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Re: Self capacitance and Medhurst
Subject:
Re: Self capacitance and Medhurst
Date:
Tue, 25 Mar 1997 07:25:55 -0500 (EST)
From:
msr7-at-po.cwru.edu (Mark S. Rzeszotarski, Ph.D.)
To:
Tesla List <tesla-at-pupman-dot-com>
Hello All,
>>Steve Falco wrote....
>>
>>> I have seen two methods of finding the self capacitance of a coil. One
>>> is closed-form:
>>>
>>> V = L/R (in inches)
>>> CD = 5.08*R*(.0563*V+.08+.38*SQR(1/V)) 'uufd.
>>>
>>> And the other is table-lookup, attributed to Medhurst:
>>>
>>> C = K x D (D in centimeters)
>>>
>>> H/D K
>>> 5.0 0.81
>>> 4.5 0.77
>>> 4.0 0.72
>>> 3.5 0.67
>>> 3.0 0.61
>>> 2.5 0.56
>>> 2.0 0.50
>>> 1.5 0.47
>>> 1.0 0.46
>>>
>>> These two methods agree at the low end of aspect ratio, but begin to
>>> diverge at the high end, with the closed-form yielding the smaller
>>> values.
>>>
>>> Does anyone on the list have a feel for which approach is more
>>> accurate? Does anyone know where the closed-form originated?
>>>
The table values are directly from Medhurst's published
experimental
work. The curve fit is an approximation to Medhurst's original table.
Malcolm Watts responded:
>>I have found Medhurst to be reliable for all the coils I've tested it
>>on (quite a few) to within a few percent. It is conditional on one end
>>being grounded though. It cannot be used to predict Cself for an
>>unearthed halfwave coil. We need to develop or find another one for
>>that.
I agree that Medhurst's formula only works for quarter wave
coils
with one end grounded or at least at low impedance relative to the other
end.
John Couture then stated:
> Capacitance is mostly dependent on the dielectric and area. For a coil self
>capacitance this would relate to the wire insulation and wire length. The
>Medhurst equation uses only radius and coil length for the coil self
>capacity. As Steve points out this can lead to some wild results.
Finally, I respond to John's comments:
I reject your hypothesis and provide the following (albeit
lengthly)
experimental data below from a number of coils I measured last night
with
different aspect ratios, some coated with polyurethane, and using a
variety
of coil former materials. Each of these coils agrees with Medhurst's
formula for distributed capacitance and Wheeler's inductance formula to
within +/- 10%. In electronics, if I can get a component value with a
10%
tolerance, I am normally pretty satisfied with it for most purposes.
For
that reason, I readily accept and rely on these formulae for coil
design. I
see no evidence of strong dependence on dielectric properties. It is an
isotropic capacitance, which depends on the current sheet enveloping the
coil, which is primarily geometry dependent.
Coil # 1
Coil Height in Inches: 22.250
Coil Diameter in Inches: 6.250
Height to Diameter Ratio: 3.56:1
Form Material(s): PVC
Wire A.W.G. Gauge: 24.
Wire Diameter in Inches: .0201
Approximate Number of Turns: 1000.
Coil D.C. Resistance in Ohms: 42.90
Coil Self-Resonant Frequency in kiloHertz: 226.
Inductance in millihenries using Wheeler's Formula: 42.00
Measured Inductance in millihenries: 41.95
Difference between LWheeler and Lmeasured: .05
Percent deviation: .12%
Predicted Distributed Capacitance (Medhurst Formula) in pF: 11.10
Distributed Capacitance Necessary to Resonate at Fself Using Lmeas:
11.82
Difference between CMedhurst and Ccalculated: -.72
Percent deviation: -6.11%
Coil # 2
Coil Height in Inches: 12.000
Coil Diameter in Inches: 3.500
Height to Diameter Ratio: 3.43:1
Form Material(s): ACR
Wire A.W.G. Gauge: 26.
Wire Diameter in Inches: .0159
Approximate Number of Turns: 700.
Coil D.C. Resistance in Ohms: 25.80
Coil Self-Resonant Frequency in kiloHertz: 667.
Inductance in millihenries using Wheeler's Formula: 11.00
Measured Inductance in millihenries: 10.22
Difference between LWheeler and Lmeasured: .78
Percent deviation: 7.63%
Predicted Distributed Capacitance (Medhurst Formula) in pF: 6.10
Distributed Capacitance Necessary to Resonate at Fself Using Lmeas:
5.57
Difference between CMedhurst and Ccalculated: .53
Percent deviation: 9.49%
Coil # 3
Coil Height in Inches: 12.000
Coil Diameter in Inches: 8.000
Height to Diameter Ratio: 1.50:1
Form Material(s): ACR
Wire A.W.G. Gauge: 16.
