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Re: [femm] how do I model a torroidal transformer ?

To: femm@xxxxxxxxxxxxxxx
Subject: Re: [femm] how do I model a torroidal transformer ?
From: Keith Gregory <k.gregory@xxxxxxxxxxx>
Date: Wed, 27 Aug 2003 07:58:08 +0100
In-reply-to: <3F4B9FE8.7010904@plix.com>
References: <web-52112482@california.com>

All,

I would use the current block for as quick model but points if I wanted to model individual turns - there could be a lot though! Anyway, I would think that a stored energy approach would give inductance with any method of representing the winding. It would be interesting to find out if anyone's got the time. I'm not sure how good inductances would be though because for a normal toroid the end winding is about the same size as the bits that are being modelled.

Keith.

At 10:59 26/08/2003 -0700, you wrote:

Robert,
I wasn't worrying about the inductance and all
that myself. There are other experts in this group
better at that than I am. I use the point currents
for other things, more to model actual turns of
wire for easier amp-turns determination. Just makes
it more of a direct calculation then. That's all.
Seems you have a different goal in mind. So go with
what works best for you.
DRS

robert Macy wrote: > Didn't realize there was an angular copy capability. > You're right looks fast. > > But then, how do you calculate the inductance? Except with > energy stored, etc > > Doesn't the A.J integral over sheets of current return > inductance? > > - Robert - > > On Tue, 26 Aug 2003 08:43:05 -0700 > Dave Squires <djsquires@xxxxxxxx> wrote: > >> >> >> >>Robert, >>Drawing point currents like this is quick and easy. >>It took me a whole 5 minutes to do this entire model. >>Perhaps you are not aware of using the radial copy >>and mirror functions? >> >>First you center this whole thing on >>the 0,0 origin.  Put in two points for the toroid >>thickness on the 0,a - 0,b  line. Select them with >>a right click. Then do mirror copy about the y axis. >>Then you enter two 180 arcs on top for the ID and OD. >>Then you mirror those two about the x axis. Toroid is >>done and takes about 30 seconds or less. >> >>Next change the grid size to what you want for wire >>diameter or something close. Put in two points say >>inside and outside on the top. Then go to the copy >>button and do an angular copy of 6 degrees and 29 >>copies. Bingo! Primary side is done. Do the same >>thing again using -6 degrees and 29 copies. Then >>delete the two initial points so you have a primary >>and secondary separated by on empty spot top and bottom. >> >>Next pick the block properties you want, air, M19 steel >>for this case.  Then set the point properties for >>the >>coils. I used plus and minus 5 amps I think it was. >> >>This whole process took about 2-3 minutes. Then >>simulating >>and displaying it another minute. Overall it took about 5 >>minutes. So it doesn't take very long to set up point >>currents and such once you learn some tricks. >> >>In any case it seems there are other ways as well >>based on what Keith and Mark came up with. >> >>DRS >> >>robert Macy wrote: >>> Brain dead here, that's set to median thickness, >>> >>> But instead of point currents which take a lot of >>time to >>> draw in, how about more curves and then use the >>"circuit" >>> properties.  That way you automatically get >>inductance per >>> turns squared.  >>> >> > > >           > >>- Robert - >>> >>> On Mon, 25 Aug 2003 10:04:51 -0700 >>>  Dave Squires <djsquires@xxxxxxxx> wrote: >>> >>>> >>>> >>>> >>>>Come on guys. This is easy. >>>>The attached file shows you how to do this. >>>>Remember this is static, not dynamic. But this >>>>will work fine for getting the field. This would >>>>be a no load condition. For a loaded case you >>>>would have to calculate the rate of change, >>>>figure the voltage induced and the current based >>>>on the load. Depending whether the field is >>>>rising or falling in the primary you can >>determine >>>>the Lenz reaction polarity accordingly to oppose >>>>or assist the primary drive. I will leave that >>>>up to the user to handle all the other details. >>>> >>>>The main trick is to use point currents for the >>>>coil windings. Just run the attached file. >>>>David Meeker can fill you in on any other way >>>>to do this. But this is one way. >>>> >>>>DRS >>>> >>>>robert Macy wrote: >>>>&gt; The torroidal transformer *is* >>axisymmetric, but >>>>when drawn >>>>&gt; that way the currents go around the >>small circle and >>>>the >>>>&gt; magnetic field is perpendicular to the >>page.&nbsp; I >>>>don't think >>>>&gt; femm solves this situation.&nbsp; >>>>&gt; >>>>&gt; Instead and approximation is to draw the >>cross >>>>sectional >>>>&gt; view in x-y form and set the total >>length to the >>>>median >>>>&gt; circumference.&nbsp; >>>>&gt; >>>>&gt; The &quot;crunching&quot; of the >>field at the inside >>>>curve won't show >>>>&gt; up, but it will get you >>started.