleuni gung” ( echnical commi ee on “Fo ce
and Accele a ion”) and he Wo king G oup 6 o
ISO TC 108/SC 3 “Use and calib a ion o ib a-
ion and shock measu ing ins umen s”. This will
emedy he cu en lack o alida ed p ocedu es
wi hin he o eseeable u u e.
The subsequen sec ion will p o ide an o e iew
o he cu en s a e o knowledge and will u he
gi e an ou line o wha is o be expec ed om he
u u e documen a y s anda ds.
2 Requi emen s
o Condi ioning Ampli ie s
In heo y, condi ioning ampli ie s should ha e no
in luence on he con en o he measu ed signal
in he equency ange o in e es and should only
con e he signal in he desi ed manne . Howe e ,
in eali y in luences o condi ioning ampli ie s
exis and need o be de e mined h ough p ope
calib a ion. In he ield o accele a ion measu e-
1 In oduc ion
Fo he dynamic measu emen o mechanical
quan i ies, he Eu opean esea ch p ojec T aceable
Dynamic Measu emen o Mechanical Quan i ies
wi hin he amewo k o he Eu opean Me o logy
Resea ch P og amme (EMRP) ocused on he
de elopmen o p ocedu es o aceable measu e-
men s o he quan i ies o ce, p essu e and o que
[1–3]. This Join Resea ch P ojec (JRP) conjoined
expe imen alis s and ma hema icians om nine
Eu opean Na ional Me ology Ins i u es (NMIs)
o esea ch on he measu ands o ce, p essu e and
o que. Fo dynamic measu emen s o any o hese
quan i ies, he espec i e senso ypically needs
o be complemen ed by a condi ioning ampli ie .
The e o e, hese ampli ie s we e included in he
esea ch wo k as a majo componen o he ace-
abili y chain.
The majo i y o measu emen s a e ca ied ou
wi h ansduce s ha ing a b idge-, cha ge- o
ol age ou pu . These di e en ypes o ou pu
signals need o be condi ioned in o de o be
digi ized by an analogue- o-digi al con e e o
u he p ocessing. Fo he condi ioning o he
signals, which may include he ampli ica ion, he
decoupling and he con e sion o quan i ies, signal
condi ioning ampli ie s – also called measu ing
ampli ie s – a e used. Bo h e ms will be used
synonymously in he subsequen ex . A ypical
measu ing chain ha consis s o a ansduce , an
ampli ie and a da a acquisi ion sys em (DAQ) is
depic ed in igu e1.
To ob ain aceable measu emen s, all compo-
nen s o he measu ing chain ha e o be calib a ed
and analysed ega ding hei in luence on he
Calib a ion o B idge-, Cha ge- and Vol age
Ampli ie s o Dynamic Measu emen Applica ions
Leona d Klaus*, Thomas B uns and Hen ik Volke s
* Leona d Klaus,
Wo king G oup
“Impac Dynamics”,
PTB, e-mail:
[email p o ec ed]
Rep in o he o iginal
A icle in Me ologia
52 (2015) 72–8,
DOI:10.1088/0026-
1394/52/1/72
Con en may be
used unde C ea i e
Commons (CC) 3.0
licence. Any u he
dis ibu ion o his
wo k mus main ain
a ibu ion o he au-
ho s and he i le o
wo k, jou nal ci a ion,
and DOI.
Figu e 1:
Measu ing chain consis ing o a ansduce , a measu ing
ampli ie and a da a acquisi ion sys em.
53
PTB-Mi eilungen 125 (2015), No. 2 Condi ioning Ampli ie s
men some expe ience in he dynamic calib a ion
o cha ge ampli ie s exis s. This knowledge has
now been ex ended o he de elopmen o calib a-
ion p ocedu es o a ious ypes o condi ioning
ampli ie s. Abo e all, he ollowing ypes o ampli-
ie s we e conside ed in he JRP and hence, in his
pape :
• Vol age ampli ie s
• Cha ge ampli ie s
• IEPE ampli ie s, and
• B idge ampli ie s.
In he ollowing pa ag aphs, he peculia i ies o
he di e en de ices a e b ie ly in oduced.
2.1 P ope ies o condi ioning ampli ie s
Real ampli ie s exhibi a equency-dependen
beha iou desc ibed by hei equency esponse
unc ion. This esponse may in u n depend o
some ex en on he p ope ies o he connec ed
sou ce ( ansduce ). These dependencies need o
be cha ac e ized by means o calib a ion. To be
able o calib a e a measu ing ampli ie , he de ice
should be linea and ime-in a ian (LTI).
