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

```Original poster: "Bart Anderson" <classi6-at-classictesla-dot-com>

Hi Dan,

Good point and true. I performed my setup by making all 3 coils the
same. I started measurements last night. There are some interesting
scenario's with magnifiers, and especially in my little situation. For
example, although all 3 are at 180kHz on my own, with the extra coil
over the driver, when the base is driven I'm meausuring 142 kHz (i.e.,
2 coils in series and a single topload affecting both). That kind of
thing. Fun stuff! I'll post details once I have them.

Take care,
Bart

> 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
>  > >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
>  > >
>  > >
>  > >
>  > >
>  >
>  >
>  >
>  >
>
>
>
>

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