ENGR 1121 Real World
MeasurementsFranklin Olin College of Engineering, Spring 2011
The Op Amp and Differential Amplifier – the workhorses
of Analog Sensor Interfaces
Hazards of not understanding electrical interfacesFrom the Arkansas Democrat Gazette, July 25, 1996:
“Two Local Men Injured in Freak Truck Accident Cotton Patch, Ark.”
“Two local men were seriously injured when their pick-up truck left the road and struck a tree near Cotton Patch on State Highway 38 early Monday morning.
“Thurston Poole, 33, of Des Arc and Billy Ray Wallis, 38, of Little Rock are listed in serious condition at Baptist Medical Center.
“The accident occurred as the two men were returning to Des Arc after a frog gigging trip. On an overcast Sunday night, Poole's pick-up truck headlights malfunctioned. The two men concluded that the headlight fuse on the older model truck had burned out. As a replacement fuse was not available, Wallis noticed that the .22 caliber bullet from his pistol fit perfectly into the fuse box next to the steering wheel column. Upon inserting the bullet, the headlights again began to operate properly and the two men proceeded on east-bound toward the White River bridge.
“After traveling approximately twenty miles and just before crossing the river, the bullet apparently overheated, discharged and struck Poole in the right testicle. The vehicle swerved sharply to the right exiting the pavement and striking a tree. Poole suffered only minor cuts and abrasion from the accident, but will require surgery to repair the other wound. Wallis sustained a broken clavicle and was treated and released.
"Thank God we weren't on that bridge when Thurston shot his nuts off or we might both be dead stated Wallis. "I've been a trooper for ten years in this part of the world, but this is a first for me. I can't believe that those two would admit how this accident happened", said Snyder.
“Upon being notified of the wreck, Lavinia, Poole's wife, asked how many frogs the boys had caught and did anyone get them from the truck.”
Factoid I :Almost all modern sensors are intended to ultimately generate an electrical output.
Factoid 2 :The sensor generates one of the following, which is a function of the phenomenon being measured:• a very small voltage or current• a variable resistance• a variable capacitance or inductance• a variable periodic pulse width or frequency
Basic types of sensor interface circuits• Differential Amplifier- Best for sensors with neither output wire internally grounded. Often produces very small voltages or currents susceptible to noise.• Balanced Resistive (Wheatstone) Bridge - For variable resistance sensors, or measuring a voltage against a reference.• Balanced Resonant Bridge - For variable inductance or capacitance sensors.• Optical Interface - For measurement of variable light transmission• Counter/timer Circuits - For totaling, timing or digitally integrating outputs of sensors that produce pulses.• Direct Digital Interface - When the native phenomena is already in binary format
Sensors, detectors and transducers that produce small voltages or currents
Examples: Thermocouple, photovoltaic (solar) cell, automotive exhaust oxygen sensor, microphone, guitar pickup, phono cartridge, piezo-electric (crystal) strain sensors, magnetic tape or computer hard drive head, pH probe, ECG or EEG measurements from skin contacts, capacitive switch, Geiger–Müller counter, magnetic position sensor.
Sensor usually produces a weak voltage.
Thevenin equivalent circuit
Sensor impedance
_
+
_+
Induced noise appears on both input wires if they are run close together
Example: Thermocouple
Some commonly used thermocouples:
Type Material Wire Color Temperature Range (deg C, deg F)
J Iron Constantan* Red/White 0 to 750C 32 to 1382F
K Chrome Alumel** Red/Yellow 200 to 1250C 328 to 2282F
T Copper Constantan Red/Blue 200 to 350C 328 to 662F
E Chrome Constantan Red/Purple 200 to 900C 328 to 1652F
* 55% copper and 45% nickel alloy** 95% nickel, 2% manganese, 2% aluminium, 1% silicon alloy
http://www.omega.com/techref/themointro.html
Two different metals welded together to form a junction (e.g., Iron-Constantan, Chromium-Alumel)
Measurement of small voltages: single-ended connection
Single-ended (grounded) sensor connection.Noise reduction method: passive EMI shielding
A voltage-producing sensor or transducer
+
_
grounded sensor
Single signal wire, often run in a shielded cable
shield
Op amp circuit amplifies signal and induced noise equally
Improved measurement of small voltages: differential connectionDifferential (floating) sensor connections.Noise reduction method: Common Mode Rejection (CMR).
