An amplifier is an analogue circuit. This page is about a summing amplifier based on an inverting amplifier. The output voltage (V_{out}) of the circuit depends on the input voltage of two separate inputs (V_{A} and V_{B}) and the Gain of each input.

It is a good idea to read the amplifier basics and the Inverting Amplifier pages first.

For all the circuits shown below, the amplifier is assumed to have a positive and a negative power supply, usually ±15 V, so that the output voltage can be both positive and negative.

The circuit is based on an inverting amplifier

The output voltage (V_{out}) depends on each of the two input voltages (V_{A} and V_{B}) and the ratio of the input resistors (R_{A} and R_{B}) and the feedback resistor (R_{f})

The voltage gain of each input can be calculated separately as the two inputs are completely independent and do not affect each other in any way

The output voltage is given by:

−V_{out} / R_{f} = V_{A} / R_{A} + V_{B} / R_{B}

If all the resistor values are equal:

−V_{out} = V_{A} + V_{B}

In this case the output voltage is the sum of the input voltages

Note: R_{A}, R_{B} and R_{f} should all be > 1 kΩ and < 10 MΩ

The summing amplifier multiplies each input voltage by the gain of that input and then adds them together to give the output voltage. Input voltages can be both positive and negative and the summing amplifier takes account of this. Input voltages can be fixed or changing with time, analogue or digital.

The timing diagram shows two input voltages to a summing amplifier and the output voltage assuming the gain of each input is −1

V_{A} is a constant voltage of +2 V

V_{B} is a square wave that oscillates between +1 V and −1 V

V_{out} is the inverted sum of the two inputs. Initially V_{A} = +2 V and V_{B} = +1 V and therefore V_{out} = −3 V

After some time V_{A} = +2 V and V_{B} = −1 V and therefore V_{out} = −1 V

The equation to calculate the output voltage can be rearranged to give:

−V_{out} = V_{A} (R_{f} / R_{A}) + V_{B} (R_{f} / R_{B})

Consider the following example. What is the output voltage?

For input A, the gain is 470 kΩ / 220 kΩ = × 2.14

For input B, the gain is 470 kΩ / 10 kΩ = × 47

The output voltage is therefore −(+3 × 2.14 + −0.2 × 47) = −3 V

Each input has a gain defined by the input resistor and the feedback resistor.

The gains for each input do not have to be the same.

A Summing Amplifier can be used to mix two signals, such as in the music industry. The circuit shown has an input for a line source such as a CD player or guitar and a separate input for a microphone (Mic).

The input capacitors (nominally 1 µF) block any D.C. bias

The 47 kΩ Logarithmic potentiometers act as volume controls

The gain of the Mic input is ×10 so an input of 100 mV will give an output of 1 V

The gain of the Line input is ×1 so an line level input of 1 V will give an output of 1 V

The summing amplifier mixes the two signals so, using the numerical values given, the maximum output would be 2 V

The output capacitor and resistor block any D.C. bias being presented to the next subsystem

Just like the Inverting Amplifier, the Summing Amplifier uses negative feedback to keep the inverting input at almost zero volts. The inverting input is a virtual earth. As both inputs are connected, through their respective input resistors, to this virtual earth they do not affect each other - the voltage at input A does not affect the voltage at input B and vice versa.

**The Gain Equation**

- The current flowing in to input A is I
_{A}= V_{A}/ R_{A} - The current flowing in to input B is I
_{B}= V_{B}/ R_{B} - The current flowing in the feedback resistor is I
_{f}= −V_{out}/ R_{f} - No current flows into the inverting input and therefore I
_{f}= I_{A}+ I_{B}

Combining the above equations gives:

−V_{out} / R_{f} = V_{A} / R_{A} + V_{B} / R_{B}

© Paul Nicholls

December 2018

Electronics Resources by Paul Nicholls is licensed under a Creative Commons Attribution 4.0 International License.