4.2 Theory of Operation

The DAC is used to create a current source. Although the DAC outputs a voltage signal V₀, the resistors in the circuit will create a current I₀ that is given by:

$I_0=\frac{V_0}{R_1+R_{SENSE}+R_2}$

The voltage divider rule gives the following equation for the voltage drop across R_SENSE:

$V_{SENSE}=V_0\times \frac{R_{SENSE}}{R_1+R_{SENSE}+R_2}$

If the expression for I₀ is substituted (the same current flows through all the resistors), the following expression is obtained:

$V_{SENSE}=I_0\cdot R_{SENSE}$

This, in turn, leads to:

$I_0=\frac{V_{SENSE}}{R_{SENSE}}$

Since R_SENSE is known, measuring the voltage drop across R_SENSE may determine the current.

With the output voltage V₀ set to 1V (DAC0 OUT) and using the resistor values as listed, the following result is obtained:

$V_{SENSE}=V_0\times \frac{R_{SENSE}}{R_1+R_{SENSE}+R_2}=1.0V\times \frac{10k\mathrm{\Omega }}{100k\mathrm{\Omega }+10k\mathrm{\Omega }+100k\mathrm{\Omega }}=47.6mV$

$I_0=\frac{V_{SENSE}}{R_{SENSE}}=\frac{47.6mV}{10k\mathrm{\Omega }}=4.8\mu A$