Linea i y:
he ou pu scaling ac o should no depend on he
le el o he inpu signal o he ampli ie .
Time in a iance:
he equency esponse unc ion should no
change o e ime.
The assump ion o an LTI beha iou o condi ion-
ing ampli ie s is a p e equisi e o he applicabil-
i y o he calib a ion p ocedu es desc ibed in his
pape .
2.2 Di e en ypes o ampli ie s
used o dynamic measu emen s
2.2.1 Vol age ampli ie
Vol age ampli ie s a e used o condi ion inpu
ol ages o p opo ional ou pu ol ages. Two main
applica ions exis :
• Fo small inpu ol ages, ol age ampli ie s a e
used o signal ampli ica ion.
• They a e also used as uni y-gain ollowe s o
a decoupling o inpu and ou pu in case o
load-sensi i e ansduce ou pu s o o adap
he sou ce impedance o he connec ed da a
acquisi ion channel.
2.2.2 Cha ge ampli ie
These de ices a e used in conjunc ion wi h
piezo elec ic ansduce s o con e he cha ge
gene a ed by he ansduce o a p opo ional low
impedance ol age ou pu . The in e nal ci cui y
o he inpu s age o hese de ices ypically exhibi s
ei he high-pass cha ac e is ics, o d i beha iou ,
i he high pass is compensa ed o [5].
2.2.3 IEPE ampli ie
Piezoelec ic ansduce s may be supplied wi h
embedded in eg a ed elec onics (in eg a ed elec-
onic piezoelec ic, IEPE), which may be named
ICP®, Del a on®, Piezo on®, o simila , depending
on he manu ac u e . The speci ica ions o IEPE
ansduce s and hei powe supply a e no de ined
in a s anda d speci ica ion and may di e in de ail
om manu ac u e o manu ac u e . Howe e ,
he known ypes ollow a common p inciple. The
powe supply o such a ansduce is ealized using
a wo-wi e connec ion wi h a cons an cu en
eed. The ol age be ween he ails used o he
powe supply changes, depending on he measu ed
quan i y. I has a bias ol age le el o ypically 8V
o 12V, which co esponds o he ze o poin o
he measu ed quan i y. The ol age will change
p opo ionally o he measu ed quan i y in a ange
o ypically 0.5 V (minimum ol age, minimum
alue o he measu and) o 24 V (supply ol age,
maximum alue o he measu and). Besides he
cu en supply and he bias ol age le el, he
wo king p inciple o an IEPE condi ioning ampli-
ie is ela ed o ha o a ol age ampli ie used o
decoupling o inpu and ou pu .
2.2.4 B idge ampli ie
B idge ampli ie s a e used o he signal condi ion-
ing o he Whea s one b idge ou pu s o s ain
gauge o o piezo esis i e ansduce s. The ampli-
ie eeds he ansduce ’s b idge ci cui wi h a
supply ol age. The ol age ou pu o he b idge is
dependen on he de uning o he b idge’s esis-
o s and addi ionally p opo ional o he supply
ol age. The e o e, he ou pu o a ansduce
is a a iome ic quan i y and is usually gi en as
he a io o he b idge ou pu ol age and supply
ol age in mV/V. Fo co ec signal condi ioning,
b idge ampli ie s should implemen his a iome -
ic p inciple by no only aking he ou pu signal
o he ansduce in o accoun , bu by including
he supply ol age le el as well. I should be no ed
ha o he scope o he wo k de sc ibed he e, only
ampli ie s p o iding a DC supply ol age a e con-
side ed. So-called ca ie equency b idge ampli-
ie s a e ypically dedica ed o s a ic measu emen
exe cises and he e o e a e no discussed he e.
54
PTB-Mi eilungen 125 (2015), No. 2Dynamic Measu emen o Mechanical Quan i ies
Ca ie equency b idge ampli ie s can be used in
a equency ange o only abou 20 % o he ca ie
equency, which is usually below 5 kHz. E en
hen, de ia ions o mo e han 10 % in he magni-
ude esponse ha e o be aken in o accoun [6].
Fu he mo e, i should be no ed ha acco ding o
he common uni s o he inpu in mV/V and he
ou pu in V, he uni o he equency esponse
unc ion o hese de ices is, in ac ,
V
(mV/V)
.
