Maths question....

Discussion in 'General Off-Topic Chat' started by UltraMagnus, Mar 15, 2009.

Mar 15, 2009

Maths question.... by UltraMagnus at 9:03 PM (535 Views / 0 Likes) 2 replies

  1. UltraMagnus
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    Member UltraMagnus hic sunt dracones

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    I need to work this out for my electronic design corsework...

    If I am working out the voltage out using the simple voltage divider rule, with a calculation something like

    Vout= ((R3 + R4 + R5)/(R2 + R3 + R4 + R5)) * Vin

    and each resistor (R2, R3, etc) has a 5% tolerance, how do I work out the total tolerance of Vout?

    thanks in advance.
     
  2. FAST6191

    Reporter FAST6191 Techromancer

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    I am going to find this hard to tell you how without giving a direct answer but OK.
    Long story short you need to work out the maximum difference, this is the tolerance.

    There are rules of thumb but they break down after you get anywhere fun (logarithms, non linear error curves (semiconductors are great for this), non linear behaviour of multiple systems comprising a whole and so on) so I do not suggest using them, also while extremes are useful you occasionally want realism (probability distributions of errors, worst case scenario is too expensive) and others want safety factors (in electronics you want to look at Zener diodes for safety factors and capacitors for fully charged/discharged despite being at 95%).
    Basically what I am saying is learn the theory behind it before venturing out into the world.

    Back on topic basic factoring of equations and percentages as a multiple is what you need here

    15%= 1.15 (I know it is not 15%, this is just an example)
    (R1+15%)=1.15 x R1

    Scaled up

    1.15 x R1 + 1.15 x R2 + 1.15 x R3 =1.15(R1 + R2 + R3)
    Just to try and get you thinking about it if you found a 10% resistor (call it R3) you could no longer factor it as nicely as you can there, just use the 10% in the calculation and it will come out fine.

    Obviously dividing by a larger number is not the thing to do if you want to make a maximum difference in this case* so you have to spin it, in this case you want to take it. Continuing with the example the 15% would then become 0.85 with the same idea as before.

    *Vout/Vin = 1.15 (R3 + R4 + R5) / 1.15 (R2 + R3 + R4 + R5) will have the 1.15 cancel out leaving you with the original equation.

    Also check the inverse (top half 5% below, bottom %5 above).

    Although I dislike rules the following guides are pretty good:
    http://documents.wolfram.com/applications/...orAnalysis.html
    http://www.shef.ac.uk/physics/teaching/fir..._hand_outs1.ppt
    http://www.carlton.srsd119.ca/chemical/Sig...ntal_errors.htm
     
  3. UltraMagnus
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    Member UltraMagnus hic sunt dracones

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    Thanks for that, it helped me figure it out finally.
     

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