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