Maxwell-Wien bridge...



Hi,

I trying to find out whether there is a 'neat' solution to the
following (and if so, how to get to it):

My starting point is the following equation (its the formula for the
Maxwell-Wien bridge):
(Vab/Vcd) = (R3/(R1+j*w*L1+R3)) - (R4/(R2+R4+j*w*R2*R4*C4))

Equation in Latex:
\[ \frac{V_{ab}}{V_{cd}} = \left(\frac{R_3}{R_1 + j \omega L_1 + R_3}
- \frac{\frac{R_4}{1 + j \omega R_4 C_4}}{R_2 + \frac{R_4}{1 + j
\omega R_4 C_4}} \right) \]

I want to differentiate the norm of Vab/Vcd with respect to R2. I've
managed to figure out that:

|Vab/Vcd| = sqrt(((R3*R2 - R4*R1)^2 + (R4*w*L1 -
R3*w*R2*R4*C4)^2)/(((R1 + R3)^2 + (w*L1)^2)((R2 + R4)^2 +
(w*R2*R4*C4)^2)))

Latex:
\begin{eqnarray*} \left\|\frac{V_{ab}}{V_{cd}}\right\| =
\sqrt{\frac{(R_3 R_2 - R_4 R_1)^2 + (R_4 \omega L_1 - R_3 \omega R_2
R_4 C_4)^2}{((R_1 + R_3)^2 + (\omega L_1)^2)((R_2 + R_4)^2 + (\omega
R_2 R_4 C_4)^2)}}
\end{eqnarray*}

The trouble is that the formula isn't getting any smaller and I am not
really in the mood to spend more hours trying to derive the answer. So
is there anyone who has a better way of deriving what I want to know
(am I missing an obvious simplification or something)? Is there a neat
analytical solution? Or should I just let Maple get me the values I
need and give up?

(BTW I've already tried Maple, but it doesn't really seem to be able
to make good simplifications... well, at least not the ones I'm
interest in, or maybe its just my Maple skills that suck. Did give me
the answer I needed though. :) ).

Any help is appreciated (and when I say 'any help' I mean help that is
useful. :) ).
.



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