3 P ocedu es o Dynamic Calib a ion
The goal o a calib a ion is he de e mina ion
o he p ope ies o in e es o he de ice unde
es (DUT) wi h a known measu emen unce -
ain y. Fo he condi ioning ampli ie , which can
p esum ably be desc ibed as an LTI sys em, he
p ope y o in e es is he equency esponse
unc ion.
3.1 F equency esponse unc ion
The complex- alued equency esponse unc ion
H (iω) desc ibes he ime-dependen inpu –ou pu
beha iou o an LTI sys em in he equency
domain o an angula equency ω = 2π , whe e
is he equency in Hz. Fo con inuous sys ems,
he equency esponse unc ion is de ined as he
a io o he ou pu Y (iω) o e he inpu X (iω) as
H(i )=
Y(i )
X(i ) .
(1)
I s magni ude A(ω) is gi en by
AH
HH
ωω
ωω
()
=
()
=
()
()
+
()
()
|i|i iRe Im
22
(2)
and desc ibes he con e sion and scale- o gain
ac o o he de ice. The phase esponse unc ion
φ(ω) is gi en by
ϕ
(
ω
)= an−1Im(H(i
ω
))
Re(H(i
ω
))
⎛
⎝
⎜⎞
⎠
⎟
(3)
and cha ac e izes he signal delay be ween inpu and
ou pu .
To de i e he phase angle om he complex
equency esponse unc ion, a ou -quad an
in e se angen calcula ion should be applied. I he
wo-quad an in e se angen calcula ion is used,
a co ec ion o φ o ± π may be necessa y as his
unc ion is only de ined in he ange −π/2<φ<π/2.
3.2 Exci a ion signal
The dynamic exci a ion o he measu ing ampli-
ie ’s inpu quan i y used o calib a ion can be
ca ied ou in di e en ways, e.g. by ansien ,
andom noise o pe iodic exci a ion signals. The
mos commonly used exci a ion signal is he mono-
equen sinusoidal exci a ion. I s ad an ages a e
he selec able exci a ion equency, du a ion and
magni ude, bu he compa ably long measu emen
ime o ob ain he comple e equency esponse
unc ion is disad an ageous. Since non-sinusoidal
exci a ions can usually be ela ed o sinusoidal exci-
a ions by Fou ie me hods, all subsequen consid-
e a ions will be ocused on he la e .
Fo an exci a ion signal x( ) o a sinusoidal
exci a ion wi h he magni ude Ax, he angula e-
quency ω and he phase φx is desc ibed by
x( )=Ax · sin(ω +φx)=ax sin (ω )+bx cos(ω ) , (4)
wi h Ax= a
x
2+b
x
2and φx = an−1(ax /bx) . The
ou pu signal can be desc ibed acco dingly as
y( )=Ay· sin(ω +φy) =ay sin (ω )+by cos(ω ) . (5)
Wi h his de ini ion he equency esponse unc-
ion can be w i en in he o m
H
A
A
y
x
ie
i
yx
ωω
ω
ϕω
ϕω
()
=
()
()
⋅
()
−
()
()
. (6)
The exci a ion equency should be chosen
app op ia ely o he la e applica ion. The ecom-
mended equency alues o en used in acous ics
and ib a ion calib a ions a e gi en in ISO 266 [7].
These ecommended equencies a e equally spaced in
he equency domain on he loga i hmic scale. The
wid h be ween he equency s eps can be chosen
based on he desi ed numbe o equency s eps o a
ixed in e al.
3.3 Ampli ie se ings
A calib a ion esul can only be alid o one ce ain
se o se ings o he ampli ie unde es , which
include gain, co ne equencies o high-pass and
low-pass il e s, ansduce sensi i i y and possibly
o he pa ame e s. I is essen ial o documen he
se ings a which he ampli ie was calib a ed. These
se ings should be chosen acco ding o he la e
applica ion.
3.4 Linea i y
Fo he abo e-men ioned equency esponse unc-
ion used o desc ibe he dynamic beha iou , he
55
PTB-Mi eilungen 125 (2015), No. 2 Condi ioning Ampli ie s
linea i y o he DUT is manda o y and should be
ensu ed du ing calib a ion. Nonlinea i ies cause
dis o ions o he sinusoidal shape o he ou pu
signal and can be es ima ed by analysing he ha -
monic signal componen s.
