I) INTRODUCTION TO DIELECTRIC & MAGNETICDISCHARGES IN ELECTRICAL WINDINGSby Eric Do Hard, © 1982

II) ELECTRICAL OSCILLATIONS IN ANTENNAEAND INDUCTION COILSby John Miller, 1919

PART I

INTRODUCTION TO DIELECTRIC & MAGNETICDISCHARGES IN ELECTRICAL WINDINGSby Eric Dollard, (c) 1982

1. CAPACITANCE

2. CAPACITANCE INADEQUATELY EXPLAINED

3. LINES OF FORCE AS REPRESENTATION OF DIELECTRICITY

4. THE LAWS OF LINES OF FORCE

5. FARADAY'S LINES OF FORCE THEORY

6. PHYSICAL CHARACTERISTICS OF LINES OF FORCE

7. MASS ASSOCIATED WITH LINES OF FORCE IN MOTION

8. INDUCTANCE AS AN ANALOGY TO CAPACITANCE

9. MECHANISM OF STORING ENERGY MAGNETICALLY

10. THE LIMITS ZERO AND INFINITY

11. INSTANT ENERGY RELEASE AS INFINITY

12. ANOTHER FORM OF ENERGY APPEARS

13. ENERGY STORAGE SPATIALLY DIFFERENT THAN MAGNETIC ENERGY STORAGE

14. VOLTAGE IS TO DIELECTRICITY AS CURRENT IS TO MAGNETISM

15. AGAIN THE LIMITS ZERO AND INFINITY

16. INSTANT ENERGY RELEASE AS INFINITY

17. ENERGY RETURNS TO MAGNETIC FORM

18. CHARACTERISTIC IMPEDANCE AS A REPRESENTATION OFPULSATION OF ENERGY

19. ENERGY INTO MATTER

20. MISCONCEPTION OF PRESENT THEORY OF CAPACITANCE

21. FREE SPACE INDUCTANCE IS INFINITE

22. WORK OF TESLA, STEINMETZ, AND FARADAY

23. QUESTION AS TO THE VELOCITY OF DIELECTRIC FLUX

APPENDIX I

0; Table of Units, Symbols & Dimensions

1) Table of Magnetic & Dielectric Relations

2) Table of Magnetic, Dielectric & ElectronicRelations

FART II

ELECTRICAL OSCILLATIONS IN ANTENNAE & INDUCTION COILS

J.M. Miller

Proceedings, Institute of Radio Engineers, 1919

P.0. BOX 429 • GARBERVILLE, CA 95440-0429 * U.S.A.

1. CAPACITANCE

The phenomena of capacitance is a type of electrical energy

storage in the form of a field in an enclosed space. This space

is typically bounded by two parallel metallic plates or two

metallic foils on an intervening insulator or dielectric. A

nearly infinite variety of more complex structures can exhibit

capacity, as long as a difference in electric potential exists

between various areas of the structure. The oscillating coil

represents one possibility as to a capacitor of more complex

form, and will be presented here.

2. CAPACITANCE INADEQUATELY EXPLAINED

The perception of capacitance as used today is wholly inadequate

for the proper understanding of this effect. Steinmetz mentions

this in his introductory book "Electric Discharges, Waves and

Impulses". To quote, "Unfortunately, to a large extent in dealing

with dielectric fields the prehistoric conception of the electro-

static charge (electron) on the conductor still exists, and by its

use destroys the analogy between the two components of the electric

field, the magnetic and the dielectric, and makes the consideration

of dielectric fields unnecessarily complicated."

3. LINES OF FORCE AS REPRESENTATION OF DIELECTRICITY

Steinmetz continues, "There is obviously no more sense in

thinking of the capacity current as current which charges the

conductor with a quantity of electricity, than there is of speaking

of the inductance voltage as charging the conductor with a quantity

of magnetism. But the latter conception, together with the notion

of a quantity of magnetism, etc., has vanished since Faraday's

representation of the magnetic field by lines of force."

4. THE LAWS OF LINES OF FORCE

All the lines of magnetic force are closed upon themselves,

all dielectric lines of force terminate on conductors, but may

form closed loops in electromagnetic radiation.

These represent the basic laws of lines of force. It can be

seen from these laws that any line of force cannot just end in

space.

5. FARADAY AND LINES OF FORCE THEORY

Faraday felt strongly that action at a distance is not possible

thru empty space, or in other words, "matter cannot act where it

is not." He considered space pervaided with lines of force.

Almost everyone is familiar with the patterns formed by iron filings

around a magnet. These filings act as numerous tiny compasses

and orientate themselves along the lines of force existing around

the poles of the magnet. Experiment has indicated that a magnetic

field does possess a fiberous construct. By passing a coil of wire

thru a strong magnetic field and listening to the coil output in

headphones, the experimenter will notice a scraping noise. J. J.

Thompson performed further experiments involving the ionization of

gases that indicate the field is not continuous but fiberous

(electricity and matter, 1906).

6. PHYSICAL CHARACTERISTICS OF LINES OF FORCE

Consider the space between poles of a magnet or capacitor

as full of lines of electric force. See Fig. 1. These lines

of force act as a quantity of stretched and mutually repellent

springs. Anyone who has pushed together the like poles of two

magnets has felt this springy mass. Observe Fig. 2. Notice the

lines of force are more dense along A B in between poles, and

that more lines on A are facing B than are projecting outwards to

infinity. Consider the effect of the lines of force on A.

These lines are in a state of tension and pull on A. Because more

are pulling on A towards B than those pulling on A away from B,

we have the phenomena of physical attraction. Now observe Fig. 3.

Notice now that the poles are like rather than unlike, more

or all lines pull A away from B; the phenomena of physical

repulsion.

7. MASS ASSOCIATED WITH LINES OF FORCE IN MOTION

The line of force can be more clearly understood by representing

it as a tube of force or a long thin cylinder. Maxwell presented

the idea that the tension of a tube of force is representative of

electric force (volts/inch), and in addition to this tension,

there is a medium through which these tubes pass. There exists

a hydrostatic pressure against this media or ether. The value of

this pressure is one half the product of dielectric and magnetic

density. Then there is a pressure at right angles to an electric

tube of force. If through the growth of a field the tubes

of force spread sideways or in width, the broadside drag through

the medium represents the magnetic reaction to growth in intensity

of an electric current. However, if a tube of force is caused

to move endwise, it will glide through the medium.with little or

no drag as little surface is offered. This possibly explains why

no magnetic field is associated with certain experiments performed

by Tesla involving the movement of energy with no accompanying

magnetic field.

8. INDUCTANCE AS AN ANALOGY TO CAPACITY'

Much of the mystery surrounding the workings of capacity

can be cleared by close examination of inductance and how it

can give rise to dielectric phenomena. Inductance represents

energy storage in space as a magnetic field. The lines of force

orientate themselves in closed loops surrounding the axis of

current flow that has given rise to them. The larger the space

between this current and its images or reflections, the more

energy that can be stored in the resulting field.

9. MECHANISM OF STORING ENERGY MAGNETICALLY

The process of pushing these lines or loops outward, causing

them to stretch, represents storing energy as in a rubber band.

A given current strength will hold a loop of force at a given dis-

tance from conductor passing current hence no energy movement.

If the flow of current increases, energy is absorbed by the field as

the loops are then pushed outward at a corresponding velocity.

Because energy is in motion an E.M.F, must accompany the current

flow in order for it to represent povrer. The magnitude of this EMF

exactly corresponds to the velocity of the field. Then if the current

FIG. Z. Fia. 3.

