Tests and Measurements |

A model or simulation is meaningless unless there is firm experimental evidence that its predictions agree with reality. This page provides a summary of the comparison tests which have been applied to this model.

Notes |

Results are presented for

Resonant frequencies, the lowest few overtones are compared.

Voltage profiles, detailed voltage profile measurements by Terry Fritz.

Current profiles, detailed current profile measurements by Terry Fritz.

Transimpedance, and effective series inductance, requiring measurements of top voltage
and base current.

Energy storage inductance, requiring measurements of input impedance and Q factor.

Coils are identified by a 'system name', the first two letters of which indicate who provided the measurements, according
to the following table:

md | Marco Denicolai |
---|---|

mm | Marc Metlicka |

mw | Malcolm Watts |

mz | Mark Rzeszotarski |

pn | Paul Nicholson |

sk | Kurt Schraner |

tf | Terry Fritz |

We use the abbreviations f1, f3, f5, etc to indicate the resonant mode in terms of the number of electrical quarter-waves involved in the whole resonator, ie topload included.

Resonant Frequencies |

Unless otherwise stated, these resonant frequency results apply to the base fed model configuration. Results shown are all computed with version 0.9d of the model - a version which is set up for a fairly quick calculation, at the expense of accuracy. Coils are listed in order of reducing h/d ratio.

measured modeled error mm2: bare d=0.108m h/d=9.97 sr=0.81 b/h=0.31 turns=1700 f1 276.9kHz 272.7kHz -1.5% f3 711.8kHz 696.9kHz -2.1% mm1: bare d=0.091m h/d=8.92 sr=0.76 b/h=0.41 turns=1221 f1 455.5kHz 464.1kHz +1.9% sk16b55: bare d=0.161m h/d=8.71 sr=0.90 b/h=0.39 turns=1976 f1 161.4kHz 155.5kHz -3.7% f3 386.4kHz 385.5kHz -0.2% f5 562.0kHz 566.7kHz +0.8% f7 710.3kHz 725.2kHz +2.1% mm4: bare d=0.114m h/d=6.78 sr=0.83 b/h=0.39 turns=1600 f1 237.0kHz 241.9kHz +2.1% tfsm1: bare d=0.108m h/d=6.14 sr=0.91 b/h=0.03 turns=1176 f1 358.8kHz 357.2kHz -0.5% f3 883.1kHz 882.3kHz -0.1% f5 1265.5kHz 1295.0kHz +2.3% f7 1602.5kHz 1628.9kHz +1.6% sk12b49: bare d=0.121m h/d=4.83 sr=0.92 b/h=0.84 turns=894 f1 405.1kHz 405.9kHz +0.2% mm3: bare d=0.221m h/d=4.66 sr=0.93 b/h=0.35 turns=2989 f1 61.9kHz 63.4kHz +2.5% f3 157.9kHz 157.4kHz -0.3% f5 229.7kHz 229.3kHz -0.2% f7 294.4kHz 295.0kHz +0.2% f9 355.6kHz 358.7kHz +0.9% mwa1-4hd0: bare d=0.168m h/d=4.00 sr=0.92 b/h=0.74 turns=1106 f1 224.0kHz 224.1kHz +0.1% mwa2-4hd0: bare d=0.168m h/d=4.00 sr=0.49 b/h=0.74 turns=1106 f1 220.0kHz 224.0kHz +1.8% sk20b49: bare d=0.205m h/d=3.26 sr=0.90 b/h=0.73 turns=943 f1 217.2kHz 206.4kHz -5.0% f3 497.8kHz 488.8kHz -1.8% f5 709.9kHz 716.8kHz +1.0% tfltr: bare d=0.261m h/d=2.92 sr=0.67 b/h=0.03 turns=1000 f1 148.4kHz 146.5kHz -1.3% f3 353.4kHz 353.4kHz +0.0% f5 513.8kHz 522.7kHz +1.7% f7 666.4kHz 674.0kHz +1.1% f9 819.8kHz 850.0kHz +3.7% f11 977.4kHz 1015.1kHz +3.9% f13 1133.1kHz 1188.5kHz +4.9% pn2: bare d=0.580m h/d=2.84 sr=0.88 b/h=0.08 turns=725 f1 92.0kHz 91.2kHz -0.9% f3 213.0kHz 217.9kHz +2.3% f5 320.0kHz 322.7kHz +0.8% pn1: bare d=0.590m h/d=1.36 sr=0.91 b/h=0.05 turns=356 f1 150.7kHz 152.2kHz +1.0% f3 360.0kHz 367.1kHz +2.0% f5 543.0kHz 573.8kHz +5.7%

