I have an Op-amp that looks like this:
and I am trying to derive this equation for Ix:
\(I_{x} = (V_{s})\frac{R_{1}R_{3}}{R_{x}(R_{1}R_{3} - R_{2}R_{4}) + R_{1}R_{3}R_{4}}\)
Here is what I have so far:
\(V_{-} = (V_{o})\frac{R_{1}}{R{1} + R_{2}}\)
\(V_{-} = V_{+}\)
I1 going through R4 is:
\(I_{1} = \frac{V_{s} - (V_{o})\frac{R_{1}}{R{1} + R_{2}}}{R_{4}}\)
I2 going through R3 is:
\(I_{2} = \frac{(V_{o})\frac{R_{1}}{R{1} + R_{2}} - V_{0}}{R_{3}}\)
Then Ix is:
\(I_{x} = I_{1} - I_{2}\)
I am not sure if this is correct up to here?
and I am trying to derive this equation for Ix:
\(I_{x} = (V_{s})\frac{R_{1}R_{3}}{R_{x}(R_{1}R_{3} - R_{2}R_{4}) + R_{1}R_{3}R_{4}}\)
Here is what I have so far:
\(V_{-} = (V_{o})\frac{R_{1}}{R{1} + R_{2}}\)
\(V_{-} = V_{+}\)
I1 going through R4 is:
\(I_{1} = \frac{V_{s} - (V_{o})\frac{R_{1}}{R{1} + R_{2}}}{R_{4}}\)
I2 going through R3 is:
\(I_{2} = \frac{(V_{o})\frac{R_{1}}{R{1} + R_{2}} - V_{0}}{R_{3}}\)
Then Ix is:
\(I_{x} = I_{1} - I_{2}\)
I am not sure if this is correct up to here?