&nbsp; >>>>&gt; >>>> >>> >>> >> > > &gt;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>> >>>>- Robert - >>>>&gt; >>>>&gt; On Mon, 25 Aug 2003 03:16:32 -0000 >>>>&gt;&nbsp; &quot;Dr Mark >>Snoswell&quot; >>>>&lt;mark@xxxxxxxxxxxxxxx&gt; wrote: >>>>&gt; >>>>&gt;&gt; >>>>&gt;&gt; >>>>&gt;&gt; >>>>&gt;&gt;How do I model the field of a >>torroidal >>>>transformer? ... >>>>&gt;&gt;it's axi >>>>&gt;&gt;symetric but I can't quite see >>hwo to model it. >>>>&gt;&gt; >>>>&gt;&gt; >>>>&gt;&gt; >>>>&gt;&gt; >>>>&gt;&gt; >>>>&gt;&gt; >>>>&gt;&gt; >>>>&gt;&gt; >>>>&gt;&gt; >>>>&gt;&gt; >>>>&gt;&gt; >>>>&gt;&gt; >>>>&gt;&gt;Yahoo! Groups Sponsor >>>>&gt;&gt; >>>>&gt;&gt; >>>>&gt;&gt; >>>>&gt;&gt; >>>>&gt;&gt; >>>>&gt;&gt; >>>>&gt;&gt; >>>>&gt;&gt; >>>>&gt;&gt; >>>>&gt;&gt; >>>>&gt;&gt; >>>>&gt;&gt; >>>>&gt;&gt;Your use of Yahoo! Groups is >>subject to the >>>>Yahoo! Terms >>>>&gt;&gt;of Service. >>>>&gt;&gt; >>>>&gt;&gt; >>>>&gt;&gt; >>>>&gt;&gt; >>>>&gt; >>>>&gt; >>>>&gt; >>>>&gt; >>>>&gt;&nbsp; >>>>&gt; >>>>&gt; Your use of Yahoo! Groups is subject to >>>>http://docs.yahoo.com/info/terms/ >>>>&gt; >>>>&gt; >>>>&gt; >>>> >>>> >>>>&nbsp; ---------- >>>> >> > > >>[Format]&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>=&nbsp; 3.3 >>>>[Frequency]&nbsp;&nbsp; =&nbsp; 0 >>>>[Precision]&nbsp;&nbsp; =&nbsp; >>1e-008 >> > > >>[Depth]&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>=&nbsp; 1 >>>>[LengthUnits] =&nbsp; inches >>>>[ProblemType] =&nbsp; planar >>>>[Coordinates] =&nbsp; cartesian >>>>[Comment]&nbsp;&nbsp;&nbsp;&nbsp; >>=&nbsp; &quot;Add >>>>comments here.&quot; >>>>[PointProps]&nbsp;&nbsp; = 2 >>>>&nbsp; &lt;BeginPoint&gt; >>>>&nbsp;&nbsp;&nbsp; >>&lt;PointName&gt; = >>>>&quot;Primary-plus&quot; >>>>&nbsp;&nbsp;&nbsp; >>&lt;I_re&gt; = 5 >>>>&nbsp;&nbsp;&nbsp; >>&lt;I_im&gt; = 0 >>>>&nbsp;&nbsp;&nbsp; >>&lt;A_re&gt; = 0 >>>>&nbsp;&nbsp;&nbsp; >>&lt;A_im&gt; = 0 >>>>&nbsp; &lt;EndPoint&gt; >>>>&nbsp; &lt;BeginPoint&gt; >>>>&nbsp;&nbsp;&nbsp; >>&lt;PointName&gt; = >>>>&quot;Primary-minus&quot; >>>>&nbsp;&nbsp;&nbsp; >>&lt;I_re&gt; = -5 >>>>&nbsp;&nbsp;&nbsp; >>&lt;I_im&gt; = 0 >>>>&nbsp;&nbsp;&nbsp; >>&lt;A_re&gt; = 0 >>>>&nbsp;&nbsp;&nbsp; >>&lt;A_im&gt; = 0 >>>>&nbsp; &lt;EndPoint&gt; >>>>[BdryProps]&nbsp;&nbsp; = 0 >>>>[BlockProps]&nbsp; = 2 >>>>&nbsp; &lt;BeginBlock&gt; >>>>&nbsp;&nbsp;&nbsp; >>&lt;BlockName&gt; = &quot;Air&quot; >>>>&nbsp;&nbsp;&nbsp; >>&lt;Mu_x&gt; = 1 >>>>&nbsp;&nbsp;&nbsp; >>&lt;Mu_y&gt; = 1 >>>>&nbsp;&nbsp;&nbsp; >>&lt;H_c&gt; = 0 >>>>&nbsp;&nbsp;&nbsp; >>&lt;H_cAngle&gt; = 0 >>>>&nbsp;&nbsp;&nbsp; >>&lt;J_re&gt; = 0 >>>>&nbsp;&nbsp;&nbsp; >>&lt;J_im&gt; = 0 >>>>&nbsp;&nbsp;&nbsp; >>&lt;Sigma&gt; = 0 >>>>&nbsp;&nbsp;&nbsp; >>&lt;d_lam&gt; = 0 >>>>&nbsp;&nbsp;&nbsp; >>&lt;Phi_h&gt; = 0 >>>>&nbsp;&nbsp;&nbsp; >>&lt;Phi_hx&gt; = 0 >>>>&nbsp;&nbsp;&nbsp; >>&lt;Phi_hy&gt; = 0 >>>>&nbsp;&nbsp;&nbsp; >>&lt;LamType&gt; = 0 >>>>&nbsp;&nbsp;&nbsp; >>&lt;LamFill&gt; = 1 >>>>&nbsp;&nbsp;&nbsp; >>&lt;BHPoints&gt; = 0 >>>>&nbsp; &lt;EndBlock&gt; >>>>&nbsp; &lt;BeginBlock&gt; >>>>&nbsp;&nbsp;&nbsp; >>&lt;BlockName&gt; = &quot;M-19 >>>>Steel&quot; >>>>&nbsp;&nbsp;&nbsp; >>&lt;Mu_x&gt; = 4416 >>>>&nbsp;&nbsp;&nbsp; >>&lt;Mu_y&gt; = 4416 >>>>&nbsp;&nbsp;&nbsp; >>&lt;H_c&gt; = 0 >>>>&nbsp;&nbsp;&nbsp; >>&lt;H_cAngle&gt; = 0 >>>>&nbsp;&nbsp;&nbsp; >>&lt;J_re&gt; = 0 >>>>&nbsp;&nbsp;&nbsp; >>&lt;J_im&gt; = 0 >>>>&nbsp;&nbsp;&nbsp; >>&lt;Sigma&gt; = 0 >>>>&nbsp;&nbsp;&nbsp; >>&lt;d_lam&gt; = 0 >>>>&nbsp;&nbsp;&nbsp; >>&lt;Phi_h&gt; = 0 >>>>&nbsp;&nbsp;&nbsp; >>&lt;Phi_hx&gt; = 0 >>>>&nbsp;&nbsp;&nbsp; >>&lt;Phi_hy&gt; = 0 >>>>&nbsp;&nbsp;&nbsp; >>&lt;LamType&gt; = 0 >>>>&nbsp;&nbsp;&nbsp; >>&lt;LamFill&gt; = 1 >>>>&nbsp;&nbsp;&nbsp; >>&lt;BHPoints&gt; = 13 >> > > >>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.29999999999999999&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>>>39.78875 >> > > >>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.80000000000000004&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>>>79.577500000000001 >> > > >>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1.1200000000000001&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>159.155 >> > > >>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1.3200000000000001&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>318.31 >> > > >>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1.46&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>795.77499999999998 >> > > >>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1.54&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>1591.55 >> > > >>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1.6187499999999999&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>>>3376.6669999999999 >> > > >>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1.74&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>7957.75 >> > > >>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1.8700000000000001&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>15915.5 >> > > >>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1.99&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>31831 >> > > >>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2.0459640000000001&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>>>55102.040000000001 >> > > >>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2.0800000000000001&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>79577.5 >>>>&nbsp; &lt;EndBlock&gt; >>>>[CircuitProps]&nbsp; = 0 >>>>[NumPoints] = 114 >> > > >>-1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-1.75&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>1.75&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.18192272946553939&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.85587915064207998&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.38983442028329873&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1.8340267513758857&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.27038987007807896&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.83217445175825933&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.57940686445302636&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1.7832309680534129&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.35589456269132513&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.79935227543727572&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.76263