3.5 S abili y
The equi emen o he ime-in a ian beha iou
can be p o ed by epea ed calib a ions o e a p o-
longed pe iod o ime.
4 Calib a ion Se -Ups
4.1 Vol age ampli ie calib a ion se -up
Fo he calib a ion o ol age ampli ie s, a calib a ion
se -up as depic ed in igu e2 can be used. The ime-
dependen ol age ou pu Ugen o he signal gene a o
is coupled di ec ly o he inpu o he ol age ampli-
ie unde es (in he case o small gain ac o s) o
can be down-con e ed by means o a calib a ed
ol age di ide (in he case o la ge gain ac o s).
The measu ands o his se -up a e he inpu
ol age o he ampli ie Uin( ), which may be cal-
cula ed om a calib a ed gene a o ol age and he
ou pu ol age Uou ( ) o he ampli ie . In e ms o
equa ions (4) and (5), his means
x( )=Uin · sin(ω +φin) and (7)
y( )=Uou · sin(ω +φou ) . (8)
4.2 Cha ge ampli ie calib a ion se -up
In o de o calib a e a cha ge ampli ie i is neces-
sa y o con e he gene a o ol age om he
p e iously desc ibed se -up o an inpu cha ge
q e [8]. Fo his pu pose, a high p ecision capaci-
ance C e is employed as shown in igu e3.
Assuming ha he inpu impedance o he
cha ge ampli ie is negligible, he e e ence cha ge
q e o he cha ge ampli ie unde es can be
de i ed as
q e ( ) = Ugen( ) · C e . (9)
In e ms o equa ion (4) he inpu measu and is
gi en as
x( ) = Ugen · C e · sin(ω + φin) . (10)
Unde his assump ion, pa allel capaci ies Cpa
(e.g. om he ansduce cable) will no in lu-
ence he amoun o cha ge a he ampli ie inpu .
Howe e , i was ound ha he o al capaci ance
a he inpu (C e + Cpa ) may in luence he cha ge
ampli ie ’s equency esponse unc ion [9]. This
e ec is ypically small, bu may no be negligible
in applica ions wi h a demand o low measu e-
men unce ain ies.
4.3 IEPE ampli ie calib a ion se -up
IEPE condi ioning ampli ie s can be calib a ed
using a measu ing se -up simila o a se -up o
low gain ol age ampli ie s. Ins ead o a di ec
connec ion o he signal gene a o and he ampli-
ie unde es , an IEPE simula o is connec ed
be ween he signal gene a o and he IEPE condi-
ione [10], con e ing he gene a ed ol age in o
an IEPE ansduce -like ou pu signal. This se -up
is depic ed in igu e4.
Fo he de e mina ion o he equency
esponse unc ion o an IEPE signal condi ione ,
wo connec ion schemes a e possible wi h such a
se -up:
• Calib a ion wi h a calib a ed IEPE simula o .
I he IEPE simula o ’s equency esponse
Figu e 2:
Schema ic ep esen-
a ion o a calib a ion
se -up o ol age
ampli ie s using a
signal gene a o and
a ol age di ide
(le ), o a signal ge-
ne a o only ( igh ).
Figu e 3:
Schema ic diag am
o a calib a ion
se -up o cha ge
ampli ie s.
56
PTB-Mi eilungen 125 (2015), No. 2Dynamic Measu emen o Mechanical Quan i ies
unc ion was de e mined p io o he cali-
b a ion o he IEPE condi ioning ampli ie ,
a known inpu ol age can be used o he
exci a ion ollowing
x( )=Ugen · sin(ω +φin) (11)
and applying a co ec ion acco ding o he
p ocedu es desc ibed in sec ion 9.
• Calib a ion by measu ing Uin ins ead o Ugen.
I he ou pu signal o he IEPE simula o is
acqui ed ins ead o he inpu signal, he in lu-
ences o he IEPE simula o a e excluded om
he measu emen .
x( )=Uin · sin(ω +φin) + Uo se (12)
Howe e , i has o be kep in mind ha he e
will be a ol age o se Uo se due o he IEPE
eeding, which can lead o educed ol age
measu emen p ecision due o he disad an a-
geously la ge inpu ol age anges o he da a
acquisi ion de ice. Addi ional in luences due
o he ol age measu emen in he measu ing
chain mus be analysed as well.
