Inductors and Loading Coil Current (Mobile and Coil Loaded Antennas)

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Related pages:

Mobile
antenna FS
comparisons   
Loading
Inductors    
Inductor
Spice
Model         

W7EL’s
Measurements and
comments   
Constructing
an RF Current Meter

Time
Delay Through Coil

How Does
an Inductor or
Loading Coil
Work? 

Much of the data
below also applies
to inductors in
equipment, such as
tank circuits.

The most common
questions are:

What
does the coil do? 
A normal physically
small (physically small compared to antenna length or wavelength) loading coil
or loading inductor does not replace a missing fraction of a wavelength. A
physically small loading coil simply inserts
a series inductive
reactance that
cancels capacitive
antenna reactance.
When a 150-ohm
reactance inductor
is inserted in
series with a 150-ohm capacitive load
(like an antenna) reactances cancel. Only the resistive
parts
remain.  

What
determines current
distribution in a
loading coil? 
Current distribution is determined by stray capacitance to
the outside world
and the impedance
terminating the loading coil. The current in
any inductor would
be equal at each end
except for
displacement
currents. Displacement
currents are
“imaginary
currents” that
flow through a
capacitance. A
changing electric
field is
tied to these
currents.

How
much level difference is
there in loading
coil current
entering the coil
and loading coil
current exiting the
far end?
If the antenna
beyond the coil has
low self-impedance
compared to the
impedance of stray capacitances
that shunt current
from the coil to
“ground”,
currents at each end
of the coil will be
essentially equal.
The current taper effect is not
caused by the
“missing
antenna length”
the coil replaces.
Current taper is
determined by the
ratio of termination
impedance to stray
capacitance from
parts of the
coil to
surroundings. If the
portion of antenna
above or beyond the
loading coil is long
or has a large
physical area
compared to the
physical size of the
coil, coil current
will be essentially
equal throughout the
coil and at each
end. In tank
circuits, inductor
current is equal at
each end unless the
tank capacitors have
a very low value
compared to the tank
inductor’s stray
capacitance to the
chassis. This is one
reason why we do not
want to mount an
inductor close to
sheet metal.

What
does significant
current taper in the
loading or tank coil
indicate?
Large differences in
end
currents on an
inductor are strong
indicators of poor
antenna or tank
circuit layout or design. An
example would be a
situation where a
loading coil or tank
coil has high stray
capacitance to other
areas of the system
(like the
groundplane or
surrounding objects)
compared to
capacitive reactance
of the system at the
high impedance ends
of the inductor.
Significant current
taper indicates poor
inductor, layout, or
antenna construction
or
design.     

click
to view typical
installation
measurements 

The Difference
Between a Loading
Coil and a Normal
Inductor

There really
isn’t any difference
between a
loading  coil
and a conventional
inductor or coil
used in other
systems, except the
impedances and
surroundings are
different. The
inductor or loading coil
behaves the same way
whether the load is
a radiating antenna
or an electronic
circuit. An inductor
is an inductor, it
doesn’t change characteristics
depending on
end-use, although
different designs
can work better with
different reactance
and circuit requirements.

Mobile loading
coils or loading
coils for short
antennas often have
very high reactance.
They often have
extremely low capacitance at
one
end, and this makes
stray capacitance
throughout the
inductor a concern.

Stray capacitance
from turn-to-turn
increases
circulating
currents.
Turn-to-turn
capacitance
increases effective
inductance and
effective
resistance, yet at
the same time
unnecessary stray
capacitance reduces
system bandwidth
and (contradictory
as this sounds) also
reduces
effective Q.

Stray capacitance
to the outside world
causes the coil to
behave like an
L-network, and
transform impedances
instead of providing
a pure series
reactance. 
This is why the
optimum form factor
of a coil becomes
longer compared to
the diameter with
any inductor having
very high
reactance. This
is also why
inductors (RF
chokes), at high
enough frequencies,
behave like
back-to-back L
networks. We call this
effect “series
resonance” when
discussing power
amplifier plate chokes.

Inductors with
low inductive reactance are
much less critical
of internal and
external stray
capacitances.
Optimum form-factor
in a low reactance
inductor leans
towards a short coil
with the diameter
nearly equaling
length. In tank
circuits, or with loading
coils used with
longer antennas or
with capacitance
hats, the optimum
inductor shape
becomes shorter
and larger in
diameter. In a short
mobile antenna or
very high impedance
tank system or
circuit, optimum
inductor form factor
becomes longer when
compared to
diameter. Long high
inductance coils are
generally good,
compact large
diameter inductors
often work better in
low inductance
ranges. 

Most optimized-form
air core
inductors fall
between 1:1 and 4:1
length to diameter
ratios, the exact
value depending on
inductor and
terminating
reactances. A coil
behaves the same way
regardless if used as a
loading coil or used
as a tank
inductor.   

