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Im currently working on an assignment for my EEE systems engineering module, in which iv ran into a few problems that the limited notes and email ignoring lecturer cant solve. The topic in question is using extreme value analysis to calculate the tolerance of the frequency cutoff of a low pass filter given its component tolerances, so f=1/2piRC.
The first question I have is should the resulting frequency tolerance be equal either way, such as +-10%? I ask because all my results seem to be coming out at something like +10% -8%, despite equal component tolerances.
This then leads on to my second problem, where I am asked to find a function for Δf using ΔR and ΔC (Δ meaning tolerance). The problem is that Δf changes depending on which extremes of ΔR and ΔC are taken like in the question above, meaning I cant see how Δf, ΔR and ΔC can be linked in an equation. The nearest I got is f=1â„(2Ï€*R(1±∆R)*C(1±∆C) ), but i dont see how I can continue from here to get Δf as a constant (eg ±∆f)
I hope I've explained the problem well enough, just ask if i havent :)
Oh and also, im pretty sure this is going to be a simple answer or something iv completely missed, so im asking you in advance not to rub it in too hard please :)
Registered Member #30
Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706
I think the proper name for this is uncertainty analysis.
To get delta f, write your above equation twice. Once for the unperturbed value, which is just f= 1/(2 pi R C) and once for the perturbed value- f+ delta f = 1/(2 pi (R+ delta R) (C+ delta C))
Then subtract them to get delta f as a function of delta R and delta C. This is a continuous function, that will tell you delta f for any delta R and delta C you care to put in. So you can try positive and negative values of delta R and C to find the worst case delta f.
The other way to do it is use partial differentiation to find df/dR and df/dC, then compose the answers. You're assuming delta R is small compared to R, so second order terms like delta R delta C can be neglected, making the math far easier.
The common sense approach: R and C are multiplied together, so the worst case tolerance for frequency is twice the tolerance of the components. Eg, 5% components gives 10% frequency. (The derivative of x.x is 2x)
Radiotech is not mental, there is actually such a thing as a Schmoo plot, you can make one with the Monte Carlo option in any good circuit simulator.
I tried doing ∆f=1/2piRC - 1/2pi(R+∆R)(C+∆C), but i constantly keep ending up with R∆C and C∆R terms that i cannot get rid of, what am i missing?
Registered Member #30
Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706
If the tolerances are in percent, and you want an answer in percent, you should maybe be substituting deltaR/R and deltaC/C, and solving for delta f/f. Hopefully that'll get rid of the unwanted terms.
After all if a resistor changes by 5% then deltaR = 0.05R, or deltaR/R = 0.05
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Extreme value analysis
