"H. F. Resistance and Self-Capacitance of Single-Layer
[Rosa 1908] "The Self and Mutual Inductances of Linear Conductors."
[see also "Inductance of a Straight Wire", by Tim Healy]
Jennings Technology Website: Vacuum capacitors and relays: Technical information and data sheets..
Mechanics, Leonard I Schiff, 3rd edition 1968, McGraw-Hill,
Tokyo. Library of Congress cat. No.: 68-25665.
Ch 9, Section 39 (p344): "As originally derived in optics by Krönig and Kramers, the analytic behaviour underlying the dispersion relation was inferred from causality: the statement that a light signal has a limiting speed c, so that the scattered electromagnetic radiation cannot outrun the incident wave."
 "Skin Effect", Nick Wheeler, Electronics World, Sept 1997. p780-781.
Discussion of skin effect in audio and RF cables. Silver plating starts to be useful at about 1MHz.
 "Conductors for HF Antennas", Rudy Severns N6LF, QEX Nov/Dec 2000 p20-29
Resistivities of common conductors [states that "silver oxide" is a better conductor than copper oxide, incorrectly implying better ageing of silver conductors]. Skin effect (detailed analysis). Comparison of wire losses for various types and diameters of wire in a variety of antennas (copper, copperweld, aluminium, iron). Flat conductors. Comparison of various wire types by winding coils and comparing the Q at 1.8MHz (table 6) [unfortunately uses PVC former, but the trend is unaffected], e.g., AWG12 Soft Cu: Q=410, AWG13 iron fence wire: Q=25 (!). Oxidation increases losses. The difficulty of making good connections to aluminium.
 "Insulators, Conductors and RF efficiency". "Wires for antennas". Pat Hawker, G3VA, Technical Topics, Rad Com. Aug. 2003. p71-73.
Interesting roundup of unspeakably bad practices [article unfortunately repeats the folklore about testing materials in a microwave oven, and repeats the assumption that silver is better than copper at maintaining its surface conductivity]. Refers to article "Conductors for HF antennas", by Richard Gamble, ZL1BNQ, Break-In, Jan/Feb 2003, p10-11 [which is a simplified version of the QEX article of same title by N6LF above]. Reproduces table 6 from from the N6LF QEX article.
 "Simple formulae for Skin effect", Leslie Green, Electronics World, Oct 2003, p44-46.
Discussion of the accuracy of various formulae. Useful references.
 Advanced Level Physics, M Nelkon and P Parker, 3rd edition (SI) 1974, Heinemann, London. ISBN 0 435 68636 4.
Ch 31: Capacitors. Parallel plate capacitor p771. Permittivity p772. Dielectrics p773.
Ch 32: Current Electricity. Resistivity p788. Joule's Law p790.
Ch 37: Magnetic Fields of Current-Carrying Conductors (Biot-Savart law).
Ch 38: Magnetic properties of materials.
 CRC Handbook of Chemistry and Physics, 63rd edition. 1982-83 (CRC press, Florida) [Newer editions exist].
C779-788: Properties of commercial plastics. E50: Spark-gap voltages. E56: Properties of dielectrics. E81: Resistivity of metals. F131: Resistance of` wires. F133: Resistivity of chemical elements. E112-118: Magnetic materials. E118-134: Magnetic susceptibility of the elements and inorganic compounds. [In this edition, magnetic susceptibility is given as the molar magnetic susceptibility χM in cgs units. To obtain the dimensionless susceptibility in the SI system, use the formula:
χ = 4π χM ρ / WM
where ρ is the density in g/cm³, and WM is the molar mass in grams, (i.e., the atomic or molecular weight)]
of Physical and Chemical Constants, Originally compiled
by G W C Kaye and T H Laby. 15th edition [SI Units]
1986 (reprinted with amendments 1993). Longman, UK. ISBN 0-582-46354-8.
1.8.1: Electrical resistivities, resistivities of metallic elements.
1.8.3: Resistivity of insulators.
1.8.5: Dielectric properties of materials [commentary by J H Calderwood], tables of εr' and tanδ.
1.8.6: Magnetic properties of materials.
2.1.2: Properties of the elements.
2.11.1: Properties of polymers.
[8a] Tables of Physical and Chemical Constants, Originally compiled by G W C Kaye and T H Laby. 12th edition 1959, Longmans, Green & Co. London.
p14-15: EMF of the Weston Standard Cell.
p90-95: Dielectric properties [commentary by L Hartshorn of NPL].
and Waves in Communication Electronics, 3rd Edition,
Simon Ramo, John R.Whinnery, Theodore Van Duzer, 3rd edition.
