lecture 4: sensor interface circuits - texas a&m...

Intelligent Sensor SystemsRicardo Gutierrez-OsunaWright State University

1

Lecture 4: Sensor interface circuitsg Review of circuit theory

n Voltage, current and resistance

n Capacitance and inductancen Complex number representations

g Measurement of resistancen Voltage dividers

n Wheatstone Bridgen Temperature compensation for strain gauges

g AC bridgesn Measurement of capacitancen Measurement of impedance


2

Voltage, current, resistance and powerg Voltage

n The voltage between two points is the energy required to move a unit of positive charge from a lower to a higher potential. Voltage is measured in Volts (V)

g Currentn Current is the rate of electric charge through a point. The unit of measure is the

Ampere or Amp (A)

g Resistancen Given a piece of conducting material connected to a voltage difference V, which

drives through it a current I, the resistance is defined as

g As you will recall, this is known as Ohm’s Lawg An element whose resistance is constant for all values of V is called an ohmic resistor

n Series and parallel resistors…

g Powern The power dissipated by a resistor is

RIRV

VIP 22

===

IV

R =


3

Kirchhoff’s Lawsg 1st Law (for nodes)

n The algebraic sum of the currents into any node of a circuit is zerog Or, the sum of the currents entering equals the sum of the currents leavingg Thus, elements in series have the same current flowing through them

g 2nd Law (for loops)n The algebraic sum of voltages in a loop is zero

g Thus, elements in parallel have the same voltage across them.

I1

I2

I3

I1=I2+I3I1

I2

I3

I1=I2+I3

VA VB

VCVD

VAB+ VBC+VCD+VDA=0

VA VB

VCVD

VAB+ VBC+VCD+VDA=0


4

Capacitors and inductorsg A capacitor is an element capable of storing charge

n The amount of charge is proportional to the voltage across the capacitor

g C is known as the capacitance (measured in Farads)

n Taking derivatives

n Therefore, a capacitor is an element whose rate of voltage change is proportional to the current through it

g Similarly, an inductor is an element whose rate of current change is proportional to the voltage applied across it

g L is called the inductance and is measured in Henrys

CVQ =

( )dtdV

CIdtCVd

dtdQ =⇒=

dtdI

LV =


5

Frequency analysisg Consider a capacitor driven by a sine wave voltage

n The current through the capacitor is

g Therefore, the current phase-leads the voltage by 900 and the ratio of amplitudes is

g What happens when the voltage is a DC source?

CV(t)=V0sin(ωt)

I(t)

CV(t)=V0sin(ωt)

I(t)

( )( ) t)cos(VC�sinVdtd

CdtdV

CI 00 ===

C1

I(t)

V(t)=


6

Voltages as complex numbersg At this point it is convenient to switch to a complex-number

representation of signalsn Recall that ejϕ=cosϕ+jsin ϕ

g Applying this to the capacitor V(t)/I(t) relationship

Circuit voltage versus time:V(t)=V0cos(ωt+ϕ)

Complex numberrepresentation:V0ejϕ=a+jb

Multiply by ejϕ and take real part

V0cos(ωt+ϕ)⇓

V0ejϕ

( ) ( )Cj

1HC1

Ce

eC��Wcos

t)cos(VCWsinV

IV

t)cos(VCdtdV

CI

�� j

�� j

j00

0

0

===−==

⇓

==

−

−

From [HH89]


