# Op Amp Summing Amplifier: Virtual Earth Mixer

## The op amp circuit for an inverting amplifier can be used to create a simple high performance linear virtual earth mixer or summing amplifier.

The properties of the op amp circuit for an inverting amplifier mean that it lends itself to being the ideal platform for a summing amplifier.

In this configuration the operational amplifier inverting amplifier is used as a virtual earth mixer. It finds many uses where several analogue signals need to be summed. One is as an audio mixer, although it is widely used in many other areas of electronic circuit design.

The advantage of using an op-amp inverting amplifier is that the summing point is virtually at earth potential and therefore the settings and signals from each different channel do not affect each other. In this way each channel can be summed or mixed regardless of the signal level, source impedance and the like.

## What is a linear mixer or summing amplifier

With electronics there are two types of circuit that can be described by the world mixer:

• Linear mixer:   The linear mixer is a summing amplifier which is used widely in audio and other applications to sum signals. Audio mixers used in studios and many other areas use this technology. It is this type of mixer that is uses a summing amplifier, i.e. each signal is summed in a totally linear fashion.
• Multiplying mixer :   This type of mixer is used in RF applications. It uses the non-linear characteristics of a circuit to multiply two signals together and in this way generate further frequencies. This type of mixer is used for applications including frequency changing.

An ideal linear mixer or summing amplifier should be able to take almost unlimited number of inputs, and none of one input should appear at another input.

Also any additional inputs that may be included should not alter any of the settings of the existing controls.

## Op amp virtual earth amplifier as summing amplifier

The op amp inverting amplifier configuration lends itself to being used as a summing amplifier because of the fact that it has a virtual earth point.

Consider the case of a series of resistors used to sum different voltages.

Using a resistor network like this, it can be seen that it appears like a potential divider for each signal source. A voltage is developed across the load resistor (which could be the input impedance of the amplifier stage). This voltage also then feeds out to the other signal sources. Also the overall load resistance is a combination of the actual amplifier load resistance and all the inputs in parallel. Thus adding an extra input will also the settings.

This is clearly not a satisfactory state of affairs.

The op amp virtual earth amplifier makes an ideal summing amplifier. If the summing point is taken as the virtual earth point, then there is no interaction between the different inputs.

## Op amp summing amplifier

The op amp summing amplifier or virtual earth mixer uses the non-inverting amplifier configuration.

The key change to the inverting amplifier is that several series resistors are added to the virtual earth or virtual ground point formed at the inverting input.

The output from any given input can be calculated from the formula below:

$Av=-\frac{\mathrm{R2}}{\mathrm{R1x}}$

Where:
Av = voltage gain
R2 is the feedback resistor value
R1x is the value of the resistor for input x

## Op amp audio mixer

The op amp inverting amplifier provides an ideal platform for an analogue audio mixer. As shown above the various inputs can be taken via a suitable resistor to the virtual earth point. By using the virtual earth of the inverting amplifier, the level for one input is not dependent upon the conditions for any other input. Accordingly all the controls can be set totally independently.

Using an op amp summing amplifier as a virtual earth mixer provides the ideal solution for an audio mixer. The mixer can have as many inputs as required within reason and each one can be controlled independently by the value of the input resistor.

Contribution to output from Va is:

$Vo=-{V}_{a}\left(\frac{{R}_{2}}{{R}_{a}}\right)$

Contribution to output from Vb is:

$Vo=-{V}_{b}\left(\frac{{R}_{2}}{{R}_{b}}\right)$

And so forth for each input . . . . . .

As a result of the capabilities of the inverting amplifier, a mixer is able to have a large number of inputs each of which is individually controllable.

During the electronic circuit design for an audio mixer summing amplifier using an op amp circuit, thought has to be put into the way in which the gain of each channel is controlled. The obvious place to place a potentiometer is on the input as shown. If this is to be done, then the value of the resistor R1x must be sufficiently higher than that of the potentiometer, otherwise the position of the potentiometer will also have an impact on the gain as it will vary the overall input resistance.

As the potentiometer slider travels towards ground, so the resistance to ground decreases and this will increase the gain of the channel - the gain for that channel is controlled by the resistor R1x and the value of the resistance from the centre of the potentiometer to ground.

If the potentiometer value is ten times that of R1x then this should be sufficient for the effect to be sufficiently small not to be noticed unduly in most cases.

The op amp based summing amplifier provides the ideal solution to many analogue summing applications, from summing voltages for use in measurement, or for other situations and of course the classic application for the op amp summing amplifier is within audio mixers. The op amp inverting amplifier provides the ideal basis to provide an analogue summing amplifier.

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