Publ. John Wiley & Sons Inc. 1994. ISBN 0-471-58551-3.
The symbol means "equal by definition".
3.16 (p149-153): Penetration of Electromagnetic Fields into a Good Conductor (skin effect).
3.17 (p153-155): Internal impedance of a plane conductor.
4.4 (p180-182): Skin effect in practical conductors.
4.5 (p182-186): Impedance of round wires.
[9a] Fields and Waves in Communication Electronics, Simon Ramo, John R.Whinnery, Theodore Van Duzer, Publ. John Wiley & Sons Inc. 1965. Library of congress cat. card no. 65-19477.
4.12 (p249-254): Penetration of Electromagnetic Fields into a Good Conductor (skin effect). 5.16 (p291-293): Current distribution in a wire of circular cross section.
5.17 (p294): Internal impedance of a round wire.
5.19 (p298-301): Impedance of a coated conductor.
5.20 (p301-303): Impedance of a thin-walled tubular conductor.
5.24 (p309-311): External inductance of a circular loop.
5.25 (p311-313): Inductance of practical coils.
6.04 (p330-334): Imperfect Dielectrics and Conductors (Kramers-Krönig relations).
6.13 (p358-361): Refractive index.
8.17 (p467-470): The idealized helix and other slow-wave structures.
Field Theory, R D Stuart, Addison-Wesley Publ. Co. inc.
Ch 7, The Calculation of Resistance, Capacitance, and Inductance: Guard-ring capacitor 7.2.
Ch 9, Waves and Radiation: Waves in a dielectric 9.3. Skin effect 9.6.
 Physical Chemistry, P W Atkins, Oxford University Press, 1978.
23.4 Magnetic properties [of molecules]. Gouy balance p778.
Bob Pearson, Electronics World, Letters Oct 1997, p861
[12b] "Silver [and other matters]", Doug Self, Electronics World, Letters Nov 1997 p965.
The brown/black tarnish layer which forms on silver is silver sulphide.
[12c] "Silver's not sterling", Jim Ussalis, Electronics World, Letters Apr 1998 p350.
Referring to microwave components: "Initially, coin silver provided a lower loss circuit than unplated copper. But with time, and a bit of tarnish, the situation would reverse". A rhodium flash [thin top-coat] may combat the sulphide contamination problem when silver plating is used. Gold plating of copper does not reduce losses because gold has lower conductivity than copper.
[12d] "Housekeepers will, without doubt, thank us for informing them that the black sulphide of silver, which forms on plated and silver wares, door plates and knobs, may at once be removed by wiping the surface with a rag wet with aqua ammonia (the ammonia should be very weak). This black film is no evidence that the silver is impure, for it forms as quickly on fine silver as on that which is alloyed with copper. After rain, much sulphide of hydrogen is disengaged from the soil of our streets."
Scientific American, October 1858, reprinted October 2008, p9.
of Silver Sulphide, etc. Private communication from Andy
Cowley, M1EBV, 25 Apr. 2003.
Re: Communication from Roy Lewallen, W7EL, which was as follows: AgS has a resistivity of 1.5 - 2.0Ωm, and is believed to be the most common silver tarnish. Cu2O is 10 - 50Ωm, CuO is 6KΩm, CuS is 0.3 - 83μΩm (source: 1993 CRC Handbook of Chemistry and Physics). The trick is translating this into loss. If the coating is a perfect insulator or a perfect conductor it causes no loss. Loss is a maximum at some intermediate value, which depends on frequency, layer thickness and base material - not a trivial calculation.
at 136KHz", Paolo Antoniazzi and Marco Arecco, Electronics
World, Jan 2001, p16-22. [erratum: the correct picture for fig.
10 is reproduced on page 1 of the magazine].
Very short vertical antennas, ground resistance, propagation, noise, design of high Q loading coils (skin effect, proximity effect, dielectric loss, form factor, test setup for measuring Q). Use of 42×0.18mm Litz wire dramatically increases Q at 136KHz. Use of PVC in coil formers gives very poor Q - winding coils on wooden pegs with wooden end-cheeks is better.
[14b] "The Art of Making and Measuring LF Coils", Paolo Antoniazzi IW2ACD and Marco Arecco IK2WAQ, QEX Sept/Oct 2001, p26-32.
4W linear amplifier for 136KHz. The problem of ground resistance with very short vertical antennas. Antenna efficiency. Coil design: skin effect, proximity effect, dielectric losses. Use of Litz wire. Poor Q obtained with PVC former. Best Q obtained by winding on 8 wooden dowels. Replacing the dowels with PVC rods reduces the Q by 30%.
[14c] "The Art of Making and Measuring LF Coils", David Bowman, G0MRF, QEX (Letters to the Editor) Nov/Dec 2001, p61.
Cautions against the use of wood in coil-formers, and insufficient insulaton of enameled copper wire [although we must take issue against the recommendation of PVC insulation].
[14d] "The Art of Making and Measuring Low-Frequency Inductors", Chan Shaw WA6EWY, QEX (Letters to the Editor), Jan/Feb 2002, p61-62.
On the virtues of basket-weave coils (reduced proximity effect and self capacitance). Some notes on litzendraht and bunch-wire.
Designer's Handbook, Ed. Fritz Langford-Smith. 4th edition.
4th impression (with addenda), Iliffe Publ. 1957 [A later reprint
exists (1967) ISBN 0 7506 36351]
Chapter 11: Design of radio Frequency Inductors. Section 11.2 (ii), p451: Medhurst's formula. Section 11.5: Short-Wave Coils [uses SWG wire sizes, but SWG diameters in mils (1 mil=0.001"=25.4μmm) are given in section 38.19, p1409.].
[Erratum: In chapter 36, Design of FM receivers, by E Watkinson: Rosa's formula for the inductance of a wire has been transcribed incorrectly, and the subsequent example on p1287 is incorrect.].
 "Optimum Wire Size for RF Coils", Charles J Michaels, W7XC, QEX, Aug 1987, p6-7.
Skin effect: Ferromagnetic materials make poor RF conductors. The higher the conductivity, the thinner the skin, thus the advantages of using silver over copper is not as great as the ratio of their conductivities might suggest. [states incorrectly that silver has a slight advantage over copper because its surface corrosion products are conductive, whereas those of copper are not]. For a given coil form: if the wire is too thin the RF resistance will be large, if the wire is too thick, the proximity effect will be large. Therefore there is an optimum wire size for every coil form. Gives Butterworth's formula for optimum wire diameter: dopt=la/N, where a is a fudge parameter depending on the l/D ratio of the coil (a=0.615 for l/D=1). Advises against using hard-drawn copper for high Q coils.
 "How Long is L?", Ian Hickman, Electronics World, May 1999 p386-389.
Discussion of inductance, mutual inductance, inductance of a wire.
 Radio-Frequency Measurements by Bridge and Resonance Methods, L. Hartshorn (Principal Scientific Officer, British National Physical Laboratory), Chapman & Hall, 1940 (Vol. X of "Monographs on Electrical Engineering", ed. H P Young). 3rd imp. 1942.
Ch V1, section 4: The guard ring.
Ch VI, section 6, Table II: Properties of Insulating Materials.
Ch VIII, section 3: Inductance of single turn loop.
 Inductance Calculations: Working Formulas and Tables, F W Grover, 1946 and 1973. Dover Phoenix Edition 2004. ISBN: 0-486-49577-9.
 "Resistor Measurements", Bob Botos [of Hewlett-Packard], Electronic Product Design, July 1981, p89-93.
Resistance of carbon resistors (film and slug types) decreases with frequency - "Boella Effect" caused by shunting by distributed capacitance of dielectric binder. Effect is greater for higher value resistors. C film resistors have less capacitance than slug types, 0.2-0.5pF for ½W RF types. Precision wirewound: pi-section and Ayrton-Perry non-inductive winding. Reactance of ordinary (inductive) wirewound resistors. Metal-film resistors: principal parasitic is capacitance, 0.2-0.6pF. Resistor model and ESR. Resistor measurements.
 "PEP Wattmeter" Thomas V Cefalo WA1SPI, Ham Radio, Oct 1989 p76-80.
Introduction dispenses with the idea of resistive voltage sampling by giving impedance analyser measurements of a 10KΩ carbon composition resistor.
Resistors - Trimmed and Otherwise" Albert E Weller WD8KBW,
QEX July 1985, p9-10.
On the problem of obtaining precision resistors usable at RF. Carbon composition resistors of 10 to 1000Ω have reasonably good RF characteristics, but have poor tolerance ratings and are often out of spec. from new. Composition resistors can be adjusted to a particular value by notching with a file, but may vary by as much as 8 or 9% due to changes in humidity. They are of little value in high precision applications.
