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1Sensors and Interfacing Loading effect
Loading Effects
The output of a sensor device may deviate from the correct value due to loading effect. We can categorize two types of loading effect:
• Inter element loadingA given element in the system may modify the characteristics of the previous element.
• Process loadingThe introduction of the sensing element into the process or system being measured causes the value of the measured variable to change.
2Sensors and Interfacing Loading effect
Electrical loading (two-port networks)
A. A sensor device is represented by Thevenin equivalent circuit
Eth: Voltage source, open circuit voltage of the network across theoutput terminal.All voltage sources reduced to zero and replaced by their internal impedance.
Zth: The impedance looking back into the terminal.
circuit equivalentThevenin theof loading
,ZZ
ZEiZVLth
LthLL +
==
ZL≧Zth, VL→ETH
maximum voltage transfer from the network to the load.
3Sensors and Interfacing Loading effect
Example: Temperature measurement system
4
4
L6
66
IN 1075101000V ,
20102102T1040V
+=
+××
×= −INV
LM 25VT =
0.0075Terror loading 0.99257T,1075
1020102
1021000T251040 4
4
6
66
==+
×+×
×××××= −
4Sensors and Interfacing Loading effect
Use of buffer amplifier to reduce loading effects
• PH transducer (glass electrode): use of Buffer AmplifierSensitivity: Eth = 59 PH(mV) or 1 PH →59mV Sensitivity=59mV/PH
Zth = 109Ω
Indicator : Zth = RL =104Ω
PH10591)
101010(59 PH
PH/mV 591 :y sensitivit Scale
594
4PH
M−≈×
+=
5Sensors and Interfacing Loading effect
Buffer Amplifier
→ Buffer Amplifier
Loading error: -0.002 PH
0.998003591
101010
10101059PH 4
4
912
12
M =×+
×+
×=
6Sensors and Interfacing Loading effect
Loading Effect of Potentiometer
• The fraction displacement: x = d/dT
• total resistance: RP Ω
xVER
xRVE ?E sth
p
p
s
thth =⇒==•
Open circuit voltage across the output thermals AB
7Sensors and Interfacing Loading effect
Loading Effect of Potentiometer
• R th =?
⎩⎨⎧
==
0impedance internal0Vs
8Sensors and Interfacing Loading effect
Loading Effect of Potentiometer
x)(1R1
xR1
R1
ppth −+=
x)-x(1Rx)1(xRxx)R-(1R
R pp
ppth =
−+=
1x)x(1RR
1xVRx)x(1R
RxVRR
REV
L
ps
Lp
Ls
thL
LthL
+−=
+−=
+=•
9Sensors and Interfacing Loading effect
Loading Effect of Potentiometer
• Loading effectthe relationship between VL and x is non-linear, the amount of non-linearity depending on the ratio RP/PL
1x))x(1
RR
(
1x1VVEN(x)
L
psLth
+−−=−=
10Sensors and Interfacing Loading effect
Loading Effect of Potentiometer
11Sensors and Interfacing Loading effect
Loading Effect of Potentiometer
Design
N(x) has a maximum value of
when x = 2/3 , as a percentage of full-scale deflection
x))x(1
RR
(1
)RR
x)(-(1xVN(x)
L
p
L
p2
s−+
=
1RR
ifL
p ≤
)x)(xRR
(VN(x) 32
L
ps −≈
)RR
(V274N
L
ps=ˆ
percent RR
15oo
RR
27400N
L
p
L
p ≈=ˆ
12Sensors and Interfacing Loading effect
Loading Effect of Potentiometer
= 2 ﹪dT = 10 cm RL = 10 K Ω 1K potentiometer (=RP)
→ the greater VS, the higher sensitivity
But considering the power dissipation
→ Sensitivity = 1.0 Vcm-1
N Ω101520R2
RR15 3
PL
P ×≤⇒≤→
sL V
dxdV
≈
0.1WRV
P
2S ≤
10V100.1V 3S ≤×≤⇒
13Sensors and Interfacing Loading effect
Norton equivalent circuit
• Norton equivalent circuit
ZN: the impedance looking back into the output terminals with all voltage source reduced to zero and replaced by their internal impedance.iN: the current which flows when the terminals are short circuited.
14Sensors and Interfacing Loading effect
Norton equivalent ckt
ZL << ZN, VL→iNZLmaximum current through the load.
LN
LNNL
LN
NL
ZZZZiV
Z1
Z1
Z1
ZiV
+=
⎪⎭
⎪⎬⎫
+=
=
15Sensors and Interfacing Loading effect
Differential Pressure Transmitter
Output: 4 ~ 20 mA currentInput: differential pressure 0~2 × 104 Pa N/m2
16Sensors and Interfacing Loading effect
Differential Pressure Transmitter
the recorded voltage derivates from the desired range of 1 to 5 volts by 0.05 ﹪
RC
R
L
RRR
RVV
+=
RNRCN
NRNR Ri 0.995
RRRRRiV =
++=
RCN
RCNNL RRR
)R(RRiV+++
=
total load = RC+RR
17Sensors and Interfacing Loading effect
Piezoelectric Force Measurement
LCN R
1sCsCZ1
++=1s)RC(C
RZLCN
L
++=
1s)RC(CR
(s)Δi(s)ΔV
LCN
L
N
L
++=
dt
Influence the dynamic characteristics
18Sensors and Interfacing Loading effect
Process Loading
Process F = kPx+FS
FS = ksx
We want : ks>> kP in order to minimize loading error.
sS
Sp F)
kF(kF +=
)k
kk(F
S
Sps
+=
Fkk
kFSp
SS +=
19Sensors and Interfacing Loading effect
Mechanical impedance
kxdtdx
dtxdmF ++= λ
2
Mechanical impedance =mZ skmss
x
F++=
Δ
Δ•
λ)(
)()()( sxskmssF
•
Δ++=Δ λ
20Sensors and Interfacing Loading effect
Equivalent Ckt
∫++= idtC
RidtdiLV 1
Electrical impedance CsRLs)s(
iVZE
1++==
ΔΔ
)s(i)Cs
RLs()s(V ΔΔ 1++=
⎪⎪⎭
⎪⎪⎬
⎫
⎪⎪⎩
⎪⎪⎨
⎧
→
→→
Ck
RLm
1λ
Equivalent Ckt
i
V
L
R
x&
k1
λF
m
21Sensors and Interfacing Loading effect
General Transducer
ZM V
i
iN ZNF
•
x
F ZM
Eth
V
i
Zth
•
x
F Vi
•
x
22Sensors and Interfacing Loading effect
Process Loading
23Sensors and Interfacing Loading effect
Process Loading
Process impedance
Sensor impedanceS
kλsm(s)Z PPpMP ++=
Skλsm(s)Z S
SSMS ++=
(s)FΔZZ
Z(s)FΔMPMS
MSS +
=
SpppFFdtkλ
dtdm ∫ −=++
••
•
xxx
SSSsFdtkλ
dtdm ∫ =++
••
•
xxx
S
p
PFΔ-FΔ)Δ
Sk
λ(mps =++•
x
S
S
SFΔ)Δ
Skλ(mss =++
•
x
•••
=−− xxsSSS
mλxkF
•••
=−− xxpSpp
mFxk- Fprocess λ