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.
deflection bridge and non-linearity
- Thread starter liniams
- Start date
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.
panic mode
- Joined Oct 10, 2011
- 2,749
how did we go
from R1=R2=R3=R0
to R1+R2+R3=Ro
from R1=R2=R3=R0
to R1+R2+R3=Ro
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?
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?
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.
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.
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.
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.
