# Understanding the odd behavior of this current loop transmitter

In my assignment, I want to study this current transmitter circuit shown in the figure 1. The goal of this circuit is to output a constant load current $$\ i_L\$$ (denoted by $$\ I_L\$$ in the diagram) controlled by $$\ v_S\$$ (operating within a certain range of $$\ v_S\$$ and $$\ R_L\$$). I derived the expression for relating $$\ v_S\$$ and $$\i_L\$$; that expression is (see figure 2) $$\dfrac{i_L}{v_S}=-\dfrac{1}{R_2}$$ The circuit simulation can be found on Multisim online here.

In the assignment question, the circuit is specified to work for $$|v_S|<1 V, R_L < 1k\Omega$$ However, the circuit does not behave according to the relation $$\ i_L/v_S=-1/R_2\$$ at those extreme conditions (being $$\v_S=1 V, R_L = 1k\Omega\$$), and it's probably because the op-amp output voltage $$\ V_o\$$ saturates at $$\\pm \$$15 V. The expression that relates $$\ V_o\$$ with $$\ v_S\$$ and $$\ R_L\$$ is (see figure 3) $$V_o = -(2 v_S \times R_L/R_2 + v_S)$$ And this must stay within saturation limits. At $$\v_S=1 V, R_L = 1k\Omega, V_o=-21\$$ V, so that explains the odd behavior there. My concern is that, for a value of $$\ V_o\$$ within limits, specified by some $$\ v_S\$$ and $$\ R_L\$$ pair, the output is still anomalous. For example, when $$\ v_S=0.8 V\$$ and $$\ R_L=300 \Omega\$$, $$\ V_o=-5.6 V\$$, but simulated $$\i_L=-5.66\$$ mA as opposed to being -8 mA, and I can't think of any reason why we're deviating from the expected results.

## 2 Answers

I did a simulation Dynamic DC Analysis with microcap v12 and a old 741.

Here is what I get ... EE&O, 10 < R5 < 10k (log stepping *2).

For another configuration of resistors (1 k)

And here is a Maple sheet ... for analytical results.

Both the results you cited are correct. The 1k results show a voltage out that's below the negative rail, but that's the simulator's fault. I think your problem is that you aren't considering RL's effect on the positive feedback voltage. In both cases IL is -10*Vs ma.