0
$\begingroup$

I have this expression:

$$PB=\frac{(R3 + R4) R6}{R4 R5 + R4 R6 + C2 R2 R3 R5 S + C2 R2 R4 R5 S + C1 C2 R1 R2 R3 R5 S^2 + C1 C2 R1 R2 R3 R6 S^2}$$

I need to put it in this form:

$$PB=\frac{\frac{(R3 + R4) R6}{C1 C2 R1 R2 R3 (R5 + R6)}}{\frac{R4}{C1 C2 R1 R2 R3} + \frac{(R3 R5 + R4 R5)}{C1 R1 R3 (R5 + R6)}S + S^2}$$

I made this code:

In[]:T=(R3 + R4) R6/(R4 R5 + R4 R6 + C2 R2 R3 R5 S + C2 R2 R4 R5 S + C1 C2 R1 R2 R3 R5 S^2 + C1 C2 R1 R2 R3 R6 S^2);
     Den = Cancel[Collect[Denominator[T] /aux, S]]

And I obtained as output:

$$\frac{R4}{C1 C2 R1 R2 R3} + \frac{(R3 R5 + R4 R5)}{C1 R1 R3 (R5 + R6)}S + S^2$$

Then I made:

In[]:Num = Cancel[Numerator[T]/aux]

And I obtained as output:

$$\frac{(R3 + R4) R6}{C1 C2 R1 R2 R3 (R5 + R6)}$$

But when I made:

PB=Num/Den

The output was:

$$\frac{(R3 + R4) R6}{C1 C2 R1 R2 R3 (R5 + R6)(\frac{R4}{(C1 C2 R1 R2 R3)} + \frac{(R3 R5 + R4 R5) S}{C1 R1 R3 (R5 + R6)} + S^2)}$$

My question is: Is there a way to put the expression in the form I need?

$\endgroup$

1 Answer 1

2
$\begingroup$
Clear["Global`*"]

T = (R3 + 
     R4) R6/(R4 R5 + R4 R6 + C2 R2 R3 R5 S + C2 R2 R4 R5 S + 
      C1 C2 R1 R2 R3 R5 S^2 + C1 C2 R1 R2 R3 R6 S^2);

eq = 1/T == (b + c*S + S^2)/a;

sol = Solve[CoefficientList[#, S] & /@ eq, {a, b, c}][[1]] /.
   Rule[lhs_, rhs_] :> 
    Rule[lhs, Simplify[Numerator[rhs]]/Simplify[Denominator[rhs]]];

T2 = HoldForm[a]/(b + c*S + S^2) /. sol

enter image description here

T2 // ReleaseHold

enter image description here

EDIT: To keep S separate

(T3 = HoldForm[a]/(b + HoldForm[c]*S + S^2) /. sol) // TraditionalForm

enter image description here

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

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