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'[EE]:Formula for unbalanced bridge Rx-> V - take 2'
2001\02\26@090653 by mike

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I think I got the formula wrong last time...

Treating each side as a potential divider : Vout = Vin(R3/R1+R3) - Vin(R2/Rx+R2)

R1=R2, so this is now :
Vout=Vin(R3/R1+R3) - Vin(R1/Rx+R1)

Vout = Vin((R3/R1+R3) - (R1/Rx+R1))
We want the answer for Rx given the Vout/Vin ratio- call this ratio V,
so this becomes :

V = (R3/R1+R3) - (R1/Rx+R1)

..and this is where my algebraic ability grinds to a halt..!

So the question is how do you juggle this to get either  :
Rx = function_of(V)
Or (better, if possible)
Rx/R3 = function_of(V)

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2001\02\26@092721 by mike

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Oops - mixed up Rx and  R2 - let's try again...

Vin
R1 R2
+--|--
|  +-- Vout
R3 Rx
0V

Treating each side as a potential divider : Vout = Vin(R3/R3+R1) - Vin(Rx/Rx+R2)

Vout = Vin((R3/R1+R3) - (Rx/Rx+R2))
We want the answer for Rx given the Vout/Vin ratio- call this ratio V,
so this becomes :

V = (R3/R1+R3) - (Rx/Rx+R2)

..and this is where my algebraic ability grinds to a halt..!

So the question is how do you juggle this to get either  :
Rx = function_of(V)
Or (better, if possible)
Rx/R3 = function_of(V)
..and can it be simplified further if R1=R2 ?

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2001\02\26@093511 by wzab

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On Mon, Feb 26, 2001 at 02:12:12PM +0000, Mike Harrison wrote:
{Quote hidden}

OK, so let's do it once again with maxima (alfa is Rx/R3, so Rx=alfa*R3):
(C1) V1 : Vin*R3/(R1+R3);

                                   R3 Vin
(D1)                                -------
                                   R3 + R1
(C2) V2 : Vin*alfa*R3/(R2+alfa*R3);

                                alfa R3 Vin
(D2)                             ------------
                                alfa R3 + R2
(C3) solve(V=(V1-V2)/Vin,alfa);

                              (R2 R3 + R1 R2) V - R2 R3
(D3)                 [alfa = - -------------------------]
                                  2
                               (R3  + R1 R3) V + R1 R3
--
                               HTH
                             Wojciech M. Zabolotny
       http://www.ise.pw.edu.pl/~wzab  <--> spam_OUTwzabTakeThisOuTspamise.pw.edu.pl

http://www.debian.org  Linux - free OS for free people!

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