Topic 7  Summing Amplifier

At the end of this Topic you should be able to:

  • Draw and recognise a summing amplifier circuit.

  • Describe and explain applications including mixing audio signals and digital to analogue conversion

  • Calculate resistor values for the above applications.

  • Use the formula Vout = -Rf[(V1/R1) + (V2/R2) + (V3/R3)].

 

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

 
 

 

 

 

 

 

 

 

You can see that this circuit is like an inverting amplifier.  It 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?  ANSWER

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

 Question 2 What does this mean in simple terms?  

ANSWER                                                        

So we can use Ohm’s law to rewrite this in terms of voltage and resistance. 

 Question 3  What is the formula for Ohm's Law?  ANSWER

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   therefore   Vout = - Rf (V1 + V2 + V3)

             Rf       R1     R2     R3                                           R1     R2     R3

 

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 Can you explain why the statement Vout = -(V1 + V2 + V3) is true?  ANSWER

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.

 
 

 

 

 

 

 

 

 

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?

ANSWER

Question 6 Suppose V = 5 volts and R = 10 k and Rf = 1k.  Use these to work out Vout for the binary word 1101.  ANSWER                                                                                                           

  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 a Hi-Fi) 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!

 

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