L12_load

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.


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.


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

==+

×+×

×××××= −


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−≈×

+=


Buffer Amplifier

→ Buffer Amplifier

Loading error: -0.002 PH

0.998003591

101010

10101059PH 4

4

912

12

M =×+

×+

×=


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



• R th =?

⎩⎨⎧

==

0impedance internal0Vs



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

+−=

+−=

+=•



• 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

+−−=−=





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



= 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 ≤×≤⇒


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.


Norton equivalent ckt

ZL << ZN, VL→iNZLmaximum current through the load.

LN

LNNL

LN

NL

ZZZZiV

Z1

Z1

Z1

ZiV

+=

⎪⎭

⎪⎬⎫

+=

=


Differential Pressure Transmitter

Output: 4 ~ 20 mA currentInput: differential pressure 0~2 × 104 Pa N/m2


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


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


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 +=


Mechanical impedance

kxdtdx

dtxdmF ++= λ

2

Mechanical impedance =mZ skmss

x

F++=

Δ

Δ•

λ)(

)()()( sxskmssF

•

Δ++=Δ λ


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


General Transducer

ZM V

i

iN ZNF

•

x

F ZM

Eth

V

i

Zth

•

x

F Vi

•

x


Process Loading


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

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L12_load