Hello again,
Knowing the math behind something like a circuit can be very very useful.
It can help a person get something similar to real life experience just from
running through a set of equations a few times. The math doesnt even
have to be perfect sometimes, just close enough to get a 'feel' for how
the circuit works and how it changes with component values so we know
about how it would work out in real life.
A good example where math pays off big might be this...
We need to select a resistor value that is to be used in series with a thermistor
so that we can use this simple circuit to measure temperature with an AD
converter, measuring the voltage at the junction. The question is, what
is the best value for this resistor? Many resistor values will work, because
we will always get a voltage out of the circuit, so the problem is to find the
best resistor value.
As it turns out, we can graph the temperature, AD converter value, and
resistance for this circuit to get a 'feel' for where this is going to take us.
But before we go there, try to take a guess for what this value would be.
If you already have experience with this circuit you might know the
answer already, or if you are a lucky guesser
But what if we forgot what the best value was or we just want to prove what
it is? That's where the graph comes in.
See the attached picture.
In this picture we have temperature vs AD count vs resistor value.
We can see that for values of 10k and 100k we get an AD count that is
quite non linear. What this would mean is we would have to put up with
that or else work out the math for eliminating this in the micro controller
program, but looking again we can see parts of this surface that have a linear
character over most of the range of the AD converter count. Also, the
end application would only need a temperature range of about plus and minus
20 degrees for temperature fault detection (for example), so what would
the best resistor value be now, looking at the graph?
We can see that the part of the surface that curves less with change of AD count
is in the center of the resistor values, around 40k to 60k. Since these choices
give the best linearity, we choose 50k and this gives us very good linearity
even without any additional calculations that would have to be done by the uC.
Now we can see that we found the right value, and how did we get there?
We used math to graph the function and found the right value that way.
This took knowing the curve of the thermistor too.
What if we didnt have this math, what then?
Well, we would have to try a resistor value and then vary the temperature over the
required range and measure values, then plot the curve, then try another resistor
value, etc., untill we could find one that gave what looks like the best linearity.
Math, in this case, payed off big even though the math equations are not perfect
(the thermistor character varies a little from theoretical) but we were still able to
get enough 'experience' to find the right value. This graph took the place of
hours and hours of testing and retesting.
Knowing the math behind something like a circuit can be very very useful.
It can help a person get something similar to real life experience just from
running through a set of equations a few times. The math doesnt even
have to be perfect sometimes, just close enough to get a 'feel' for how
the circuit works and how it changes with component values so we know
about how it would work out in real life.
A good example where math pays off big might be this...
We need to select a resistor value that is to be used in series with a thermistor
so that we can use this simple circuit to measure temperature with an AD
converter, measuring the voltage at the junction. The question is, what
is the best value for this resistor? Many resistor values will work, because
we will always get a voltage out of the circuit, so the problem is to find the
best resistor value.
As it turns out, we can graph the temperature, AD converter value, and
resistance for this circuit to get a 'feel' for where this is going to take us.
But before we go there, try to take a guess for what this value would be.
If you already have experience with this circuit you might know the
answer already, or if you are a lucky guesser
But what if we forgot what the best value was or we just want to prove what
it is? That's where the graph comes in.
See the attached picture.
In this picture we have temperature vs AD count vs resistor value.
We can see that for values of 10k and 100k we get an AD count that is
quite non linear. What this would mean is we would have to put up with
that or else work out the math for eliminating this in the micro controller
program, but looking again we can see parts of this surface that have a linear
character over most of the range of the AD converter count. Also, the
end application would only need a temperature range of about plus and minus
20 degrees for temperature fault detection (for example), so what would
the best resistor value be now, looking at the graph?
We can see that the part of the surface that curves less with change of AD count
is in the center of the resistor values, around 40k to 60k. Since these choices
give the best linearity, we choose 50k and this gives us very good linearity
even without any additional calculations that would have to be done by the uC.
Now we can see that we found the right value, and how did we get there?
We used math to graph the function and found the right value that way.
This took knowing the curve of the thermistor too.
What if we didnt have this math, what then?
Well, we would have to try a resistor value and then vary the temperature over the
required range and measure values, then plot the curve, then try another resistor
value, etc., untill we could find one that gave what looks like the best linearity.
Math, in this case, payed off big even though the math equations are not perfect
(the thermistor character varies a little from theoretical) but we were still able to
get enough 'experience' to find the right value. This graph took the place of
hours and hours of testing and retesting.
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