4.4 Dynamic b idge s anda d calib a ion se -up
Fo he dynamic calib a ion o b idge ampli ie s,
di e en calib a ion se -ups ha e been de eloped
a he NMI le el. They all ea u e a a iome ic
measu emen p inciple. An olde app oach gene -
a es he small exci a ion ol ages by means o an
induc i e coupling, which is limi ed a low equen-
cies [11]. The e o e, no DC measu emen ( = 0 Hz)
is possible.
A new app oach gene a es he b idge signals by
using wo mul iplying digi al-analogue con e e s
(MDACs) and a esis i e ol age di ide [12–13].
The p inciple is depic ed in igu e5. Wi h his p in-
ciple, b idge exci a ion equencies down o DC a e
possible; in ac , a bi a y signals could be gene a ed
as well. As pa o wo k package 4 o he a o emen-
ioned EMRP p ojec , he dynamic b idge s anda ds
we e u he de eloped o enable phase measu e-
men s and a aceable calib a ion was ca ied ou .
An in e na ional bila e al compa ison o he di -
e en dynamic b idge s anda ds is cu en ly unde
way o ensu e compa abili y in he ange o he
es ima ed measu emen unce ain ies.
The dynamic b idge s anda d simula es he
ou pu signal o a s ain gauge ansduce . The
de ice is connec ed o he b idge ampli ie unde
es and p o ides a simila inpu esis ance o a
s ain gauge ansduce . The ou pu ol age o he
simula ed b idge depends di ec ly on he b idge
supply ol age, because he supply ol age is he
e e ence ol age o he mul iplying DACs. In he
case o b idge ampli ie s equipped wi h a con ol o
he b idge exci a ion ol age by means o a 6-wi e
connec ion using sense wi es, hese wi es a e con-
nec ed o he MDACs in he b idge s anda d so as
o beha e simila ly o a eal ansduce .
As he dynamic b idge s anda d gene a es he
p ede ined aceable ol age a io, he measu and
o a magni ude calib a ion o a b idge ampli ie is
solely he ou pu ol age o he ampli ie . In o de o
de e mine he phase esponse, he dynamic b idge
s anda d supplies a complemen a y no malized
signal ou pu , which p o ides a signal synch onous
o he ol age a io. Wi h e e ence o his ‘synch o-
niza ion signal’, he ime delay and he e o e he
phase esponse o he ampli ie can be calib a ed.
Figu e 4:
Calib a ion se -up o
IEPE condi ioning
ampli ie s including
an IEPE simula o .
Figu e 5:
Schema ic ep e-
sen a ion o a b idge
ampli ie calib a ion
se -up wi h an MDAC
dynamic b idge
s anda d.

57
PTB-Mi eilungen 125 (2015), No. 2 Condi ioning Ampli ie s
5 Da a Acquisi ion and Analysis
The me hodology p esen ed he e is implemen ed in
he espec i e labo a o ies o PTB and oou knowl-
edge in many o he NMI labo a o ies, namely in
he ield o ib a ion me ology. Ne e heless, o he
alid se -ups and me hods a e concei able.
To calcula e he equency esponse unc ion (see
equa ion (1)), he inpu and ou pu quan i ies ha e
o be acqui ed wi h wo measu emen channels. Fo
p ope signal acquisi ion, se e al c i e ia should be
complied wi h:
• Common sample clock o he wo channels (o
sample clocks o an in ege a io).
• Synch onous s a o sampling.
• Common sampling in e al (window wid h) o
an in ege mul iple o he mains pe iod.
• Sample equency ha co e s he bandwid h o
he nominal equency and exis ing ha monics
(Nyquis c i e ion).
Conside ing his in all o he p e iously desc ibed
se -ups, wo sampled ime se ies o sinusoidal
ol age signals {xi} and {yi} a e acqui ed1, which is –
i espec i e o a cons an ac o (e.g. C e ) – adisc e-
ized ealiza ion o he con inuous signals x( ) and
y( ) (see equa ions (4) and (5)).
Th ough he applica ion o a linea leas squa es i
o he named equa ions o he sampled ime se ies,
he pa ame e s ax, bx and ay, by can be de e mined
easily. Wi h he ans o ma ions gi en in sec ion
3.2, he equency esponse unc ion is hus de i ed
acco ding o equa ion (6) by subsequen measu e-
men s a all desi ed angula equencies ω.
