Op Amp: Differential Voltage To Current Converter (Grounded Load Voltage Fed Back As Offset)

This is a differential voltage to current converter (differential voltage-controlled current source). The first operational amplifier works as a difference amplifier which mainly amplifies the difference between the two input signals Viniv (noninverting input voltage) and Viinv (inverting input voltage). The second operational amplifier buffers the voltage drop across the grounded load back to the first operational amplifier circuit where it serves as an offset to the difference amplifier. Therefore, apart from the amplified difference between the main input signals Viniv and Viinv, the output of the difference amplifier has an offset equal to the load voltage. This effectively makes the net voltage drop across Rset equal only to the amplified difference between Viniv and Viinv. Thus the current through Rset and to the load is simply equal to the amplified difference between the main control signals divided by Rset. Iload = Iset Iload = (Vout1 - Vload) / Rset Vout1 = [(Riinv + Rf) / Riinv] Vniv1 - (Rf / Riinv) Viinv Vout1 = [(Riinv + Rf) / Riinv] {[Roffs / (Roffs + Riniv)] Viniv + [Riniv / (Riniv + Roffs)] Vout2} - (Rf / Riinv) Viinv Vout1 = [(Riinv + Rf) / Riinv] (Roffs · Viniv + Riniv · Vout2) / (Riniv + Roffs)] - (Rf / Riinv) Viinv When Riniv = Ri = Riinv and Rf = Rfoffs = Roffs Vout1 = [(Ri + Rfoffs) / Ri] (Rfoffs · Viniv + Ri · Vout2) / (Ri + Rfoffs)] - (Rfoffs / Ri) Viinv Vout1 = [(Rfoffs · Viniv + Ri · Vout2) / Ri] - (Rfoffs / Ri) Viinv Vout1 = (Rfoffs / Ri) (Viniv - Viinv) + Vout2 But Vout2 = Vload Vout1 = (Rfoffs / Ri) (Viniv - Viinv) + Vload Iload = {[(Rfoffs / Ri) (Viniv - Viinv) + Vload] - Vload} / Rset Iload = [(Rfoffs / Ri) (Viniv - Viinv) + Vload - Vload] / Rset Iload = (Rfoffs / Ri) (Viniv - Viinv) / Rset Iload = [Rfoffs / (Ri · Rset)] (Viniv - Viinv) With the saved values of this particular circuit Iload = [20 kΩ / (10 kΩ · 1 kΩ)] (Viniv - Viinv) Iload = 2 (Viniv - Viinv) / 1 kΩ Typically Riniv = Riinv = Rf = Roffs which would make the gain of the difference amplifier (U1 circuit) equal to 1 and adjustment of the overall transfer function (transconductance) is made only through Rset. The saved values of the circuit exemplifies that the gain of the difference amplifier is a parameter available for juggling when fiddling with the circuit.