STEORN DEMO LIVE & STREAM in Dublin, December 15th, 10 AM

[Omnibus]

@teslaalset,

Now I used your corrected spreadsheet but made it for one only cycle. The last cycle in yours wasn't finished. I also changed it for 700kHz, 100pF and 1.2 and 2Ohms.

[Omnibus]

I have attached the mathematical equation for the energy equation. Basically it's the indefinite integral of the integrals I have been using. When you plot these equations you get the energy plots you guys have been sharing but without needing discrete data points. When you use them be carefull to get everything right as it's easy to make a slip and throw everything off.

The C's at the end are integration constants. They need an initial condition at t = 0 for instance to fill out.

That's a very good warning. I can't agree more. Now, regarding discreteness, I think Mathematica also uses discrete math. Like I said, the real killer would be if all this can be solved analytically without using numerical methods (Mathematica due to its very essence uses numerical methods; in this respect it's no different than Excel). We need a mathematician to discuss this and it very well may turn out that it's practically impossible to solve this analytically. That's the reason those numerical methods in applied math emerged -- numerous otherwise unsolvable engineering problems could be tackled with ease by using the discrete math of computers. Anyway, that was a slight off topic rumination. Now back to the problem at hand.

[broli]

That's a very good warning. I can't agree more. Now, regarding discreteness, I think Mathematica also uses discrete math. Like I said, the real killer would be if all this can be solved analytically without using numerical methods (Mathematica due to its very essence uses numerical methods; in this respect it's no different than Excel). We need a mathematician to discuss this and it very well may turn out that it's practically impossible to solve this analytically. That's the reason those numerical methods in applied math emerged -- numerous otherwise unsolvable engineering problems could be tackled with ease by using the discrete math of computers. Anyway, that was a slight off topic rumination. Now back to the problem at hand.

I'm confused here. Surely the mathematical equations of Mathematica has produced are all analytical. Definite integrals have indeed numerical solutions, but indefinite ones if solvable are purely analytical.

[Omnibus]

I'm confused here. Surely the mathematical equations Mathematica has produced are all analytical.

The equations are analytical, however, the concrete data they are crunching is handled by using the methods of the discrete math. The numerical solutions, that is. Mathematica has a cute way of solving equations, say, differential equations and presenting these solutions analytically. That's really great. However, the minute you need to find numerical solutions the discrete math kicks in. Same as in Excel, MathCAD and what not.

[teslaalset]

@teslaalset,

Now I used your corrected spreadsheet but made it for one only cycle. The last cycle in yours wasn't finished. I also changed it for 700kHz, 100pF and 1.2 and 2Ohms.

Almost good, but you overlooked the time constant in cell A4.
The 800000 should be replaced by 700000.

Such errors are very easily made. That's why I made my model such that you only have to change the main parameters in the yellow highlighted cells.