Abstract: A DS4412 adjustable-current DAC is used to adjust the margin of a DC-DC converter's output voltage. This article describes how to properly select the resistor values of a DC-DC converter's feedback divider network when a DS4412 is employed in the design.

The Adjustable Power Supply

The DS4412 contains two I²C adjustable current sources capable of sinking and sourcing current. A typical application for these DACs is margining the output voltage of a DC-DC converter. (See Figure 1.)


Figure 1. DC-DC converter circuit with adjustable-current DACs used to margin the converter's output voltage.

The DS4412 sinks and sources from its OUT pins. Valid full-scale current values range from 0.5mA to 2.0mA. The value of the full-scale current, I_FS, is determined by the size of the resistor connected to the DAC's FS pin of the corresponding OUT pin. The source/sink current generated by the DS4412 is most commonly used to adjust the DC-DC converter's feedback voltage divider.

Determining the Relationship Between V_OUT and I_FS

Choosing the right I_FS depends on how much margin is desired on the DC-DC converter's V_OUT pin. To determine this margin, we must discover the relationship between V_OUT and I_FS.

Summing currents into the V_FB node, we find that:



Where:



And



However, since R_B and V_FB are constant, there is no change in I_RB. Thus:



We are looking for the relationship between the margin on V_OUT, ΔV_OUT, and the selected range of I_FS, ΔI_FS. Since we know that the change in the I_FS current equals the change in the current across R_A, we can subtract one set of V_OUT and I_RA values from another to determine the relationship between V_OUT and I_FS.

First, solving Equation 3 to find V_OUT, we find that:



Use Equation 5 to create two equations. For one equation, we chose the maximum margin on V_OUT, V_OUTMAX, and the maximum I_RA current, I_RAMAX. For the other equation, we choose the nominal values for V_OUT and I_RA, V_OUTNOM and I_RANOM. Subtracting the two equations, we get:



Using Equation 4, Equation 6 translates into the relationship:



Equation 7 shows that the relationship between the margin on V_OUT and I_FS is determined by the value of the resistor R_A.

Calculating the Right Resistor Value for the Margin on V_OUT

Now that we know the relationship between V_OUT and I_FS, we can select the correct value of R_A and, thus, R_B to generate the desired margin on V_OUT. Since the full-scale current sink/source range of the DS4412 is 0.5mA to 2.0mA, we select 1mA as the I_FS current for the DAC. To set this value, choose R_FS based on the following equation found on page 6 of the DS4412 datasheet:



With V_RFS = 0.607V, we solve Equation 8 and find that R_FS needs to be 4.612kΩ to produce a 1mA full-scale current.

With the DS4412 I_FS selected, we must determine the size of R_A to achieve the desired margin on V_OUT. A 2.0V V_OUT with a 20% margin requires ±0.4V of change. Sinking and sourcing settings of the DS4412 will manage the sign. The change in I_FS equals the I_FS value of 1mA, and the desired change in V_OUT is 0.4V. After substituting for ΔV_OUT and ΔI_FS in Equation 7, we solve for R_A and get R_A = 400Ω.

Determining the Relationship Between R_A and R_B

The feedback network of the circuit in Figure 1 is a voltage-divider with resistors R_A and R_B. Looking at Figure 1 and assuming I_FS = 0A, we can create a simple voltage-divider equation.



We assume that the desired nominal value for V_OUT is 2.0V and the DC-DC converter has a feedback voltage, V_FB, of 0.8V. Substituting the values for V_OUT and V_FB, the relationship between R_A and R_B is determined to be



We use Equation 10 to solve for R_B and get R_B = 267Ω.

Conclusion

The resistive-feedback-divider network and the current-sinking/sourcing capabilities of the DS4412 DACs control the margin of V_OUT of a DC-DC converter. The relationship between the full-scale current, I_FS, to the margin on V_OUT is determined by the value of the resistor R_A. By choosing the correct I_FS value for your application, you can determine the correct resistor values for the feedback divider network, and achieve the desired margin on V_OUT.