Common myths
about inductor
behavior:

One common
myth is loading coil
current is reduced
by standing waves or
by the fraction of
“electrical
degrees” the
inductor
“replaces”
as it passes through
the length of wire
in the coil. There
are two reasons
cited for this. One
idea is the current
is reduced because
the loading coil
replaces a certain
amount of
“electrical
degrees” of
antenna area,
substituting or
replacing
the normal current taper
seen in
an unterminated antenna. The
other idea is that
series loss
resistances cause a
current reduction.

We often find
inexperienced
builders of 5/8th wl
antennas think the
“loading
coil” needs to
contain 1/8th
wavelength of wire
in order to make the
5/8th wave antenna a
“3/4wl
resonant antenna”.
They think,  through wire
length alone, the
wire creates
a low feed impedance
by making the
antenna
three-quarters of a
wave long
electrically. In
other cases claims
are made one
half-wave of wire
wound on a compact
form causes a
180-degree current
delay, making a
compact coil useful
for phasing in a
collinear array.

The basic flaw is
the above ideas do
not account for what
actually occurs in a
coil. The flawed
viewpoint is current
goes in one end,
winds its way around
through the physical
length of wire in
the coil, and after
a time delay caused
by the copper path
length current
appears at the other
end. There is a
physical mechanism
that prevents what
we might intuitively
think happens from
actually happening.
A coil or loading
inductor has
magnetic mutual
coupling between
turns. The physical
mechanism is the
magnetic field in
the coil! 

What Really
Happens

When current
flows in the
transmitter-end of
the coil, a magnetic
field is created.
This time-varying
magnetic field
causes charges in
the other turns to
instantly move. This
effect ripples
through the length
of the coil at
light-speed, just
over 186,000 miles
per second. As long
as the magnetic flux
coupling is high,
the delay through
the coil is the
speed of light over
the physical length
of the coil. In an
inductor with good
flux coupling from
end-to-end, the
electrical time
delay in current
is very close to the
physical length of
the coil expressed
in degrees at the
operating frequency.
Note that this time
delay is NOT the
phase relationship
between voltage and
current, but the
delay time of
current appearing at
each inductor
terminal. More on
this appears later
in this text.

(Another
interesting effect
occurs. The
increasing magnetic
field sets up an
“opposing
voltage” as it
cuts across
conductors. This
opposing voltage,
created as the field
expands, is what
causes the current
to rise slower than
the applied voltage.
If the exciting
voltage is decreased
the field collapses,
and now the voltage
changes polarity and
aids current flow!
If we don’t allow
the current to flow,
the voltage will
rise until it does.
This is what causes
the kick in a relay
coil when we open
the relay coil path,
or the spark in an
ignition when the
points abruptly
open.)       

In an RF system,
the physical size of
the coil actually
does add some
“antenna
effect”. For
example, on 160
meters the
wavelength is about
550 feet. 1.5 feet
is about one
electrical degree. A
skinny one foot tall
coil, with
negligible stray
capacitance, would
have about 0.67
electrical degrees
phase delay of
current between each
terminal. This delay
occurs because to
coil occupies a
physical length of
.67 degrees. Current
at each end would be
almost perfectly
equal, the taper
would be about what
we would expect for
a
fractional-degree-long
coil. 

(In
the real world, all
components have some
stray capacitance
and flux leakage, so
they have a
different amount of
electrical length
and current taper
than the
“negligible
capacitance”
case. In good
coil designs, the
capacitance and
leakage is small and
can be ignored. I’ll
show you
measurements later
to prove this.)

Now let’s look at
an extreme case. If
the entire antenna
is
“coiled”,
like a helically
wound antenna with
no top hat or
stinger, current
would be reduced to
nearly zero at the
open end. This is
because distributed
capacitance over the
length of the
antenna is fairly
high, the shunting
capacitance has a
low impedance
compared to
impedance at the end
of the antenna, and
current is diverted
to ground in the
form of displacement
currents. The significant displacement current distributed
along the coil causes phase delay through the coil, as well as the current taper
along the length. 

Compact
loading coils are
another matter.
In
many cases phase
delay is negligible
or immeasurable by
normal
methods.. providing flux
coupling is nearly
perfect. A good
example would be a
relatively compact
toroid or a compact
nearly-square L/D
ratio loading
inductor. I’ve found
it impossible to
measure the current
taper in a toroid
and very difficult
to measure in a
compact air-core
loading coil. (The
opposite extreme
would be be a
perfectly straight
wire with no folds
or bends or the
helical antenna
described above.)

In the case of
the toroid or
compact coil, the
behavior would be
such that doubling
the turns nearly
perfectly quadruples
inductance. If we
doubled turns and
inductance simply
doubled or increased
at a much faster
rate, we should know
the coil is in a
mode other than a
pure inductor mode.
This is a strong
indicator inductor
operating Q is less
than optimum, and
the inductor might
behave less than
ideally in critical
applications. 

As a matter of
fact, observing
inductance change
while adding turns
can be an excellent
test for flaws or
shortfalls in system
design. A linear
increase in
inductance when
adding conductor
length indicates
design
problems. 