— Electric Field of Circuit.Fig.22b— Etectrie Field of Comluctor.

ceases changing in magnitude thereby becoming constant, no EMF

accompanys it, as no power is being absorbed. However, if the current

decreases and represents then a negative velocity of field as

the loops contract. Because the EMF corresponds exactly to velocity

it reverses polarity and thereby reverses power so it now moves out

of the field and into the current. Since no power is required

to maintain a field, only current, the static or stationary field,

represents stored energy.

10. THE LIMITS OF ZERO AND INFINITY

Many interesting features of inductance manifest themselves

in the two limiting cases of trapping the energy or releasing

it instantly. Since the power supply driving the current has

resistance, when it is switched off the inductance drains its

energy into this resistance that converts it into the form of

heat. We will assume a perfect inductor that has no self resis-

tance. If we remove the current supply by shorting the terminals

of the inductor we have isolated it without interrupting any current.

Since the collapse of field produces EMF this EMF will tend to

manifest. However, a short circuit will not allow an EMF to

develop across it as it is zero resistance by definition. No EMF

can combine with current to form power, therefore, the energy will

remain in the field. Any attempt to collapse forces increased

current which pushes it right back out. This is one form of storage

of energy.

1 1 . INSTANT ENERGY RELEASE AS INFINITY

Very interesting (and dangerous) phenoma manifest themselves

when the current path is interrupted, thereby causing infinite

resistance to appear. In this case resistance is best represented

by its inverse, conductance. The conductance is then zero. Because

the current vanished instantly the field collapses at a velocity

approaching that of light. As EMF is directly releated to velocity

of flux, it tends towards infinity. Very powerful effects are produced

because the field is attempting to maintain current by producing

whatever EMF required. If a considerable amount of energy exists,*

say several kilowatt hours (250 KWH for lightning stroke), the ensuing

discharge can produce most profound effects and can completely

destroy inadequately protected apparatus.

12. ANOTHER FORM OF ENERGY APPEARS

Through the rapid discharge of inductance a new force field appears

that reduces the rate of inductive EMF formation. This field

is also represented by lines of force but these are of a different

nature than those of magnetism. These lines of force are not a

manifestation of current flow but of an electric compression

or tension. This tension is termed voltage or potential difference.

* The energy utilized by an average household in the course of one day.

13. DIELECTRIC ENERGY STORAGE SPATIALLY DIFFERENT THAN MAGNETICENERGY STORAGE

Unlike magnetism the energy is forced or compressed inwards

rather than outwards. Dielectric lines of force push inward into

internal space and along axis, rather than pushed outward broadside

to axis as in the magnetic field. Because the lines are mutually

repellent certain amounts of broadside or transverse motion can be

expected but the phenomena is basically longitudinal. This gives rise

to an interesting paradox that will be noticed with capacity. This

is that the smaller the space bounded by the conducting structure

the more energy that can be stored. This is the exact opposite of

magnetism. With magnetism, the units volumes of energy can be

thought of as working in parallel but the unit volumes of energy

in association with dielectricity can be thought of as working

in series.

14. VOLTAGE IS TO DIELECTRICITY AS CURRENT IS TO MAGNETISM.

With inductance the reaction to change of field is the production

of voltage. The current is proportionate to the field strength only

and not velocity of field. With capacity the field is produced

not by current but voltage. This voltage must be accompanied by

current i-n order for power to exist. The reaction of capacitance

to change of applied force is the production of current. The current

is directly proportional to the velocity of field strength. When

voltage increases a reaction current flows into capacitance and

thereby energy accumulates. If voltage does riot change no current

flows and the capacitance stores the energy which produced the field.

If the voltage decreases then the reaction current reverses and energy

flows out of the dielectric field.

As the voltage is withdrawn the compression within the bounded space

is relieved. When the energy is fully dissipated the lines of force

vanish.

15. AGAIN THE LIMITS ZERO AND INFINITY

Because the power supply which provides charging voltage has internal

conductance, after it is switched off the current leaking through

conductancedrains the dielectric energy and converts it to heat.

We will assume a perfect capacitance having no leak conductance. If

we completely disconnect the voltage supply by open circuiting the

terminals of the capacitor, no path for current flow exists by defi-

nition of an open circuit. If the field tends to expand it will tend

towards the production of current. However, an open circuit will not

allow the flow of current as it has zero conductance. Then any

attempt towards field expansion raises the voltage which pushes the field

back inwards. Therefore, energy will remain stored in the field.

This energy can be drawn for use at any time. This is another form

of energy storage.

16. INSTANT ENERGY RELEASE AS. INFINITY

Phenomena of enormous magnitude manifest themselves when the

criteria for voltage or potential difference is instantly disrupted,

as with a short circuit. The effect is analogous with the open circuit

of inductive current. Because the forcing voltage is instantly withdrawn

the field explodes against the bounding conductors with a velocity

that may exceed light. Because the current is directly related to the

velocity of field it jumps to infinity in its attempt to produce

finite voltage across zero resistance. If considerable energy had

resided in the dielectric force field, again let us say several K.W.H.

the resulting explosion has almost inconceivable violence and can

vaporize a conductor of substantial thickness instantly. Dielectric

discharges of great speed and energy represent one of the most

unpleasant experiences the electrical engineer encounters in practice.

17. ENERGY RETURNS TO MAGNETIC FORM

The powerful currents produced by the sudden expansion of a dielecti

field naturally give rise to magnetic energy. The inertia of the

magnetic field limits the rise of current to a realistic value. The

capacitance dumps all its energy back into the magnetic field- and

the whole process starts over again. The inverse of the product of

magnetic storage capacity and dielectric storage capacity represents

the frequency or pitch at which this energy interchange occurs. This

pitch may or may not contain overtones depending on the extent of

conductors bounding the energies.

18. CHARACTERISTIC IMPEDANCE AS REPRESENTATION OF PULSATION OF ENERGY

FIELD

The ratio of magnetic storage ability to that of the dielectric

is called the characteristic impedance. This gives the ratio of maximum

voltage to maximum current in the oscillitory structure However,

as the magnetic energy storage is outward and the dielectric storage

is inward the total or double energy field pulsates in shape or size.

The axis of this pulsation of force is the impedance of the system

displaying oscillations and pulsation occurs at the frequency of

oscillation.

19. ENERGY INTO MATTER

As the voltage or impedance is increased the emphasis is on the

inward flux. If the impedance is high and rate of change is fast

enough (perfect overtone series), it would seem possible the compression

of the energy would transform it into matter and the reconversion of

this matter into energy may or may not synchronize with the cycle of

oscillation. This is what may be considered supercapacitance,

that is, stable longterm conversion into matter.

20. MISCONCEPTIONS OF PRESENT THEORY OF CAPACITANCE

The misconception that capacitance is the result of accumulating

electrons has seriously distorted our view of dielectric phenomena.

Also the theory of the velocity of light as a limit of energy flow,

while adequate for magnetic force and material velocity, limits our

ability to visualize or understand certain possibilities in electric

phenomena. The true workings of free space capacitance can be

best illustrated by the following example. It has been previously

stated that dielectric lines of force must terminate on conductors.

No line of force can end in space. If we take any conductor

and remove it to the most remote portion of the universe, no lines

of force can extend from this electrode to other conductors. It

can have no free space capacity, regardless of the size of the

electrode, therefore it can store no energy. This indicates that

the free space capacitance of an object is the sum mutual capacity of "ft

•fof all the conducting objects of the universe.

21. FREE SPACE INDUCTANCE IS INFINITE

Steinmetiz in his book on the general or unified behavior

of electricity "The Theory and Calculation of Transient Electric

Phenomena and Oscillation," points out that the inductance of any

unit length of an isolated filimentary conductor must be infinite.

Because no image currents exist to contain the magnetic field

it can grow to infinite size. This large quantity of energy cannot

be quickly retrieved due to the finite velocity of propagation of the

magnetic field. This gives a non reactive or energy component to the

inductance which is called electromagnetic radiation.

