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