A perfect
impedance squaring
effect indicates
minimal electrical
phase-delay, or
“antenna
length” of an
inductor. Impedance
squaring as turns
are doubled
indicates the
undesired inductor
stray capacitance
has a high reactance
compared to the
antenna system
beyond the loading
coil. Of course
there can be
exceptions, but it
is a good general
rule that large
current taper
indicates the
loading system is
much less efficient
than necessary.

Making a Delay
Line

It’s certainly
possible to make
a delay line from a
coil without
opposing fields
caused by a second
parallel conductor
(a transmission
line), but doing so
requires stray
capacitive reactance
to be significant
compared to the
value of distributed
inductance in the
coil. It also requires significant flux leakage. This would
occur in a very long helice, a very large
diameter helice or
loop, or an inductor
near or wound around
a large metal
counterpoise or
ground plane.

It’s important to
remember unless a
coil is
“stretched
out” or
“expanded”
a great deal, the
phase delay will not
even be close to the
physical conductor
length. (The
exception could be
if you had so much
capacitance the
inductor acted like
a series connected
string of L/C/L
networks as shown
below). 

In any case while
this effect might be
good in a collinear
antenna or plate
choke (assuming you
do it right) it is a
BAD effect in a
short loaded
antenna!

Inductor E/I
Phase shift

An inductor
delays the flow of
current in
relationship to
applied voltages as
the magnetic field
inside the coil
expands. Voltage
increases before
current starts to
flow. This phase
relationship between
voltage and current
is often confused
with time-delay
phase in the
inductor. Say we
have this simple
circuit:

Current and
voltage at V1 will
be out-of-phase by
the effect of L1
“charging”
with magnetic flux.
Current appears
AFTER voltage rises,
and falls after
voltage falls. 
Current in R1,
however, is exactly
in phase with
voltage across R1.
That’s because the
voltage across 
R1 is always E=I*R.

Every component
must follow the Laws
or electrical rules
established for that
component.

The current in R1
is delayed from
VOLTAGE rise in V1
by the voltage to
current phase delay
of L1. This does
result in a time
delay in
relationship to
voltage rise at V1,
but there is NO
current time delay
through L1! V1, L1,
and R1 all have the
same peak current at
the same time!!!

The notion that
antenna loading coil
delay current by the
same time as they
delay response to
increased voltage is
obviously nonsense.

Here is a
graph  of phase
delays in the above
system:

Current in the
load, generator, and
inductor all exactly
track in the same
relationship from dc
up. There is no
“phase
delay”. The
generator voltage is
a straight line
different than
current, and this
indicates the
generator sees a
“reactive
load”.  

This is an ideal model. It does not include shunt capacitance, or flux
leakage.

Phase Shift of
Current

What happens to
current passing
through an inductor with very tight inter-turn flux coupling?

Magnetic flux
links the ends of an
inductor. Current
does not enter one
end of the inductor,
wind through the
turns, and appear
with a time delay
related to conductor
length on the other
terminal. The
magnetic field
travels through the
coil at light speed,
and when the very
first turn is
magnetized every
turn linked by the
flux immediately has
current induced. The
delay is related to
the speed of light
and physical
distance from the
starting turn to the
ending turn. (This
assumes negligible
stray capacitance to
the outside world
compared to load
impedance.)

Here’s a SPICE
model of an inductor
(this would represent perfect coupling) showing current at
three points
indicated by A, B,
and C:

You can see A, B,
and C have the same
current and same
phase. This would be
true for forward
waves as well as
reflected waves. Of
course this is an
inductor with
perfect mutual
coupling and no
displacement
current. A real
inductor of
reasonable form
factor would have
some small phase
delay. 

Phase Shift Of
Voltage

Where does the
phase delay come in?
The voltage at
different parts of
the system is
delayed. Here are
voltage waveforms
with respect to
ground:

Spice allows us
to show phase
difference between
multiple points. The
graph to the left shows
phase difference at
three points.

The Misplaced
Notion 

Proponents of the
idea that coils
replace
“antenna
length” and equal the missing antenna length in degrees are unable to
define a set of
rules or logically demonstrate why a
current reduction
and “electrical-degree”
phase delay directly related
to the antenna area
“replaced”
occurs in a
two-terminal
component. While a
long inductor with
poor flux linkage
from end-to-end, or
an inductor with low
values of stray
capacitive reactance
to a groundplane
compared to series
impedance, can cause
SOME current
inequalities and phase delays, the amount is normally immeasurable with normal
thermal current meters when the inductor has good form
factor and
reasonable
termination
impedance above the
coil. The amount of
current taper
actually rivals the
disturbance of the
system by adding the
measurement device,
unless we construct
the measurement
device very
carefully.

