In practice, it is often necessary to obtain the difference between two signals or to superimpose and mix multiple analog signals, which requires the use of a signal superposition circuit and a difference circuit. The inverting proportional and in-phase proportional circuits shown in Figure 1 are the basic topologies of proportional arithmetic circuits, based on which signal superposition and difference circuits can be constructed using the superposition principle and Davinan’s theorem.
Figure 1 Basic topology of proportional arithmetic circuit
I. Signal superposition is divided into in-phase superposition and anti-phase superposition. Figure II shows the signal in-phase superposition circuit, whose Davinan equivalent circuit is shown on the right side of Figure II.
Figure 2 The same phase superposition and its equivalent circuit can be seen from Figure 2, the equivalent circuit is the basic homogeneous proportional circuit shown in Figure 1 (b), using the superposition principle to obtain the P-point open circuit voltage Us = 1/3 (Ui1 + Ui2 + Ui3), the equivalent internal resistance of the voltage source R0 = R//R//R; directly apply the formula of the basic homogeneous proportional circuit, we can get: Uo = (1 + R/0.5R)*Us = Ui1+Ui2+Ui3 , the output is the in-phase superposition of the three input signals.
Figure 3: Inverted Superposition and Equivalent Circuit
The output is equal to the sum of the outputs of each input signal acting alone. When Ui1 acts alone, Ui2 and Ui3 are shorted to ground, and the equivalent circuit is shown on the right side of Figure 3. Because the in-phase terminal is grounded, the in-phase terminal is a virtual location, that is, the N point is zero potential, R2, R3 on no current, R2, R3 can be considered to exist or not on the circuit has no effect, that is, can be taken out, the equivalent circuit and Figure I (a) the same basic inversion proportional circuit, directly apply the inversion proportional circuit formula, the output of Ui1 alone: Uo1 = – Rf/R1 * Ui1 ; the same can be obtained. Uo2=-Rf/R2Ui2 ; Uo3=-Rf/R3Ui3 ; total output Uo=Uo1+Uo2+Uo3 ; when Rf=R1=R2=R3, Uo=-(Ui1+Ui2+Ui3), completing the inverse superposition of the input signal.
II. Different ideas can be used to form different difference circuits. Using the idea of signal inversion and summation, the subtraction circuit shown in Figure 4 can be obtained.
Figure 4: Difference circuit realized by signal inversion and superposition
The circuit consists of two stages of op-amps, where A1 constitutes the inverter and A2 constitutes the two-signal inversion superposition circuit. The resistors connected in parallel at the same-phase end of the op-amp in the figure are for the balance of the resistances at the two inputs of the op-amp. The output of the first stage Uo1=-Ui2 ; according to the conclusion of the inverse superposition circuit, the output of the circuit is: Uo=-(Uo1+Ui1)=Ui2-Ui1 ,which realizes the difference operation of the signal.
Figure 5: Difference circuit implemented by differential circuit
Figure 5 is the combination of in-phase proportional and inverse proportional ideas, the use of differential circuit composition of the difference circuit, compared with Figure 4, only one op-amp unit, but the circuit can not use the concept of virtual ground, op-amp two inputs exist in common mode voltage, the actual use, should try to choose a high common mode rejection ratio op-amp. When Ui1 alone, the equivalent circuit as shown in Figure V (b), the basic inverse proportional circuit, when Uo1 = – Ui1 ; when Ui2 alone, using Davinan’s theorem, the circuit is equivalent to the circuit shown in Figure V (c), which is the basic in-phase proportional circuit, P point open circuit voltage Us = R / (R + R) * Ui2 = 0.5Ui2 ; equivalent power supply resistance R0 = R / / R ; Directly apply the same phase proportional circuit formula, Uo2 = (1 + R/R)*Us = Ui2 ; circuit output Uo = Uo2 + Uo1 = Ui2 – Ui1 ; to achieve the signal difference operation.
