Theory of Operation

A 4–20-mA V-to-I current transmitter takes a differential voltage as the input and outputs a current with a linear relationship from input to output. This linear relationship depends on the common-mode range of the op amp and the headroom available for the transistor and LDO. Furthermore, a current transmitter designed with a 2-wire loop requires that the quiescent current drawn from all components on the loop path consume less than the minimum output current I_{out_min} – 4 mA in this design. This includes the op amp, LDO, the current through the R₃ and R₅ branch, and any other peripherals that are on the same supply loop. As long as this requirement is met, the op amp and transistor compensate to supply the remaining current to the loop to output the correct current to the load resistor.

The output current I_out is the sum of the currents through R₃ and R₄, I₃, and I₄, respectively:

I₃ is set by R₁ and R₂, along with the input voltage V_in and regulated supply V_reg. Under ideal operation, the non-inverting terminal of the op amp has a virtual short to the local ground, I_ret. Notice also that V_reg and V_in are referenced to I_ret. I₃ is then the following:

I₄ is the sum of the local ground return current I_ret and the compensating current through the transistor T₁.

For correct operation of the op amp, the voltages across R₃ and R₄ must be equal, so we have V₃ = V₄ and it follows that:

The previous equation is rewritten as:

Combining the first equation, second equation, and previous equation, the transfer function for the circuit is derived as:

It is apparent, then, that the current through R₃ that is set by R₁, R₂, V_in, and V_reg is amplified by the factor
1 + R₃ / R₄.