Both
W7EL and myself made
independent
measurements of
current in small
loaded antennas.
These measurements
demonstrate the
“missing
electrical
degrees” in an
antenna has nothing
to do with current
distribution in the
coil. Some
people have actually
incorrectly reported
W7EL’s data! Here’s
what he had to post
on rec.radio.amateur.antenna
to
correct
misrepresented
claims. 

The Need for a
Measurement 

An
article long ago on E-ham
claimed measurements
proved a new concept
about loading coil
current.  The
E-ham article put
forth an idea that
current disappears
as it moves through
a loading inductor without a mechanism
like displacement
currents providing a
path. This claim
conflicts with
established
component behavior,
so it would indeed
be fascinating if it
were true! One
of the claims
supporting the idea
that coils in
antenna work
differently than
coils in circuits
was that a
non-radiating toroid
loading inductor
showed a current
taper when used in
an antenna.

I
recently constructed
a calibrated current
meter
that slips over whip
antennas and masts,
and is for all
practical purposes
totally immune to
variations in
voltage in the
system. It also is
mostly plastic, and
has minimal effect
on stray capacitance
of the antenna. The
resonant frequency
and currents are not
significantly
perturbed by
measurements with
this meter. When I
added a similar
meter used in the
other tests,
resonant frequency
shifted
significantly! This
is a sure sign the
meter’s capacitance
or inductance is
affecting the
system.

In
late December 2003
and early January
2004, I made
additional
measurements of
loading inductor
currents. The
results clearly
agree with the
analysis that had
been presented on
this page since
early 2003. Without
displacement
currents, currents
into and out of a
loading inductor
are equal.
That is a
hard rule, it agrees
with theories
defined by people
much smarter than
me, and I believe it
is unbendable unless
the works of
Faraday, Maxwell,
Ohm, and Kirchhoff
were
incorrect. 

A
sample of
measurements above
and below the
loading coil with
various antenna
above the coil
(current as percent
of reference)
follow: 

The
most revealing thing
was how noticeably
small changes in
stray capacitance
near the middle and
top of the loading
coil affect current
distribution. It was
quite evident
hanging a large
meter on each end of
the coil would
greatly perturb the
system.

Clearly
we do NOT want:

• A
  large hat just
  above a large
  coil
• A
  long large coil
  and a short whip
• A
  coil near large
  sheetmetal

More
data along with
photographs will
appear on a new page
over the next month
or so. Until then, I
can assure everyone
the conventional
theories presented
below are accurate,
and the theory that
“electrical
length” the
coil
“replaces”
is incorrect.
Loading coils indeed
behave like any
other inductor in
the world. 

Independent
measurements by a
reliable engineer
have agreed with my
measurements above.
Anyone doubting my
data need only read
the following e-mail
from W7EL.   

The Incorrect
Assumption

Another commonly
misconception is,
since voltage
increases at the far
end of the loading
coil, current must
logically decrease.
After all, we have a
fixed amount of
power and voltage
has increased. The
assumption is: 

1.) We multiply
voltage times
current to get
power.

2.) If voltage
increases current
must decrease. 

Unfortunately,
this is not
correct in reactive
systems! Simple P
(power) = I
(current) times E
(voltage) only works
when the system is
non-reactive. This
condition only
occurs at resonance,
and only below
the
loading coil at the
antenna
feedpoint! 

In a reactive
system, like in a
mobile whip above a
loading coil,
voltage and current
are no longer in
phase. As a matter
of fact, voltage and
current can closely
approach being 90
degrees out-of-phase
when the whip is
electrically very
short. Since the
antenna area above
the loading coil is
highly reactive
(voltage is not in
phase with current),
we can not multiply
voltage times
current without
considering phase
differences. 

You may have
heard the term
“reactive
power” or VAR
(volt-amperes-reactive).
Reactive power is
voltage times
current without
consideration of
phase angle. We can
have kilowatts of
VAR power with only
a low power
transmitter, and
that is what we
actually have in the
reactive part of the
small
antenna.   

Coil Q and
Changes in
Efficiency 

Current taper or
reduction has been
cited as a reason
coil
“Q” 
has little effect on
signal level in
mobile systems.
Speculation is only
the first few turns
of the loading coil
carry significant
current because the
coil
“leaks”
magnetic fields and
radiates, and this
is why the coil Q
has little
effect. 

Another idea
proposes the loading
coil “makes
up” a certain
missing part of the
antenna. It goes on
to conclude the
loading coil can be
accounted for in
“electrical
degrees”,
making up the
“missing
difference” in
antenna degrees.
This isn’t true
either. The inductor
doesn’t know where
it is and suddenly
change from
“x” ohms
reactance to
electrical degrees!
It responds to AC
currents and
voltages as any
inductor in any
circuit does. It
doesn’t suddenly
change measurement
units.

As an example of
this, try to define
a 45-degree
electrical length
inductor at 1.8 MHz.
That would mean it
is a capacitor at
3.61MHz, where it is
over 90-degrees
long!  How many
turns at what length
and diameter is a
45-degree
inductor?? 
Where is a formula
that allows
converting a given
size inductor to
electrical degrees?
This shows how
useless and
meaningless that
definition
is!      

