In this article, we are going to learn the most basic use case of the operational amplifier, i.e. Summing amplifier. We will discuss each and every point about summing amplifiers in detail so let’s get ready to learn.

## What is Summing Amplifier

In our earlier discussion about the **inverting operational amplifier**, we explored how it operates with a sole input voltage (V_{in}) directed to its inverting input terminal. However, by incorporating additional input resistors, each mirroring the original input resistor (R_{in}), we unveil a new configuration known as a **Summing Amplifier**, sometimes referred to as a “summing inverter” or even a “voltage adder” circuit.

The Summing Amplifier is a special setup of an operational amplifier. It's used to mix the voltages from different inputs into just one output voltage.

## Inverting Summing Amplifier

In this summing amplifier setup, the output voltage (V_{out}) is directly linked to the total of all input voltages, such as V_{1}, V_{2}, V_{3}, and so on. Consequently, we can adjust the initial equation used for the inverting amplifier to accommodate these additional inputs.

\mathbf{I_F = I_1 + I_2 + I_3 = -\left[ \frac{V_1}{R_{in}} + \frac{V_2}{R_{in}} + \frac{V_3}{R_{in}}\right ]}

Now as we know in the Inverting amplifier, the output voltage can be defined as,

\mathbf{V_{out} = -\frac{R_F}{R_{in}} \times V_{in}}

Then we can write,

\mathbf{-V_{out} =\left[ \frac{R_F}{R_{in}}V_1 + \frac{R_F}{R_{in}}V_2 + \frac{R_F}{R_{in}}V_3\right ]}

If all the input impedances (R_{IN}) have the same value, we can simplify the equation mentioned above to yield an output voltage of:

\boxed{\mathbf{V_{out} =-\frac{R_F}{R_{in}}\left[ V_1 + V_2 +V_3 + …. + V_n\right ]}}

Now, we’ve created an operational amplifier circuit capable of amplifying each individual input voltage, generating an output voltage signal proportional to the combined “SUM” of the three input voltages: V_{1}, V_{2}, and V_{3}. If necessary, we can expand this setup by adding more inputs, with each input being isolated by its respective resistance, R_{in}.

This isolation is facilitated by the “virtual short” node at the op-amp’s inverting input. Moreover, a direct voltage addition is achievable when all resistances are of equal value, and R_{ƒ} equals R_{in}.

**It’s important to note that connecting the summing point to the inverting input of the op-amp results in the circuit producing the negative sum of input voltages. Conversely, connecting it to the non-inverting input yields the positive sum of input voltages.**

If the individual input resistors are not equal, a Scaling Summing Amplifier can be constructed. In such a case, the equation needs to be adjusted to:

\mathbf{-V_{out} = V_1 \left (\frac{R_f}{R_1} \right) +V_2 \left (\frac{R_f}{R_2} \right) +V_3 \left (\frac{R_f}{R_3} \right) … etc}

To simplify the mathematics, we can rearrange the formula above to isolate the feedback resistor R_{ƒ} as the subject of the equation, resulting in the output voltage being expressed as:

\mathbf{-V_{out} =R_f \left[ \frac{V_1}{R_1} + \frac{V_2}{R_2} +\frac{V_3}{R_3} + … etc\right ]}

This setup simplifies the calculation of the output voltage when additional input resistors are connected to the amplifier’s inverting input terminal. The input impedance of each individual channel equals the value of its respective input resistor, such as R_{1}, R_{2}, R_{3}, and so forth.

Occasionally, we require a summing circuit solely for combining two or more voltage signals without any amplification. By setting all resistances in the circuit to the same value, R, the op-amp will exhibit a voltage gain of unity, resulting in an output voltage equal to the direct sum of all input voltages, as illustrated below:

The **Summing Amplifier** proves to be a highly versatile circuit, allowing us to efficiently combine multiple individual input signals through addition or summation, hence its name. When the input resistors, labeled as R_{1}, R_{2}, R_{3}, and so on, are all equal, it results in a “unity gain inverting adder.” However, if the input resistors have different values, it yields a “**scaling summing amplifier**,” producing an output that represents a weighted sum of the input signals.

## Non-inverting Summing Amplifier

Besides constructing inverting summing amplifiers, we can utilize the non-inverting input of the operational amplifier to create a **non-inverting summing amplifier**. While an inverting summing amplifier produces the negative sum of its input voltages, the non-inverting summing amplifier configuration generates the **positive sum** of its input voltages.

True to its name, the non-inverting summing amplifier is structured around the setup of a non-inverting operational amplifier circuit. Here, the input (either AC or DC) is directed to the non-inverting (+) terminal, while the desired negative feedback and gain are attained by feeding back a portion of the output signal (V_{OUT}) to the inverting (-) terminal, as depicted.

