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RG RM AI VOUT Digital Input, Di DACI Figure QI Figure QI shows the circuit used to condition the output of the n- bit Digital to Analog Converter "DACI" having a digital input value of Da. DACI may be assumed to have a voltage output with zero source resistance coded in "straight binary" such that • For a binary input of Dw000...000 the output voltage vae is 0 V

RG RM AI VOUT Digital Input, Di DACI Figure QI Figure QI shows the circuit used to condition the output of the n- bit Digital to Analog Converter "DACI" having a digital input value of Da. DACI may be assumed to have a voltage output with zero source resistance coded in "straight binary" such that • For a binary input of Dw000...000 the output voltage vae is 0 V

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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QI Ref RG RM A1 Vou VOUT Digital A DACI Input, DIN VDAC Figure QI Figure QI shows the circuit used to condition the output of the n- bit Digital to Analog Converter "DACI" having a digital input value of Dw. DACI may be assumed to have a voltage output with zero source resistance coded in "straight binary" such that • For a binary input of Dy = 000...000 the output voltage vaac is 0 V • For a binary input of Dw = 111..111 the output voltage vaac is Vn Where Vg is a positive voltage reference. Neglecting Ry and assuming that opamp Al is ideal, show that the output voltage v, is (а) OUT R. for D, - 000000 R (i) Vay- ref (ii) Vor for D,-111..111 Hence choose values of Ro and R to give an output voltage range -V Svar S (iii) Re-draw Figure Q1 to show all sources of DC opamp error and say why they have the signs you have given them. (b) Hence derive an expression for the emor in vug due to opamp DC input cur. and voltage errors including both bias and offset currents. (c) If the two resistors R and R, have a tolerance of + p% what is the error in Vour due to resistor tolerance for (d) (i) Day = 111.11? (ii) Dy= 000..000? DACI is a 16 bit DAC and Vg has a value of +4-096 V. What is the value of the minimum voltage change at vour, ie. the voltage change when Dw is increased by I bit? (e) Al is one of the three opamps indicated below in Table Q1. Choose appropriate values of Ru. Ra and Ru and explain why you chose these values. () Offset voltage, pV 20 Offset current I nA 0.5 pA 40 fA Opamp OPA277E Bias current I nA I pA AD8616ARZ 60 LMP772IMA 180 20 fA Table QI (g) (i) Using your answers from (c) and (), define a figure of merit for Al and hence select the best opamp for the circuit. (ii) How many bits of error do the opamp DC voltage and current eror contribute? (h) Resistors are available with tolerances of 1%, 0.1% and 0.01% with prices of £0.002, £0.027 and £7.60 respectively. Single turn potentiometers cost £0.07 and ten turn trimmer potentiometers cost £0.68. If the resistors must cause no more error than 1 bit, design a circuit using fixed resistors and a potentiometer to allow the output to be trimmed to within 1 least significant bit accuracy over its full range, neglecting errors other than resistor tolerance. The adjustment range of the potentiometer should be just enough to allow the output accuracy to be achieved. Specify the tolerance of all fixed resistors used. Hint: In (h), the question does not contain all the information you need to complete the design, so you will need to use your judgement on some thine These decisions should be stated and justified
Transcribed Image Text:QI Ref RG RM A1 Vou VOUT Digital A DACI Input, DIN VDAC Figure QI Figure QI shows the circuit used to condition the output of the n- bit Digital to Analog Converter "DACI" having a digital input value of Dw. DACI may be assumed to have a voltage output with zero source resistance coded in "straight binary" such that • For a binary input of Dy = 000...000 the output voltage vaac is 0 V • For a binary input of Dw = 111..111 the output voltage vaac is Vn Where Vg is a positive voltage reference. Neglecting Ry and assuming that opamp Al is ideal, show that the output voltage v, is (а) OUT R. for D, - 000000 R (i) Vay- ref (ii) Vor for D,-111..111 Hence choose values of Ro and R to give an output voltage range -V Svar S (iii) Re-draw Figure Q1 to show all sources of DC opamp error and say why they have the signs you have given them. (b) Hence derive an expression for the emor in vug due to opamp DC input cur. and voltage errors including both bias and offset currents. (c) If the two resistors R and R, have a tolerance of + p% what is the error in Vour due to resistor tolerance for (d) (i) Day = 111.11? (ii) Dy= 000..000? DACI is a 16 bit DAC and Vg has a value of +4-096 V. What is the value of the minimum voltage change at vour, ie. the voltage change when Dw is increased by I bit? (e) Al is one of the three opamps indicated below in Table Q1. Choose appropriate values of Ru. Ra and Ru and explain why you chose these values. () Offset voltage, pV 20 Offset current I nA 0.5 pA 40 fA Opamp OPA277E Bias current I nA I pA AD8616ARZ 60 LMP772IMA 180 20 fA Table QI (g) (i) Using your answers from (c) and (), define a figure of merit for Al and hence select the best opamp for the circuit. (ii) How many bits of error do the opamp DC voltage and current eror contribute? (h) Resistors are available with tolerances of 1%, 0.1% and 0.01% with prices of £0.002, £0.027 and £7.60 respectively. Single turn potentiometers cost £0.07 and ten turn trimmer potentiometers cost £0.68. If the resistors must cause no more error than 1 bit, design a circuit using fixed resistors and a potentiometer to allow the output to be trimmed to within 1 least significant bit accuracy over its full range, neglecting errors other than resistor tolerance. The adjustment range of the potentiometer should be just enough to allow the output accuracy to be achieved. Specify the tolerance of all fixed resistors used. Hint: In (h), the question does not contain all the information you need to complete the design, so you will need to use your judgement on some thine These decisions should be stated and justified
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