22. WORK OF TESLA,STEINMETZ AND FARADAY

In the aforementioned books of Steinmetz he develops some rather

unique equations for capacity. Tesla devoted an enormous portion of

his efforts to dielectric phenomena and made numerous remarkable discoveri

in this area. Much of this work is yet to be fully uncovered. It is

my contention that the phenomena of dielectricity is wide open for

profound discovery. It is ironic that we have abandoned the lines

of force concept associated with a phenomena measured in the units called

farads after Farady, whose insight into forces and fields has led

to the possibility of visualization of the electrical phenomena.

IMPORTANT REFERENCE MATERIAL

1. "Electricity and Matter/1 J. J. Thompson

New York, 1906, Scribner's Sons, and 1904, Yale University

2. "Elementary Lectures on Electric Discharges, Waves, and

Impulses and other Transients." C. P. Steinmetz, second

edition, 1914, McGraw-Hill

3. "Theory and Calculation of Transient Electric Phenomena

and Oscillations," C. P.Steinmetz, third edition, 1920,

McGraw-Hill. Section III Transients in Space, Chapter VIII,

Velocity of Propagation of Electric Field.

23. QUESTION AS TO THE VELOCITY OF DIELECTRIC FLUX

It has been stated that all magnetic lines of force must

be closed upon themselves, and that all dielectric lines of force

must terminate upon a conducting surface. It can be infered

from these two basic laws that no line of force can terminate

in free space. This creates an interesting question as to the

state of dielectric flux lines before the field has had time to

propagate to the neutral conductor. During this time it would seem

that the lines of force, not having reached the distant neutral

conductor would end in space at their advancing wave front. It

could be concluded that either the lines of force propagate instantly

or always exist and are modified by the electric force, or voltage.

It is possible that additional or conjugate space exists within

the same boundaries as ordinary space. The properties of lines

of force within this conjugate space may not obey the laws of

normally conceived space.

TABLE I.

Magnetic Field. Dielectric Field.

Magnetic flux: Dielectric llux:•t> = Li 10* lines of magnetic force. • "• Ct lines of dielectric force, or

coulombs.Inductance voltage: Capacity current:

,-=n£io-. = L£vo.t, r-J.r*.

Magnetic energy: Dielectric energy:

2ir— ^joules. ! u1 = -^-joules.

Magnetomotive force: Electromotive force:F = ni ampere turns. f = volts.

Magnetizing force: ' Electrifying force or voltage gra-p dient:

J — -r ampere turns per cm. i f' . O = j volts per cm.

iMagnetic-field intensity: | Dielcitric-field intensity:

X' = 4»/10-1 lines of magnetic ,. G .force per cmJ. A = ^ 3 10' hues of dielectric

force per cm2, or coulombsper cm:.

Magnetic density: Dielectric density:(B = MOC lines of magnetic force £> = «A' lines of dielectric force j

per cm2. i P**r cn<2' o r coulombs percm:.

I'erineubility: ^ 1 Perm ' ttivity or specific capacity: «:

Magnetic (lux: | Dielectric flux:•t> = .1(B lines of magnetic force. ; * m AD lines of dielectric force,

or coulombs.

v = 3 X 10'° = velocitv of linlit.

TABLE II.

Magnetic Circuit. Dielectric Circuit. Electric Circuit.

j Magnetic (iux ^magnetic• current):j * = lines of magneticI force.I Magnetomotive force:: F = ni ampere turns.; Permeance:

+

Inductance:

henry.Reluctance:

] Magnetic energy: |

w = — = -3j-10~* joules.

Magnetic density:

(JS = — =M,iclinespercm1.A

Magnetizing force: jF i

/ — -j- ampere turns per:cm. '

Magnetic-field intensity::

3C - AT}.

. Permeability:

„ - St.

Reluctivity:

p = <B"

Dielectric flux (dielectriccurrent):

• = lines of dielectricforce.

Electromotive force:e = volts.

Permittance or capacity:

C = -farads.e

(Elastance):I 1C = *"

Dielectric energy:Ce2 e*. ,w = -^- = ;j- joules.

Dielectric density:

D -= — = KKI ines per cm1.

Dielectric gradient:

G = -. volts per cm.

Dielectric-field inten-sity:

K = ^ H > » .

Permittivity or specificcapacity:

D

(Elaativity ?):1 K

Specific magnetic energy:; Specific dielectric energy:

10-' joules per cm1.: 2 rr'KD joules per cm*.

Electric current:

i «• electric cur-rent.

Voltage:e = volts.

Conductance:

g = - mhos.6

Resistance:

r = - ohms,i

Electric power:p = ri2 = gez =

watts.

Electric-currentdensity:

/ = 1 = yG am-

peres per cm2.

Electric gradient:

G - j volts per cm.

Conductivity:

y w — mho-cm,(xResistivity:

p^~sa — ohm-cm.7 I

Specific power:

watts par cm1.

APPENDIX I

1

,,

S••

101112

I.I1-1

15Ifi171811iU\\

Ii24252(.

2329.10i lJ2

3.!

Quantity

LCTHth

'-., , icral ionForceEnergyI'owrrChargeDielectric constant of

free spaceDielectric constant

relativeCharm density

volumesurfaceline

Electric intensityElectric rlux densityElectric fluxElectric potentialE M FCapacitanceCurrentCurrent densityResistanceResistivityCor.iuctar.eeConductivityElectric p<"il.\rizationElectric susceptibilityElectric dipole mo-

mentElectrio energy density

Sym-bol

L.1

M mf. 1

u

rwp

Q. Q

<"04

*r

ppt

fitED&Vv.r

I. iJRpG9

P^#

m.->•

mksUnit

Rationalized

nim :

m>kito^ram

' 'JCt •:.*;

newtonjouleWJltt

coulumb

farad;mfarad, mnumeric

coulomb/m'coulomb/m'coulomb/m

vnh/mcoulomb/rn2

coulombvoltVOlt

faradampere

ampere/m'ohm"

ohm-mmho

mho/mcoulomb/in*

farad/m

coulomb-mjoule '»n<

r.vPLE OF UNITS, SYMBOLS

Denning Equation

A - £»•.' "• L1

• *•> / / ia - L.T'/•• =- Ma

W =• FLP - W'TF •- Q* f (fattL*)

» - 1 /(>.«.')

tr — t/*t

P - Q/v

7t - Q/LE - F/Q - - V/LD - ,E - +/At - DAV - -EL

V, — —d&/dtC - Q/VI - Q/T •J - I/AR - V/IP - RAIL

G - 1/Kff • l/p •• J/JtP - D - t,E - pZ.x. - P/E - «.(«• - 1)

m. - QL

Dimer

AND

'iiona:• o r m u l a

Exponents of

L

123001I1220

— 3— 5

0

- 3- 2— 1

1- 2

0•12

- 20

- 223

— 2

- 3- 2- 3

1— 1

hi

0001

( 1

00

1I0

- 1- 1

I)

0n0I0011

- 100f1

- 1— 1

<)- 1

0

1

f

000(11

_ 1

.._ J

- 30

220

000

- 200

- 2- 2

2- 1— 1- I- 1

1j02

0- 2

oi-

0.

is(1

01

220

111

- 111

— 1— 1

211

— 2

_ 22212i

1

oj

DlNf ENS IONS

ci;ii emu

cmcm*i • •:-.3

v.- i tic:n s o :C n i so c *

dyne

erg.. s.ecabcculomb

abcoulumb/cm*abroulomb/cTTi*a bcou lo m b / c m

abvoh.' '.-m

a b voltabvuit

abiaradabampere

abampere/cm'abohm

abohm-cm.i b m h o

abmho/cmabcu'.nnl'/cm1

Mo. oie m u

No. cfin Its

i ' ) '1 (>•

I O ]

