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Homework Solutions 1

Homework Solutions 1 - BENG 186B Principles of...

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BENG 186B Principles of Bioinstrumentation Week 1 Review Solutions Selections from: 2012 Homework 1 2012 Homework 2
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BENG 186B Homework 1 SOLUTIONS 1. Consider the following circuit: a 1 a 0 a 2 a 3 2R 2R 2R 2R 2R R R R V out a) Calculate V out as a function of voltages a 3 , a 2 , a 1 , and a 0 . b) Assuming a n only take binary values 0V or 1V, show a table of V out for all possible combinations of the bits a n (i.e. [0000, 0001, 0010, 0011…] where a 0 is the least significant bit). c) What is the resolution of the output V out ? d) What is the worst-­૒case accuracy of the output V out when the leftmost resistor 2R has a relative error of 1%? What are the binary values of a 3 , a 2 , a 1 , and a 0 ? e) What is the worst-­૒case accuracy of the output V out when the rightmost resistor 2R has a relative error of 1%? What are the binary values of a 3 , a 2 , a 1 , and a 0 ? f) In one sentence, what is the function of this circuit?
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2. A photodiode is a semiconductor device that can be used as a light transducer. It behaves ideally in the following fashion: ! = ! ! ! !"! + ! ! ! ! ! ! 1 Where: ! ! ! !"! is the positive photocurrent, linearly proportional to the irradiance; ! ! is the thermal voltage, 25mV at room temperature; ! ! is the reverse saturation current, 100nA. a) Find the open circuit voltage V (when the photodiode is not loaded) as a function of ! ! ! !"! . Plot V for ! ! ! !"! ranging from 0 to 1uA. b) At what photocurrent and output voltage is the sensitivity maximum? What is the sensitivity there?
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