7

Impedanceg Impedance (Z) is a generalization of resistance for circuits that

have capacitors and inductorsn Capacitors and inductors have reactance, while resistors have

resistance

g Ohm’s Law generalized

g Impedance in series and parallel

RZ

�jZ

�j-

� j1

Z

R

L

C

==

==

ZIV =

N21P

N21S

Z1

Z1

Z1

Z1

ZZZZ

+++=

++=

�

�


8

Example: High-pass filterg High pass filter

n The current through cap and resistor is

n The output voltage is equal to the voltage differential across the resistor

n If we focus on amplitude and ignore phase

g Asymptotic behavior…g Corner frequency

R

VoutVin

C

&j1

R

VZV

I inin

+==

&j1

R

VRRIV in

out

+==

( ) 1RC

RC V

&

1R

VR

&j1

R

VRV

2in22

ininout

+=

+

=+

=

dB-3.01011

120log

V

V20log

RC1

10in

out10CORNER =

+=⇒=


9

Measurement circuitsg Resistance measurements

n Voltage divider (half-bridge)

n Wheatstone bridge

g A.C. bridgesn Measurement of capacitancen Measurement of impedance


10

Voltage dividerg Assumptions

n Interested in measuring the fractional change in resistance x of the sensor: RS=R0(1+x)

g R0 is the sensor resistance in the absence of a stimuli

n Load resistor expressed as RL=R0k for convenience

g The output voltage of the circuit is

g Questionsn What if we reverse RS and RL?n How can we recover RS from Vout?

Vout

VCC

RS= R0(1+x)

RL= R0k

( )( ) kx1

x1V

kRx1Rx1R

V

RRR

VV

CC00

0CC

LS

SCCout

+++=

+++=

=+

=

1 2 3 4 5 6 7 8 9 100.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

x

k=0.1

k=1

k=10

Vo

ut/

VC

C


11

Voltage dividerg What is the sensitivity of this

circuit?

g For which RL do we achieve maximum sensitivity?

n This is, the sensitivity is maximum when RL=RS

( ) ( )( )

( )2CC

2CC

CCout

kx1

kV

kx1

x1kx1V

kx1x1

Vdxd

dxdV

S

++=

=++

+−++=

=

+++==

( )( ) ( )

( ) x1k +=⇒=++

++−++⇒=

++

⇒= 0kx1

kx1k2kx10

kx1

kV

dkd

0dkdS

2

2

2CC

1 2 3 4 5 6 7 8 9 10

0.05

0.1

0.15

0.2

x

k=0.1

k=1

k=10

S


12

Wheatstone bridgeg A circuit that consists of two dividers

n A reference voltage divider (left)

n A sensor voltage divider

g Wheatstone bridge operating modesn Null mode

g R4 adjusted until the balance condition is met:

n Advantage: measurement is independent of fluctuations in VCC

n Deflection modeg The unbalanced voltage Vout is used as

the output of the circuit

n Advantage: speed

VCC

R1

R4

R2

R3= R0(1+x)

Vout

1

243out R

RRR0V =⇔=

+

−+

=43

4

32

3CCout RR

RRR

RVV


13

Wheatstone bridgeg Assumptions

n Want to measure sensor fractional resistance changes RS=R0(1+x)

n Bridge is operating near the balance condition:

g The output voltage becomes

0

2

4

1

RR

RR

k ==

( )( )

( )( ) ( )( )xk1k1

kxV

1k1

x1kx1

V

RkRR

x1RkRx1R

VV

CCCC

44

4

00

0CCout

+++=

+

−++

+=

=

+

−++

+=

1 2 3 4 5 6 7 8 9 10

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

k=0.1

k=1

k=10

Vo

ut/

VC

C

x


14

Wheatstone bridgeg What is the sensitivity of the Wheatstone bridge?

n The sensitivity of the Wheatstone bridge is the same as that of a voltage divider

g You can think of the Wheatstone bridge as a DC offset removal circuit

g So what are the advantages, if any, of the Wheatstone bridge?

