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Solving for an expression in cascades of stages and ladders

Posted 4 months ago
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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?

2 Replies

A replacement can do something like that, unless I misunderstand you:

In[7]:= Vout == 
 Simplify[Vsupply - (Vin - Vbe) ((hfe + 1)/hfe)*RC/RE /.
   Vin -> Vout/DCTransferFunction]

Out[7]= 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][[1]]]

Is the intent to eliminate the variables of interest i.e. Vout/Vin-><function of remaining variables>?

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