a. l. wicks dept. of mechanical engineering virginia tech 1 advanced instrumentation by a.l. wicks...
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A. L. Wicks Dept. of Mechanical Engineering Virginia Tech
1
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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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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