### Non-inverting Summing Amplifier Circuit

What advantages does the non-inverting configuration offer over the inverting summing amplifier configuration? Besides the straightforward fact that the output voltage V_{OUT} of the operational amplifier (op-amp) aligns with its input and the output voltage represents the weighted sum of all inputs, determined by their resistance ratios, the main advantage of the non-inverting summing amplifier lies in its significantly higher input impedance compared to the standard inverting amplifier configuration.

Moreover, the input summing section of the circuit remains unaffected even if the op-amp’s closed-loop voltage gain is altered. However, selecting the weighted gains for each individual input at the summing junction involves more mathematical consideration, especially with more than two inputs, each with a distinct weighting factor. Nonetheless, if all inputs share the same resistive values, the mathematical complexity decreases significantly.

If the closed-loop gain of the non-inverting operational amplifier matches the number of summing inputs, the op-amp’s output voltage will precisely mirror the sum of all input voltages. For instance, in a two-input non-inverting summing amplifier, the op-amp’s gain equals 2; in a three-input summing amplifier, the gain equals 3, and so forth. This occurs because the currents flowing in each input resistor are influenced by the voltage across all inputs. When the input resistances are equal (R_{1} = R_{2}), the circulating currents cancel out since they cannot flow into the high impedance non-inverting input of the op-amp, resulting in the output voltage becoming the sum of its inputs.

Thus, for a 2-input non-inverting summing amplifier, the currents flowing into the input terminals can be defined as:

If we ensure that the two input resistances have the same value, then we have R_{1} = R_{2} = R.

The typical equation for the voltage gain of a non-inverting summing amplifier circuit is expressed as:

The closed-loop voltage gain (A_{V}) of the non-inverting amplifier is determined by the formula 1 + R_{A}/R_{B}. If we set this gain to 2 by making R_{A} equal to R_{B}, then the output voltage (V_{O}) becomes equal to the sum of all the input voltages, as illustrated.

### Non-inverting Output Voltage

Therefore, for a 3-input non-inverting summing amplifier setup, adjusting the closed-loop voltage gain to 3 will result in V_{OUT} being equivalent to the sum of the three input voltages, V_{1}, V_{2}, and V_{3}. Similarly, in a four-input configuration, the closed-loop voltage gain would be set to 4, and for a five-input setup, it would be 5, and so forth. It’s worth noting that if the amplifier of the summing circuit is configured as a unity follower with R_{A} set to zero and R_{B} set to infinity, the output voltage V_{OUT} will precisely match the average value of all the input voltages, represented as

**V _{OUT} = (V_{1} + V_{2})/2**, since there is no voltage gain.

## Summing Amplifier Applications

**Summing amplifiers**, whether inverting or non-inverting, offer versatile applications. By connecting the input resistances of a summing amplifier to potentiometers, it becomes possible to mix individual input signals in varying proportions.

### Audio Mixer Circuit

For instance, in temperature measurement, you could introduce a negative offset voltage to ensure that the output voltage or display reads “0” at the freezing point. Similarly, in audio mixing, a summing amplifier can serve as an audio mixer, blending individual waveforms (sounds) from different source channels such as vocals, instruments, etc., before routing them collectively to an audio amplifier.

### Digital to Analog Converter

In this DAC summing amplifier circuit, the number of individual bits comprising the input data word—4 bits in this example—ultimately dictates the output step voltage as a percentage of the full-scale analog output voltage.

The accuracy of the full-scale analog output hinges on the voltage levels of the input bits consistently being 0V for “0” and 5V for “1”, alongside the precision of the resistance values employed for the input resistors, R_{IN}.

Fortunately, to address these potential errors, commercially available Digital-to-Analogue and Analogue-to-Digital devices come equipped with highly accurate resistor ladder networks pre-installed, alleviating concerns on our part.

### Level Shifter

Another significant application of a Summing Amplifier is as a Level Shifter. A 2-input Summing Amplifier can function as a level shifter by utilizing one input for an AC Signal and the other input for a DC Signal.

The AC Signal undergoes an offset by the input DC Signal. This type of level shifter finds prominent use in Signal Generators for DC Offset Control.

## FAQs

**What is a summing amplifier?**

The Summing Amplifier is another type of operational amplifier circuit configuration that is used to combine the voltages present on two or more inputs into a single output voltage.

**What is the summing point of an op-amp?**

The “summing point” (the negative input) of an OpAmp summer is kept at the same voltage as the positive input by the action of the negative feedback.

What are the disadvantages of the summing amplifier?

it requires a dual-polarity power supply, which can add complexity and cost to the circuit design.

**What are the different types of summing amplifiers?**

There are two types of summing amplifiers: inverting and non-inverting summing amplifiers.