9780199339136, Chapter 1, Problem 37P

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Chapter 1, Problem 37P Step-by-step solution Step of 4 Refer to the Digital-to- analog converter in Figure P1.37 in the (a) The current is the sum of currents flowing through the resistances 2R through The voltage across all the resistances is same because potential difference exists between two points is unique. Hence, by Kirchhoff's law the node, = 2R 4R 8R 2NR = +...+ 2R R = Thus, the expression for the output current is, = 2 Step of 4 (b) From the output current expression, the least significant bit (LSB) is, = 2N R Thus, the LSB is From the output current expression, the most significant bit (MSB) is, Thus, the MSB is 2R Step of 4 (c) The expression for the output current is, = Substitute 10 V for 10 kΩ for R, and 8 for N. = 10x10 10 = 10 For the maximum current, all the bits through b₈ must equal to 1. Hence, 10 = 10⁻³ = 0.99609375 mA Thus, the maximum value of current is 0.99609375 mA Step of 4 For LSB = 0: the b it The current is, = 10 = 10⁻³ = 0.9921875 mA For LSB = 1: the The current is, 11111111 = 10 = 10⁻³ = 0.99609375 mA The change in is = = -0.00390625 mA Thus, the change in is resulting from the LSB changing from 0 to 1 is -0.00390625 mA