# Develop an OpAmp circuit to measure average voltages

With four different sensors, V1, V2 V3, and V4 I need to develope an operational amplifier circuit to measure average temperature with following specifications:

1. The output voltage range of each sensor is limited to 0-5 V
2. The output voltage range of average temperature measurement circuit is 0-5V
3. The span adjustment range is +/- 1V
4. Total system accuracywith +/- 0.1% of FSO

• Your specs do not have span adjustment. Is there a typo? Dec 18, 2010 at 15:16
• This smells a bit like homework... ? Dec 18, 2010 at 19:30
• @marcus, no rule against homework, we should just avoid giving out solutions directly. Dec 19, 2010 at 0:07
• @Kortuk: That's what I meant. :) Dec 19, 2010 at 11:18

For an average voltage you need a voltage adder

Since the opamp will set the output such that $X$ is at $0V$:

$I_N = \dfrac{V_N}{R_{IN}}$

Since ideally no current flows into the opamp's input

$I_F = \Sigma I_N$

and

$V_{OUT} = -R_F \cdot I_F = -R_F \cdot \Sigma \left(\dfrac{V_N}{R_{IN}}\right)$

Therefore:

$V_{OUT}=-\dfrac{R_{F}}{R_{IN}}\times (V_1 + V_2 + V_3)$

To average N inputs $R_F$ should be 1/N-th of $R_{in}$.

For zero adjustment just add another input to which you can apply a variable voltage by means of a potmeter. You'll want to include negative voltages in the control range.
Range adjustment can be done by modifying $R_F$ (for all inputs simultaneously) or $R_{in}$ (for each input individually).

(image taken from http://www.electronics-tutorials.ws/opamp/opamp_4.html)

• Thanks Kortuk, Marcus Lindblom, stevenvh, and tyblu for your efforts. It looks the propsal of stevenvh is more likely what I required but how to limit the output of the sensors 0-5 V. I think you required the complete senario.
– Mokhtar
Dec 19, 2010 at 10:49
• @Mokhtar, There are a few ways to limit a node to a specific voltage range, each with advantages and disadvantages. Why not open a new question to get some complete answers? Dec 19, 2010 at 15:36

There are many ways of averaging voltage. Any circuit is an "op amp circuit", once it has an op amp. First, voltages average naturally, like temperature. This can be shown using a passive method, with resistors:

A high impedance voltage follower (op amp circuit) is required to maintain accuracy.

Another passive method is with capacitors, using charge redistribution. This is related to how many modern analog-to-digital converters (ADCs) are being designed today. It works by storing a voltage on a capacitor, disconnecting from the source signal, then connecting to and redistributing charge with another parallel capacitor, which halves the initial voltage. This can be extended to average four voltages by having them share and redistribute total charge:

Again, a high impedance voltage follower is required to maintain accuracy.

Either of these concepts can be improved upon in many different ways, using op amps or otherwise. Since this appears to be a homework assignment, I'll leave this bit to you!

• xxx Petroleum company required a circuit for the boiler control system which needs the average temperature from four locations. The temperature sensors make the temperature information available as voltage V1, V2, V3, and V4. Develop an operational amplifier circuit to measure avarage temperature with following specification: 1) The output voltage range of each sensor is 0-5 V. 2) The output range of average temperature meassurement circuit is 0-5 v. 3) The span adjustment range is +/- 1 v and zero adjustment range is =/- 1 v. 4) Total system accuracywith +/-0.1% of FSO.
– Mokhtar
Dec 19, 2010 at 10:49

Try the Handbook of Operational Amplifier Applications pg 65.

• -1. Sorry, krapht, but this isn't helpful if Mokhtar doesn't have the book, and you can't presume he does. Dec 18, 2010 at 15:33
• @krapht can you provide a link, I found multiple copies of the book online for free, but the author and book varied. I guessed you meant google.com/… Dec 18, 2010 at 16:41
• Ah, with the link in your answer it's completely different. When I saw the title of the book I was rather thinking of Amazon than a freely downloadable document. And that wouldn't have been helpful. Point restored. Dec 18, 2010 at 17:40
• @stevenvh, I thought I had remembered it as a free-book i had seen before, so I decided I should step in. Dec 18, 2010 at 18:36
• Thanks Kortuk, Marcus Lindblom, stevenvh, and tyblu for your efforts. It looks the propsal of stevenvh is more likely what I required but how to limit the output of the sensors 0-5 V. I think you required the complete senario.
– Mokhtar
Dec 19, 2010 at 10:33

What stevenvh has show is the classic opamp summing circuit. One advantage of such a circuit is that each signal is feeding into a virtual ground, so there is no back driving of one signal to another. Another characteristic of this circuit is that it inverts. That may or may not make a difference. If the result is going into a microcontroller, then the polarity is irrelevant as the result can be easily flipped in firmware.

However, here is another circuit that should work in this case. The assumption is that the output of the sensors is uneffected when driving a impedance above some value. In this case I put 20 KOhm resistor in series with each sensor to satisfy that requirement. All you really need in that case to get the average is 20 KOhms in series with each sensor output then all tied together. Assuming the sensors have very low output impedance, the resulting impedance will be the parallel combination of all the resistors. Since you have 4 signals being averaged, the impedance will be 5 KOhms. If that's good enough, then no opamp is required.

If you need lower impedance, then a simple unity gain buffer will do. I have made an example schematic:

http://www.embedinc.com/temp/average.gif