Measurement junction
Ungrounded sensor
Both signal wires run close to each other as a twisted pair or in a shielded cable
+
_
Op amp circuit amplifies only the difference between the two floating inputs
Example: Thermocouple
Reference junction
Floating inputs – neither is grounded so induced noise voltage appears equally on both.
Sensors, detectors and transducers that produce variable resistancesExamples: Thermistor, piezoresistor or semiconductor strain gauge or pressure gauge, carbon grain microphone (telephone), CDS photocell, photodetector or phototransistor, skin resistance, thoracic impedance (for adaptive pacemaker, start of combustion (ionization) sensor, Hall effect sensor, simple switch.
Usually less susceptible to EMI noise due to lower impedance.
_+ Noise voltage
added to input voltage.
Sensor resistance varies with
phenomenon to be
measured
Rpull-up
Vref
Voltage varies with
phenomena to be measured
Example:Strain gauge using a balanced bridge circuit.
Differential voltage
measurement
R1 R3
VCC
Adjustable pot to “balance the bridge”
Strain gauge
The Operational Amplifier – a fundamental Analog IC
Almost every analog sensor requires one or more op-amps for its interface. They are typically used as differential amplifiers, with very high input impedance, low output impedance, and high gain. With negative feedback, they are highly linear.
+
_Inverting Input v-
Non-Inverting Input v+
Output y
The Operational Amplifier(a quick review of analysis and applications)
The Ideal Op-Amp Assumptions: 1. Zero output impedance2. Infinite input impedance
3. Infinite* differential gain, GD or just G
* implies that v+ v- for VOUT in linear range
4. Zero common mode gain, GCM
These assumptions are only valid at low-medium frequencies (bandwidth limited), and if we don’t care too much about the maximum rate that the output voltage can change (slew rate). Every op amp is characterized by a Gain-Bandwidth (GBW) Product that may limit the use of the device in a high-frequency application.
The Operational Amplifier
In an inverting configuration...
+
_v-
v+
Rf
Ri
VINVOUT
INi
fOUT V
R
RV
VV
:yieldsnodeVatKCL
0
The Operational Amplifier
Ideal Op-Amp analysis of inverting configuration...
INi
FOUT
IN
F
iOUT
OUT
f
OUTRf
i
INRi
RfRi
VR
RV
V
RR
)G(
GV
)()V(G)VV(GV
R
VVI
R
VVI
)(II
,G as
11
:get eventually to (2) and (1) Combine
20
. Vfor Solve (1). intoSubstitute
10
-
+_ VOUT =
G x (V+ - V-)
v+
Rf
Ri v-
VIN
IRi
IRf
The Operational Amplifier
In a non-inverting configuration...
+
_v-
v+
Ri
VIN
VOUT
Rf
INi
FOUT
IN
iF
iOUT
OUT
f
OUTRf
iRi
RfRi
VR
RV
V
RR
RG
GV
VGVVGV
R
VVI
R
VI
II
1 ,G as
1
:get eventually to(2) and (1) Combine
)2()0()(
. Vfor Solve (1). intoSubstitute
0
)1(0
-IRf
IRi
The Operational Amplifier A special case of the non-inverting
configuration: Unity gain follower...
+
_v-
v+
VIN
VOUT
INOUT
INOUT
OUTINOUT
VV
VG
GV
VVGV
G as1
)(
No gain, so what good is this circuit?
The Operational AmplifierAn analog weighted summing amplifier...
+
_v-
v+
Rf
R1
V1
VOUT
2
21
1
VR
RV
R
RV ff
OUT
V2
R2
The Differential AmplifierIdeally, only amplifies the difference between the two inputs. Used when neither side of a sensor connection is grounded. REJECTS COMMON-MODE NOISE
121
2
12
21
1
21
2
G For
1
VVR
RV
VV
RRR
G
RRR
G
V
OUT
OUT
VOUT
R1
+
_
R1
R2
R2
V1
V2
Differential Mode v.s. Common ModeDifferential Mode: amplifies V1 - V2Common Mode: amplifies V1 and V2
small very veryis G ere wh
)( :Gain ModeCommon
:Gain Mode alDifferenti
12
121
2
Common
CommonOUT
OUT
VVGV
VVR
RV
VOUT
R1
+
_
R1
R2
R2
V1
V2
Ratio of Common Mode Gain to Differential Mode Gain is the CMRR
Demonstration: Single-ended v.s. differential mode sensor interface
Demonstration Circuit 1. Single-ended (grounded) sensor connection, 1kHz signal plus 10kHz noise.