6 In luence o he Impedance
E e y signal inpu , signal ou pu and connec ing
cable has i s inhe en complex impedance which, i
no aken in o accoun , can add sys ema ic de ia-
ions o he measu emen s. Figu e 6 shows he wo
se -ups o he ol age and o he cha ge measu e-
men s. I he ypically used coaxial cables a e signi i-
can ly sho e han he wa eleng h o he signal, hey
can be modelled by a pa allel capaci ance Z c.
The ou pu ol age Uou o a measu ing ampli ie is
dependen on he ou pu scaling ac o de sc ibed by
he equency esponse unc ion H as
U ou =H · U in (13)
o ol age ampli ica ion, and
U ou = H · q in (14)
o cha ge condi ioning, espec i ely.
The ol age a he inpu o he ampli ie U in can
de ia e om he senso ou pu ol age U s because o
he in luences o he impedances
Uin =Us1+Zs1
Zin
+1
Zc
1
. (15)
Acco dingly, he inpu q in o a cha ge measu emen
can de ia e om he ou pu cha ge q s acco ding o
θin = θs1+Zs1
Zin
+1
Zc
1
. (16)
7 Measu emen Unce ain y Con ibu ions
o Realized Calib a ion Facili ies
The measu emen unce ain ies o dynamic calib a-
ions a e based on he quali y o he de ice unde
es as well as on he calib a ion se -up. The majo
componen s o he measu emen unce ain y o he
se -up can be (see [8–12]):
• Non-linea i ies o he A/D con e sion o
single equency a io measu emen .
• Calib a ion unce ain ies o he used e e ence
capaci ance ( o cha ge ampli ie calib a ion).
• Calib a ion unce ain ies o he IEPE simula o
( o IEPE ampli ie calib a ion).
• Calib a ion unce ain ies o he dynamic b idge
s anda d ( o b idge ampli ie calib a ion).
• Noise o he inpu ol age (gene a o ) and o he
ou pu ol age (condi ioning ampli ie ).
1 In he case o he
dynamic b idge s an-
da d, he inpu is no
acqui ed bu de ined by
he p og ammed signal.
Howe e , he analysis
p ocedu e is easily
adap able.
Figu e 6.
Schema ic diag am
including impedan-
ces o cu en o
cha ge measu e-
men s (le ) and o
ol age measu e-
men s ( igh ).
58
PTB-Mi eilungen 125 (2015), No. 2Dynamic Measu emen o Mechanical Quan i ies
Hence, a ough es ima e shows ha he claims o
some 10−3 o 10−4 o ela i e combined expanded
unce ain y o magni ude a e easible o cha ge
ampli ie calib a ion [8–9] wi h he p ope equipmen
and unde good condi ions, depending, o cou se,
on he de ails o he implemen a ion. The ela i e
expanded measu emen unce ain ies o IEPE and
he b idge ampli ie s, again o magni ude calib a ion,
will be in he anges o en hs o pe cen [10–12].
No only do NMIs ca y ou aceable calib a ions
o cha ge ampli ie s, bu acc edi ed labo a o ies
also compa e hei calib a ion esul s in a na ional
compa ison p og amme [14]. The measu emen
unce ain ies o acc edi ed cali b a ion labo a o ies o
he a ailable calib a ions (cha ge ampli ie s, ol age
ampli ie s, bu no ye b idge ampli ie s) a e ypically
in he ange o 0.3 %<U(k=2)<1 % and ypically
a ailable o magni ude calib a ion only.
8 Measu emen Resul s o he Calib a ion
o Ampli ie s
To show he impo ance o a sui able calib a ion
o ampli ie s used o dynamic measu emen s,
di e en calib a ion esul s o b idge-, cha ge-,
ol age- and IEPE condi ioning ampli ie s a e
p esen ed. All analysed ampli ie s a e comme -
cially a ailable. They we e p oduced by di e en
manu ac u e s.
The cha ge-, ol age- and IEPE condi ion-
ing ampli ie calib a ions we e ca ied ou in
a equency ange om 0.1 Hz o 100 kHz. All
high- and low-pass il e s we e disabled o se o
hei lowes (high-pass il e ) o highes (low-pass
il e ) alue, espec i ely. The de ia ions in he
magni ude esponses a e gi en wi h espec o he
nominal alue, se a he ampli ie .
