# Non Inverting Summing Amplifier : Circuit, Derivation, Transfer Function, Vs Inverting Summing & Its Applications

Operational amplifiers are available in different configurations. A summing amplifier is one of the types, that is used for combining the available voltages on a minimum of two or above inputs into a single o/p voltage. Inverting op-amp has a single input voltage which is provided to the inverting input terminal. If we give several input resistors to the inverting input terminal, each input is equivalent to the original input resistor value, known as the summing amplifier. This amplifier processes adding & subtracting voltages. There are two types of summing amplifiers; inverting and non-inverting. This article provides brief information on a **non-inverting summing amplifier**, working, and its applications.

## What is a Non-inverting Summing Amplifier?

A type of an Op-Amp circuit configuration used to provide a summed output, with the same phase or polarity is known as a Non-inverting summing amplifier. These types of summing amplifiers utilize the direct coupling technique, which indicates that the source signals are connected and directed to the Op-Amp.

In this type of op-amp configuration, the inverting input of the op-amp is grounded. The non-inverting input is connected with the input voltage through a resistor or directly. This non-inverting summing amplifier’s output voltage can be determined by using the following formula:

**Vout = (1+Rf/R1)*Vin**

Where ‘Rf’ is the feedback resistor, ‘R1’ is the input resistor & Vin is the sum of applied input voltages.

#### Non-Inverting Summing Amplifier Working

A Non-Inverting Summing Amplifier provides a summed o/p of the i/p signals including the similar polarity (or) phase. This amplifier has several input sources and a single output where these inputs are connected to its non-inverting terminal through resistors.

Every input signal is directly connected to a resistor whereas the other end of every resistor is simply connected to the non-inverting terminal of the op-amp. After that, the summing junction is connected to GND through a feedback resistor. So this arrangement simply allows the operational amplifier to add various input voltages with the suitable weighting decided by the values of a resistor.

The total output of this amplifier is the sum of all the connected input voltages where the individual weights are dependent on the connected resistors with the equivalent inputs. So the input & output of this amplifier is in phase with 0°.

### Non-Inverting Summing Amplifier using Op Amp

The non-inverting summing amplifier circuit diagram is shown below. This amplifier configuration is similar to the non-inverting amplifier. The input voltages to this amplifier are given to Op Amp’s non-inverting input terminal. The output of this amplifier is fed back through voltage divider bias feedback to the inverting input terminal. This circuit has three inputs only for the sake of ease, but the number of inputs can also be added. The output voltage calculation of this amplifier is discussed below.

If the input voltage like ‘VIN’ is all the input signals combination, then this can be provided at the non-inverting pin of the op-amp. From the above non-inverting summing amplifier circuit, we can compute this amplifier’s output voltage with input pin VIN & in the feedback divider, Rf and Ri resistors are used. So the output voltage will become as;

VOUT = VIN (1 + (Rf / Ri))

Whenever the output voltage of this amplifier is figured out, then we have to decide the VIN value. If the three main input sources are V1, V2 & V3, and input resistances are; R1, R2 & R3 then the respective channel inputs are VIN1, VIN2 & VIN3 when other equivalent channels are grounded. Thus,

VIN = VIN1 + VIN2 + VIN3

Here, when the virtual ground idea doesn’t apply, all channels affect the remaining channels. First, we have to calculate the VIN1 part of the VIN and by easy math; we can easily get the remaining two values of VIN2 & VIN3.

Whenever V2 & V3 are grounded coming to VIN1, then their equivalent resistors cannot be ignored as shape a voltage divider network. Consequently,

VIN1 = V1 [(R2 || R3) / (R1 + (R2 || R3))]

Likewise, we can compute the other two VIN2 & VIN3 values as

VIN2 = V2 [(R1 || R3) / (R2 + (R1 || R3))]

VIN3 = V3 [(R1 || R2) / (R3 + (R1 || R2))]

Therefore,

VIN = VIN1 + VIN2 + VIN3

VIN = V1 [(R2 || R3) / (R1 + (R2 || R3))] + V2 [(R1 || R3) / (R2 + (R1 || R3))] + V3 [(R1 || R2) / (R3 + (R1 || R2))].

At last, we can compute the Output voltage as;

VOUT = VIN (1 + (Rf / Ri))

VOUT = (1 + (Rf / Ri)) {V1 [(R2 || R3) / (R1 + (R2 || R3))] + V2 [(R1 || R3) / (R2 + (R1 || R3))] + V3 [(R1 || R2) / (R3 + (R1 || R2))]}

If we consider the special equivalent weighted state wherever all the resistors with similar values, after that the VOUT is:

VOUT = (1 + (Rf / Ri)) ((V1 + V2 + V3)/3)

Non-inverting summing circuit design is approached by primarily designing this amplifier to have the necessary voltage gain. After that, the input resistors are chosen as large as feasible to suit the kind of operational amplifier used.

### Non-Inverting Summing Amplifier Transfer Function

The noninverting summing amplifier circuit with three inputs is shown below. If we want to add three input signals to the amplifier then the transfer function of three input noninverting summing amplifier is discussed below.

