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Logarithmic Scale Conversion

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Pero2912

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Hello people.

So I'm trying to figure this out:
here is a sensitivity characteristics of my gas sensor, and the both x and y scales are logarithmic.
sensitivity.jpg
Now, i'd like to interpolate this data but I guess I can not use simple linear method, like y=(y2-y1)/(x2-x1)*x+y1. What do you think?

Regards,

Pero
 

Thanks for answer Brad!
But, could you be so nice and provide me some explanation of why is this method legitimate? Or, link some references if it's easier for you.
 

A straight line in log-log scale corresponds to a function Y = X^a. It can be modelled in software.
 
Solved it! Thanks for advice.
but if somebody wants to know, I used analytic approximation y = C/sqrt(x),
 

I used analytic approximation y = C/sqrt(x)
Click to expand...
Slope of different curves in the above characteristic corresponds to exponents between -0.3 and -0.63, so -0.5 (1/sqrt) is well in the middle. We could try to fit the exponent in an individual calibration, but that's probably beyond reasonable efforts for this sensor.
 

Yeah, i also came up with 0.67 for alcohol. But why do you use negative coefficients? I mean, y = 0.67/sqrt(x) works fine for me.
 

sqrt(x) = x^0.5
1/sqrt(x) = x^-0.5
Thus the negative exponent.
 

Yeah, you're right. I didnt pay good attention on what you wrote above.
 

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