120576712529&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1.7128977330798767&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.43749999999999994&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.75777222831138391&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.93749999999999989&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1.6237976320958225&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.51431209575591397&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.70788987007807902&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-1.1020973480483871&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1.5169068644530266&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.58548928056400096&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.65025172229271999&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-1.2546198869228591&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1.3933965477701142&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.65025172229271988&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.58548928056400096&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-1.393396547770114&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1.2546198869228591&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.70788987007807902&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.51431209575591397&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-1.5169068644530266&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1.1020973480483871&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.7577722283113838&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.43750000000000011&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-1.6237976320958223&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.93750000000000022&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.79935227543727572&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.35589456269132519&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-1.7128977330798767&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.7626312057671254&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.83217445175825933&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.27038987007807902&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-1.7832309680534129&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.57940686445302647&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.85587915064207987&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.18192272946553953&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-1.8340267513758854&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.38983442028329895&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.8702066584472391&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.09146240535919678&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-1.8647285538155125&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.19599086862685022&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.875&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>5.3576527979729005e-017&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-1.875&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1.1480684567084787e-016&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.87020665844723921&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.091462405359196669&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-1.8647285538155127&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.19599086862685&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.85587915064207998&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.18192272946553922&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-1.8340267513758857&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.38983442028329834&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.83217445175825944&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.27038987007807891&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-1.7832309680534131&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.57940686445302625&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.79935227543727583&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.35589456269132502&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-1.7128977330798769&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.76263120576712506&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.75777222831138391&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.43749999999999978&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-1.6237976320958225&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.93749999999999956&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.70788987007807902&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.51431209575591386&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-1.5169068644530266&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-1.1020973480483869&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.65025172229271999&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.58548928056400096&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-1.3933965477701142&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-1.2546198869228591&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.58548928056400107&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.65025172229271977&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-1.2546198869228593&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-1.3933965477701138&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.51431209575591408&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.70788987007807891&