1

10*1 0 1

107

10"»

10-T10"»10"1

\0*

•\* i 101(>»! 0'

10~*10" ;

io~*10»10**1O~*10--H! 0~4

1

eft* esu

cmc m 'e n '

^r;tmsecondcm :\e.zr:r., sec1

dynee r g

statcoulomb

1

statcoulomb/cm*statcoulomb/cmJ

siatcoulomb/otnstatvolt/cm

statvoltutatvoit

statfaradsiatampere

statampe re/cm1

statohmstatohm-cm

statmhostatrr.ho/cm

statcotilomb/ era1

1

statcoulomb-cmerg 'cmJ

No. ofesu

AO. ofmkt

10 '10*10«in"

1H ) '10*10*1 0 '10'10c

4«' /10'

1

c/10'c/10'c/10lOVc

4rc/10'4x1 Oc10§/C

10'/cc'/lO*

10cc/10'I0VC10*/ c'c1/10*c'/10'c/10'

4xc'/!0'

10*c10

No. ofesu

; .o . ofemu

1111111

111

100c

100c100c100c

l / (100c)100c100c

1/dOOc)l / (100c)(100c)'

SOOc100c

1 /(100c)*l/(100c}'

(!00c)»(100c)'

100c

1

.4

!Sin

i 7

4(1

J 1I !.\ \4 4

4516474S195051525.1

54

tjuantity

P..r,1,eab;;,ly oi f r«

Permeitbilii yrcl.-.li vc

Magnetic pole

Magnetic momentMagnetic intensity

Magnetic '.ux lienaity

Magnetic rtuxM.^i^netic ,'OtentialM: , IKIntensity ^i magneti-

zationInductance

selfmutual

ReluctanceReluctivityPermeancePermittivityEMFPoyntin^'s vectorMagnetic energy den-

sityMany t-tic iusccpt i -

b.hty

Svm-bV'i

fit

p

m&

H

$V

\t

LM

¥

(PnV.y

Urn

"iksUnit

henry, .-iii i e n r v • M I

numericweber

A-eb'-'-nianiperc / m ^r

newtou wuberv.'eber, ni !

wob^r

amperewetier/m1

henryhenry

ampere/ we bermeter/henryweber/amp

henry/metervolt

watts/m1

joule/^i*henry/in

TABLE OF UNITS, SYMBOLS

Dennin* E.Taat:on

^9 - 4u/ 10'M - n/ti

P - n7i - i;8)

J/ - f . / i or/•-//>

••

* - Ji.l - [',7'6' - S - UL•y - i

M - IS - lit - m/L>

L - 0 / /.vr - 4i,/ - I K / / '(B — 3 / *« * l /«

(S> - I/iftc - I/»

& - EH

<*„ - / /B/2X*4 •* *M/H

- «(M. - 0

, AND

OimensionalP c r m u L

Exponents

/..

1

i i

2

— I

0

.'0

«

22

-212!20

- 11

1

01

10

1

1(J

(I1

1I

- 1- 1

1111

I1

T

0( i

I]

- I

_ j

- 1

- 1

- 1- 1— ]

— i

fl(I0000

_ T

- j

- 20

of

Q

. ,- 2

0- !

— 1

;

- 1

— ]i

1- 1

— 2

2- 2- 2- 1

0

ni- 2 '

DIMENSIONS

• sir. emu

pl>H»-CRt

r»en;tci3 i r;.:ubert, em

Kauss ' irrr.ax'.veH cm*

maxwellgilbert

pole/ cm1 orgauss/4*-

uhhenry. ,b:ien:y

abvohith)watt/cm*

erg/cm1

henry/m

2\'o. ul"Sffltl

No. oim k s

IU1 H

1'<)< -!r

1 •'! '' I *Ir, 1' I1

I CM

10*( r / 1 0l r / 1 0

1 0 * ' 4 T

I 0"HP

* 0*10*

1010V4»

!

cga esu

statvolt•t»twatt/cm»

etg/sm*j1

No. of

No. vin i b

10*/c*io*/c«

l»/e10*

10

!No . of

.No. r,f 1W . |

emu |

I

It

1

1 /'100c)3

l/(100c)'

l/<100c)1

1

- W I 0 ' henrys/meter. Fore - 2.998 X 16« nietori/iee, « - t/im' - l(P/Hwc') - 8.854 X 10"" farad/mewFor c 2T 3X10" moteri/sec, <j g l/t}«rlO«> farad/meter- c' - 8.98S X 10" ^ 9 X 10"

I. INTRODUCTION

In the following paper are outlined some results of the appli-cation of the theory of circuits having uniformly distributedelectrical characteristics to the electrical oscillations in antennasand inductance coils. Experimental methods are also given for de-termining the constants of antennas and experimental resultsshowing the effect of imperfect dielectrics upon antenna resistance.

The theory of circuits having uniformly distributed charac-teristics such as cables, telephone lines, and transmission lineshas been applied to antennas by a number of authors. Theresults of the theory do not seem to have been clearly broughtout, and in fact erroneous results have at times been derivedand given prominence in the literature. As an illustration,in one article the conclusion has been drawn that the familiarmethod of determining the capacity and inductance of antennasby the insertion of two known loading coils leads to results whichare in very great error. In the following treatment it is shownthat this is not true and that the method is very valuable

Another point concerning which there seems to be consider-able uncertainty is that of the effective values of the capacity,inductance and resistance of antennas. In this paper expres-sions are obtained for these quantities giving the values whichwould be suitable for an artificial antenna to represent the actualantenna at a given -frequency.

The theory is applied also to the case of inductance coilswith distributed capacity in which case an explanation of awell-known experimental result is obtained.

Experimental methods are given for determining the con-stants of antennas, the first of whirl) is the familiar methodpreviously mentioned. It is shown (hat ins- nuthud in ivalitygives values of capacity and inductance "! ihv MUt'.nna elu-c inthe low frequency or static values and may be corrected -<> as togive these values very accurately. The -crond method con-cerns the determination of the effective mine- <>i the- capacity,inductance, and resistance! of the antenna.

In the portion which deals with the resistance of antennas,a series of experimental results are given which explain thelinear rise in resistance of antennas as tile wave length is in-creased. It is shown that this eharafteristic feature <<( antennaresistance curves is caused by the presence of imprrjVct dielec-tric such as tret's, buildings, and so on, in the field of tin:antenna, which cau.-es it to behave as an absorbing condenser.

300

II. CIRCUIT WITH UNIFORMLY DISTRIBUTED INDUCTANCE AND

CAPACITY

The theory, generally applicable to all circuits with uni-formly distributed inductance and capacity, will be developedfor the case of two parallel wires. The wires (Figure 1) are oflength I and of low resistance. The inductance per unit length

FIGURE 1

••

Li is defined by the flux of magnetic force between the wires per '.',unit of length that there would be if a steady current of one ,jampere were flowing in opposite directions in the two wires. iThe capacity per unit length d is defined by the charge that ,|there would be on a unit length of one of the wires if a constant ;emf. of one volt were impressed between the wires. Further the jjquantity L0 = lLt would be the total inductance of the circuit \if the current flow were the same at all parts. This would be ljthe case if a constant or slowly alternating voltage were applied ;at i = 0 and the far end (x = l) short-circuited. The quantity pC, = /Ci would represent the total capacity between the wires ;if a constant or slowly alternating voltage were applied at x = 0and the far end were open. !

