Welcome to PPTools !
Here, you will find some help about this software, including details about how the calculations are performed.
Table Of Contents
- General concepts about the User Interface
- General concepts about numerical methods
- The RLC simulator
- The resistance calculator
- The inductance calculator
- The skin depth calculator
1. General concepts about the User Interface
Amongst all the tools grouped within this software, some principles have been kept the same:
- Balloon help is available on almost all input fields: leave your mouse cursor still on an input field, a few words of explanations will appear.
- When a button is labelled "solve", that means that you can leave any of the input fields blank and a solver will solve it (and re-write all the other values in order to make sure the form is consistent).
- When a button is labelled "calculate", that means that there is a bunch of input fields and only one result field.
- If a calculation does not converge (physically impossible set of parameters, ...), the displayed results will be obviously wrong: expect to see "NaN", "Inf" of negative numbers when they should be positive.
- Most of the tools will try to give you as much information about the calculation that has been performed as possible.
- All units are SI unless otherwise specified.
2. General concepts about the numerical methods
- Equations are solved using Newton's method with a small (non-zero) initial condition. For parameters that can only be positive, a loop will try to divide that initial condition and try again if the computed result was negative.
- Non-linear systems are solved using a method that can be found in Ortega, J and Rheinboldt, W (1970), "Iterative Solution of Non-linear equations in several variables", Academic Press, New York
- Initial values used in the above mentionned algorithms are guesses based on physical considerations. They should be close enough to the real solution, in order for the methods to converge.
- Tabulated values are computed using data tables and interpolations, knowing if one (or both) of their scale is log.
- In order to make sure data is consistent, all fields are re-calculated after solving. That could explain that some fields could be a little bit altered after solving.
3. The RLC simulator
This simulator solves the two equations describing an RLC circuit. Because there are two equations, you have to fill out all fields but two.
Please remember that you have to provide values that are physically possible !
The two equations that are solved are non-linear and are solved using an algorithm specifically designed for that kind of problems. Because that algorithm is not very robust in term of convergence, it has to be provided with very carefully chosen initial values. Such values are estimated using various physical consideration (quarter period of a pure LC circuit, fraction of the energy that could be dissipated in the resistance, ..). A few cases are solved using a simple Newton's algorithm.
4. The resistance calculator
The first section of that tab is about color coding for resistors. You can either select the color of the three rings of your resistor and it will tell you what is the value of that resistor, or enter the resistance your are looking for and it will tell you what colors you have to look for in order to come as close as possible to the value you requested (Once again, the resistance value will be updated to reflect the real resistance of the proposed choice). Sometimes, there is more than one way to code a given resistance value. The coding using the highest multiplier is prefered. If you want to see the alternate value, add a negligible value to your resistance: for example, if you want the alternate coding for 100 Ω, enter 100 in order to get the regular color coding or 100.1 in order to get the alternate coding.
The second section is about liquid resistors. You have to select the solution you are using (most of the time, copper sulfate, CuSO4, but other are available as a matter of convenience, even if they are far less interesting in term of available range). Then, fill up all but one value, then solve it and it will give you a set of consistent parameters. If the maximum solubility of the product has been reached, it will keep it at such a maximum value (measured at 20C) and finish the calculation (in order to get a consistent set of parameters). Then, you are advised to keep that maximum concentration and blank another field in order to get the result you need, knowing that you need to change one of your initial parameters (also, more details about going out of the internal tables are given when you launch pptools from the command line). If there are no empty fields, the total resistance will be calculated.
The solutions proposed in the liquid resistors section contain the following:
| Formula | Name |
|---|
| KMnO4 | Potassium permanganate |
| CuSO4 | Copper sulfate |
| ZnSO4 | Zinc sulfate |
| NaCl | Sodium cloride (Salt) |
| NH4Cl | Ammonium chloride |
5. The inductance calculator
This solver is about calculating inductance parameters knowing the geometry. First, select the geometry of your inductance. Then, fill out all but one parameters (be carreful, since L and C are equivalent, they are considered to be the same parameter), and run the solver. If you want to find some parameters in order to achieve a specific inductance or capacitance, leave one of the top fields blank, then fill out only ONE of the two bottom field (L and C) and run the solver. The equation will be solved and the other bottom parameter (L or C) will be displayed as well. If there are no empty field, the L and the C will be calculated.
All but one (the one for two spheres) of the calculations are made on the inductance and then the capacitance value is extracted using LC=ε0μ0 per unit of length. When the lenght makes sense, this calculation works fine. Some other cases are currently supposed to be wrong, because there is no concept of length and I don't have any capacitance formulas for them at the moment (like for the torus). In such a case, a warning message is displayed.
Numerically speaking, these calculations account for flux leakage. There are performed according to the Knoepfel calculations (p312-324), including all coefficients. These coefficients are tabulated in the solver, using the appropriate interpolation. A status text field will display the value of these coefficients (if relevant) as well as warning when out of tables (most of limit values beeing trivial, this going out of tables should not be a problem most of the time).
For the rectangular coil, there is no available coefficient in a very specific regime. So, a weigthed average is used instead, providing a smooth transition between the two well defined regimes at the boundaries of that regime. Such a transition seems reasonnable, but the precision of the calculation would drop in that regime, so a warning is issued.
For the helix coil, the calculation in the Knoepfel seems obviously wrong, so don't complain if the results are wrong!
6. Skin depth calculator
This solver is about magnetic field skin depth in various materials. You have to select the applied signal shape, and then enter the parameters, leaving one field blank. Since these profiles are tabulated up to T/2, don't expect any relevant results at time greater than T/2!
This solver gives you the value of a "flux skin depth". This is the distance such as Sum(B) from 0 to d = Sum(B) from 0 to infinite / e. Practically speaking, this is equivalent to the length defined page 54 of the Knoepfel. It allows the skin depth to be meaningfull at times greater than T/4 and is specially suited for inductance calculations (because it is based on the flux). For a more detailed explanation of such a concept, please have a look at the Knoepfel or at my PhD thesis (p278, "La compression de flux magnétique dans le régime sub-microseconde pour l'obtention de hautes pressions et de rayonnement X intense", Paris XI, July 2002, Mathias Bavay)
Thank you for using PPTools !