Tutorial 7 F - Summing Amplifier

Learning Objectives



This kind of amplifier is used in digital to analogue conversion, or as a mixer in an audio system.



This circuit uses negative feedback into the inverting input, but instead of one input, there are three inputs.


Question 1

What does this circuit remind you of?



Kirchhoff I tells us that Itot = I1 + I2 + I3


Question 2

What does this mean in simple terms?



So we can use Ohmís law to rewrite this in terms of voltage and resistance. 


Question 3

What is the formula for Ohm's Law?



Notice that in the next step we use the minus sign because X is at a virtual earth so we have to climb the potential difference hill to get to Vout.  This is Kirchhoff II.


-Vout = V1 + V2 + V3      

                               Rf       R1     R2     R3                              



Vout = - Rf (V1 + V2 + V3)

                  R1     R2     R3


For any number of resistors, the equation becomes:



If the values of all the resistors are the same:


Vout = -(V1 + V2 + V3)


The output is the sum of all the input signals but is of opposite polarity.


Summing amplifiers are found in mixing desks which add together the inputs from several different audio sources.


Question 4

Explain why the statement Vout = -(V1 + V2 + V3) is true.


Digital to Analogue Conversion

There are many occasions in which digital signals are converted to analogue.  Computers know two states, ON and OFF, but the signals that we pick up and use are analogue.  So the output of a computer (or a CD deck) is pretty meaningless without some kind of digital to analogue conversion.


A summing amplifier can be used, which gives an output equal to the sum of the digital signals.




In the diagram, msb means most significant bit, while lsb means least significant bit.


Since the inverting input is a virtual earth, we can say that the total current Itot is given by:

Vout = - Itot Rf


= - Rf(I1 + I2 + I3 + I4)

= - Rf(V1 + V2 + V3 + V4)

         R       2R     4R    8R


For every change in one bit, there is a voltage change of 0.0625 V.  For an eight bit word it is 1/256 = 0.00390625 V.  For a 16 bit word the smallest voltage change is 1/216 = 1/65536 = 0.0000152 V.  You can see that the more bits there are, the smaller the voltage change per bit, leading to greater resolution.


Question 5 

An op-amp has 2 inputs, one having a resistance of 1000 W and the other having an input resistance of 5000 W.  The two inputs have a voltage of + 4 V and + 5 V respectively.  The feedback resistance is 2000 W.  What is the output voltage?




Question 6

Suppose V = 5 volts and R = 10 k and Rf = 1k.  Use these to work out Vout for the binary word 1101.



The diagram here shows the digital output converted to an analogue wave pattern:



You can see that the output wave is similar to the input, but would result in some distortion.  This can be reduced markedly by increasing the resolution.  However there will always be an element of this kind of distortion.  Audiophiles (people who like listening to music on High-Fidelity music reproduction equipment) reckon that analogue-recorded music sounds more natural than digitally recorded music and argue that a vinyl LP played on a high quality record deck sounds better than a compact disc.  This is not true for a vinyl LP played on an inferior groove-grinder!  A CD sounds better any day!


When these notes were originally written, the vinyl LP had almost completely been superseded by CDs.  Now many music companies are re-issuing albums on vinyl, and manufacturers are again making high quality record decks.  Why?  People prefer the sound!




  • Summing op-amp uses negative feedback

  • Equation

  • Digital to Analogue Converter



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