Let us assume, without defining the condition of the circuitat x = /. that a sinusoidal emf. of periodicity r« = 2 r / i s impressedat .i" = 0 giving rise to a current of instanhuieou.s value i at A and ,a voltage between .1 ami I) equal to v. At II the eiim-nt will he

i-| dx and the voltage from B to C will IK1 C + -~ <ti.d x • dxThe voltage around the rectangle .1 BCD will be equal to

the rate of decrease of the induction thru the rectangle; hence

dx 01 v

Further the rate of increase of the irhargc q on the ulementarylength of wire .-l.fi will be equal to the excess in the currentflowing in at .4 over that flowing out at B.

301

Hence

di dv~Tx'Tt (2)

These equations (1) and (2), determine, the propagation of thecurrent and voltage waves along the wires. In the case ofsinusoidal waves, the expressions

v = cox ait (A cos to \/('xL\X+B xin <o y/V\L\X) (3)

i= sin ID t . /—' (.1 xin iu \/('i /', i X — H co* <« \/V', L, .r) (4)

are solutions of the above equations as may lie verified by sub-stitution. The quantities .4 and B are constants dependingupon the terminal conditions. The velocity of propagation ofthe waves at high frequencies, is

111. Tin: ANTKNNA

1. KKAI TANCK OF THE AK.RIAI.-( ! HolNI) PMKTIO.N

The aerial-frrouml poition of the antenna <('!) ill Figure 2lwill be treated as a line with uniformly distributed inductance,capacity and resistance. As is common in the treatment of

• • B. C '.

l - ' l U ' H K - ' — \ t l " ! i t l : t I t l ' J T i — f l l t i i t a - i [ . I I L I 1 t t i l h

( " i i i f i i n i i D i - : n i . i i t i i i n "1 l l n l u c l ; t m i : i i i . i ( ";. i »:t • i l V

* d i o r i i c i i J t s . t h e r i • - 1 ~ 1 : 1 1 M I • w i l l l > r I ' M i i - i d i [ " « - • 1 " « i I " ' s u I « » W a >

not to affect the fn-qiii-iwy of the u-i-iHatinti- "i1 'hf disirilnttionof fiiri-ftil and Vdltatr--. Tin- lead-in IU' I'ijiiiri' 2i will In-

considered to he fret: from inductance or capacity excepting asinductance coils or condensers are inserted (at --1) to modify tlieoscillations.

Applying equations (.3) ami (4) to the aerial of the antenna Iand assuming that x = 0 is the lead-in end while x = l is the farend which is open, we may introduce the condition that the ,'current is zero for .r = l. From (4) ]

~ = cot to \ A \ L, / (5) •i

Now the reactance of the aerial, which includes all of the an-tenna lint the lead-in, is given l>y the current and voltage at.r = (). These are, from 1.3), (,4), and (.">),

<•„ = .4 con en I = H cot at y/C\ L\ I coy <o t '

1(T ' !

'„ = — \h~ M *in tu t

T h e c u r r e n t l e a d s t h e vo l tage w h e n I he co tangent i s p o s i t i v e ,

a n d hijrs when t h e cotangent is n e g a t i v e . T h e r e a c t a n c e ot t h e J

a e r i a l , g iven liy t h e r a t io of 1 lu- maxiinlltll va lues o\ i\ tn ('., is

-V = - x ; ^ cot w \T\L; I !

o r i n t e i m s n t ' ' . , = / ( ' : a n d / . „ = / / . ,

X = - xiL- cot ,o V J...

V „

or since 1 =v M',

A'= - / . , Vcot'" \•>', l.s IA< g iven liy •). >. StitneJ

AI low !rei|iielicii"" tile reai'ialice I- negat ive and hence1

the aerial lu-liaves as a capacity. At the frequency i'= —

t h e r e a c t a n c e l i f c m n e s Kent a n d l i e v m n l ' h i - Irecpi ' -ney is p o - i ! t v e1

o r i n d u c t i v e u p t o i h e I r e q i i e i i c v / = . , , . • • •'•'•• w i n c h t h e r e -

a c t a n e e l ) e c o i n e ~ i n f i n i t e . I h i s v a r i a t i o n ol th«.- a e r i a l i'ea1"-

t a n c e w i t h t h e l ' r<- ' | ucncy i~ - l iovvn l iy t h e c o t a n g e n t c u r v e s in

Figure :{.!Si,,i|(.. J. s.: •"l"i:iii~ liil. ilkr i "••nan1""." Si. I..M11-. .",. |». Vi.': l"tM

|

i 10 12 i* 2+ zaxio'u

L.. 50^K

C.COOOS^

Fiiil'itK 3—Variation i;f the Keactanee of the Aeri:il of :m Antenna withthe l're<|iioiiry

2. XATIRAL FHEUUE.MIES OF OSCILLATION

Those frequpneics :>t which the reactance uf the aerial, assiiven by equation (G). becomes equal to zero are the naturalfrequencies of oscillation of the antenna (or frequencies of re-sonance) when the lead-in is of zero reactance. They are givenin Figure 3 by the points of intersection of the cotangent curveswith the axis of animates and by the equation

The corresponding wave length.* are jjiven by

'' ~ f ~ f VC. L,, in

\. v.. 4 1 .4 3. 4 5. 4 7. i-tr., times the length of ilie aerial. If.liiiwi'ver, the lead-in has a reactance A",., the natural frequenciesof oscillation are determined by the condition that the totalreactance of lead-in plus aerial shall be zero, that is:

.YX+.Y=O

p r o v i d e d the reactances are in se r ies w i t h t h e d r i v i n g einf.fai LOADING CuiL IN LKAII- IX. The most important prac-

tical cast- i- that in which an inductance roil is inserted in the

lead-in. If the foil lias an inductance L its reactance A";=<»L.This is u positive reactance increasing linearly with the fre-quency ami represented in Figure 4 by a solid line. Those fre-quencies at which the reactance of the coil is equal numericallybut oppositt- in sign to the reactance of the aerial, arc the naturalfrequencies of oscillation of the loaded antenna since the totalreactance XL-\- X = (). Graphically these frequencies are deter-

inE 4—Curves of Aerial ;ind Loading Coil Reactances

mined by the intersection of the straight line — A'/, = — to L!shown by a (lashed line in Figure 41) with the cotangent curvesrepresenting A". It is evident that the frequency i> lowered l>ythe insertion of the loading foil and that the higher natural fre-quencies of oscillation are no longer integral multiples of thelowest frequency.

The condition AL-f-A=0 winch determiner: the natural fre-quencies of oscillation leads to the equation

w L — » -'," col in V('«L,, = 0

orcot m

Thi." initiation lias IHH'II given by CSuvati* and L. Cohen.1 Itdetermine* the periodicity m and hence the frequency and wavelength of the possible natural modes of oscillation when thedistributed capacity and inductance of the aerial and the in-ductance of the loading coil arc known. Tin's equation cannot,however, be solved directly; it may be solved graphically asshown in Figure1 4 or a table may be prepared indirectly which

r

gives the values of <o \Zc,,L0 for different values of--, from

which then to, f or /. may be determined. The second columnof Table I gives these values for the lowest natural frequencyof oscillation, which is of major importance naturally.

(l>) CONDKNSEH IN' LEAD-IN. At times, in practice, a con-denser is inserted in the lead-in. If the capacity of the condenser

is C. its reactance is A'c = - • This reactance is shown in<o(

Figure .") by the hyperbola drawn in solid line. The intersection

I

1>1

4 \

c 1 C. &a**mMf

I ' n . t KK (_ 'u rvcs ;jf A i r , : i l :i

ul the tu'jsittvo of tins curve (drawn in dashed linei with thoft.ttaiijn.'iil i*urve.-r leprocntmi; A." gives the frequenetes (or which

•'(iu\;;!!. A.: "l.n.'iurrc Ki>i'tri<|iu*, ' l">, I> !•!: It'll.; { ' . i ! a - n , I . . ; " K k f t r i r a l Wrirl«i."' O.'i, |». _'sr, : | « l | . 1 .