The inductor adds
a certain amount of
series reactance,
that’s all. A 300uH
inductor is not
20-degrees long, nor
is it 80-degrees
long, so far as
radiation goes
unless it is really
that long physically. It
is a certain number
of ohms reactance at
a certain frequency,
or a certain number
of units called
Henries. It is not
“electrical
degrees” that
it adds, it is a
non-dissipative
reactance (in
combination with a
loss resistance
because of finite
quality) at a
certain frequency!

A loading
inductor can
“insert” a
large amount of
phase shift, but the
phase shift is
between voltage and
current. The only
exception to this
would be if the
inductor had
considerable
distributed shunt
capacitance to the
outside world, and
acted like a string
of series inductors
(with the antenna)
and shunt capacitors
(shunting to the
ground system). In
that case we could
expect coil Q to be
extremely low, since
it would be the
electrical
equivalent of a
lossy transmission
line. That’s either
an awful loading
coil, or it is a
less-efficient
helical loaded
antenna!

The Correct
View  

Another group of
people don’t argue
against established
and proven circuit
theory. They
understand charges
flowing into one end
of the loading coil
must have someplace
to branch off (a
virtual third
terminal), or they
must flow out the
other end. Without
that additional
“virtual”
path, charges
flowing into the
coil would always
equal charges
flowing out. This is
true regardless of
radiation, losses,
or induction fields.

This makes
perfect sense when
we think of any dc
circuit, antenna, or
RF system.
Electrical rules are
satisfied, the
system behaves as it
does in the real
world. 

There is very
little change in
current, unless the
coil is physically
very long compared
to the rest of the
antenna above the
coil or unless the
coil is laid right
against
“grounded”
conductors and the
whip above the coil
is very short. This
fits perfectly with
helical verticals,
where the coil is
“stretched
out” over the
length of the
antenna. 

It also agrees
with base loaded
antennas, which have
nearly as much
current into the
antenna above the
coil as at the
feedpoint. It agrees
with center loaded
antennas, where
current below the
coil is essentially
uniform and the whip
above has triangular
distribution.  

Current can
be different in
various areas of an
inductor, but only
if shunting
capacitances
(impedances) to the
outside world are
significant compared
to load capacitance
(impedance). Another
condition where
current can vary
substantially is
with operation near
the condition of
self-resonance in
what is normally
considered or
defined as a
“series-resonant”
mode. This
would be a very poor
and inefficient
loading inductor,
such as when a
160-meter antenna is
used at a secondary
resonant frequency
in upper HF.

Circuit Model of
a Mobile Antenna

This model
represents what might be
a typical mobile
antenna
installation if the coil is compact and has very good flux coupling through the
length of the coil.

1. Rgnd ground
   resistance of
   vehicle
   normalized to
   feedpoint
2. V1 coaxial
   feed line
3. C2 base
   capacitance
4. Rrbase Radiation
   resistance
   of the base area
   of the antenna
5. L1 loading
   coil
6. Rcoil coil
   equivalent
   series loss
   resistance
7. C3 coil shunt
   C to ground
8. Rr top area radiation
   resistance
9. Cant
   equivalent
   antenna
   capacitance
   above coil area

My 160 Mobile
Antenna

I’ve worked all
continents except
Africa while
160-meter mobile. I
have CW contacts at
over 10,000 miles,
and SSB as far as
Europe (4000 miles).
My mobile antenna
consists of an
eight- foot antenna
with a six-foot hat
(made from surplus
Ford or Chrysler car
antennas) at the
top. The loading
coil is at 5 feet.

This antenna has
been on the truck
for thousands of
miles, without
mechanical failure.
It is mounted at the
upper left corner of
the truck bed, about
one foot back from
the cab. 

The following is
a model of the
current antenna
system on my Ford
F-250 HD long bed
super cab truck:

The base
impedance in the
model is:

Frequency = 1.854
MHz.
Source 1 Voltage =
24 V. at 2.35 deg.
Current = 1 A. at
0.0 deg.
Impedance = 23.98 +
J 0.9853 ohms
Power = 23.98 watts
SWR (50 ohm system)
= 2.087

Actual
measurement at my
Johnstonville, GA
farm in open flat
pastures on August
17 at 8AM. Wet
soil  25.8 ohms
0j base impedance,
pretty close
agreement to EZNEC
model and earlier
data! (I
did have to adjust
the model for very
low ground
conductivity,
otherwise the
resistance was far
too low. It’s my
belief that NEC-2
underestimates
ground losses in
small radial or
counterpoise systems
that are close to
earth.) Earlier text
shows a base
resistance of 28
ohms, that
was dry soil with a
slightly different
loading coil and
antenna.  

