Understanding Summing Amplifier Voltage Adders

A summing amplifier is a type of operational amplifier circuit that can sum multiple input signals. It is also referred to as a voltage adder because it adds multiple input voltages and provides a single output voltage that is the summed total.

In this comprehensive guide, we will dive deep into summing amplifier voltage adders, covering:

• What is a summing amplifier voltage adder
• Summing amplifier configurations
  • Non-inverting summing amplifier
  • Inverting summing amplifier
• Summing amplifier calculations and equations
• Selecting feedback and input resistor values
• Applications of summing amplifiers
  • Audio mixing
  • Sensor signal combining
  • DC level shifting
  • Analog computing circuits
• Advantages and disadvantages of summing amplifiers
• Summing amplifier examples and simulations

What is a Summing Amplifier Voltage Adder?

A summing amplifier is an op amp circuit that can sum several input voltages applied to one or more of its input terminals and produce an output voltage that is proportional to the negative or positive sum of the input voltages.

Summing amplifiers are based around an operational amplifier, which is a high gain differential amplifier. By using negative feedback via an appropriately valued resistor, the high gain of the op amp is controlled and we can configure the circuit to perform mathematical operations on the input signals.

The basic concept behind a summing amplifier is that it creates a virtual ground at the inverting input terminal of the op amp. This allows multiple input voltage sources to be connected from ground to the virtual ground point. Currents from each source flow through resistors into the summing point and the op amp adjusts its output to maintain the virtual ground, effectively summing the currents. The feedback resistor then converts this summed current into an output voltage.

Depending on whether the input voltages are connected to the inverting terminal or non-inverting terminal of the op amp, we have two types of summing amplifier configurations:

1. Non-inverting summing amplifier
2. Inverting summing amplifier

Summing Amplifier Configurations

There are two basic summing amplifier configurations that give different polarity outputs.

Non-Inverting Summing Amplifier

In the non-inverting summing amplifier, the input voltages to be summed are applied to the non-inverting (+) input terminal of the op amp through resistors, while feedback is applied from the output to the inverting terminal.

The output voltage of a non-inverting summing amplifier is given by:

Vout = (Rf/R1)(V1 + V2 + V3 + ...)

Where:

• Vout is the output voltage
• Rf is the feedback resistor
• R1, R2 etc are the input resistor values
• V1, V2, V3 are the input voltage sources

This shows that the output voltage is a positive scaled sum of the input voltages.

The scaling factor is determined by the resistor values. Typically Rf and all the input resistors R1, R2 etc are chosen to be equal so the output is just the simple sum of the input voltages.

Inverting Summing Amplifier

In the inverting summing amplifier, the input voltages are instead applied to the inverting (-) input terminal through input resistors, with feedback taken from the output to the non-inverting (+) terminal.

For the inverting configuration, the output voltage equation is:

Vout = -(Rf/R1)(V1 + V2 + V3 + ...)  

The output voltage is a negative scaled sum of the input voltages. Again, choosing Rf = R1 = R2 ensures Vout is simply the negation of the total of all the inputs.

Summing Amplifier Equations and Calculations

Now let‘s examine the analysis behind these summing amplifier configurations and equations in more detail. We will focus on the standard case where the input resistors share a common, equal value R and the feedback resistor also has the same resistance Rf.

Non-Inverting Summing Amplifier Analysis

Here is the standard non-inverting summing amplifier again for reference:

We know that due to the virtual ground at the inverting input, Vin-=0V. Therefore:

V+ = I1R + I2R + ... + InR

Where I1, I2 etc are the input currents through each input resistor. Also, as total current into the non-inverting input is 0, we can state:

0 = I1 + I2 + ... + In

Substituting Ohm‘s law for the resistor currents gives:

V+ = V1/R + V2/R + ... + Vn/R
V+ = (V1 + V2 + ... + Vn)/R

For an ideal op amp, V+=Vout. Also, we know Vout=V+ (1 + Rf/R) from the non-inverting op amp gain equation.

Therefore:

Vout = V+ (1 + Rf/R)
     = (V1 + V2 + ... + Vn) (Rf/R)

This derivation matches our non-inverting summing amplifier voltage equation.

Inverting Summing Amplifier Analysis

Analyzing the inverting summing amplifier:

As before, we use Ohm‘s law and the virtual ground concept to give:

V- = I1R + I2R + ... + InR 
0 = I1 + I2 + ... + In

Therefore:

V- = -(V1/R + V2/R + ... + Vn/R) 
   = -(V1 + V2 + ... + Vn)/R

And as Vin-=Vout(R/Rf) from the standard inverting op amp configuration:

Vout = -Vin-(Rf/R)
    = -(V1 + V2 + ... + Vn)(Rf/R)  

So again, the mathematical analysis aligns with the standard equation for an inverting summing amplifier.

This shows how the choice of summing amplifier configuration gives both an inverting and non-inverting summing amplifier from essentially the same resistor-based analysis.

