Digital Electronics: Principles, Devices and Applications

474 Digital Electronicshow different bits in the digital input data contribute a different quantum to the overall output analoguevoltage or current, and also that the LSB has the least and the MSB the highest weight.12.1.1 Simple Resistive Divider Network for D/A ConversionSimple resistive networks can be used to convert a digital input into an equivalent analogue output.Figure 12.1 shows one such resistive network that can convert a three-bit digital input into an analogueoutput. This network, however, can be extended further to enable it to perform digital-to-analogueconversion of digital data with a larger number of bits. In the network of Fig. 12.1, if R L is muchlarger than R it can be proved with the help of simple network theorems that the output analoguevoltage is given byV A = V 1/R + V 2 /R/2 + V 3 /R/41/R + 1/R/2 + 1/R/4= V 1/R + 2V 2 /R + 4V 3 /R1/R + 2/R + 4/R= V 1 + 2V 2 + 4V 37(12.1)(12.2)(12.3)which can be further expressed asV A = V 1 × 2 0 + V 2 × 2 1 + V 3 × 2 22 3 − 1(12.4)The generalized expression of Equation (12.4) can be extended further to an n-bit D/A converter toget the following expression:V A = V 1 × 2 0 + V 2 × 2 1 + V 3 × 2 2 + ··· +V n × 2 n−12 n − 1(12.5)In expression (12.5), if V 1 = V 2 = = V n = V , then a logic ‘1’ at the LSB position would contributeV/(2 n − 1) to the analogue output, and a logic ‘1’ in the next adjacent higher bit position wouldV 3R LV AV 2V 1R/4R/2RFigure 12.1Simple resistive network for D/A conversion.