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-1.1020973480483873&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-1.5169068644530264&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.43749999999999994&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.75777222831138391&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.93749999999999989&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-1.6237976320958225&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.35589456269132536&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.79935227543727572&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.76263120576712584&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-1.7128977330798765&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.27038987007807908&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.83217445175825933&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.57940686445302658&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-1.7832309680534129&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.18192272946553939&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.85587915064207998&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-0.38983442028329873&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-1.8340267513758857&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.18192272946553939&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.85587915064207998&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.38983442028329873&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1.8340267513758857&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.27038987007807896&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.83217445175825933&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.57940686445302636&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1.7832309680534129&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.35589456269132513&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.79935227543727572&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.76263120576712529&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1.7128977330798767&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.43749999999999994&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.75777222831138391&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.93749999999999989&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1.6237976320958225&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.51431209575591397&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.70788987007807902&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>1.1020973480483871&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1.5169068644530266&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.58548928056400096&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.65025172229271999&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>1.2546198869228591&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1.3933965477701142&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.65025172229271988&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.58548928056400096&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>1.393396547770114&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1.2546198869228591&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.70788987007807902&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.51431209575591397&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>1.5169068644530266&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1.1020973480483871&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.7577722283113838&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.43750000000000011&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>1.6237976320958223&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.93750000000000022&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.79935227543727572&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.35589456269132519&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>1.7128977330798767&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.7626312057671254&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.83217445175825933&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.27038987007807902&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>1.7832309680534129&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.57940686445302647&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.85587915064207987&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.18192272946553953&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>1.8340267513758854&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.38983442028329895&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.8702066584472391&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.09146240535919678&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>1.8647285538155125&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.19599086862685022&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.875&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>5.3576527979729005e-017&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>1.875&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1.1480684567084787e-016&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.87020665844723921&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.091462405359196669&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>1.8647285538155127&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.19599086862685&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.85587915064207998&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