Selecting Feedback and Input Resistor Values

The equations above for Vout show that the scaling factor applied to the summed voltages is determined by Rf/R.

• For an exact voltage summation when using equal value input resistors R, we simply select Rf=R.

• If Rf>R, the circuit will provide amplification as well as summation.

• Values of Rf

There are a few factors that guide the selection of suitable resistor values:

• Input Impedance – We generally want high input impedance looking back into the amplifier inputs to avoid loading down voltage sources. Lower resistor values give higher impedance, so there is motivation to keep R small, usually ≤ 10 kΩ.

• Noise and Bandwidth – Smaller resistor values generate higher noise as this sets the noise gain. But larger resistors reduce bandwidth, so there is a tradeoff. For audio signals, 1 kΩ is common. Higher frequencies may necessitate smaller resistors.

• Non-ideal Op Amp Gain – The open loop gain A of real op amps is finite. So this will create a small scaling error if A(Rf/R) >> 1. In this case, slightly lower R values help minimise the issue.

• DC Offset Errors – Input bias currents flowing through the resistor network can induce DC offset voltages. Lower resistor values help reduce offsets.

• Power Consumption – Smaller resistors increase power use in the amplifier due to higher bias currents. Though this is generally insignificant for most applications.

In summary, good design practice is to start with resistor values in the 1 kΩ to 10 kΩ range unless other constraints dictate otherwise.

Applications of Summing Amplifiers

The ability to sum several analog input signals while controlling scaling makes summing amplifiers useful for many applications, including:

Audio Mixing

Summing amplifiers provide audio mixing functionality for sound recording or live music applications. Multiple analog signals from microphones, instruments, effects units etc can be summed to create a composite mix:

If all resistors are equal, the output level corresponds to the number and amplitude of inputs added. Adjusting certain input resistor values allows control of the mix contributions from each source as well.

Sensor Signal Combining

Sensor systems may rely on several transducers to measure parameters. Summing amplifiers allow consolidating multiple sensor outputs into a single aggregated signal for simplified processing:

Here a temperature sensor, pressure sensor and airflow sensor generate separate analog voltages that represent their measured values. The summing amplifier merges these together into one mixed signal carrying the composite sensor data.

DC Level Shifting

A fixed DC voltage can be injected into an AC signal using a summing configuration to provide level shifting:

This shifts the AC signal up from 0V to sit at a higher DC bias point defined by Vdc. This is important for interfacing between circuits operating a different voltage levels.

Analog Computing Circuits

More advanced analog computing systems leverage op amp summation capabilities to execute mathematical operations. Simple functions like addition, subtraction, logarithms, differentiation and integration can be achieved by specialized multi-amplifier circuits before the advent of digital computing.

These technique are still used for small analog computers or to offload tasks from digital systems. Summing amplifiers provide the fundamental building block to enable complex analog computation.

Advantages and Disadvantages of Summing Amplifiers

Advantages

Summing amplifier configurations offer useful functionality and have some key benefits:

• Allows summing of voltages from multiple separate sources
• Flexible control of scaling using resistor ratios
• High input impedance for voltage sources
• Unwanted signals can be excluded by omitting connections
• Inverting and non-inverting outputs available
• No adjustments needed for number of inputs

Disadvantages

There are also some limitations to be aware of when working with these amplifiers:

• Output loading from low resistor values
• Noise and offsets may be increased
• Bandwidth can be lower for higher R values
• Input and output dynamic range is constrained
• AC coupling may be required in some cases

So in applications where these disadvantages can be mitigated through good design, summing amplifiers provide an efficient analog solution for combining multiple voltages.

Summing Amplifier Examples and Simulations

To demonstrate summing amplifiers further, here are some examples of SPICE simulations showing these amplifiers in action combining multiple input waveforms:

Non-Inverting Summing Amplifier

This simulation shows a non-inverting summing amplifier combining a DC signal, sine wave, triangle wave and square wave:

The output voltage is the positive sum of the inputs. Adjusting the phase and magnitude of the waveforms shows how synchronization affects the signal addition.

Try the non-inverting summing amplifier simulation »

Inverting Summing Amplifier

Similarly, this simulated inverting summing amplifier combines a different set of waveforms:

Here the output is the negative sum of the input voltages. The resistors are varied to demonstrate weighted scaling factors as well.

Try the inverting summing amplifier simulation »

In both cases, the live circuit simulations let you adjust component values and signals to explore the operational dynamics. The visualizations clearly show the summing effects in action.

Conclusion

Summing amplifiers provide a flexible solution for analog voltage summation applications. By leveraging resistor feedback around an op amp, multiple input signals can be added either in inverted or non-inverted form.

Careful selection of resistor values allows both scaling and simple resistor-based summing implementations. These amplifiers find use for audio mixing, sensor signal aggregation, DC level shifting and analog computing operations.

Through SPICE simulations, we demonstrated both non-inverting and inverting summing amplifiers combining various waveforms. The ability to freely adjust circuit parameters gives further insight into the operational dynamics of these useful summation amplifiers.