Please show DETAILED work and explanation: The summing amplifier below can be us

Question

Please show DETAILED work and explanation:

The summing amplifier below can be used as a digitally controlled volume control. The switches either connect to ground (mid) or the input signal (one). How many possible input combinations are there for this circuit? What is the output voltage if the input data is 0110 (depicted) if vs(t) = sin( 4000 pi t)? What is the frequency (f) in Hertz for the above input signal? What is the output voltage if the input is 1011? Make a table showing all possible combinations. (Better be sure to get the right answer for questions!)

Explanation / Answer

Please ask if you have any doubt. I will help you.

Note that the non inverting terminal( + ) is at ground ,which in an ideal op amp indicates that the inverting terminal ( - ) is also at ground.

V(-) = V(+) = 0.

Thus unless the inputs are at higher vlotage they dont come into play .

If 2 or more inputs come into play then the summing amplifier concept helps.

First lets calculate the Vo due to each single source individually.

For 0001 :

The line with 16R is activated and other lines are off .

Thus the current flows through 16R and then R to output.

(Vi - V(-))/16R = (V(-) - Vo)/R

Gives Vo = - Vi/16

For 0010 :

The line with 8R is activated and other lines are off .

Thus the current flows through 8R and then R to output.

(Vi - V(-))/8R = (V(-) - Vo)/R

Gives Vo = - Vi/8

For 0100 :

The line with 4R is activated and other lines are off .

Thus the current flows through 4R and then R to output.

(Vi - V(-))/4R = (V(-) - Vo)/R

Gives Vo = - Vi/4

For 1000 :

The line with 2R is activated and other lines are off .

Thus the current flows through 2R and then R to output.

(Vi - V(-))/2R = (V(-) - Vo)/R

Gives Vo = - Vi/2

a) inputs = 4 .24 = 16 combinations are possible.

b) for 0110 :

Vo = -(1/8 + 1/4)Vi

Vo = -(3/8)sin(4000t)V

c) Frequency = /2 = 4000/2 = 2000 Hz.

d) For 1011 :

Vo = -(1/2 + 1/8 + 1/16 )Vi

Vo = -(11/16)sin(4000t)

e) possible inputs      output values

    0000                    0

    0001                  -(1/16)Vi

    0010                  -(1/8)Vi

    0011                  -(3/16)Vi

    0100                  -(1/4)Vi

    0101                  -(5/16)Vi

    0110                  -(3/8)Vi

    0111                  -(7/16)Vi

    1000                  -(1/2)Vi

    1001                  -(9/16)Vi

    1010                  -(5/8)Vi

    1011                  -(11/16)Vi

    1100                  -(3/4)Vi

    1101                  -(13/16)Vi

    1110                  -(7/8)Vi

    1111                  -(15/16)Vi

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