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Q2 R R-A VIN) O A2 VOUT VIN(+) O R R+ 4 Figure Q2 (a) (a) Figure Q2 (a) shows the circuit diagram of part of an instrumentation amplifier. (i) Derive expressions for the differential and common-mode gains of the circuit. (ii) State the values of 4 for the three cases that the resistors have a tolerance of 1%, 0.1% and 0.01%. (b) Draw the diagram of a traditional three-opamp instrumentation amplifier. Write down expressions for the differential and common-mode gains of the complete circuit, including the circuit fragment shown in Figure Q2(a). A "Scanning Thermal Microscope" is used to image the temperature of a surface by moving a small thermometer across it. The thermometer consists of a small resistance element whose resistance changes with temperature such that (c) RSTEM = R, + aT {Equation 2} Where Ro = 1102 a= 0.2 Q/ °C The sensor has a thermal resistance to ambient of 2 × 10$ °C/W. The resistance is to be measured using a resistance bridge with three equal resistors as well as the probe. Design the bridge choosing values for the bridge resistors and bridge voltage given that the probe temperature should rise by no more than 0.5°C due to heating from the current flowing through it.

Q2 R R-A VIN) O A2 VOUT VIN(+) O R R+ 4 Figure Q2 (a) (a) Figure Q2 (a) shows the circuit diagram of part of an instrumentation amplifier. (i) Derive expressions for the differential and common-mode gains of the circuit. (ii) State the values of 4 for the three cases that the resistors have a tolerance of 1%, 0.1% and 0.01%. (b) Draw the diagram of a traditional three-opamp instrumentation amplifier. Write down expressions for the differential and common-mode gains of the complete circuit, including the circuit fragment shown in Figure Q2(a). A "Scanning Thermal Microscope" is used to image the temperature of a surface by moving a small thermometer across it. The thermometer consists of a small resistance element whose resistance changes with temperature such that (c) RSTEM = R, + aT {Equation 2} Where Ro = 1102 a= 0.2 Q/ °C The sensor has a thermal resistance to ambient of 2 × 10$ °C/W. The resistance is to be measured using a resistance bridge with three equal resistors as well as the probe. Design the bridge choosing values for the bridge resistors and bridge voltage given that the probe temperature should rise by no more than 0.5°C due to heating from the current flowing through it.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Q2 R R- A VIN(-) A2 VOUT VIN(+) R R+ 4 Figure Q2 (a) (a) Figure Q2 (a) shows the circuit diagram of part of an instrumentation amplifier. (i) Derive expressions for the differential and common-mode gains of the circuit. (ii) State the values of 4 for the three cases that the resistors have a tolerance of 1%, 0.1% and 0.01%. (b) Draw the diagram of a traditional three-opamp instrumentation amplifier. Write down expressions for the differential and common-mode gains of the complete circuit, including the circuit fragment shown in Figure Q2(a). A “Scanning Thermal Microscope" is used to image the temperature of a surface by moving a small thermometer across it. The thermometer consists of a small resistance element whose resistance changes with temperature such that (c) R- RSTHM + aT {Equation 2} Where Ro = 1102 α- 0.2 Ω/ C The sensor has a thermal resistance to ambient of 2 x 105 °C / W. The resistance is to be measured using a resistance bridge with three equal resistors as well as the probe. Design the bridge choosing values for the bridge resistors and bridge voltage given that the probe temperature should rise by no more than 0.5°C due to heating from the current flowing through it.
Transcribed Image Text:Q2 R R- A VIN(-) A2 VOUT VIN(+) R R+ 4 Figure Q2 (a) (a) Figure Q2 (a) shows the circuit diagram of part of an instrumentation amplifier. (i) Derive expressions for the differential and common-mode gains of the circuit. (ii) State the values of 4 for the three cases that the resistors have a tolerance of 1%, 0.1% and 0.01%. (b) Draw the diagram of a traditional three-opamp instrumentation amplifier. Write down expressions for the differential and common-mode gains of the complete circuit, including the circuit fragment shown in Figure Q2(a). A “Scanning Thermal Microscope" is used to image the temperature of a surface by moving a small thermometer across it. The thermometer consists of a small resistance element whose resistance changes with temperature such that (c) R- RSTHM + aT {Equation 2} Where Ro = 1102 α- 0.2 Ω/ C The sensor has a thermal resistance to ambient of 2 x 105 °C / W. The resistance is to be measured using a resistance bridge with three equal resistors as well as the probe. Design the bridge choosing values for the bridge resistors and bridge voltage given that the probe temperature should rise by no more than 0.5°C due to heating from the current flowing through it.
(d) Derive expressions for the common mode and differential voltages produced by your bridge as a function of temperature, accurate to first order in temperature. You may wish to make use of the binomial theorem (e) The output of your bridge is to be amplified using an instrumentation amplifier. Design the instrumentation amplifier to meet the following specifications Vour = 10mV ´T Where Tis the temperature in °C as defined in {Equation 2} The error due to the common-mode rejection of the instrumentation amplifier is specified to be no more than 0.1°C in measured temperature The gain error of the system is no more than 2% The system is powered by a + 5V power supply Design the instrumentation amplifier including the values and tolerances of all components. (f) The three opamps used in this instrumentation amplifier are one of the types shown in Table Q2. Without detailed calculation, pick an opamp type and justify your choice Component CMRR (dB) Price (£) LT1180 116 2.08 TLC2201 85 4.2 LMH6642 95 0.6 AD8091 88 1.28 Table Q2
Transcribed Image Text:(d) Derive expressions for the common mode and differential voltages produced by your bridge as a function of temperature, accurate to first order in temperature. You may wish to make use of the binomial theorem (e) The output of your bridge is to be amplified using an instrumentation amplifier. Design the instrumentation amplifier to meet the following specifications Vour = 10mV ´T Where Tis the temperature in °C as defined in {Equation 2} The error due to the common-mode rejection of the instrumentation amplifier is specified to be no more than 0.1°C in measured temperature The gain error of the system is no more than 2% The system is powered by a + 5V power supply Design the instrumentation amplifier including the values and tolerances of all components. (f) The three opamps used in this instrumentation amplifier are one of the types shown in Table Q2. Without detailed calculation, pick an opamp type and justify your choice Component CMRR (dB) Price (£) LT1180 116 2.08 TLC2201 85 4.2 LMH6642 95 0.6 AD8091 88 1.28 Table Q2
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