This may be a dumb question, but I often need to solve expressions for something other than a variable. As a trivial example, say we have a common-emitter amplifier:
Vout = Vsupply - (Vin - Vbe)((hfe + 1)/hfe) * RC/RE
And I want to solve it for the DC transfer function Vout/Vin. Can Mathematica do this, at all?
Now, I understand there is actually no solution here, but a small change makes it solvable (and still easy to reason around):
Vout = - (Vin - Vbe)((hfe + 1)/hfe)*RC/RE
Now, this simple example I can solve easily. But there are complex expression created in cascades of stages and ladders that get a bit more complex in hurry... But even being to solve the simple problems would be nice as a "calculator" function. I can calculate square roots and look up logarithms in tables myself also, but I sure prefer to work with a calculator.
Any ideas? Maybe I just missed something obvious?
A replacement can do something like that, unless I misunderstand you:
In:= Vout ==
Simplify[Vsupply - (Vin - Vbe) ((hfe + 1)/hfe)*RC/RE /.
Vin -> Vout/DCTransferFunction]
Out= Vout == ((1 + hfe) RC (DCTransferFunction Vbe - Vout))/(
DCTransferFunction hfe RE) + Vsupply
You can leave it to Mathematica to find the replacement with Solve:
Vout == Simplify[
Vsupply - (Vin - Vbe) ((hfe + 1)/hfe)*RC/RE /.
Solve[Vout/Vin == DCTransferFunction, Vin][]]
Is the intent to eliminate the variables of interest i.e. Vout/Vin-><function of remaining variables>?
Vout/Vin-><function of remaining variables>