[22b] "Composition Resistors - A Dying Breed" Dave Andrus WB6VYN, QEX Correspondence Oct 1985, p2, contd p5. On the poor tolerance and high capacitance of composition resistors and the superiority of carbon film.
[22c] "Composition Resistor Gains Wide Acceptance", Steve Lund WA8LLY, Leroy E Smith WB0LTV, Albert E Weller WD8KBW. QEX Correspondence, Nov 1985, p2-3.
On the poor accuracy and humidity performance of carbon composition resistors, the inductance of spiral-cut resistors, and the superiority of metal-film. Four-terminal measurements using a power-supply and a voltmeter give more accurate results than an Ohmmeter.
Long-Term Resistance Increases in Resistors", Aaron
D Karty KD4BYW, QST April 2002 p70-71.
Resistance of composition resistors increases with time due to moisture absorption.
 Measurements in Radio Engineering, Frederick Emmons Terman, McGraw-Hill, 1st edition, 1935.
Ch 4, sec. 23: Wirewound resistors. Low-inductance winding (Ayrton-Perry, Bifilar, etc.) p92.
 Electrical Measurements and Measuring Instruments, E. W. Golding. 3rd edition, Pitman, London, 1949.
Chapter IV: Condensers, Capacity, and Dielectrics [i.e., Capacitors, Capacitance, and Dielectrics]. Guard-ring capacitor p140.
 The Feynman Lectures on Physics, Richard P Feynman, Robert B Leighton, and Matthew Sands. Addison-Wesley. Vol I 1963 ISBN 0-201-02010-6-H, 0-201-02116-1-P. Vol II 1964 Lib Congress Cat# 63-20717. Vol III 1965 ISBN 0-201-02118-8-P 0-201-02114-9-H.
Vol II, 6-10: Condensers; parallel plates. Non uniform field near the edge of the plates. 6-11: High-voltage breakdown. Ch 10: Dielectrics. Ch 11: Inside Dielectrics. 11-7 Ferroelectricity of BaTiO3.
 Radio Engineering, Frederick Emmons Terman, McGraw-Hill, 3rd edition 1947.
Section 2-4: Condensers and Dielectrics, p23-26 (Polar and Nonpolar Dielectrics p26.). General behaviour of dielectric constant and power factor with changing temperature for polar materials.
capacitors", Cyril Bateman, Electronics World, Dec 1997
p998-1003. Feb 1998 p126-132. Apr 1998 p324-333. May 1998 p391-396.
Jun 1998 p495-503. July 1998 p594-599. Aug 1998 p640-644. See
also letters: Jan 1998 p45, July 1998 p613, Oct 1998 p859.
Dec 97: Capacitor basics: dielectric absorption, phasor diagram, equivalent circuit. Feb. 98: Mica capacitors (k(μr)=5.4, tanδ=0.0003, dielectric strength 200V/μm), paper capacitors, capacitors for connection to the AC mains supply. Capacitor ionisation and self-healing. Apr. 98: Ceramic capacitors. May 98: Plastic film capacitors (errata see Jun 98 p503). June 98: Electrolytic capacitors. July & Aug. 98: Models and measurement techniques.
[29a] "Power dissipation in capacitors", Cyril Bateman, Electronics World, April 1995 p287-290
Capacitor equivalent circuits. Method for calculating power dissipation in capacitors subjected to non-sinusoidal waveforms.
[29b] "Looking into impedance", Cyril Bateman, Electronics World, Aug 1997 p635-640.
Terminology. Four terminal measurements. Transposing Impedance. Wheatstone bridges. Reflection bridges.
[29c] "Fazed by Phase?", Cyril Bateman, Electronics World, Nov 1997 p907-911.
Accurate low-cost phase meter for audio and Tanδ measurements up to 1MHz.
Crystals and Their Application to Ultrasonics, Warren
P Mason (Bell Labs), Van Nostrand Co. Inc. 1950.
Ch XI: Theory of Ferroelectric Crystals.
 Ultrasonic Engineering, Julian R Frederick, Wiley & Sons Inc, 1965. Library of Congresss Cat Card No. 65-14257.
4.6 Piezoelectric transducers. 4.7 Magnetostriction transducers.
 Automatic Control Handbook, Ed. G A T Burdett, Newnes, London, 1962.