The modeled
current distribution
for 1-ampere applied
at the base (in
1-foot intervals)
is:

 
1ft=
1.0031                      

2 ft= 1.0091

3ft= 1.0178

4ft= 1.0318

<Coil>

5ft= 1.0175

6ft= .97512

7ft= .92984

8ft = .89522

Measuring the
current into and out
of the loading coil
with a small
thermocouple RF
meter, I detect no
difference This is
in close agreement
with the
model.  

The efficiency of
this antenna knowing
coil Q, radiation
resistance, and base
resistance
calculates just
under 1 percent. The
model indicates
about 1/3 percent
efficiency. This is
reasonably
close.  

Removing the hat
(in the model only)
shows the following
changes:

1ft = 1.0043
2ft = 1.0133
3 ft= 1.0279
4 ft= 1.0566

<coil>

5 ft= .95508
6 ft= .72232
7 ft= .27813 
8 ft = open
  

I haven’t tested
the above, but with
the same loading
coil loss resistance
the model says
efficiency is now
around 3dB worse.
Removing the hat,
with NO change in
coil resistance,
shows nearly loss
nearly doubles. Of
course the coil
resistance would
increase, because
the loading coil
nearly quadruples in
size. Bandwidth is
less and efficiency
is less, even if I
could maintain the
same coil
resistance.

Examples of
Unequal
Current 

In the above
models, we see that
current into and out
of the one-foot long
coil is about the
same. There is only
about 2%
change in current
even though the coil
occupies 12% of
antenna length in
the
“hat-loaded”
antenna, but in
fairness I couldn’t
resolve that change
with a reasonably
good RF current
meter. 

The model
predicts 10%
change in a non-hat
antenna, but
I never measured
that antenna to
confirm it. 

Clearly there is
no basis to the
claim current is
high only in the
first few turns of
an inductor, or that
current tapers in
relationship to
“electrical
degrees”. The
most accurate way to
state the effect
would be to say:
“When the
loading coil is
short and the
capacitance of the
antenna beyond the
coil is reasonable
(in this case 3000
ohms Xc or less),
there is an
immeasurable
reduction in current
in the coil. When
the required loading
reactance is very
high (in this case
8000 ohms), the
reduction in current
is about what we
would expect for an
equivalent length of
antenna replacing
the
coil.”  

Degrees Vs
Radiation Resistance

This upper four
feet of this antenna
resonates near 24
MHz with the hat. We
can assume it is 90
degrees long at 24
MHz, which would
translate to 6.9
degrees on 1.85 MHz.
Following that same
logic, this would
mean the loading
coil would be about
83 degrees long
electrically. Using
the incorrect logic
proposed by others
where the loading
coil “makes up
the difference in
electrical
degrees”, there
would be almost no
current past the
loading coil.
Obviously this is
not the case, the
loading coil has
very little
“electrical
length”. 
As a matter of fact,
in this case because the inductor is terminated in a fairly low capacitance and
the inductor is compact with good flux linkage
through all the turns, electrical
length is much closer to the
physical length of the coil than the “missing antenna length” in degrees!

This goes back to
radiation theory,
and my favorite
saying: “Five
hundred feet of wire
in a one foot long
tube is still one
foot of
antenna”. Some
CB manufactures sell
antennas to
consumers with the
claim they use 5/8
or 3/4 wavelength of
wire in an
eight-foot
fiberglass whip, so
the antenna has more
gain. Obviously this
is not true. Let’s
not let such silly
claims spread into
amateur radio!

Related topics:

Inductors 

The spice
inductor model shows
one example of how
unequal current is
created. The model
demonstrates a coil
having significant
distributed
capacitance to the
point of current
return in the system
compared to
terminating
impedance of the
coil. In a monopole
this return path
would be to the
groundplane, or
anything closer to
the potential of the
groundplane than the
area above the
loading coil’s
position in the
antenna system.

Another
Practical Antenna
Example

Let’s assume we
have a lossless 15.3
foot long 0.2 inch
diameter conductor
over a perfect
groundplane. Eznec
gives the 1.821 MHz
base impedance as
.3004 -2169j. In
other words, the
antenna “looks
like” .3004
ohms of load
resistance in series
with 40.32pF on
1821kHz. The return
path for current is
through the .3004
ohm resistance and
40.32pF capacitance,
back to the ground
of the antenna (it
is a Marconi
antenna).

Such a
termination (load)
would require a
series inductance of
2169j (189.57µH) to
cancel feedpoint
capacitive
reactance. A typical
190µH inductor
would be rather
large, requiring
somewhere around 53
turns when using a
4″ by 4″
form factor. One
would expect a
physically large
inductor to have
noticeable but very
small displacement
currents to the
groundplane, when
the small stray coil
capacitance is
compared to the
40.32pF termination
capacitance. This
raises two very
important design
guidelines:  

• When
  installing a
  loading coil of
  substantial
  inductance in an
  electrically
  short antenna,
  sheetmetal and
  dielectrics
  should be kept
  away from the
  coil and areas
  of antenna above
  the loading
  coil. This would
  include
  dielectrics on
  or near the
  inductor, since
  the presence of
  dielectrics
  would increase
  undesirable
  capacitance.
• When
  inductive
  reactance
  requirements are
  large, as when
  short thin
  “stingers”
  without hats are
  used above a
  coil, the coil
  form factor
  should lean more
  towards long and
  thin.
  Capacitances
  near the open
  end of the coil
  (high voltage
  end) should be
  minimized. This
  would be true
  even when the
  coil length
  increase results
  in a small
  reduction in
  mutual turns
  coupling, since
  the stray
  capacitance may
  result in a
  larger loss
  penalty 
  than the slight
  increase in
  accumulated
  resistance from
  additional wire
  length.