TABLE I

DATA !OR LOADKD ANTENNA CALCULATIONS

0 . 0.1*>

Ti.4.",ii

<l1)

.1.)

4.",

.(i

.7

.S«.l

2.0. ' .11.2i ••

! 4.' ."J ii> ~

| s:.'.i: o

lllllll

:.71till:514

•220142077021

. l l . i lN'.MMill

.SAXMI4

. 77U—«—

.~'M\-

. 7 1 7(>!>ft(is:?

.WIKfiji3(i4O1127lil."

.1104. ."'.IM.Yv I

;"i7-l."ii i 1

"lill i. " 17

1

1 Ti"1 ")l!l1 .'(li'li :liu1 . IKS1 O'.l."i

1 KVi.'.IS4

I).;!)

'. l(«1

.Mil!

s:;.-SHS

7(i07M'I

!nii701

(iS'lJi.'l.jIi4 1

'.i¥£<l i l l i

.till."

r.ni.V>!- ~ j

.".!.."i

..Vrfi", (v

Differ-ence, |>er

cunt

10i;4:{•>

I1l

.,

:J•i

()

41[|~-

-

444;j

;{

i{;\

U:i;j:5:i• >

;{

41•5-Ii

(11~

ssr>

'•') < (1• j• >

•_>•J•_'_•

111

| 101 u

2:;i_")i7sij

21)

rj

;j

.4

.5l>

.S

.0

II-

.0."l

.0,-,

o. ,*i().-,0II

.0(1(1

II

IIII1)I)

(1

• j —

ii.rv.lfi

.">24

. > 17.'31(1:>041077

'.•tsm4MI1

0

.454S j. l;>:>04141 '

;}S2ti.i(iO:5:i.->74ii4li->;;:{l»(i j

III Ml:>111

. 2 0 7 2 :

.2s.">0 '

. 2711 :

2i i l 1.2."i."(i2 17'i

. 2 1 0 2

'' '77221'.'

_ l ^ _ l Differ-/ {J i e n c e , | ier

")40

.Viii

.") 1S• i l l5O4

rent

0 . 11

.11

.10

4!I7'.» i .04".»1'.» : .11

. |S(MI 04SO4 I i)4.'il'.l IIi:;:;o n

. . . . ji

.1U7

Af + A = (). and hence the natural frequencies of oscillation ofthe antenna. The frequencies are increased (the wave lengthdecreased) by the insertion of the condenser and the oscillationsof higher frequencies arc not integral multiples of the lowest.

The condition Xc+ X = 0 is expressed by the equation

£ (9)

which has been given by Guy an. Equat ion (9) may be solvedgraphically as above or a table similar to Table I may be prepared

Z,,LO for different values of — . More complicatedgiving

circuits may be solved in a similar manner.

."3. EFFECTIVE RESISTANCE, INDUCTANCE, AND CAPACITY

In the following, the most important practical case of a load-ing coil in the lead-in and the natural oscillation of lowest fre-quency will alone be considered. The problem is to replacethe antenna of Figure (> (a) which has a loading coil L in the lead-in and an aerial with distributed characteristics by a circuitFigure 6 (,b) consisting of the inductance L in series with lumpedresistance It,, inductance Lc. capacity (\. which are'equivalentto the aerial. It i.s necessary, however, to state how theseeffective values arc to be defined.

I'lGlP.E 0

Iii practice the quanti t ies which an- of importance, in anantenna are the resonant wave length or frequency and tin:current at the current maximum. The quantifies />, and <\.are, therefore, defined as those which will give the circuit (b) the

same resonant frequency as tho antenna in (a). Further thethree quantities L,, C,, and If, must be such that the current in(b) will be the same as the maximum in the antenna for thesame applied emf. whether undamped or damped with anydecrement. These conditions determine Le, Ct, and Re uniquelyat any given frequency, and arc the proper values for an arti-ficial antenna which is to represent an actual antenna at a particu-lar frequency. In the two circuits the corresponding maximaof magnetic energies and electrostatic energies and the dissipa-tion of energy will be the same.

Zenneck.4 has shown how these effective values of inductancecapacity and resistance can be computed when the current andvoltage distributions are known. Thus, if at any point x onthe oscillator, the current i and the voltage >> are given by

i

where I is the value of the current at tin; current loop and 1'the maximum voltage, then the differential equation of theoscillation is

where the integrals are taken over the whole oscillator. If wewrite

R.~Sll>f{xydx (10)Lt=/Uj{x)-dx (11)

the equation becomes

P d l • ! d'il ^ ' - . 1d t 0 /- ( ,

which i> tlie differential c(|uaiii>n of oscillation of a simple cir-

cuit with lumped resistance, iniluetanee, and capacity of values

/? , . Ln a n d ("c a n d in which tin- current is ihe s a m e as t h e uiaxi-

inuii] in t h e d i s t r i b u t e d caw . In o n l r i tn I'valuate t l iese quan-

tit ies , it is necessa ry only to determine / i.r) and <£ | . r ) ; t h a t is,

the funct ions which specify the distribution uf current a n d vol-

tajio on t he osci l la tor . In t i n - i-uiinectiuii it will !<e assumed

that the resistance is not uf importance in determining thesedistributions.

'Zi-miM-k, "Wireless Tclcf;r:i|)li\ ' 'Tniiislutwl Uy A. H. ^celigi, Note 10,p. 411).

At the far end of the aerial the current is zero, that is forx = l; ii = Q. From oquations (3) and (4) for x = l

v, = cos to t (A cos to \/C\Li I+B sin to \/c7Z[I)

i'i = sin w t yj -'- (A sin to \/Ci Lx I —B cos to \/C\ L\ I)

and since it = QA sin w \/C\L\ I =B cos to y/C\ L\ I

From (3) then we obtainc = r, cos (to "s/C\ L\ I — io y/Ct L\ x)

Hence 4> (x) =cos (at y/C\L\. I—to \/C\Li x)

Now for x = 0 from (4) we obtain

io = -B -Jj! sin tot=-A Jy-1 Ian to VCTLI I sin to t\ L i \ L \

whence _ . xin ("^VCiL, / — <o \//(\Lix)sittm-\/CiLil

and , , _ sin (to Vc \L\l —1» \/C\L, x)J \-r) — : / ., , , • ""

sin to VC iL\'W e c a n n o w e v a l u a t e t h e e x p r e s s i o n s ( 1 0 ) . ( 1 1 ) , a n d ( 1 2 ) . F r o m(10 )

p — Cp s*ni ((0 v^^'' i ^ ~'» >/Ci L\x) d xsin- tu s/C\Li Isin

sm- ,„ v 'C, L, I L2 4 a, VjCijL,

~ 2 [x//i*w y/c.,L, w\/C~,L,

ami fri'iu 1111 which contains tin1 same form nf inlegnil

2 Lv?''5 tu V C L« w V C, L,,and from (12)

__ i ./".;('• cos {(o y'f/, Lt I-io \Zr~i /.i -r)'/-r 1 •y ' < ' i ( • ( ; • , • ( C M \ / T , L I / - < • > V ' C , / „ ' , - r ) ' / x

, .. xiirja

/ / , »/« 2

\2 4-(',. _ (15')

<"\ C,,L.,(2

310

,,L.

