A summing amplifier is an adaptation of the inverting amplifier in which the output voltage is the result of summing the results due to each separate input signal – hence the name. This is a useful circuit which combines a number of separate signals together, with the option to apply a different scale factor to each input.
The above illustration shows a circuit with three inputs, although a fewer or greater number may be connected, as required. The output voltage for this case is given by:
Worked Example 1
Calculate suitable component values to produce the expression Vout = − (0.1 V1 + 0.2 V2 + 0.5 V3).
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Begin by choosing a reasonable value for Rf, such as Rf = 1 kΩ.
Next, calculate values for R1, R2 and R3 to give the required ratios of Rf / R1 = 0.1 (1/10), Rf / R2 = 0.2 (1/5) and Rf / R3 = 0.5 (1/2) respectively.
Hence, Rf = 1 kΩ, R1, = 10 kΩ, R2 = 5 kΩ and R3 = 2 kΩ.
To understand the circuit operation, begin by considering the case where only a single input V1 is applied. This is the same as an inverting amplifier so Vout = V1 × −Rf / R1. Similar expressions are derived if V2 or V3 are the only inputs.
To analyse the operation of the circuit with multiple active inputs, it is useful to apply a couple of op-amp assumptions. Firstly, the voltage on the inverting input (V−) of the op-amp will be 0 V due to the virtual earth principle. The input currents through R1, R2 and R3 may then be calculated as I1 = V1 / R1 · · · (1), I2 = V2 / R2 · · · (2) and I3 = V3 / R3 · · · (3) respectively.
Secondly, we assume that the input impedance of the op-amp is infinite, so the input current to the inverting input of the op-amp will be zero. We can then apply Kirchhoff's Current Law to the virtual earth node, showing that the three currents flowing into the junction (I1, I2 and I3) will equal the single current flowing out through the feedback resistor, Rf. Hence, I1 + I2 + I3 = If · · · (4).
Based on the assumed direction of If, Vout = 0 − If × Rf, since the left end of Rf is at virtual earth potential. Hence If = −Vout / Rf · · · (5).
Finally, the overall expression for Vout may be found by substituting Equations 1, 2, 3 and 5 into Equation 4, in order to eliminate all currents from the relationship.
Simplified Summing Amplifier Circuits
If it is not necessary to individually scale input values, then all input resistors may be set to a common value, Rin. The expression for Vout then simplifies to:
This may be simplified even further if no overall scaling is required, in which case Rin = Rf and the expression for Vout becomes: