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Austria
9 Posts

 Posted - Sep 23 2021 :  16:48:14 Hi,first of all thanks to the FastFieldSolvers Team for making this software available to us!I am trying to see if I can benefit from the 2D capabilities of FasterCap, so I am poking around with simple structures to try and understand the fundamentals of the tool.In this phase, I am really hoping to leverage the (simpler) framework of a 2D simulation.I have been experimenting with a model for a parallel plates capacitor and I would have a few questions on it, but I'll leave that for later as here I would like to understand more about the capacitance matrix.For a structure with only two conductors, FasterCap returns a 1x1 matrix, as I would expect: just the cap between the two conductors I created.For a structure with two conductors over a gnd plane (i.e. a segment of conductor of larger size than the two conductors above it), the output is a 2x2 matrix.Now, I am referencing Enrico's white paper here: ht*ps://w*w.fastfieldsolvers.com/Papers/The_Maxwell_Capacitance_Matrix_WP110301_R02.pdfWhere the Maxwell Capacitance Matrix is explained with a 4-conductors example. The features I extract from the picture are:1. Each conductor has a 'self capacitance', i.e. a capacitance with respect to infinity2. Each conductor has N-1 (=3 in this case) mutual capacitances with all other conductors in the geometry.I have a little issue with this 'self capacitance', why it's needed, why it's there, so maybe that's the issue here.However, if I apply this scheme for a situation where I have two conductors, I would say that each conductor should have, again,1. A self capacitance (towards infinity)2. A mutual capacitance towards the other conductorTherefore, a 2x2 matrix. However, the output of FasterCap is a 1x1 matrix.Similarly, for a 2 conductors + gnd plane, you have 3 conductors (also gnd is a conductor, right?), so again if I follow the pattern explained in the white paper, I would expect a 3x3 matrix, not 2x2.What is the rationale behind this 'dimensional reduction'? Or maybe it's my input file incorrect?Thanks for helping!MicheleHere the file, for reference:(last version, two conductors and gnd plane)* 2D - Cap of two metal rods on a gnd surface --> 2x2 matrix?** data is included in a single file** Natural units are metres: how does cap scale?*C rectangle.txt 1 -6 0.0C rectangle.txt 1 5 0.0C gnd.txt 1 0 -10File rectangle.txt0 conductor strip*S microstrip 0.0 0.0 0.0 1.0S microstrip 0.0 1.0 1.0 1.0S microstrip 1.0 1.0 1.0 0.0S microstrip 1.0 0.0 0.0 0.0EndFile gnd.txt0 gnd plane*S gnd -10 0.0 10 0.0End

447 Posts

Austria
9 Posts

 Posted - Sep 27 2021 :  19:54:42 Dear Enrico,many thanks for your explanation and references, I'll look them up!In the few days from my post to now, I think I got to something similar reasoning by myself, although I couldn't figure out the log(1/r) dependency on my own ;-)If I understand you right, then, the 2x2 matrix obtained from my arrangement, in 2D, is of the form:Q1 = c11*Vd1 + c12*Vd2Q2 = c21*Vd1 + c22*Vd2with the 'implicit' constraint that Q1+Q2=-Q3and Vd1 and Vd2 being deltas among the three conductors' voltages.Is this correct? If so, I would then ask: how are Vd1 and Vd2 defined?Meaning:1. What in the file determines them?2. How does the simulator communicate the choice, in its output?For the file I posted in the OP, the results of the matrix are:g1_microstrip 1.48869e-011 -4.3045e-012 g2_microstrip -4.31433e-012 1.48527e-011Could you explain that the 'gx_microstrip' label means?Thanks again!Michele

447 Posts

 Posted - Sep 28 2021 :  15:51:33 Hi Michele,I think I see your point - you are wondering where's the voltage of the third conductor. You're absolutely right in asking, as I'm afraid we kept it implicit i.e. it is not documented (actually it appears as a comment in the source code, but of course I don't expect anyone to browse the sources just to use the software..).In fact, in the 2D simulation one conductor is always considered ground, meaning that its potential is never raised to 1V. The voltage of this conductor is the famous one that is subtracted from the other to achieve the 'trick'. Now, FasterCap simply assumes that the last conductor that is defined in a list file is the ground conductor (I believe this is the missing piece of information you needed). If you check the 2D input file examples that are installed with the software, you will see in fact that the gnd definition always comes last.So in a nutshell, the Maxwell capacitance matrix you see for your 3 conductor example file refers to the first two conductors vs. the gnd plane (that you defined correctly as last conductor). So the C11 element is the sum of the capacitance per unit length to the second conductor and to the gnd plane and the C12=C21 element is the capacitance per unit length between the two conductors. Note by the way that this definition of the Maxwell capacitance matrix allows to invert the matrix to find also the inductance per unit length of the transmission line, if you assume TEM propagation (for the rigorous treatment again see C. Wei, R. F. Harrington, J. R. Mautz, T. K. Sarkar, "Multiconductor transmission lines in multilayered dielectric media", IEEE Transactions on Microwave Theory and Techniques, Vol. 32, No. 4, Apr 1985, that contains the proof).For what regards instead the g1_ and g2_ prefixes, this is not related to 2D or 3D extraction. In fact, these are prefixes that are added to the conductor name when you use the same conductor definition multiple times, to distinguish between the conductors. In your case you are using the rectangle.txt file twice, and the conductor name in the file is always 'microstrip'. To avoid shorting the two conductors together unintentionally, the name is prefixed by an incremental g_ string, where 'g' means 'group' and is simply a number.If you want specific names, you need to use files containing different names.Finally, let me just add a small remark about the sum of the charges; what you say is correct if you have no dielectric. In presence of a dielectric, you need to zero the sum of the total charges, i.e. including also the polarization charges at all interfaces. This is not (only) the free charge at the conductor surface; but this is a detail you can safely ignore, as it is not impacting at all your results or how you will use them.Hope this clarifies a bit,Enrico

Austria
9 Posts

 Posted - Sep 28 2021 :  19:33:44 Hi Enrico,many thanks for your detailed explanation. It makes perfect sense now!In the mean time, I gathered some other questions on my journey with the tool, but I'll start a new thread for those.Thanks!Michele
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