The expressions (14) and (15) should lead to the same valuefor the reactance X of the aerial as obtained before. It is rendilyshown that

X = <»Le — = -\\j7 cot <o(I) C , Vtg

agreeing with equation ((>).It is of interest to investigate the values of these quantities

at very low frequencies (<u = 0), frequently called the staticvalues, and those corresponding to the natural frequency ofthe unloaded antenna or tlie so-called fundamental of the an-tenna. Substituting n» = 0 in (13), (14), and (15) and evaluatingthe indeterniinant which enters in the first two cases we obtainfor the low frequency values

L,

R,," 3

L,,

(\=C\, (10)At low frequencies, the current is a maximum at the lead-inend of the aerial and falls off linearly to zero at the far end.The effective resistance nnd inductance are one-third of thevalues which would obtain if the current were the same thruout.The voltage is, however, the same at all points and hence theeffective capacity is the capacity per unit length times thelength or ('„.

At the fundamental of the antenna, the reactance X of

equation f'fi) becomes equal to zero and hence «> \/C,. L. = ., •

Substituting this value in (13). (14), and (15)

( I

Hence in going from low frequencies up to that of the funda-mental of the antenna, the resistance (neglecting radiation andskin effect.) and the inductance Sneglecting ^kin effect) increase byfifty per cent., the capacity, however, decreases by about twenty

2 2per cent. The incorrect values - /„,, and -C,, have been fre-

R,=

U =

r.-=

R,,2

28

(•

qucntly given and commonly used as the values of the effectiveinductance and capacity of the antenna at its fundamental.

These lead also to the incorrect value Le=-^ for the low fre-

quency inductance5.The values for other frequencies may be obtained by sub-

stitution in (13), (14), (15). If the value L of the loading coilin the lead-in is given, the quantity <o y/CoLo is directly obtainedfrom Table 1.

4. EQUIVALENT CIRCUIT WITH LUMPED CONSTANTS

Insofar as the frequency or wave length is concerned, theaerial of the antenna may be considered to have constant valuesof inductance and capacity and the values of frequency or wavelength for different loading coils may be computed with slighterror using the simple formula applicable to circuits with lumpedinductance and capacity. The values of inductance and capacity

ascribed to the aerial are the static or low frequency, that is, —-°

for the inductance and Co for the capacity. The total inductance

in case the loading coil has a value L will be L+ ~ and the

frequency is given by

(18)

or the wave length in meters by

/. = ISS4 \' L+^)<\. 110)

where the inductance is expressed in microhenry* and the capacityin microfarads. The accuracy with which this formula givesthe wave length can be determined by comparison with theexact formula (8). In the second column of Table I are given

I. It. E." .'). |>.:!ss»,v fur the reactance of•as verified by the ex-iltl be corrert forau ar-:a\inium m the actual

' T h e s e v a l u e s a r c Jj ivpl i b y if. I I . M o i c c i v . l ' t ill I ' rl'.'lT. It may bo shown that they lead to correct vuhlthe aerial ami henee to correct values uf frequency a.s >pornnents They are not, however, the. values which wotificial antenna in which the current must. l'((l!:;l tlie i .antenna and m which the energies must also !>e i'*|Ual to 'hose ill the antenna.Tht" resi.-tance values yiven i>v 1'rof. Mmccnift agrif with these requirementsar.d with the values obtained here.

Values fur the effective inductance and capacity in agreement with tho>cof equation (17) above have been (liven by (.i. \\•". 0. Howe. "WaHwmk ofWireless Tfk-eraj i l iy and T e l c p l m n y , " |tuuf fet ' . \\»\~.

the values of <o\/C0L0 for different values of Lo as computed byformula (8). Formula (18) may be written in the form

so that the values of <o y/C»Lu, which arc proportional to thefrequency, may readily be computed from this formula also.These values are given in the third column of Table I and theper cent, difference in the fourth column. It is seen that formula(18) gives values for the frequency which are correct to less thana per cent., excepting when very close to the fundamental of theantenna, i. c., for very small values of L. Under these con-ditiom the simple formula leads to values of the frequencywhich arc too high. Hence to the degree of accuracy shown,which is amply sufficient in most practical cases, the aerial can

be re]>rcsentcd by its static inductance —- with its static capacity Cuo

in series, and the frequency of oscillation with a loading coil Lin the Icad-m can be computed by the ordinary formula applicablelu circuits with lumped constants.

In an article by L. Cohen,6 which has been copied in severalother publications, it was stated that the use of the simple wavelength formula would lead to very large errors when appliedto the antenna with distributed constants. The large errorsfound by Cohen are due to his having used the value Lo for the

inductance of the aerial, instead of -—> in applying the simpleo

formula.

IV. THK INIH'CTANI E COIL

The transmission line theory can also he applied to thetreatment of the effects of distributed capacity in inductancecoils. In Figure 7 la) is represented a -single layer solenoidconnected to a variable condenser ('. A and /? are the terminalsof the coil, D the middle, and the condensers drawn in dottedlines are supposed to represent the capacities between the dif-ferent parts of the coil. In Figure 7 ili.i the same coil is repre-sented as a line with uniformly distributed inductance andcapacity. These assumptions art- admittedly rough, but aresomewhat justified by the known similarity of the oscillations inlong solenoids to those in a simple antenna.

6 Svc foot-note •!.

,-'

Finnic 7—Inductance Coil Represented as a Line with UniformDistribution of Inductance and Capacity

1. REACTANCE OF THE COIL

Using the same notation as before, an expression for thereactance of the coil, regarded from the terminals AB(x = 0),will be determined considering the line as closed at the far endD{.t = l). Equations (3) and (4) will again be applied, takingaccount of the new terminal condition, that i . for ,r = /: r = 0.Hence

A cos (o \ / C i L\ I = —B sin i<> \/C'i L\ I

and for x =0

v0 = A cos (o I = — B Ian m y/Ci L\ I cos w t

io= - sin <ot

which gives for the reactance of the coil regarded from theterminals .4 B,

or

X' = -^

A"

\ '•,/-;'

v l\. L,, ;20)

2. NATURAL FUKQCKKCJES OF OSCILLATION

At low frequencies, the reactance of the coil is very smalland positive, but increases with increasing frwjucncy and becomes

infinite when <M V ('„/-„= ^- This represents the lowest fre-quency of natural oscillation of the coil when the terminals areopen. Above this frequency the reactance is highly negative,approaching zero at the frequency cu v COL, = ~. In this rangeof frequencies, the coil behaves as a condenser and would require

an inductance across the terminals to form a resonant circuit.At the frequency u>y/CaLo = - the coil will oscillate with itsterminals short-circuited. As the frequency is still further in-creased the reactance again becomes increasingly positive.

(a) CONDENSER ACROSS THE TERMINALS. The natural fre-quencies of oscillation of the coil when connected to a condenserC arc given by the condition that the total reactance of thecircuit shall be zero.

X'+X^O

From this we have<rr j

. I — Ian t» %/(.'„ Lu - —7,

or CO'<"> /C7L^ = £ .U C ^ '

This expression is the same as (8) obtained in the case of theCloaded antenna, excepting that — occurs on the right-hand side

instead of —> and shows that the frequency is decreased and

wave length increased by increasing the capacity across the coilin a manner entirely similar to the decrease in frequency pro-duced by inserting loading coils in the antenna lead-in.

3. EQUIVALENT CIRCUT WITH LUMPED CONSTANTS

It is of interest to investigate the effective values of induc-tance and capacity of the coil at very low frequencies. Expand-ing the tangent in equation (20) into a scries we find

.j

and neglecting higher power terms this may be written

, - /

This is the reactance of an inductance L» in parallel with aC •

capacity —' which shows that at low frequencies the coil may beo

r e g a r d e d a s a n i n d u c t a n c e L u w i t h a c a p a c i t y •— a c r o s s t h e

terminals and. therefore, in parallel with the external condenser315

FURTHER DISCUSSION* ON

"KI.K1THICAL OSCILLATIONS IN ANTENNAS ANDINDUCTION COILS" BY JOHN M. MIl.LKH

BY

JOHN IT. MCIHF.CUOKT

1 was isla<l to sec an article by Dr. Miller on the subject ofOscillations in coils and antennas because of my own interestin the subject, and also because, of the able manner in which Dr.Miller handles material of this kind. The paper is well worthStudying.

