Date: Tue, 21 Oct 1997 10:01:29 -0400 (EDT)
From: "Mark S. Rzeszotarski, Ph.D."
To: tesla@pupman.com
Cc: terryf@verinet.com
Subject: Non-Linear Coil Winding Measurements
Hello All,
Terry Fritz built a really great coil winder
(see http://www.verinet.com/~terryf/Tesla/Projects/CoilWind/Winder.html) and
he was kind enough to ship me three coils, two of which are wound with
nonlinear pitch. They exhibit some very interesting behaviors. All coils
are wound with 300 turns of 30 AWG enamel wire on 3 inch diameter cardboard
coil forms with a winding length of 10 inches, using about 236 feet of wire.
I used a BK Precision 878 LCR meter (1% accuracy) and an HP 4193A
vector impedance meter for measurements. I also used an oscilloscope and HP
signal generator to verify that I was operating at the 1/4 wave frequency.
Coil #1 - linear wound with equal spacing
I measured: Rdc=26.57 ohms, L=1.955 mH Fres=1615 kHz
I calculated Cdistributed=4.97 pF ignoring the A.C. resistance of the wire.
Coil #2 - winding spacing proportional to d=cos(x) where x is the distance
along the height of the coil. Windings are bunched at the top of the coil.
Coil upright:
I measured: Rdc=26.62 ohms, L=2.041 mH, Fres=1844 kHz
I calculated Cdistributed=3.71 pF ignoring the A.C. resistance of the wire.
Coil inverted so bunched turns are at the base:
I measured: Rdc=26.62 ohms, L=2.041 mH, Fres=1420 kHz
I calculated Cdistributed=6.27 pF ignoring the A.C. resistance of the wire.
Coil #3 - winding spacing proportional to d=cos(x)^2 where x is the distance
along the height of the coil. Windings are very bunched at the top of the coil.
Coil upright:
I measured: Rdc=26.60 ohms, L=2.192 mH, Fres=1840 kHz
I calculated Cdistributed=3.41 pF ignoring the A.C. resistance of the wire.
Coil inverted so bunched turns are at the base:
I measured: Rdc=26.60 ohms, L=2.041 mH, Fres=1273 kHz
I calculated Cdistributed=7.13 pF ignoring the A.C. resistance of the wire.
These numbers are basically in agreement with those obtained by Terry Fritz.
The question arose as to whether the A.C. resistance of the coils was
affecting the resonant frequency Fres=sqrt[1/LC-(R/2L)^2], or was it due to
a change in distributed capacitance, or both. To gain some insight on this
question I conducted two experiments.
Experiment #1
Add noninductive resistance to the base of the coil and remeasure resonant
frequency to see if the R is shifting it substantially. Based on prior
calculations, I suspected the A.C. resistance of the linear wound coil to be
around 350 ohms, due in large part to the very high operating frequency. I
experimented with resistor values in the range from 0 to 2400 ohms. The
results for 546.9 ohms are representative:
Coil #1 upright: Fres=1615 kHz @ 0 ohms, Fres=1633 kHz @ 546.9 ohms
Coil #2 upright: Fres=1844 kHz @ 0 ohms, Fres=1846 kHz @ 546.9 ohms
Coil #2 inverted: Fres=1420 kHz @ 0 ohms, Fres=1424 kHz @ 546.9 ohms
Coil #3 upright: Fres=1840 kHz @ 0 ohms, Fres=1850 kHz @ 546.9 ohms
Coil #3 inverted: Fres=1273 kHz @ 0 ohms, Fres=1292 kHz @ 546.9 ohms
I conclude that the A.C. resistance is not significantly impacting
resonant frequency. With 72 ohms added, the shift is only 1-2 kHz. At
around 2400 ohms, the threshold for oscillation was attained.
Experiment #2
Use Howe's method to measure the distributed capacitance. This method
consists of measuring the resonant frequency of the coil while loaded with
additional capacitance. A plot of (1/F)^2 versus added capacitance should
yield a straight line. The negative x-axis intercept is the estimated
distributed capacitance. I used two capacitors to take measurements, one at
15.0 pF and the other at 30.0 pF, measured using my BK 878. The capacitors
were variable air transmitting types which were adjusted until the
appropriate readings were obtained. Then, they were switched in or out of
the circuit using alligator clips.
Cdis = calculated distributed capacitance using measured Fres and L
and ignoring Rac.
CHowe = measured distributed capacitance based on Howe's method
Coil #1 upright: Fres=1615 kHz Cdis=4.97 pF CHowe=5.88 pF
Coil #2 upright: Fres=1844 kHz Cdis=3.71 pF CHowe=4.65 pF
Coil #2 inverted: Fres=1420 kHz Cdis=6.27 pF CHowe=7.73 pF
Coil #3 upright: Fres=1840 kHz Cdis=3.41 pF CHowe=4.37 pF
Coil #3 inverted: Fres=1273 kHz Cdis=7.13 pF CHowe=8.77 pF
In comparing the upright coil measurements, there is a systematic
error of about 0.9 pF between Cdis and CHowe. It is greater for the
inverted coil measurements. This is probably due to the capacitive effects
of the alligator clip leads, especially the one from the top of the coil
down to the capacitor. This is known to add capacitance to the circuit.
Medhurst's formula predicts a distributed capacitance of 4.95 pF for the
linear wound coil, in close agreement with the Cdis for Fres, ignoring Rac,
for the linear wound coil #1. Medhurst makes no mention of nonlinear coil
winding effects :(.
I conclude that the effect is real and appears to be primarily
capacitive in nature. The next step is to fire these little coils single
shot and see if there are performance differences. I would like some advice
on experimental setup for this next series. At the moment I plan to fix
K=0.05 or so (not close to critical coupling), fix Zsurge for all three
coils to a value of 30-100 ohms depending on which capacitors I can
scrounge, use the same spark gap for each, and operate without a top toroid
since the top windings might be affected by the proximity of the toroid.
The primary will be a 4.25 inch diameter solenoid using 16 AWG wire
closewound to yield the appropriate Lp value. The elevation will be
adjusted to yield K=0.05. I will employ a D.C. supply through a charging
resistor such that the repetition rate is no more than about one pulse per
second. Comments/flames welcome.
Thanks again to Terry Fritz for shipping me these most interesting
coils.
Regards,
Mark S. Rzeszotarski, Ph.D.