# Using the DS4412 to Margin the Output Voltage of a DC-DC Converter

### 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.)

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}.