ENGR 1121 Real World Measurements Franklin Olin College of Engineering, Spring 2011

1. ENGR 1121 Real World Measurements Franklin Olin College of Engineering, Spring 2011 The Op Amp and Differential Amplifier – the workhorses of Analog Sensor Interfaces

2. Hazards of not understanding electrical interfaces From 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.”

3. 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

4. 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

5. 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 impedance + Sensor usually produces a weak voltage. Induced noise appears on both input wires if they are run close together _ + _ Thevenin equivalent circuit

6. Example: Thermocouple Two different metals welded together to form a junction (e.g., Iron-Constantan, Chromium-Alumel) 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

7. Measurement of small voltages: single-ended connection Single-ended (grounded) sensor connection. Noise reduction method: passive EMI shielding shield _ Single signal wire, often run in a shielded cable + A voltage-producing sensor or transducer Op amp circuit amplifies signal and induced noise equally grounded sensor

8. Improved measurement of small voltages: differential connection Differential (floating) sensor connections. Noise reduction method: Common Mode Rejection (CMR). Example: Thermocouple Floating inputs – neither is grounded so induced noise voltage appears equally on both. Measurement junction _ + Op amp circuit amplifies only the difference between the two floating inputs Both signal wires run close to each other as a twisted pair or in a shielded cable Ungrounded sensor Reference junction

9. Sensors, detectors and transducers that produce variable resistances Examples: 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. Vref Rpull-up Voltage varies with phenomena to be measured Sensor resistance varies with phenomenon to be measured Noise voltage added to input voltage. + _

10. Example: Strain gauge using a balanced bridge circuit. VCC R1 R3 Adjustable pot to “balance the bridge” Strain gauge Differential voltage measurement

11. 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. + Non-Inverting Input v+ Output y _ Inverting Input v-

12. The Operational Amplifier(a quick review of analysis and applications) • The Ideal Op-Amp Assumptions: • Zero output impedance • Infinite input impedance • Infinite* differential gain, GD or just G • * implies that v+ v- for VOUT in linear range • 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.

13. The Operational Amplifier In an inverting configuration... Rf Ri v- _ VIN v+ VOUT +

14. The Operational Amplifier Ideal Op-Amp analysis of inverting configuration... Rf IRf Ri v- VIN IRi + VOUT = G x (V+ - V-) _ v+

15. The Operational Amplifier In a non-inverting configuration... v+ + VIN v- _ VOUT IRf Rf Ri IRi

16. The Operational Amplifier A special case of the non-inverting configuration: Unity gain follower... v+ + VIN v- _ VOUT No gain, so what good is this circuit?

17. The Operational Amplifier An analog weighted summing amplifier... Rf R1 V1 v- _ V2 v+ VOUT + R2

18. The Differential Amplifier Ideally, only amplifies the difference between the two inputs. Used when neither side of a sensor connection is grounded. REJECTS COMMON-MODE NOISE R2 R1 _ V1 + VOUT V2 R1 R2

19. Differential Mode v.s. Common Mode Differential Mode: amplifies V1 - V2 Common Mode: amplifies V1 and V2 R2 R1 _ V1 + VOUT V2 Ratio of Common Mode Gain to Differential Mode Gain is the CMRR R1 R2

20. Demonstration: Single-ended v.s. differential mode sensor interface

21. Demonstration Circuit 1. Single-ended (grounded) sensor connection, 1kHz signal plus 10kHz noise. Rf R1 Vsignal v- _ VNoise v+ VOUT + R2

22. Demonstration Circuit 2. Differential amplifier (neither signal input grounded), 1kHz signal plus 10kHz noise. R1 Rf Vsignal + Note: R2 doesn’t matter R2 v- _ VNoise R2 v+ VOUT + R1 Vsignal -

23. 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 . R2 R1 _ V1 + VOUT V2 R1 R2 VRef

24. Q: V1 = 1 and V2 = 5, what is VOUT? Note that the input resistances are not equal. R3=3K R1=1K _ V1 + VO V2 R2=2K R3=3K

25. Q: V1 = 1 and V2 = 5, what is VOUT? Note that the input resistances are not equal. A: Vout = 9 V R3=3K R1=1K _ V1 + VO V2 R2=2K R3=3K

26. Improving the input impedance and gain of the differential amplifier 3-Op Amp Instrumentation Amplifier. Commonly used for sensor interfacing, especially biomedical applications. R4 V1 + _ R3 R2 _ R1 R2 + VOUT R3 _ + V2 R4

27. Why is it so awesome? High CMRR, high gain, and high input impedance. V1 R4 + _ R3 R2 _ R1 R2 + A sensor that produces a tiny voltage, like a strain gauge or thermocouple R3 _ + R4 V2

28. Q: R2=R3=R4=100K. Specify R1 such that the instrumentation amplifier below produces a differential gain of 40 dB. R4 V1 + _ R3 R2 _ R1 VOUT R2 + R3 _ + V2 R4

29. Q: R2=R3=R4=100K. Specify R1 such that the instrumentation amplifier below produces a differential gain of 40 dB. A: R1= 2020 ohms R4 V1 + _ R3 R2 _ R1 VO R2 + R3 _ + V2 R4

30. Q: What if R2a not the same as R2b ? How does this affect the differential gain? R4 V1 + _ R3 R2a _ R1 VOUT R2b + R3 _ + V2 R4

31. Q: What if R2a not the same as R2b ? How does this affect the differential gain? A: Doesn’t matter! R4 V1 + _ R3 V’1 R2a _ i R1 VOUT R2b + So why do we set R2a =R2b ? R3 _ + V2 R4 V’2

32. Q: Why do we set R2a = R2b ? A: Maximum internal headroom. Consider V’1 andV’2 individually... R4 V1 + _ R3 V’1 R2a _ i R1 R2b + VO R3 _ + V2 R4 V’2