# Shunt voltage reference bias resistor calculator

Voltage reference

Part Nº

Voltage reference part number

$$V_{ref(min)}$$

Reference voltage (min)

$$V_{ref(max)}$$

Reference voltage (max)

$$I_{refmin(max)}$$

Reference minimum operating current (max)

Supply

$$V_{supply(min)}$$

Supply voltage (min)

$$V_{supply(max)}$$

Supply voltage (max)

$$I_{load(max)}$$

Bias resistor

$$R_{bias(max)}$$

Resistance (max)

Exact
Standard

$$P_{bias(max)}$$

Resistor power dissipation (max)

Exact
For chosen standard values
Voltage reference

$$P_{ref(max)}$$

Reference power dissipation (max)

Exact
For chosen standard values
Total

$$P_{total(max)}$$

Total power dissipation (max)

Exact
For chosen standard values

## Discussion

The bias resistor for a shunt reference must guarantee that current through the reference never falls below its minimum operating current.

Shunt reference works by sinking precisely the right amount of current to establish voltage $$V_{ref}$$ on its reference lead: \begin{aligned} I_{bias} & = I_{ref} + I_{load} \\ V_{supply} & = V_{ref} + R_{bias} I_{bias} \\ \Rightarrow I_{ref} & = {{V_{supply} - V_{ref}} \over R_{bias}} - I_{load} \end{aligned}

$$I_{ref}$$ is required to remain above the minimum reference operating current $$I_{refmin}$$; the maximum value for the minimum reference operating current, $$I_{refmin(max)}$$, is given in datasheet. The lowest value of $$I_{ref}$$ occurs when supply voltage is at a minimum, reference voltage is at a maximum and load current is at a maximum.

Component parameters that determine minimum viable value of the external resistor are:

• Maximum reference voltage $$V_{ref(max)}$$
• Maximum of minimum reference operating current $$I_{refmin(max)}$$
• Minimum supply voltage $$V_{supply(min)}$$
• Maximum load current $$I_{load(max)}$$

Therefore:

\begin{aligned} I_{ref} & \ge {{V_{supply(min)} - V_{ref(max)}} \over R_{bias}} - I_{load(max)} \ge I_{refmin(max)} \\ \Rightarrow R_{bias} & \le {{V_{supply(min)} - V_{ref(max)}} \over {I_{load(max)} + I_{refmin(max)}}} = R_{bias(max)} \end{aligned}

Both the bias resistor and the voltage reference will dissipate some power.

\begin{aligned} P_{bias} & = {V_{bias}^2 \over R_{bias}} \\ & = {(V_{supply} - V_{ref})^2 \over R_{bias}} \\ & \le {(V_{supply(max)} - V_{ref(max)})^2 \over R_{bias(min)}} = P_{bias(max)} \\ P_{ref} & = V_{ref} I_{ref} \\ & = V_{ref} ({{V_{supply} - V_{ref}} \over R_{bias}} - I_{load}) \\ & \le V_{ref(max)} {{V_{supply(max)} - V_{ref(max)}} \over R_{bias(min)}} = P_{ref(max)} \end{aligned}

## Acknowledgements

This calculator and the discussion are based on Maxim Application Note 4003.

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