A. L. Wicks Dept. of Mechanical Engineering Virginia Tech

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Advanced Instrumentation

By

A.L. Wicks

Department of Mechanical EngineeringVirginia Tech

A course in current techniques of measurement, acquisition and processing test data

A. L. Wicks Dept. of Mechanical Engineering Virginia Tech

2

Amplifiers

Amplifiersignalsource

Load

+

-

v in

+

_vo=A v(v in)

Ideal amplifier

Amplifier has gain A

)()( tAvtv SL In this case, the gain relates the output of the source to the voltage delivered to the load

This is in contrast to the input voltage and output voltage of the amplifier

A. L. Wicks Dept. of Mechanical Engineering Virginia Tech

3

Amplifiers

+

-

+

-

R loadvo

vs

R s

R i

+

-

v i Avin

SiS

ii v

RR

Rv

outLoad

LoadinO RR

RAvv

Rout

sLoadoutiS

LoadiO v

RRRR

RRAv

))((

What are the desirable characteristics of an amplifier?

small very large very outi RR

A. L. Wicks Dept. of Mechanical Engineering Virginia Tech

4

Amplifiers

+

-

V 0A v(OL) V in

R outR in

+

-

V in

I in

+

-

Operational amplifier

)()( vvAv OLvout

A. L. Wicks Dept. of Mechanical Engineering Virginia Tech

5

AmplifiersDevelopment of summing point constraint

Consider the following amplifier with feedback

-

+

R s

R f

V s V o

fOLv

o

f

o

sOLv

o

s

s

fs

f

of

s

ss

OLvo

OLvo

RA

v

R

v

RA

v

R

v

ngsubstituti

ii

R

vvi

R

vvialso

Avv

groundedvnote

vvAv

)()(

)(

)(

,

/

)( 0

)(

ss

fo

OLv

vR

Rv

Afor

4)( 10

A. L. Wicks Dept. of Mechanical Engineering Virginia Tech

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Definition of Gain

• Voltage gain is equal to the ratio of voltage output to voltage in.

• Power gain is equal to the ratio of output power to power input.

in

out

V

VGain ls) (decibe

V

V Gain=

in

out

log20

in

out

P

PGain )log10 els (decib

P

P Gain=

in

out

A. L. Wicks Dept. of Mechanical Engineering Virginia Tech

7

Amplifiers

-

+

R 1

R f

V s

V oV i

Non-inverting amplifier

ff

s

o

of

sio

s

of

i

RRR

aRRR

a

a

v

vA

vRR

Rvaavv

vv

vRR

Rv

vvv

1

1

1

1

1

1

1

1

11

1

)(

1

1limR

RA f

a

Gain for the non-inverting amp

A. L. Wicks Dept. of Mechanical Engineering Virginia Tech

8

Amplifiers

-

+

V s

V oV i

Voltage follower

Often referred to as a buffer

A=1

0

o

i

R

R

A. L. Wicks Dept. of Mechanical Engineering Virginia Tech

9

Amplifiers

-

+

R f

V o

R 1

R 2

R 3

V s1

V s3

V s2

Summing amplifier

3

32

21

1

vR

Rv

R

Rv

R

RV fff

o

A. L. Wicks Dept. of Mechanical Engineering Virginia Tech

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AmplifiersDifferential Amplifier

R1

Vin

-

+ Vout

R2

R3

R4

Assuming the op amp is ideal

1

2

3

4 alsoR

R

R

R

)( 121

2 vvR

Rvout

A. L. Wicks Dept. of Mechanical Engineering Virginia Tech

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AmplifiersDifferential Amplifier

Differential mode and Common Mode components

2/

2/

2/)(

2

1

21

12

dmcm

dmcm

cm

dm

vvv

vvv

vvv

vvv

)( Recall 121

2 vvR

Rvo Assume some error in R2

21

2

21

21

1

2 2

21

RR

RA

RR

RR

R

RA

vAvAv

cmdm

cmcmdmdmo

12R

R1

-

+ Vout

R2

R4

Vdm/2

Vdm/2

Vcm

R3

A. L. Wicks Dept. of Mechanical Engineering Virginia Tech

12

AmplifiersDifferential Amplifier

Differential mode and Common Mode components

12

212

1

2

/1log20

)/(

log20

RRCMRR

RRR

RR

A

A

A

ACMRR

cm

dm

cm

dm

For 1 % resistors the CMRR= 48.5 dB

Note The larger the differential gain R2/R1 the higher the CMRR

A. L. Wicks Dept. of Mechanical Engineering Virginia Tech

13

AmplifiersDifferential Amplifier

Use of differential amplifiers to eliminate ground loops

R 1

-

+ V out

R 2

R 1

R 2

Z gnd

+V gnd -

V in

R 1

-

+ V out

R 2

Z gnd

+V gnd -

V in )(1

2gndio vv

R

Rv

io vR

Rv

1

2

Note differential amp removes the ground loop

A. L. Wicks Dept. of Mechanical Engineering Virginia Tech

14

AmplifiersCharge amplifiers

Some transducers such as piezoelectric accels operate by converting force to charge

-

+

C f

V sV o

C s

sf

so C

C

vv

Piezo model

Thevinin equiv.

Is C s

Norton equiv. model

Note: charge amps requirehigh input impedance commonto have FET circuits

A. L. Wicks Dept. of Mechanical Engineering Virginia Tech

15

Amplifiers

-

+

C f

V sV o

C s R 1

R 2

Charge amplifiers

Practical circuit for a charge amp.

R2 provides a dc shunt for the input bias current. Without thisresistor, the bias currents would charge Cf to saturation

R1 stabilizes the feedback

Resistor criteria

fCR

1

2 sC

R

11

R2 1M-1G ohmsR1 100 ohms

sf CRf

CR 12

11

A. L. Wicks Dept. of Mechanical Engineering Virginia Tech

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• Comparator

A. L. Wicks Dept. of Mechanical Engineering Virginia Tech

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