Th ee o he ou cha ge ampli ie s show a
ypical high-pass beha iou in hei ampli ude
esponse ( igu e7). Cha ge ampli ie 2 has he
op ion o disable i s high-pass il e , which esul ed
in a much be e low- equency beha iou bu
also in a d i ing DC bias ol age (which does
no become ob ious om he equency esponse
da a). I was ound ha e en wi h high-pass il e s
se a he lowes alue, he il e se ings can s ill
in luence he measu ing esul s in he equency
ange up o 10Hz. The low-pass il e s o h ee
ampli ie s (ampli ie s 2, 3, 4) show a signi ican
o e shoo ing beha iou , which should be con-
side ed wi h cau ion. The co esponding phase
esponse o he same ou cha ge ampli ie s is
shown in igu e8. The phase and he magni ude
esponses can di e subs an ially om ampli ie o
ampli ie .
The calib a ion esul s o he magni ude
( igu e9) and phase esponse ( igu e10) o ou
di e en ol age ampli ie s show he smalles e-
Figu e 7:
Magni ude espon-
ses o ou di e en
comme cially a ail-
able cha ge ampli-
ie s in he equency
ange o 0.1 Hz o
100 kHz.
Figu e 8:
Phase esponses o
ou cha ge ampli-
ie s in he equency
ange o 0.1 Hz o
100 kHz.
59
PTB-Mi eilungen 125 (2015), No. 2 Condi ioning Ampli ie s
quency-dependen de ia ions a low equencies.
Again, he low-pass il e can p oduce signi ican
o e shoo ing e en in a equency ange o a ew
hund ed he z ( ol age ampli ie 4), which a ec s
he phase esponse acco dingly.
All in es iga ed IEPE condi ioning ampli ie s
ha e a signi ican high-pass beha iou as depic ed
in igu es 11 and 12, which can a ec low e-
quency measu emen s.
In igu es 13 and 14, he magni ude and phase
esponse o ou b idge ampli ie s a e shown.
The calib a ion measu emen s we e ca ied ou
using he dynamic b idge s anda d o PTB in a
equency ange o 10 Hz o 10 kHz. The exci a ion
le el was 2 mV/V; all il e s we e swi ched o o
se o hei highes alue a ailable.
I becomes ob ious om he calib a ion esul s
ha b idge ampli ie s can ha e a signi ican
a ying magni ude esponse e en in low equency
egions, which shows he impo ance o dynamic
calib a ions. The phase esponses o he ou
analysed ampli ie s show signi ican ly di e ing
beha iou . The ou b idge ampli ie s unde es
had a phase delay o a leas 15° o 20° a 10 kHz.
Bu b idge ampli ie 2 exhibi ed a much s onge
phase delay.
Figu e 9:
Magni ude espon-
ses o ou di e en
comme cially a aila-
ble ol age ampli ie s
in he equency
ange o 0.1 Hz o
100 kHz.
Figu e 10:
Phase esponses o
ou ol age ampli-
ie s in he equency
ange o 0.1 Hz o
100 kHz.
Figu e 11:
Magni ude espon-
ses o ou di e en
comme cially a aila-
ble IEPE condi io-
ning ampli ie s in he
equency ange o
0.1 Hz o 100 kHz.
60
PTB-Mi eilungen 125 (2015), No. 2Dynamic Measu emen o Mechanical Quan i ies
9 Co ec ion o he F equency-dependen
Beha iou
The calib a ion esul s can be used o co ec he
dynamic in luences o he ampli ie in he meas-
u emen chain. In case he magni ude esponse
unc ion Acal(ω) and he phase esponse unc ion
φcal(ω) o an ampli ie a e known om calib a ion,
he magni ude Ameas(ω) and phase φmeas(ω) o he
measu ed da a can be co ec ed in he equency
domain as
Aco (ω) = Ameas(ω) · Acal(ω)−1 (17)
and
φco (ω) = φmeas(ω) − φcal(ω) . (18)
I should be kep in mind ha he equency
esponse unc ions o he measu ing ampli ie s
ha e o be assigned wi h hei measu emen unce -
ain y and will he e o e in luence he co ec ed
da a’s unce ain y acco dingly.
Figu e 12:
Phase esponses o
ou IEPE condi io-
ning ampli ie s in he
equency ange o
0.1 Hz o 100 kHz.
Figu e 13:
Magni ude espon-
ses o ou di e en
comme cially a aila-
ble b idge ampli ie s
in he equency
ange o 10 Hz o
10 kHz.
Figu e 14:
Phase esponses o
ou b idge ampli ie s
in he equency
ange o 10 Hz o
10 kHz.