By using the superposition theorem, first, we will leave simply ‘V1’ within this circuit, and V2 and V3 made zero by connecting R2 & R3 resistors to GND.

For a perfect operational amplifier, the input current of the non-inverting terminal is considered zero. So, R1, R2 & R3 resistors will make a voltage attenuator through R2 & R3 resistors in parallel. So ‘Vp’ is;

Vp = V1 R2 || R3/ R1+ R2|| R3

Where with R2 || R3 we have noticed that the parallel R2 and R3 values.

With the V1 input source, the output of an operational amplifier can be noted through VOUT1 & it can be written as;

VOUT1 = Vp [1+ Rf2/Rf1]

By substituting the Vp value in the VOUT1 equation, we can get;

VOUT1 = V1 (R2 || R3/ R1+ R2|| R3) [1+ Rf2/Rf1]

Likewise, we can write VOUT2 & VOUT3 when the input signals only are; V2 & V3 correspondingly.

VOUT2 = V2 (R1 || R3/ R2+ R1|| R3) [1+ Rf2/Rf1]

VOUT3 = V3 (R1 || R2/ R3+ R1|| R2) [1+ Rf2/Rf1]

By adding the above VOUT1, VOUT2 & VOUT3 equations, the transfer function of a noninverting amplifier including three input signals will become as;

VOUT = [1+ Rf2/Rf1] V1 (R2 || R3/ R1+ R2|| R3) + V2 (R1 || R3/ R2+ R1|| R3) + V3 (R1 || R2/ R3+ R1|| R2).

## Difference between Inverting and Non-Inverting Summing Amplifier

The main difference between Inverting & Non-Inverting Summing Amplifiers is discussed below.

Inverting Summing Amplifier |
Non-Inverting Summing Amplifier |

All the input signals in this circuit are given to the inverting input terminal of the op-amp whereas the non-inverting terminal is grounded. | All the input signals in this circuit are given to the noninverting input terminal of the op-amp whereas the inverting terminal is grounded. |

This summing amplifier works simply similar to the inverting op-amp | This non-inverting summing amplifier works similarly to the non-inverting op-amp. |

Inverting the summing amplifier inverts the output signal’s phase. | Non-inverting summing amplifier maintains a similar phase to the input signal. |

This amplifier configuration gives the negative sum of its applied input voltages. | Non-inverting summing amplifier configuration gives the positive sum of its applied input voltages. |

The phase difference in this amplifier is 180° between the input & output signal. | The phase difference in this amplifier is 0° in between the input & output signal. |

The feedback in this amplifier is provided where the input signal is provided. | The feedback and input signal in this amplifier are connected simply to different terminals. |

The ‘+’ terminal is connected to GND. | In this amplifier, the ‘-’ terminal is connected to GND. |

In this amplifier, the feedback cannot be connected to GND. | The feedback in this amplifier is connected to GND with a resistor. |

This amplifier gives an inverted output with negative (-ve) polarity. | The output produced by this amplifier is non-inverted & expressed with +ve polarity. |

The gain polarity of this amplifier is (-) negative. | The gain polarity of a non-inverting amplifier is (+) positive. |

This amplifier’s gain is < or > or = to unity (1). | The gain is always > 1. |

### Advantages

The **advantages of a non-inverting summing amplifier** include the following.

- This summing amplifier voltage gain is positive.
- The output signal can be obtained without inversion of phase.
- Its input impedance value is high.
- The voltage gain is variable.
- In this amplifier, superior impedance matching can be attained.

The **disadvantages of a non-inverting summing amplifier** include the following.

- This amplifier has a main drawback where the circuit gain will be twice for the remaining channel connected if one of the inputs is detached.
- It’s not suggested to go away from the floating of non-inverting pins while detaching all inputs.
- Possible interference between the input & other inputs could be present with changing amounts of severity.
- Introducing a third input can result in a drop in gain within the first two channels, which could have implications based on the particular application.
- If there is a link to any source that has a variable output impedance value, then it affects the remaining two channels’ amplification, which may not be popular.

### Applications

The **applications of non-inverting summing amplifiers** include the following.

- Noninverting summing op-amp circuits are applicable wherever high input impedance is required.
- These circuits can be used as a voltage follower by simply providing the o/p to the inverting input like an inverter.
- These circuits help in isolating the particular cascaded circuits.
- This amplifier is used to provide a summed output for the applied input signals with the same phase or polarity.

Thus, this is an overview of non-inverting summing amplifiers, circuits, derivation, differences, transfer function, advantages, disadvantages, and their applications. This is a type of summing amplifier with several inputs to the +ve non-inverting input. The summing amplifier can be utilized as a non-inverting summing amplifier by simply connecting various input signals throughout resistors to the op-amp’s non-inverting input.

The output voltage of this summing amplifier is the amount of the input voltages, biased by the resistor’s values. Every input signal of this amplifier can be connected simply to a resistor whereas the remaining terminal of each resistor can be connected to the non-inverting terminal of the operational amplifier. After that, the summing junction is connected to GND through a feedback resistor. So, this arrangement allows the operational amplifier to include various input voltages through the suitable weighting decided through the resistor values. Here is a question for you, what is a summing amplifier?