Design Ideas: March 28, 1996
An R-2R resistive ladder network with a matched feedback resistor (Figure 1) is the core of the typical D/A converter, whether fabricated in discrete, hybrid, or CMOS-monolithic form. In this configuration, thermal effects can degrade performance, causing poor settling characteristics and transfer-function nonlinearity in the low-frequency range. The addition of a second feedback resistor, R2, can reduce the degradation.Assuming the analog input VREF is constant, the power dissipation in the ladder is also constant. That is, no thermal transients occur in the ladder's resistors when the digital-input code changes. However, the power in feedback resistor R1 varies significantly as a function of the digital-input code. The effects of this thermal phenomenon are difficult to detect. You won't catch the effects with any standard, high-speed dynamic test procedures. The problem is that the thermal inertia of the feedback resistor produces power averaging, thereby masking the thermal effects. Only low- and ultra-low-frequency testing can reveal the degradation.
If you connect R2 to a second op amp, IC2, and thermally couple R2 to R1, the total power in the feedback resistor will be less dependent on the digital-input code than if R1 stands alone. The proof is as follows: In a standard R-2R ladder (without R2), the total power in the ladder resistors is constant, namely P=V2/R, where V is the reference voltage. However, the power in R1 varies from zero to approximately V2/R, the power in the entire ladder of resistors.
After adding the second feedback resistor R2, and assuming R2=R1=R, the equation for power in the feedback resistors is:
where Di designates the binary coefficients of the input code. This function varies from a minimum of V2/2R to V2/R. The variation in power vs input code is thus reduced substantially.