This circuit permits to add voltages from different voltage sources. It allows also to adjust the amplification for each one.

1. Can this circuit have a linear functioning ?
    Is it an inverting configuration ?

2. Use the model of the ideal op-amp and the circuit laws to show that :
   
   Considering this expression, justify the name "inverting adder" given to this configuration...

3. Inverting adder and amplifier.

   3.1. If R2 = 10 kΩ, what should the value of R1 and R1’ be in order to realize an inverting adder having an amplification factor of 5, that is
   
   3.2. Ve is a triangular signal having a peak to peak amplitude of 1V and V’e is a continuous voltage of -1V. Represent Ve, V’e and Vs.
   Verify these results in the virtual lab.

   3.3. If Vecrête = 3V, represent Ve, V’e and Vs.
   (we will choose Vsat = 14V)
   Identify the instants where the op-amp shows a linear functioning and then a non-linear functioning.
   Verify these results in the Virtual Lab.

4. Averager.

   4.1 If R2 = 5kΩ, what should be the values of R1 and R’1 in order to obtain an inverting averager, that is
   

    4.2. Ve is a triangular signal having a peak to peak amplitude of 4V and V’e is a continuous voltage of 2V. Represent Ve, V’e and Vs.

    4.3. Verify these results in the Virtual Lab.

5. Mixer. The adder configuration is used to mix the sounds coming from two musical instruments. All the resistors are variable.     5.1. Which resistance should we adjust in order to separately modify the sound volume of each instrument ? In order to increase the sound volume, should we increase or decrease the resistance value ?     5.2. Which resistance is used to adjust the global sound volume ? In order to increase the sound volume, should we increase or decrease the resistance value?     5.3. Verify these configurations in the Virtual Lab.