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In the following circuit, compute the values of R_{1} and R_{3} in terms of R_{2} and R_{4}, such that v_{o} is always equal to v_{1}  5v_{2}.
I have marked 3 nodes, A, B and C. v_{+} = v_{} as assumption for the opamp.
Consider node A.
v_{} = v_{+} = v_{1} × (R_{2} / (R_{1}+R_{2}))
Consider node B and C.
(v_{}  v_{2}) / R3 = (v_{o}  v_{}) / R4
I now stick at here...
I can write R_{1} in terms of R_{2}, but there exist v_{} and v_{1}.
And for R3, the same problem exists.
First, is there anything wrong in my above computations?
Second, can I express R_{1} and R_{3} in terms of R_{2} and R_{4} without using other unknowns?
I have marked 3 nodes, A, B and C. v_{+} = v_{} as assumption for the opamp.
Consider node A.
v_{} = v_{+} = v_{1} × (R_{2} / (R_{1}+R_{2}))
Consider node B and C.
(v_{}  v_{2}) / R3 = (v_{o}  v_{}) / R4
I now stick at here...
I can write R_{1} in terms of R_{2}, but there exist v_{} and v_{1}.
And for R3, the same problem exists.
First, is there anything wrong in my above computations?
Second, can I express R_{1} and R_{3} in terms of R_{2} and R_{4} without using other unknowns?
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