Build Coarse/Fine DAC Control

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 V_in = 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:

V_out = -D_A V_in - D_B V_in \[R₂/(R₁ + R₂)\] where D_A and D_B are the fractional representations of the digital input code N in decimal (i.e., D_A = N_A/256 and D_B = N_B/256), and where R₃ = R₄ = R₁ R₂ /(R₁ + R₂).

Reference:

1. "Input Resistor Stabilizes mDAC's Gain," A. Paul Brokaw, EDN, January 7, 1981, p. 210.