A simple coarse/fine audio or signal attenuator can be built by combining two 8-bit DACs to yield an effective resolution of up to 14 bits (see the figure). Taking a close look at the figure, resistors R1 and R2 are all that's needed to combine the current outputs of a dual 8-bit DAC like the AD7528.
R1 and R2 attenuate the input signal into DAC B by the desired amount. For example, if R1 = 63 × R2, then ideally the "fine" reference voltage of DAC B is 1/64 the "coarse" reference of DAC A, and the total range covered by DAC B is equal to 4 LSBs of DAC A. To illustrate further, if Vin = 2.56 V, then the reference voltage of DAC B is 40 mV and the theoretical LSB size for DAC B is 156 mV. Whether or not all of DAC B's bits are usable (their combined output remains monotonic) depends on the ratio of R1 and R2, and the input offset voltage of amplifier A1, which contributes a code-dependent noise gain term.
There are a number of drawbacks to consider, however, when dealing with this circuit. First, the "fine" DAC reference voltage isn't simply a function of the ratio of R1 to R2. It must also include the loading effect of the DAC reference input resistance appearing across R2. Getting a precise, repeatable reference for DAC B is extremely difficult. The problem is defused somewhat by making the value of resistor R2 much lower than the minimum DAC ladder resistance.
A second problem is that the temperature coefficient (TC) of R1 and R2 won't match that of the DAC ladder. This will cause a shift in the value of the "fine" DAC reference, and thus a shift in the DAC B's weight.
These problems can be overcome by including R3 in series with RFB A, which is the on-chip feedback resistor of DAC A. R3 must have a value equal to the parallel combination of R1 and R2.1 Choosing this value ensures that the DAC ladder resistance's value drops out of the circuit transfer function, making the DAC B reference voltage solely a function of the ratio of R1 to R2. R3 should also have a similar TC to R1 and R2, but these TCs don't have to match the TCs of the DACs at this moment. R , in series with the DAC A reference input and equal to R3, compensates for R3 in the A1 feedback loop.
The output voltage expression for the complete circuit is:
Vout = -DA Vin - DB Vin \[R2/(R1 + R2)\] where DA and DB are the fractional representations of the digital input code N in decimal (i.e., DA = NA/256 and DB = NB/256), and where R3 = R4 = R1 R2 /(R1 + R2).
1. "Input Resistor Stabilizes mDAC's Gain," A. Paul Brokaw, EDN, January 7, 1981, p. 210.