measured modeled error mdthor: toroided d=0.400m h/d=3.94 sr=0.86 b/h=0.05 turns=939 f1 65.5kHz 66.5kHz +1.5% f3 222.8kHz 240.0kHz +7.8% f5 346.3kHz 371.2kHz +7.2% tfltr45: toroided d=0.261m h/d=2.92 sr=0.67 b/h=0.03 turns=1000 f1 97.9kHz 95.3kHz -2.6% f3 321.4kHz 327.4kHz +1.9% f5 490.2kHz 506.3kHz +3.3% pn2t: toroided d=0.580m h/d=2.84 sr=0.88 b/h=0.08 turns=725 f1 66.7kHz 66.2kHz -0.7% f3 193.3kHz 206.2kHz +6.6% f5 307.0kHz 316.4kHz +3.1%

We are having some difficulties at small radius and high elevation, as can been seen from the following results:

measured modeled error sk5b185: bare d=0.051m h/d=8.03 sr=0.91 b/h=0.45 turns=934 f1 919.5kHz 958.5kHz +4.3% mz1: bare d=0.051m h/d=6.00 sr=0.92 b/h=2.33 turns=875 f1 885.0kHz 1041.2kHz +17.7% f3 2338.0kHz 2520.5kHz +7.8% f5 3436.0kHz 3673.9kHz +6.9% mz2: bare d=0.051m h/d=6.00 sr=0.87 b/h=2.33 turns=1310 f1 645.0kHz 699.9kHz +8.5% f3 1627.0kHz 1694.6kHz +4.2% mz3012-1: bare d=0.089m h/d=3.18 sr=0.88 b/h=0.07 turns=622 f1 647.8kHz 695.7kHz +7.4% f3 1575.4kHz 1669.6kHz +6.0% f5 2264.1kHz 2461.5kHz +8.7% mz3012-5: bare d=0.089m h/d=3.18 sr=0.88 b/h=1.97 turns=622 f1 665.9kHz 714.9kHz +7.4% f3 1591.1kHz 1687.2kHz +6.0% f5 2277.9kHz 2474.2kHz +8.6% mwa1-1hd0: bare d=0.168m h/d=1.00 sr=0.91 b/h=3.94 turns=272 f1 600.0kHz 633.3kHz +5.5%

In some cases these discrepancies are caused by the model's failure to take into account lead wires and fittings near the top of
the coil. Failure to account for the coil former's dielectric properties may also be a contributing factor.
At high elevation the coil's capacitance is hard to determine accurately. Work is ongoing to resolve these difficulties, but
there is as yet no evidence that these poor results invalidate either the model or the theory.

Estimate of prediction error limits, for coils b < h, h/d > 1.5, and d > 0.1 are

1/4 wave, +/- 4%; 3/4 wave, +/- 3%; 5/4 wave, +/- 3%;

when using the following resolutions:

M: turns x turns, Cint: 32 x 512, Cext: 512, Ctor: 32

Difficulty accounting for the coil's surroundings is the reason behind the poorer estimation at f1.

For h/d < 1.5 the internal capacitance begins to dominate and the model tends to over-estimate the
higher mode frequencies, we think because we are not allowing for the permittivity of the coil former
dielectric. A first order correction for this is in the pipeline.

Transfer Impedance |

The equivalent series inductance L_{es} is related to the forward transfer impedance by

`Z _{ft} = j w L_{es}`

so that

Therefore by simultaneously measuring the top voltage and base current at f1 to obtain Z

Terry Fritz measured his small coil to obtain the comparisons

measured modeled error tfsm1p: probed d=0.108m h/d=6.14 sr=0.91 b/h=0.01 turns=1176 f1: 310.9 kHz 310.9 kHz 0.0% Ctop adjusted to match: 3.145 pF f3: 847.8 kHz 828.4 kHz -2.3% Zft: 34450 ohms 34874 ohms +1.2% Les: 17.64 mH 17.85 mH +1.2%

Equivalent Energy Inductance, Lee |

The energy storage inductance is related to Q factor and input resistance at f1 by

`Rin = w L _{ee}/Q`

By taking simultaneous readings of Rin and Q at f1, we can measure L

Terry Fritz has provided the following comparisons for his small coil.

measured modeled error Lee: 13.58 mH 13.66 mH +0.6%

Maintainer