( )( )( )( ) ( )

( ) ( )

( )2CC

22CC

CCout

xk1

kV

xk1k1

k1kxxk1k1kV

xk1k1kx

dxd

Vdx

dVS

++=

=+++

+−+++=

=

+++

==


15

Voltage divider vs. Wheatstone for small xg The figures below show the output of both circuits for small fractional

resistance changesn The voltage divider has a large DC offset compared to the voltage swing, which

makes the curves look “flat” (zero sensitivity)g Imagine measuring the height of a person standing on top of a tall building by running

a large tape measure from the street

n The sensitivity of both circuits is the same!g However, the Wheatstone bridge sensitivity can be boosted with a gain stage

n Assuming that our DAQ hardware dynamic range is 0-5VDC, 0<x<0.01 and k=1, estimate the maximum gain that could be applied to each circuit

0 0.002 0.004 0.006 0.008 0.010

0.2

0.4

0.6

0.8

1

x0 0.002 0.004 0.006 0.008 0.01

0

0.5

1

1.5

2

2.5x 10

-3

x

Wh

eats

ton

e

Div

ider

k=10

k=1

k=0.1

k=0.1

k=1

k=10

0 0.002 0.004 0.006 0.008 0.010

0.2

0.4

0.6

0.8

1

x0 0.002 0.004 0.006 0.008 0.01

0

0.5

1

1.5

2

2.5x 10

-3

x

Wh

eats

ton

e

Div

ider

k=10

k=1

k=0.1

k=0.1

k=1

k=10


16

Compensation in a Wheatstone bridgeg Strain gauges are quite sensitive to temperature

n A Wheatstone bridge and a dummy strain gauge may be used to compensate for this effect

g The “active” gauge RA is subject to temperature (x) and strain (y) stimulig The dummy gauge RD, placed near the “active”gauge, is only subject to

temperature

n The gauges are arranged according to the figures belown The effect of (1+y) on the right divider cancels out

VCC

R0

R0 RA= R0(1+x)(1+y)

Vout

RD= R0(1+y)

From [Ram96]


17

AC bridgesg The structure of the Wheatstone bridge can be used to measure

capacitive and inductive sensorsn Resistance replaced by generalized impedance

n DC bridge excitation replaced by an AC source

g The balance condition becomes

n which yields two equalities, for real andimaginary components

g There is a large number of AC bridge arrangementsn These are named after their respective developer

VAC

Z1

Z4

Z2

Z3

Vout3

2

4

1

ZZ

ZZ =

42423131

42423131

RXXRRXXR

XXRRXXRR

+=+−=−


18

AC bridgesg Capacitance measurement

n Schering bridge

n Wien bridge

g Inductance measurementn Hay bridge

n Owen bridge

C1

R1

C4

R2

Cx

Rx

VAC

Schering

C1

R1

C4

R2

Cx

Rx

VAC

Schering

R1

Cx

Rx

VAC

C4

R4

R2

Wien

R1

Cx

Rx

VAC

C4

R4

R2

Wien

C1

R1R3

Lx

Rx

VAC

Hay

R4

C1

R1R3

Lx

Rx

VAC

Hay

R4

C1 R3

Lx

Rx

VAC

Owen

R4

C1 R3

Lx

Rx

VAC

Owen

R4


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References[HH89] P. Horowitz and W. Hill, 1989, The Art of Electronics, 2nd

Ed., Cambridge University Press, Cambridge, UK[Ram96] D. C. Ramsay, 1996, Principles of Engineering

Instrumentation, Arnold, London, UK[Maz87] F. F. Mazda, 1987, Electronic instruments and

measurement techniques, Cambridge Univ. Pr., New York[Die72] A. J. Diefenderfer, 1972, Principles of electronic

instrumentation, W. B. Sanuders Co., Philadelphia, PA.[PAW91] R. Pallas-Areny and J. G. Webster, 1991, Sensors and

Signal Conditioning, Wiley, New York[Gar94] J. W. Gardner, 1994, Microsensors. Principles and

Applications, Wiley, New York.[Fdn97] J. Fraden, 1997, Handbook of Modern Sensors. Physics,

Designs and Applications, AIP, Woodbury, NY

lecture 4: sensor interface circuits - texas a&m...

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