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Figure Q2a shows the circuit diagram of part of an instrumentation amplifier. Show that the differential and common mode gains of the circuit are given by 2R,+R, and Aey1 respectively. R,

Figure Q2a shows the circuit diagram of part of an instrumentation amplifier. Show that the differential and common mode gains of the circuit are given by 2R,+R, and Aey1 respectively. R,

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
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Q2 Vi (+) O- VOUT (+) A2a RA RA A2b VOUT-) Figure Q2a (a) Figure Q2a shows the circuit diagram of part of an instrumentation amplifier. Show that the differential and common mode gains of the circuit are given by 2R,+R and 4,cu =1 respectively. R, 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 Q2a. (b)
Transcribed Image Text:Q2 Vi (+) O- VOUT (+) A2a RA RA A2b VOUT-) Figure Q2a (a) Figure Q2a shows the circuit diagram of part of an instrumentation amplifier. Show that the differential and common mode gains of the circuit are given by 2R,+R and 4,cu =1 respectively. R, 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 Q2a. (b)
Q2 (d) The resistance of the PTI00 element varies such that RR+ BT+CT BRIDGE Ro R where R,- 1002 "Sense" C=-5.75 - 10'Q'C Vor VOUT A2 Tis the temperature in "C "Ref" And therefore 8(r)- 8T +Cr* Ro Ro Using your answer to part e) derive an expression for the differential voltage at the input of the instrumentation amplifier A2. V as a function of the temperature in "C, accurate to second order including both nonlincarities due to the bridge and the sensor. () (u) Calculate the nonlincarity eror of the system (expressed as a temperature eror) at 20°C (ie. the deviation in temperature reading due to the size of the nonlinear signal at 20°C). Figure Q2e Figure Q2e shows a resistance bridge incorporating a platinum resistance thermometer, PTI00", which is a resistor whose resistance R, varies as a (i) The current through R, is Ima at O°C. What is the common-mode voltage at the amplifier input? Q2 (c) (e) function temperature such that R, -R +8(T) where 8(T)<R () What is the gain required to give a lincar output signal of 100mVrC? Amplifier A2 is the instrumentation amplifier you described in part b) By making use of the binomial theorem or otherwise, derive a polynomial expression for V as a function of R, correct to second order. The binomial theorem states that: (ii) If the error due to common mode rejection of A2 must be 001'C what is the CMRR roquired for A2? Design the instrumentation amplifier A2 including all resistor values and tolerances. (1+x) =t+ pr+ Plp-1), 2!
Transcribed Image Text:Q2 (d) The resistance of the PTI00 element varies such that RR+ BT+CT BRIDGE Ro R where R,- 1002 "Sense" C=-5.75 - 10'Q'C Vor VOUT A2 Tis the temperature in "C "Ref" And therefore 8(r)- 8T +Cr* Ro Ro Using your answer to part e) derive an expression for the differential voltage at the input of the instrumentation amplifier A2. V as a function of the temperature in "C, accurate to second order including both nonlincarities due to the bridge and the sensor. () (u) Calculate the nonlincarity eror of the system (expressed as a temperature eror) at 20°C (ie. the deviation in temperature reading due to the size of the nonlinear signal at 20°C). Figure Q2e Figure Q2e shows a resistance bridge incorporating a platinum resistance thermometer, PTI00", which is a resistor whose resistance R, varies as a (i) The current through R, is Ima at O°C. What is the common-mode voltage at the amplifier input? Q2 (c) (e) function temperature such that R, -R +8(T) where 8(T)<R () What is the gain required to give a lincar output signal of 100mVrC? Amplifier A2 is the instrumentation amplifier you described in part b) By making use of the binomial theorem or otherwise, derive a polynomial expression for V as a function of R, correct to second order. The binomial theorem states that: (ii) If the error due to common mode rejection of A2 must be 001'C what is the CMRR roquired for A2? Design the instrumentation amplifier A2 including all resistor values and tolerances. (1+x) =t+ pr+ Plp-1), 2!
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