Using the Summing Amplifier as an Average Amplifier

Sometimes people ask how can one use a summing amplifier as an average amplifier. The answer is simple, provided that one knows what kind of average one needs.

The summing amplifier can output the average of two, three or more signals. This is different than a signal average. The summing amplifier cannot, for example, output the average of a triangle signal. For that, you need an integrator to perform the average in the analog realm, or you need to sample the signal and calculate the average with a microcontroller. This type of average is the signal average in the time domain. I will write an article about the average of a signal in a near future.

In this post I will show you how to average two or more signals with a summing amplifier. In How to Derive the Summing Amplifier Transfer Function I wrote that the summing amplifier shown in Figure 1

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Design a Bipolar to Unipolar Converter with a 3-input Summing Amplifier

Since the publication of Design a Bipolar to Unipolar Converter to Drive an ADC, several readers contacted me with requests to help in solving their particular converter. The common problem they had was the fact that the components’ calculation resulted in a negative value for at least one resistor.

To provide a solution, first we need to understand the root cause of the problem. Let’s take one of the circuits I received and analyze it.

The reader wrote that he would like to drive an ADC with the input range of 0 to 2.5V from a signal with the range of –5V to +5V, connected at V1 (see Figure 1).

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Bipolar to Unipolar Converters Based on a Summing Amplifier Configuration

In a previous article, Design a Bipolar to Unipolar Converter to Drive an ADC, I presented a method for designing a bipolar to unipolar converter using a summing amplifier. In this article I am going to show more examples of bipolar to unipolar converters which are based on a summing amplifier configuration. You can adapt them to your needs if you use the method I described in the previous article.

Input -1V to +1V, Output 0V to +5V, Reference voltage +5V


Figure 1

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Design a Bipolar to Unipolar Converter to Drive an ADC

Most Analog to Digital Converters have a unipolar input that can be a problem when designing bipolar circuits.  Some common ADC input voltage ranges are 0 to 2.5 V, or 0 to 5 V.  However, the analog circuit that drives the ADC can have voltage swings of, –1 V to +1 V, –2 V to +2 V , –5 V to +5 V, and so on.  Bringing the ADC input below ground is a big No-No, because the current from input will flow through the chip substrate creating irreversible changes in the ADC and damage it.  So, how do we connect a bipolar front end circuit with a unipolar ADC?  Enters the bipolar to unipolar converter.  Let’s design one.

The converter can be designed with a summing amplifier, as in Figure 1.  How do we calculate the resistors?


Figure 1

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Differential Output Circuit

One of my readers asked me to explain how I designed a circuit I posted in a forum, as a solution to one of the member’s question.  The problem was about designing a circuit with 3 input signals, VA, VB and VCM.  The circuit had to output the sum and difference between VCM and the average of VA and VB as in the following expressions:

image0011 (1)

The solution I posted is the circuit in Figure 1.


Figure 1

What is the easiest way to design this circuit?

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Solving the Summing Amplifier

How to Design a Summing Amplifier Based on the Input and Output Voltage Level Requirements

In forum a member asked how can he drive a MOSFET that needs a voltage range of 4V to 5V with a DAC with the output range of 0V to 5V?

Initially I thought he should use a differential amplifier.  However, based on the articles I published, Solving the Differential Amplifier – Part 1, Part 2 and Part3 the solution based on a differential amplifier would require a negative voltage level in the input.   Although V1 can be the input from 0V to 5V, V2 has to be negative, so that the output shifts to positive values.

Then I thought of the Summing Amplifier, or the Non-Inverting Summing Amplifier, which is shown in Figure 1.  It is called a summing amplifier, because two signals are summed in one of the amplifier inputs.  In this case, V1 and V2 are summed in the non-inverting input.

summing_amplifier1Figure 1

The summing of V1 and V2 is not direct.  Resistors R1 and R2 make a weighted sum and this is what makes this amplifier very useful.  As in the case with the differential amplifier, one can use this circuit to achieve any linear function.  This article shows you how to design a summing amplifier based on the input and output requirements.  You can also solve your amplifier with the calculator I posted here: Summing Amplifier Calculator.

The transfer function of the summing amplifier is as follows.

image002 (1)

You can find its demonstration in this article, How to Derive the Summing Amplifier Transfer Function.

Let’s write down what we know:

If Vin1 = 0V then Vout1 = 4V and
If Vin2 = 5V then Vout2 = 5V,

where by Vin1 and Vin2 I noted the input range limits, and by Vout1 and Vout2 I noted the output range limits.

Let’s choose one of the summing amplifier inputs to be Vin, say V1.

Because we have two instances that we know, Vin1 and Vin2 and the corresponding outputs, Vout1 and Vout2, let’s rewrite equation (1) using these two instances.

image0072 (2)

This is a linear system of two equations with a lot of unknowns: R1, R2, R3, R4 and V2.  However, we can simplify our life by grouping the resistors in ratios.  The equations can be rewritten like this,

image0081 (3)

where by k1 and k2 I noted:

image0091 (4)

Now we are left with three unknowns, k1, k2, V2.  I can simply consider V2 as a known value, because I can connect to R2 any voltage I want or, more conveniently, a voltage that I already have in the circuit.  I will target for V2 = 5V, since there is already a DAC in this circuit with an output range of 0 to 5V.  So I can assume there is a 5V reference in this circuit.

If k1 and k2 are the remaining unknowns, then (3) is a system of two equations and two unknowns as in (5), which can be easily solved.

image0103 (5)

It can be easily seen that the second equation becomes

image0111 (6)

so k2 has to be zero.

The result is k1 = 1/4 and k2 = 0.

This result shows that we do not need the resistors R3 and R4. Also, the ratio between R2 and R1 is 1/4.  We can choose R2 = 1 kohm and a standard value for R1 = 4.02 kohm with a 1% tolerance.

The final circuit is shown in Figure 2.

circuitFigure 2

Since k2 is zero, R3 is zero, configuring U1 as a repeater for the summed voltage in the non inverting input.

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