To analyze this circuit, the operational amplifier is assumed to be ideal, meaning:
In these formulas, \(I_{Rx}\) represents the current flowing through \(R_1\) or \(R_2\).
\(U_D\) is the voltage difference between the non-inverting (+) and inverting (-) terminals.
\(U_{inx}\) and \(U_{out}\) are the input and the output voltages, respectively and \(U_{+}\) and \(U_{-}\) are the non-inverting and inverting input voltages of the opamp.
$$ U_+ = {R_4 \over {R_4+R3}*}U_{in2} $$ $$ 0 = -U_{in1} +U_{R1}+U_+ $$ $$ I_{R1}={-U+U_{in1}\over R_1} $$ $$ 0 = -U_{out}+U_{R2}+U_+ $$ $$ I_{R2}={-U_{out}-U_+\over R_2} $$ $$ I_{R2}=-I_{R1} $$ $$ -{-U_{out}-U_+\over R_2} = {-U+U_{in1}\over R_1} $$ $$ Uo =U_{in2} *{R_4 \over R_4+R3} *(1+{R_2 \over R1})-U_{in1}*{R_2 \over R_1}$$ $$ Uo =U_{in2} *{R_4 \over R_4+R3}*{R_1+R_2 \over R1}-U_{in1}*{R_2 \over R_1}$$ These formulas illustrate the calculation of the output voltage. By selecting \(R_1\) = \(R_2\) and \(R_3\) = \(R_4\) the amplification factor becomes 1 and the circuit functions as a subtractor.
- The differential input voltage \(U_D\) is zero, implying no input offset voltage.
- The output offset voltage is zero.
- The input current is negligible (zero). / The input resistance is infinite.
- The output resistance is zero.
- The open-loop gain is infinite.
In these formulas, \(I_{Rx}\) represents the current flowing through \(R_1\) or \(R_2\).
\(U_D\) is the voltage difference between the non-inverting (+) and inverting (-) terminals.
\(U_{inx}\) and \(U_{out}\) are the input and the output voltages, respectively and \(U_{+}\) and \(U_{-}\) are the non-inverting and inverting input voltages of the opamp.
$$ U_+ = {R_4 \over {R_4+R3}*}U_{in2} $$ $$ 0 = -U_{in1} +U_{R1}+U_+ $$ $$ I_{R1}={-U+U_{in1}\over R_1} $$ $$ 0 = -U_{out}+U_{R2}+U_+ $$ $$ I_{R2}={-U_{out}-U_+\over R_2} $$ $$ I_{R2}=-I_{R1} $$ $$ -{-U_{out}-U_+\over R_2} = {-U+U_{in1}\over R_1} $$ $$ Uo =U_{in2} *{R_4 \over R_4+R3} *(1+{R_2 \over R1})-U_{in1}*{R_2 \over R_1}$$ $$ Uo =U_{in2} *{R_4 \over R_4+R3}*{R_1+R_2 \over R1}-U_{in1}*{R_2 \over R_1}$$ These formulas illustrate the calculation of the output voltage. By selecting \(R_1\) = \(R_2\) and \(R_3\) = \(R_4\) the amplification factor becomes 1 and the circuit functions as a subtractor.
