Re: AC Resistance of wires - was 8 kHz Tesla Coil

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: "Kurt Schraner" <k.schraner@xxxxxxxxxxx>

Hi Bart,Gerry,

Medhurst's empirical Method for HF-Resistance of solenoids is 
implemented in my TC-Plan Excel:
http://home.datacomm.ch/k.schraner/TCplan.zip
The relevant sheets are "Skineff." and "Proxi-eff.", whose results are
transferred to "TC calc."' cells E34:E38. In the light of more up to date,
more general methods, Medhurst may soon become of lesser relevance, 
but I've tried to compare results from it, with Q of some of my 
coils, estimated from bandwidth measurements at Fres. A summary Excel 
of the results can be had at:
http://home.datacomm.ch/k.schraner/Qsec2.xls
or here (view in fixed width font, sorry for the possible mess!):

     TC-Secondary Q-Estimation by Medhurst's Empirical Method
      for some of my Coils

     Geometric Data
     Secondary Diameter Length Aspect L/D Turns
     Name      [cm]     [cm]     [ - ]    [ - ]
     Sk-Seibt   4      150.3     37.58     4187
     Sk-UBTT  12.54     60.3      4.81     1680
     Sk-5cm    5.11     41.1      8.04      934
     Sk-12cm  12.12     58.5      4.83      894
     Sk-Long  16.1     140.2      8.71     1976
     Sk-20cm  20.52     66.8      3.26      943
     Sk-38cm  38.4      44        1.15      346
     Sk-B&W *)40.13    177        4.41      813
     Sk-B&W *)40.13    177        4.41      813

     Geometric Data (cont.)
     Secondary Wire-Copper  Pitch Comment
     Name        [mm]       [mm]
     Sk-Seibt   0.319       0.359 Big error unexplained!
     Sk-UBTT    0.319       0.359 Test-signal via low-Z amp.
     Sk-5cm     0.4         0.434 no experiment
     Sk-12cm    0.6         0.654 Test-signal via low-Z amp.
     Sk-Long    0.64        0.71  Test-signal via low-Z amp.
     Sk-20cm    0.63        0.708 no experiment
     Sk-38cm    1           1.2   cardoard/cotton insul. wire
     Sk-B&W *) 1.268        2.177 Test-signal via low-Z amp.
     Sk-B&W *) 1.268        2.177 if R Sig-Gen=136 Ohm


     Electrical Data
     Secondary at1kHz  Fres,bare DC Resist. Wire straigt
     Name    Lexp[mH]  exp.[kHz] exp.[Ohm]  with Skineff.
     Sk-Seibt 18.13   366.11     114        240.82
     Sk-UBTT  66.59   205.4     147.8       147.86
     Sk-5cm   5.203   923.8      21.7        n.a.
     Sk-12cm  18.2    402.8      21         27.61
     Sk-Long  67.7    147.4      55.2       61.05
     Sk-20cm  49      202.7      34.8       40.5
     Sk-38cm  28.12   217.95      9.2       16.32
     Sk-B&W *)54.67   119        14.5       22.3
     Sk-B&W *)54.67   119      14.5+136     22.3+136

     Electrical Data (cont.)
     Secondary Rac-calc. Qexp     Qmedh. Qerror
     Name    with Proxy.E  [ - ]  [ - ]    [%]
     Sk-Seibt    698.9     156.5  70.8    54.8%
     Sk-UBTT     440.65    211.8  186     12.2%
     Sk-5cm       n.a.      n.a.   n.a.    n.a.
     Sk-12cm     91.01     269    270     -0.4%
     Sk-Long     190.6     164.4  168.4   -2.4%
     Sk-20cm     128.0      n.a.  478.3    n.a.
     Sk-38cm     49.79     104.3  803.7  -670.6%
     Sk-B&W *)   44.02     141.7  576    -306.5%
     Sk-B&W *) 44.02+136   141.7  141.7    0.0%


The method seems to underestimate Q of my small diameter coils, and to
(heavily) overestimate the Q of the big diameter coils. What seems obvious
is the dominant proximity effect over skineffect for usual TC frequencies,
as mentioned before on the relevant treads. Maybe dielectric loss, not
considered in the calculations, come to play here...

*) For the bandwidth measurements it seems important using a low-Z signal
source (--> Terry's low-Z amp), which was not the case for "Sk-B&W".
Otherwise the generators internal resistance will reduce measured Q value.
Anyway, bandwidth measurements seem prone to higher error, 'cause of
amplitude reading on the scope and frequency precision reading from the
sig-gen.

Well ... my 2cents for the interesting threads about coil Q. If I see 
coming out a method estimating Q with perhaps 10% error, I'd readily adapt it!

Best regards
Kurt