Efficiency

Efficiency in any
antenna near earth
is almost always
dominated by ground
related losses,
short-height Marconi
antennas are no
exception. The
overall effect of
loading inductor Q
and matching system
losses are
“diluted”
or
“swamped-out”
by ground losses.
Ground losses cause
most systems to have
greatly reduced
sensitivity to
inductor design.

The only
consistently
predictable factor
in efficiency in
fractional
wavelength Marconi
antennas with
limited size ground
systems is radiation
resistance.
Efficiency increases
almost directly in
proportion to
radiation
resistance.

Radiation
Resistance and Power
Radiated

Radiation
resistance is
probably the most
poorly defined term
used with antennas.
The lack of clear
definition creates
errors and
misjudgments when
predicting antenna
performance. If you
wish more detailed
information, this
page contains
information on
radiation
resistance. For the
purposes of this
discussion and to
avoid pitfalls
associated with
using feedpoint
impedance as
radiation
resistance, I’ll use
the same definitions
Jasik, Balmain, and
others have used.
This definition is
based on the IRE
definition of
radiation resistance
being equal to the
net or effective
current causing
radiation squared
divided by the power
radiated as EM
energy, or
Rr=Pr/I^2.

Using this
definition, a folded
dipole has a
radiation resistance
identical to a
conventional dipole
of the same physical
dimensions ( ~70
ohms).

Radiation is
caused by charge
acceleration,
there is no magic.
The only thing
affecting radiation
resistance in a
short vertical
antenna near ground
is current
distribution over
the linear area
occupied by the
radiation portion of
the antenna. The
general rules are:

Radiation
resistance of a
Marconi vertical in
the maximum possible
radiation resistance
case for a given
height (this is the
case where current
is uniform
throughout the
structure) is equal
to 1580*(H/L)^2
where H equals
height and L equals
wavelength and both
are expressed in the
same units. Using
degrees, we see a
10-degree tall
antenna has a
maximum possible
radiation resistance
of 1580*(10/360)^2
or 1580*.000772 =
1.22 ohms. This
would apply even if
the antenna is a
vertical, DDRR,
Fractal, or folded
unipole with
considerable top
loading.

If current is
triangular,
radiation resistance
would decrease by a
factor of four to
0.305 ohms.

Power radiated is
given by I^2*Rr

With 100-watts
applied to a
10-degree tall
antenna, net current
in a lossless
antenna with uniform
current distribution
would be 9.05
amperes. With
triangular
distribution, such
as appears in a
small diameter short
base loaded whip,
current would be
approximately 18.1
amperes. We are in
serious problems if
the inductor reduces
current along its
length, since the
only possible way to
radiate 100 watts
would be to have
somewhere around 9
amperes of effective
current integrated
over the 10-degree
vertical area of
space for the
radiator!    

Ground Losses

All current
flowing (or
displaced)
vertically into the
antenna must equal
current flowing out
of the ground or
counterpoise system.
Even though ground
losses are
distributed losses,
we must normalize
all losses to the
feedpoint in order
to compare systems.
There are cases
where this will not
always occur,
causing us to
falsely assume we
have lower losses
than really
exist. 

In this tutorial
and comparison, I
have normalized
ground losses to the
same point where
radiation resistance
is
considered.   

System Losses

(Measured
data below of actual
antenna given below
was from 1995 data
taken at a different
location near
Atlanta with a
slightly different
loading coil and
antenna. There is a
slight disagreement
with current data. I
left this all in so
you can see the
departure from
measurements and
models using 8 year
old data.) 

Base Loaded
(Triangular Antenna
Current
Distribution) with
no ground loss

Assuming we have
a base-loaded
antenna, and the
operating frequency
has a wavelength of
550 feet (around the
160-meter band), a
15.3 foot vertical
would fit the above
10-degree value.
Interestingly enough
when we compare
Eznec to formulas
available in older
(1950 vintage)
engineering
textbooks, we find
radiation resistance
predicted by Eznec
is .3003 ohms while
the triangular
current estimate for
the same height
radiator is .305
ohms! This is an
amazing degree of
agreement,
illustrating what we
could do before
modeling programs
became available.
(With perfect top
loading, both Eznec
and longhand
calculations show
approximately 1.2
ohms of radiation
resistance.)

