RE: Calculating and Measuring Resonant Frequency / Inductance of Secondary Coil (magnifier)

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Mccauley, Daniel H" <daniel.h.mccauley-at-lmco-dot-com> 



Thanks Bart.
However, the primary coil doesn't have to be at the resonant frequency of 
the secondary coil.
The primary coil should more closely match the tertiary coil's resonant 
frequency.
But thanks for the calculations.  I'm getting closer to finding out the 
discrepancy.

Because the frequency difference is a factor of 2, this turns out to be 
only a 25% difference in
self-capacitance, which could be a possibility.  Both the tesla cad 
programs and my impedance plot
show about 9mH inductance, so perhaps it is the self-capacitance which is 
the culprit.

Dan


 > Hi Dan,
 >
 > I ran your specs from your page in Javatc. I'll pop in the
 > inputs I used
 > and show the outputs below. The 606kHz your showing is about
 > double what it
 > should show. I showed 312 kHz on the driver. The primary is
 > down around 178
 > kHz at 7 turns, so you'll have to tap somewhere around 3.5. turns.
 > Something else to note: k at 7 turns is at 0.361 which looks
 > pretty good!
 > But, once you tap to resonance, k will drop to 0.288 (so you
 > will probably
 > end up raising the primary). BTW, maximum coupling on the
 > system (as is)
 > would be 0.466 (when the primary is centered in the middle of
 > the secondary).
 >
 > Take care,
 > Bart
 > PS: Thanks for putting up your maggy page!
 >
 > Units = inches
 > ----------------------------------------------------
 > Surrounding Inputs:
 > 100 = Ground Plane Radius
 > 100 = Wall Radius
 > 150 = Wall Height
 > 100 = Ceiling Radius
 > 150 = Ceiling Height
 > ----------------------------------------------------
 > Secondary Coil Inputs:
 > Current Profile = G.PROFILE_LINEAR
 > 8 = Radius 1
 > 8 = Radius 2
 > 5 = Height 1
 > 29 = Height 2
 > 216 = Turns
 > 14 = Wire Awg
 > ----------------------------------------------------
 > Primary Coil Inputs:
 > 11.75 = Radius 1
 > 11.75 = Radius 2
 > 5 = Height 1
 > 10.5 = Height 2
 > 7 = Turns
 > 0.5 = Wire Diameter
 > 0.0185 = Primary Cap (uF)
 > 0 = Desired Coupling (k)
 > ----------------------------------------------------
 > Top Load Object Inputs (dimensions & topload or ground connection):
 >
 > Toroid #1: minor=2, major=20, height=31, topload
 > Disc #1: inside=0, outside=16, height=31, topload
 > ----------------------------------------------------
 > Secondary Outputs:
 > 311.87 [kHz] = Secondary Resonant Frequency
 > 90 [deg°] = Angle of Secondary
 > 9 = Turns Per inch
 > 1.5 = H/D Aspect Ratio
 > 2.29 [ohms] = DC Resistance
 > 16157 [ohms] = Reactance at Resonance
 > 8.245 [mH] = Les-Effective Series Inductance
 > 9.577 [mH] = Ldc-Low Frequency Inductance
 > 31.585 [pF] = Ces-Effective Shunt Capacitance
 > 70.614 [pF] = Cdc-Low Frequency Capacitance
 > ----------------------------------------------------
 > Primary Outputs:
 > 178.23 [kHz] = Primary Resonant Frequency
 > 90 [deg°] = Angle of Primary
 > 0.286 [inch] = Average spacing between turns (edge to edge)
 > 3.75 [inch] = Primary to Secondary Clearance
 > 43.102 [uH] = Ldc-Low Frequency Inductance
 > 231.63 [uH] = Lm-Mutual Inductance
 > 0.361 [k] = Coupling Coefficient
 > 2.77 = Number of half cycles for energy transfer at K
 > 7.12 [uS] = Time for total energy transfer (ideal quench time)
 >
 >
 > Tesla list wrote:
 >
 > >Original poster: dhmccauley-at-spacecatlighting-dot-com
 > >In the midst of my magnifier design, I came up with a discrepancy.
 > >
 > >Secondary Coil Specifications:
 > >Coilform Diameter:  16"
 > >Wire Gauge:  14 AWG (0.064" wire diameter)
 > >Turns per Inch:  9T (based on my finished magnifier)
 > >Winding Length:  24"
 > >
 > >When I calculate the inductance and resonant frequency of my
 > secondary coil
 > >(in magnifier coil) using either calculations, or TeslaCad,
 > or WinTesla, I
 > >get the following
 > >numbers:
 > >
 > >Inductance:  9.76mH
 > >Fres:  365kHz
 > >*************************************************************
 > ***************
 > >*
 > >Now, when I measure this secondary coil using an Impedance
 > Analyzer, I get
 > >the following:
 > >
 > >Plot of Impedance vs. Frequency
 > >http://www.easternvoltageresearch-dot-com/images/mag1_sec_response.jpg
 > >(Note:  Top vertical line of graph is 14mH and each vertical
 > division is
 > >2mH)
 > >
 > > >From graph, the flat portion of impedance curve is about
 > 9.5mH which
 > >corresponds to what I calculate.
 > >However, when impedance is minimum (-2mH), the frequency is
 > about 606kHz.
 > >I'm using this minimum impedance point as
 > >where the resonant frequency occurs.
 > >
 > >These frequencies don't match one another, yet I would
 > expect them to.  Am I
 > >missing or doing something incorrectly here?
 > >(The secondary coil was placed directly across the two probes of the
 > >impedance analyzer when measuring.)
 > >
 > >Thanks
 > >Dan
 > >
 > >
 > >
 > >
 >
 >
 >
 >