Wire Diameter in Inches: .0508
Approximate Number of Turns: 225.
Coil D.C. Resistance in Ohms: 2.10
Coil Self-Resonant Frequency in kiloHertz: 692.
Inductance in millihenries using Wheeler's Formula: 5.30
Measured Inductance in millihenries: 4.96
Difference between LWheeler and Lmeasured: .34
Percent deviation: 6.85%
Predicted Distributed Capacitance (Medhurst Formula) in pF: 9.70
Distributed Capacitance Necessary to Resonate at Fself Using Lmeas:
10.66
Difference between CMedhurst and Ccalculated: -.96
Percent deviation: -9.05%
Coil # 4
Coil Height in Inches: 17.938
Coil Diameter in Inches: 4.125
Height to Diameter Ratio: 4.35:1
Form Material(s): CDB PU
Wire A.W.G. Gauge: 24.
Wire Diameter in Inches: .0201
Approximate Number of Turns: 800.
Coil D.C. Resistance in Ohms: 21.90
Coil Self-Resonant Frequency in kiloHertz: 510.
Inductance in millihenries using Wheeler's Formula: 14.20
Measured Inductance in millihenries: 13.02
Difference between LWheeler and Lmeasured: 1.18
Percent deviation: 9.06%
Predicted Distributed Capacitance (Medhurst Formula) in pF: 8.10
Distributed Capacitance Necessary to Resonate at Fself Using Lmeas:
7.48
Difference between CMedhurst and Ccalculated: .62
Percent deviation: 8.29%
Coil # 5
Coil Height in Inches: 26.250
Coil Diameter in Inches: 8.000
Height to Diameter Ratio: 3.28:1
Form Material(s): ACR PU
Wire A.W.G. Gauge: 21.
Wire Diameter in Inches: .0285
Approximate Number of Turns: 870.
Coil D.C. Resistance in Ohms: 22.30
Coil Self-Resonant Frequency in kiloHertz: 217.
Inductance in millihenries using Wheeler's Formula: 38.10
Measured Inductance in millihenries: 38.65
Difference between LWheeler and Lmeasured: -.55
Percent deviation: -1.42%
Predicted Distributed Capacitance (Medhurst Formula) in pF: 13.70
Distributed Capacitance Necessary to Resonate at Fself Using Lmeas:
13.92
Difference between CMedhurst and Ccalculated: -.22
Percent deviation: -1.57%
Coil # 6
Coil Height in Inches: 3.500
Coil Diameter in Inches: 8.500
Height to Diameter Ratio: .41:1
Form Material(s): ACR
Wire A.W.G. Gauge: 26.
Wire Diameter in Inches: .0159
Approximate Number of Turns: 200.
Coil D.C. Resistance in Ohms: 18.40
Coil Self-Resonant Frequency in kiloHertz: 482.
Inductance in millihenries using Wheeler's Formula: 9.40
Measured Inductance in millihenries: 9.25
Difference between LWheeler and Lmeasured: .15
Percent deviation: 1.62%
Predicted Distributed Capacitance (Medhurst Formula) in pF: 11.60
Distributed Capacitance Necessary to Resonate at Fself Using Lmeas:
11.79
Difference between CMedhurst and Ccalculated: -.19
Percent deviation: -1.59%
Inductance measurements were made with a BK Precision Model 878 LCR
meter
with 1% accuracy.
A Digital Frequency counter with 5 digit accuracy was used to measure
resonant frequency.
Coil Form Materials:
PVC means 3/16 inch thick polyvinyl chloride pipe.
ACR means 1/4 inch thick clear acrylic tubing.
PU means the unit was coated with 3 coats of polyurethane both before
and
after winding the coil.
CDB means 1/8 inch thick cardboard tubing.
The test coil was placed at least 3 feet from any metal or test
equipment.
No top capacitance was added. The base of the coil was driven by a 50
ohm
output impedance signal generator. Resonance was observed using an
oscilloscope with the probe placed free in air 3 feet from the coil.
The
top of the coil was left floating.
Apologies to those folks in the world who use real (S.I.) units of
measurement.
Flames, comments welcolmed,
Mark S. Rzeszotarski, Ph.D.