Question

Design a circuit using Op amp that will combine four voltages according to the following ratio. You can only use invertor amplifier . All input voltages are positive and you cannot tamper with the sources V_o = 4V₁ - V₂ - 8V₃ - 2V₄

Answer 1

The design can be implemented using a different version of summing circuit which is quite straightforward to analyse(though there are some limitations). In case of a summing circuit for an inverting amplifier all voltages are generally inverted but we need a non inverted voltage for V₁ in case of this problem mentioned above. Thus we remove the ground terminal from the non inverting input of generalized op-amp summer circuit which basically feeds the invertor amplifier summer network from the + or non inverting input without tampering the nature of source voltages(that is all source voltages are positive). The redesigned circuit can be drawn as follows:

The unknowns in this problem are R_f, R₁, R₂and R₃ respectively.

The output voltage genaralized equation for such a network can be deduced in simplified form as follows:

According to the problem given,

Now comparing this with the generalized equation we get the following relations,

From eq.2, eq.3, eq.4 we get

Now solving for eq.1 we get

  

Putting the values of R₁, R₂ and R₃ with respect to R_f in this equation we get,

Putting this value on to eq5, eq6, eq7 we get,

These are the required unknowns for the design which needs to be implemented in the summer circuit given above.

IMPORTANT NOTE:

In case of any doubt or clarification regarding any of steps provided above, you can always comment below without any sorts of hesitation.