1
$\begingroup$

$$\frac{V_o-\frac{A \left(R_{\text{int}} \left(V_s-V_1\right)\right)}{R_{\text{int}}+R_s}}{R_o}+\frac{V_o}{R_L}+\frac{V_o-V_1}{R_1}=\frac{V_1-V_s}{R_{\text{int}}+R_s}+\frac{V_1-V_o}{R_1}+\frac{V_1}{R_2}$$

I'm trying to rewrite the above expression in terms of V_o/V_s, but am having trouble figuring out to do this in mathematica. I tried using solve twice, first for V_o and then for V_s and doing Simplify[] on the quotient but my answer was insanely complex and I'm assuming not a correct solution to my homework problem. Is there a more direct way to do this?

Improve this question
$\endgroup$
2
  • 1
    $\begingroup$ Please include your equation as a Mathematica expression, so people don't have to retype it in order to try and help you. $\endgroup$ – MarcoB Oct 7 '15 at 18:44
  • $\begingroup$ Do you need things in terms of V1/V_s too (because that makes more sense)? $\endgroup$ – march Oct 7 '15 at 19:17
2
$\begingroup$

This will get you started. Per my comment (which to me makes sense), I am going to put things in terms of V1/Vs as well. Feel free to alter the solution to your heart's content.

expr = (Vo - (A (Rint (Vs - V1)))/(Rint + Rs))/Ro + Vo/RL + (Vo - V1)/R1 == (V1 - Vs)/(Rint + Rs) + (V1 - Vo)/R1 + V1/R2;
expr2 = Map[Simplify[#/Vs /. {Vo -> x Vs, V1 -> y Vs}] &, %, {2}]
expr2 /. {x -> Vo/Vs, y -> V1/Vs}

results in

enter image description here

Solving for x instead:

Simplify /@ Collect[x /. First@Solve[expr2, x] // Expand, y] /. y -> V1/Vs

results in

enter image description here

You don't need to do the Simplify if you don't want.

Improve this answer
$\endgroup$
5
  • $\begingroup$ I'm trying to get an expression of the form Vo/Vs={expr in terms of other variables}. The problem is to calculate the gain of an amplifier circuit so I want the output voltage over the signal voltage. $\endgroup$ – nw. Oct 7 '15 at 20:00
  • $\begingroup$ @nw. Okay: "rewriting the expression in terms of..." is what I did. So really, you mean, "solve for...". Please re-write your question to make this clear, and also follow MarcoB's suggestion to include the Mathematica code in your question. $\endgroup$ – march Oct 7 '15 at 20:21
  • $\begingroup$ Yes sorry, that is what I meant. $\endgroup$ – nw. Oct 7 '15 at 20:25
  • $\begingroup$ @nw. I updated the answer. I'm not sure if you saw it. $\endgroup$ – march Oct 8 '15 at 18:39
  • $\begingroup$ Thanks! That's the same thing I got with solve, just couldn't believe they'd give us something that nasty, especially since most of my class is doing algebra by hand! $\endgroup$ – nw. Oct 8 '15 at 23:03

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.