.18192272946553922&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>1.8340267513758857&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.38983442028329834&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.83217445175825944&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.27038987007807891&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>1.7832309680534131&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.57940686445302625&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.79935227543727583&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.35589456269132502&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>1.7128977330798769&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.76263120576712506&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.75777222831138391&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.43749999999999978&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>1.6237976320958225&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.93749999999999956&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.70788987007807902&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.51431209575591386&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>1.5169068644530266&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-1.1020973480483869&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.65025172229271999&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.58548928056400096&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>1.3933965477701142&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-1.2546198869228591&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.58548928056400107&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.65025172229271977&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>1.2546198869228593&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-1.3933965477701138&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.51431209575591408&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.70788987007807891&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>1.1020973480483873&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-1.5169068644530264&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.43749999999999994&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.75777222831138391&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.93749999999999989&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-1.6237976320958225&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.35589456269132536&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.79935227543727572&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.76263120576712584&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-1.7128977330798765&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.27038987007807908&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.83217445175825933&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.57940686445302658&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-1.7832309680534129&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.18192272946553939&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-0.85587915064207998&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0.38983442028329873&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-1.8340267513758857&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>2.5&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>-2.5&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >>>>[NumSegments] = 0 >>>>[NumArcSegments] = 6 >> > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>180&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>3&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>180&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>180&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>3&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>180&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>113&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>112&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>180&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>10&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>112&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>113&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>180&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>10&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >>>>[NumHoles] = 0 >>>>[NumBlockLabels] = 3 >> > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1.375&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.050000000000000003&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.375&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >> > > >>2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0.375&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>-1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > > >>0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; > >>0 >>>> >>>> >>>>[Non-text portions of this message have been >>removed] >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>>Yahoo! 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Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/


Dr. Keith Gregory
Senior Lecturer
Department of Electronic & Electrical Engineering
Loughborough University
Loughborough
Leicestershire
LE11 3TU
UK

Phone: +44 (0) 1509 227025 Fax: +44 (0) 1509 227014
Department web: http://www.lboro.ac.uk/departments/el/

References:
- Re: [femm] how do I model a torroidal transformer ?
  - From: robert Macy
- Re: [femm] how do I model a torroidal transformer ?
  - From: Dave Squires

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