+
_v-
v+
Rf
R1
Vsignal
VOUT
VNoise
R2
Noise
fSignal
fOUT V
R
RV
R
RV
21
Demonstration Circuit 2. Differential amplifier (neither signal input grounded), 1kHz signal plus 10kHz noise.
+
_v-
v+
RfR1
VOUT
R2
Vsignal +
VNoise R2
Vsignal -
R1
)(1
SignalSignal
fOUT VV
R
RV
Note: R2 doesn’t matter
What if single-supply OP amp? (output can’t go below ground)
Use VRef instead of ground for non-inverting input. Note that new pseudo-ground will be Vref .
121
2Re
12
21
1
21
2
1
VVR
RVV
VV
RRR
G
RRR
G
V
fOUT
OUT
VOUT
R1
+
_
R1
R2
R2
V1
V2
VRef
VO
R1=1K
+
_
R3=3K
R3=3K
V1
V2
Q: V1 = 1 and V2 = 5, what is VOUT? Note that the input resistances are not equal.
R2=2K
VO
R1=1K
+
_
R3=3K
R3=3K
V1
V2
Q: V1 = 1 and V2 = 5, what is VOUT? Note that the input resistances are not equal.
R2=2K
A: Vout = 9 V
Volts9155
43
R
R
algebra... some0 Vset
0 Vat KCL
Vat KCL
1232
31
1
3
-
32
2
31
1-
VVRR
RRV
,V
R
V
R
VV
V,R
VV
R
VV
O
o
Improving the input impedance and gain of the differential
amplifier3-Op Amp Instrumentation Amplifier. Commonly used for sensor interfacing, especially biomedical applications.
+
_
R2 VOUT
+
_R3
+
_
V1
V2
R1
R3
R4
R4
R2
Why is it so awesome? High CMRR, high gain, and high input impedance.
+
_
R2A sensor that produces a tiny voltage, like a strain gauge or thermocouple
+
_R3
+
_
V1
V2
R1
R3
R4
R4
R2
+
_
R2
+
_R3
+
_
V1
V2
R1
R3
R4
R4
R2
VOUT
Q: R2=R3=R4=100K. Specify R1 such that the instrumentation amplifier below produces a differential gain of 40 dB.
Q: R2=R3=R4=100K. Specify R1 such that the instrumentation amplifier below produces a differential gain of 40 dB.
+
_
R2
+
_R3
+
_
V1
V2
R1
R3
R4
R4
R2
VO
A: R1= 2020 ohms
211
21
3
4o
'2
'1
3
4o
211
21'2
'1
1
21
21
'2
'1
VVR
2RV
VV V:stage Second
VVR
2RVV
R
VV
2R
VV :stage First
R
R
R
R
R
R
R
ohms202100R
20R
1
1
40R
20R
1
1log 20 Want
11
1
1
110
RK
or
dBK
Q: What if R2a not the same as R2b ? How does this affect the differential gain?
+
_
R2b
+
_R3
+
_
V1
V2
R1
R3
R4
R4
R2a
VOUT
Q: What if R2a not the same as R2b ? How does this affect the differential gain?
A: Doesn’t matter!
+
_
R2b
+_
R3
+
_
V1
V2
R1
R3
R4
R
4
R2a
VOUT
211
12b2a
3
4o
'2
'1
3
4o
211
12b2a'2
'1
1
21
212a
'2
'1
VVR
RRRV
VV V:stage Second
VVR
RRRVV
R
VV
R R
VV :stage First
R
R
R
R
R b
V’1
V’2
So why do we set R2a = R2b ?
i
Q: Why do we set R2a = R2b ?A: Maximum internal headroom.
Consider V’1 and V’2
individually...
+
_
R2b
+_ R3
+
_
V1
V2
R1
R3
R4
R
4
R2a
VO
213
4o
'2
'1
12b2a
'2
'1
12b2a
21
211
2b22b2
'2
211
2a12a1
'1
1
21
VV10K
30K Vcases, both In
volts 2 at center 101V
5221V
10R0R20R :Unequal
volts 0 at center 321V
321V
10RRR :case Balanced
1V1 VSuppose
VVR
RVRVV
VVR
RVRVV
R
VV i
R
R
K,,K
K
,
i
i
V’1
V’2
i
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