# deflection bridge and non-linearity

Discussion in 'Homework Help' started by liniams, May 16, 2015.

1. ### liniams Thread Starter New Member

May 16, 2015
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0
Can anybody help with this problem? I've followed it through and found the values of Vc and Va therefore found the actual value of Vo. However I'm at a loss when it comes to comparing the ideal to the actual value to find error and Non-linearity.

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2. ### WBahn Moderator

Mar 31, 2012
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First, what do the terms "non-linear error" and "non-linearity" mean? What is the mathematical definition you are using over those two concepts?

3. ### liniams Thread Starter New Member

May 16, 2015
7
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Non linear error where ideal is O=KI + a and the actual being O=KI + a +N(I) where N is the non linear error. Non-linearity is (Nmax/span)*100. I having trouble finding this error and Non-linearity as there is no given resistor values?

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4. ### WBahn Moderator

Mar 31, 2012
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Ask if your answer makes sense. The ideal result is zero if ΔR is zero. You are claiming that the actual result is infinite if ΔR is zero. Does that make sense?

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5. ### liniams Thread Starter New Member

May 16, 2015
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So my analysis is incorrect?

6. ### WBahn Moderator

Mar 31, 2012
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Uhm, unless it makes sense that the output voltage goes to infinity for ΔR = 0 and unless it makes sense that the output voltage goes to zero as ΔR goes to infinity, yeah, that would indicate that your analysis is incorrect.

7. ### liniams Thread Starter New Member

May 16, 2015
7
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Okay thankyou.

8. ### panic mode Senior Member

Oct 10, 2011
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how did we go
from R1=R2=R3=R0
to R1+R2+R3=Ro

9. ### liniams Thread Starter New Member

May 16, 2015
7
0
it is supposed to be &. I wrote this in a rush, I've redone it using nodal for points A & C now.

10. ### WBahn Moderator

Mar 31, 2012
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And...?

What is the result?

11. ### liniams Thread Starter New Member

May 16, 2015
7
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Does this look correct?

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12. ### WBahn Moderator

Mar 31, 2012
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Ah. Thanks. I'll take a look at it and get back shortly.

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13. ### WBahn Moderator

Mar 31, 2012
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Nope. You've still got problems, though they are more subtle now.

You know that the ideal response, since it is given, is

$
V_0 \; = \; \frac{V_B}{4} \cdot \frac{\Delta R}{R_0}
$

So any thing you get that is not close to that is highly suspect.

Is

$
V_0 \; = \; V_B \cdot \frac{\Delta R}{R_0}
$

close to that?

Also, you know that you are exploring the nonlinearity of the response. Does you result show any nonlinearity at all? Another reason to be highly suspicious.

Your very first node equation makes no sense. You say

$
\frac{V_A - V_B}{R_2} \; + \; \frac{V_A}{R_0 + \Delta R} \; = \; V_A $$\frac{1}{R_0} \; + \; \frac{1}{R0} \; + \;\frac{1}{\Delta R}$$
$

Note that I'm using V_B and leaving out the phi, which you have someplaces and not others.

The left hand side is the sum of the currents leaving Node A and it is just fine. But where on earth does the right hand side come from and what is it supposed to represent?

14. ### liniams Thread Starter New Member

May 16, 2015
7
0
Sorry that may have been my presentation, there was a mistake there I had split my fraction incorrectly tried again however I may be going backwards now

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15. ### WBahn Moderator

Mar 31, 2012
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How are you going from your second line (the one with the arrow to the left of it) to the third line?

Be much more explicit in going between those two and you should see your mistake. If not, by showing your steps more explicitly, it will be easier to point it out to you.

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16. ### WBahn Moderator

Mar 31, 2012
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Oh, and again the "does it make sense" rule comes into play.

In your last expression for Va, you have it that Va = 2Vb when ΔR is zero. Does that make sense? If not, then STOP and don't go further until you have something that makes sense.

You should be checking your units and asking if the results are making sense throughout your work.