I was somewhat startled, however, to find out from theauthor that. I was in error in some of the material presented inmy paper in the PROCEEDINGS OF THE IXSTITUTK OK RADIO

ENC.INKERS for December. 1917, especially as I had at the timeI wrote my paper thought along similar lines as does Dr. Millerin his treatment of the subject: this is shown by my treatmentof ihe antenna resistance.

A> to what the effective inductance and rapacity nl an an-tenna arc when it is oscillating in its fundamental mode is, itseems to me, a matter of viewpoint. Dr. Miller concede.- thatmy treatment leads to correct predictions of the behavior oftlii' antenna and I concede the same to him: it is a question.therefore, as to which treatment, is the more logical.

From the author's deductions we must conclude that atqtwirirr wave length oscillations

Tin- value ot L really comes from a consideration ol 111 «.•inaiiiniic energy in the anlenna keeping the current in theartificial antenna the same a> the maximum value i< had in '-!.••actual antenna , and then selecting the capacity oi suitable valueto jrive the artificial antemia the same natural prriml us theactual an tenna . This method i,f proccilurc will, us the au thorstates, itivr :in artificial antenna having (he same natural tre-i|iienry. maBiH-tie etterjjy. and electrostatic euerjry. as the aetitalantenna, kei'pinjj the current in the artificial aiiteima the -atneas tlie inaxiinuin i-iinvnt in the actual antenna.

• It. . . \ v . l l . \ i ln IMi i . i r . J i im- Ji;, l'.'l'.i

l l w s u p p o s e lie luul a t t a c k e d t h e p r o b l e m from the v i e w p o i n t

of eirclrost.-itic energy instead of electromagnetic energy, andlluit lie had obtained tlie constants of his artificial intenna tosatisfy these conditions (which are just as fundamental andreasonable as those he did satisfy); same natural frequency,same magnetic; energy, same electrostatic energy and the samevoltage across the condenser of the artificial as the maximumvoltage in the actual antenna. He would then have obtainedt h e rel:i.i.n.iis

Mow <i | i iat ions (3) a n d (4) a i e just as correct as are (, I) aiui

;2) and moreove r the artificial a n t e n n a luiilt wi th the c o n s t a n t s

given in (31 a n d (4) would duplicate the ac tua l a n t e n n a jus t as

well as tlii- imc built accord ing In the retail ions given ill ( 1) a n d (2) .

1 h:u! these two possibil i t ies j u niind when wri t ing in m y

original ar t icle " a s the e lec t ros ta t i e energy is a function of t h e

potent ia l cu rve a n d the magne t i c energy is the same funct ion

of the current cu rve , a n d h o t h these curves have the same s h a p e .

M is logical, and so on." Needless to say. I -till consider it

logical, ii.ui! af ter r ead ing this discussion I am sure Dr . Mil ler

will see i,,y leasons for so t h ink ing .

When applying t he t heo ry of uniform lines to coils 1 t h ink

a vety u.rjie er ror is m a d e at once, which v i t i a tes very largely

any conclusions reached. T h e L and ( ' of the coil, per c e n t i m e t e r

lengf,!,. :,:i- by no means uniform, a neeessury condi t ion in the

llictirv i.i uniform hues : in :i limit solenoid tiie /. per cent ime te r

in-:,i t in f i ' i i t er of I h e co i l is n e a r l y t w i c e re* m e a t ; i - t h e L | iei

e e n t i m e l e ! : i ! I h e e n d s . :i facl w i n c h f o l l o w s f r o m e l e m e n t a r y

theory and one which has been verified in our laboratory byI 1 1 1 • : i s - 1 1 > • i i i • _ • i h e w a v e l e n g t h i > l a h i g h I r e t | i i e i i e y w a v e t r u v e l i n ^

a l o n g s u i li a - o l e n o i d . I ' IM' w a v e l e n g t h is imi t ' l i - l i o r t e i ' i n t h e

c e n l e r ol t h e co i l t h a n i t is n e a i t h e e n d s . W h a t - t h e c a p a c i t y

p e r c e n t i i M - i e r o f a s o l e n o i d i - h a s n e v e r b e e n m e a s u r e d . I t h i n k ,

b u t it is, l i ' n i o i i b t e i l l y a r e a t e r i n t h e c e n t e r o f t h e co i l t h a n n e a r

I In- endsTlii" conclus ions he l e a r l i e - trolii his e<(ii:iiu>!: '22 '• thai even

ai its n a t u r a l f r e q u e n c y t h e / . of I he coil m a y be r e g a r d e d :i>

c t | ua l iii !!;!• low f re( | i ienev v a l u e of L is v a l u a b l e in so far a»

II eii;ilil<-» ••;[{• b e t t e r to p red ic t I he b e h a v i o r uf (he coil, but !!

should be- krpt in mind that really the value t>f L of the uotl,when defined as does the author in the first part of his paper interms of magnetic energy and maximum current, in the coil.at the high frequency, is very milch le-ss than it. is at the lowfrequency.

One point mi which I differ very materially with the authoris the question of the reactance of a coil and condenser, con-nected in parallel, and excited by a frequency the same as thenatural frequency of the circuit. The author gives the react-ance as infinity at this frequency, whereas it is actually zeroWhen the impressed frequency is slightly higher than resonanifrequency there is a high capaeitive reaction and at a frequencyslightly lower than resonant frequency there is a high inductivereaction, but at the resonant fiequency the reactance of the cir-cuit is zero. The resistance of the circuit becomes infinite aithis frequency, if the coil and condenser have no resistance,but for any value of coil resistance, tin- reactance of the com-bination is zero :it resonant frequency.

TESLA'S LONGITUDINAL ELECTRICITYA Laboratory Demonstration withEric Dollard & Peter Lindemann.

If you've ever wondered if there are more uses to a TeslaCoil than just making big sparks then this video is definitelyfor you. Borderland Labs presents a series of experiments basedon actual Tesla patents providing the researcher with insightsinto the reality of Tesla's theories of electricity.

You will see physical experiments with Tesla's concepts,some done for the first time, on The One-Wire ElectricalTransmission System, The Wireless Power Transmission System andthe Transmission of Direct Current Through Space.

You will see a novel form of radiant electric light whichattracts material objects but produces a repelling pressure on ahuman hand! This light has the characteristics of sunlight andopens research into true full spectrum incandescent lighting.

You will see DC broadcast through space in the form of adark discharge from a plasma column transmitter picked up by asimilar receiver. You will see a capacitor charged through spacewith DC from a lightbulb utilizing Tesla Currents.

You will see a longitudinal shortwave broadcast fromBorderland Labs to a nearby beach, using the Pacific Ocean as anantenna! This heralds the beginning of the end of using largeradio towers for shortwave broadcasting. This experiment is donefor the first time on this video so you can learn as we did.This is simply another day at the lab!

These experiments are done so that they canany competent researcher, no secrets here!equipment from the surplus yards.

be reproduced byEric built his

Today's conceptions of a Tesla Coil provide the researcherwith little practical material. Eric Dollard reintroduces the"pancake" Tesla Coils in a series of experiments taken directlyfrom Tesla's work. No modern interpretations needed, we went tothe source and the equipment works! Construction details aregiven so you can do it yourself!

If you want to do some practical work with Tesla's theoriesthen this video will give you a good start. IE you are a Teslafan then you will be happy to see Tesla's work and conceptionsvindicated with physical experiments. Either way you will, findthat this is some of the most incredible Tesla material nowavailable to the public!!

60 mins, color, VHS, ISBN 0-945685-89-0.

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