Design of Digital to Analog Converters with Arbitrary Radix

There are DAC structures available in the literature for radix r = 2, 3, and 4; but how they are arrived at is missing. No general structure is available for any radix r. The aim of the paper is, therefore, to fulfil these gaps. To start with, the design relations are derived for the simplest possible attenuator circuit when connected to a voltage source V and a series resistance R, such that the complete circuit offers the Thevenin resistance R. Spread relations for this attenuator are derived. An example when 3 such attenuators with different attenuation constants are connected in cascade is given. Interestingly, the two attenuators with attenuation factors 1/2 and 1/3 have the same spread of 2. A generalized attenuator is then obtained when N number of identical attenuators are connected in cascade. This is modified to derive a digital to analog converter for any radix r.