9.24 Piezo-electric transducers, 9.25-28 Ferroelectric Transducers.
 Amplifier Handbook, Ed. Richard F Shea. McGraw Hill, 1965.
Ch 16: Ceramic Devices, (Stephen W Tehon).
 "Quartz Crystals, A resumé", Ian Poole G3YWX, Communications Quarterly, Summer (July) 1999, p35-42.
Properties of quartz. Manufacture of quartz crystals. Piezoelectric effect. Crystals cuts. Overtones. Equivalent circuit. Temperature stability. Aging. Oscillators. Filters.
 "Quartz Crystal Parameter Measurement", Jack Hardcastle G3JIR, QEX Jan/Feb 2002, p7-11.
Methods for measuring series and parallel resonance and ESR using simple test equipment.
 The ARRL Handbook 2000, 77th edition. ARRL publ. 1999, ISBN: 0-87259-183-2.
Ch 6: AC Theory and Reactive Components. Capacitance and capacitors p6.6-6.14. Table 6.4: dielectric constants (including BaTiO3). Inductance of a wire [Rosa's formula] p6.22 & 10.10.
Ch 10: Real-World Component Characteristics. Table 10.3: Dielectric strength. Thermal considerations p10.16-19.
Ch 14: Oscillators and Synthesisers. p14.21-24 Quartz crystals in Oscillators (equivalent circuits, overtones, spurious resonances).
Ch 16: Filters. Quartz crystal filters p16.17-19.
Analyzer Tips, Tricks and Techniques", QST Sept. 1996
Crystal Checking, p39-40. A 50Ω resistor is placed in series with the crystal.
[37b] "SWR Analyzer Checks Crystals", Mitchell Lee KB6FPW (Hints & Kinks) QST Dec 2000 p66.
The oscillator in an antenna analyser may have a tendency to 'lock' to the crystal when it is set close to a crystal resonance.
Muscles", Steven Ashley, Scientific American, Oct 2003,
Roundup of developments in the field of electro-active polymers.
 "Armed, yes, but not very dangerous", Duncan Graham-Rowe, The Guardian, 10th March 2005. Life p8-9.
Details of an arm wrestling match against a robot arm powered by electroactive polymer muscles.
 Modern Plastics Encyclopaedia, 1981-1982, Mc Graw Hill, New York.
Section 3: Engineering Data Bank. Plastic films and composites.
 Physics of Semiconductor Devices, S. M. Sze, Wiley & Sons, New York, 1969. SBN 471 84290 7.
Section 8.2: Schottky Effect.
 Physical Electronics, C L Hemenway, R W Henry, M Caulton, Wiley & Sons, New York, 2nd edn. 1967. Library of Congress cat. card no. 67-23327.
Section 4.4: The influence of electric fields on electron emission, p68-73.
 Synthetic Rubber, American Chemical Society, G S Whitby, C C Davis, R F Dunbrook (editors), Wiley, New York, 1954. Library of congress cat. card 54-10308.
Ch 22: Neoprene. A M Neal & L R Mayo, Du Pont Co.
 Synthetic Rubber Technology, W S Penn, Maclaren Ltd, London, 1960.
Table 32.2: General properties of Silicone Rubbers.
 "Collective electrodynamics. Quantum Foundations of Electromagnetism". Carver A Mead. MIT Press 2002. ISBN 0-262-13378-4 (hc) 0-262-63260-8 (pb).
von Klitzing resistance (quantised Hall resistance) p69-72.
on the design of AC susceptometers is given in the references
below. Note that eddy-current effects will dominate AC measurements
made on conducting materials; and so the method is primarily
of interest for the characterisation of high-resistivity materials,
or for finding the transition temperatures of superconducting
materials without the need to measure resistance directly. AC
relative permeability (and hence susceptibility) is strictly
complex; the existence of an imaginary component reflecting the
fact that some energy is lost in the process of magnetising and
demagnetising materials. In this chapter however, since we are
interested in the properties of conductors, we ignore magnetic
losses and treat permeability as a purely real quantity.
[50a] "Superconductivity: A guide to ac susceptibility measurements and ac susceptometer design". Martin Nikolo. American Journal of Physics. 63 (1) Jan. 1995. p57-65.
[50b] " A moving coil ac magnetic susceptometer" R R de Souza, C J Magon. Review of Scientific Instruments, 69 (2) Feb. 1998 p431-436.
| "Coppers for Electrical Purposes", V A Callcut, IEE Proc. Vol. 133, Pt. A, No. 4, June 1986.|