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Maths problem
Nov. 17th, 2008 11:25 pm
I want to solve a tricky maths problem. I really need an engineering solution, and at a pinch I could make adequate approximations, but it would be much better to have a more accurate formula so that I can get very close to the optimum solution before building a magnetic component and doing measurements.
What is happening physically is that there is a magnetic component that transfers a small amount of energy from its input to its output each time the input current is switched on and off, (and rises from zero to a controlled level, then declines back to zero, before immediately doing the same again, in a repeated triangular waveform).
The peak current follows a half sinusoid, and the energy transferred is proportional to the square of the current, so you might think that the power should be:
frequency * some_constant * integral_from_0_to_PI_(sin(x)^2 dx)
The tricky part is that the frequency itself depends on the point on the half sinusoid, and not quite linearly. I could approximate sin(x)^3 as the overall function, but that would not be quite correct - it is probably more like sin(x)^2.7 or something even worse. I need both a way to decide on the correct function for the frequency dependence, and then how to integrate fractional powers of sin(x).
I am more a consumer than a producer of maths, so now I go: "EEK!"
Can anyone help at all?
What is happening physically is that there is a magnetic component that transfers a small amount of energy from its input to its output each time the input current is switched on and off, (and rises from zero to a controlled level, then declines back to zero, before immediately doing the same again, in a repeated triangular waveform).
The peak current follows a half sinusoid, and the energy transferred is proportional to the square of the current, so you might think that the power should be:
frequency * some_constant * integral_from_0_to_PI_(sin(x)^2 dx)
The tricky part is that the frequency itself depends on the point on the half sinusoid, and not quite linearly. I could approximate sin(x)^3 as the overall function, but that would not be quite correct - it is probably more like sin(x)^2.7 or something even worse. I need both a way to decide on the correct function for the frequency dependence, and then how to integrate fractional powers of sin(x).
I am more a consumer than a producer of maths, so now I go: "EEK!"
Can anyone help at all?