Assuming our 15.3
foot tall
(10-degree)
base-loaded antenna
uses a coil Q of
200, the coil has
10.845 ohms of ESR.
Total resistance
with a perfect
ground would be
10.85+.3= 11.15
ohms. Current into
this system with 100
watts applied would
be around 3 amperes,
resulting in ~2.7
watts radiated and
~97.3 watts lost as
heat in the
inductor.

Doubling coil Q
(400) would provide
5.73 ohms of base
resistance with 4.18
amperes. Power
radiated would be
5.2 watts, power
lost as heat would
be 94.8 watts.
Efficiency does not
quite double,
changing from 2.7 to
5.2%. This results
in a 2.8dB change in
signal
level.    

Top Loaded (with
no ground loss)

If we added a
four-wire hat with
15-foot wires,
current would no
longer be
triangular. While we
wouldn’t quite reach
the optimum uniform
distribution,
current at the top
would be about 78%
of current at the
antenna base.
Feedpoint impedance
would become 0.97
-551j, and the
antenna would look
like 0.97 ohms in
series with 159pF.

Using a coil Q of
200, we would now
have 2.76 ohms of
inductor loss.
Current becomes 5.18
amperes. Radiated
power is 26 watts,
while power lost as
heat becomes 74
watts. Even in the
perfect ground case,
the change in
efficiency caused by
top loading is
large. Top loading
(with only the hat)
results in 9.8 dB
change in signal
level when compared
to the base loaded
case when coil Q
remains 200.
Efficiency is 26%.
The coil remains
at  ground
level for easy
matching and
frequency change.

In this case
current at each
terminal of the
loading coil would
be essentially the
same regardless of
poor coil mounting
techniques. In order
to have significant
current taper in the
coil or in the
bottom of the mast,
shunt capacitance
would have to be a
significant compared
to 160pF. The
antenna’s high input
capacitance relaxes
inductor and antenna
mounting electrical
requirements.

Base Loaded
(high ground loss)

My F-250HD Super
Cab pickup truck,
when parked over
open medium quality
pasture land, has a
ground resistance of
about 20 ohms
(normalized to the
feedpoint) on 160
meters. Applying
this ground loss to
the base loaded
antenna, the system
has a feedpoint
resistance of
20+.3=20.3 ohms.
(This is reasonably
close to actual
feedpoint
resistances measured
with a similar
operating antenna.)
Adding coil losses,
the system has
20.3+10.85=31.15
ohms. (NOTE:
Current coil is ~8
ohms ESR, 10.85 ohms
is from ~8 year old
data) Current is
sqrt (100/31.15) or
1.79 amperes.

This results in
.96 watts radiated,
and 99.04 watts lost
as heat. Efficiency
is now around .96%.

Substitution of a
coil with a Q of 400
results in 25.7 ohms
feed resistance, or
1.97 amperes antenna
current at 100
watts. In this case
efficiency is now
1.16% for 1.16 watts
radiated. The change
caused by doubling
coil Q with high
system ground losses
is about 0.8dB,
compared to almost
3dB in the perfect
ground case! With a
poor ground (in this
case typical of a
very large vehicle),
a large change in
coil Q produces
little change in
system efficiency.

Another Top
Loaded (high ground
loss) System Example
(made prior to the
EZNEC model above)

Using a large hat
isn’t practical in a
moving mobile,
although it could
apply to fixed
stations suffering
with poor ground
systems. When the
hat is smaller, such
as a mobile
requires, the
loading inductor can
be moved higher in
the system. Such a
move would produce
uniform current
below the loading
coil, with a current
shape above the coil
dictated by the
construction of the
upper portion of the
antenna. My own
mobile uses a
six-foot diameter
hat manufactured
from stainless steel
automobile antennas
arranged in a spoke.
I have no problems
with wind or
occasional
obstructions. While
unsightly, a modest
hat is workable.

In order to keep
the systems
comparable I’ll use
the same radiation
resistance provided
by a large hat, but
intentionally add
high ground loss as
a lumped resistance.
This model ignores
field losses near
the antenna.

In this case we
have 0.97 -551j as
the inductor
termination
presented by the
antenna. With ground
losses normalized at
20 ohms and an
inductor Q of 200,
we have 20+2.76+.97
= 23.73 ohms of
feedpoint
resistance. Current
is 2.05 amperes, and
power radiated is
4.1 watts. Power
lost is 95.9
watts. 

Efficiency is
4.1%, a 6.3dB
increase over a
base-loaded
triangular current
system with the same
lossy ground. This
system is  8dB
down from the same
“top-loaded”
distribution using a
perfect ground.

When the system
has significant
fixed losses,
increasing radiation
resistance four
times by top loading
provides a similar
dividend in system
efficiency. At the
same time a
substantial increase
in coil Q provides
only minimal change
in field
strength.  

Current Through
Coil

Related pages:

Inductor
spice model

There has been
some speculation
that current is high
only in the first
few turns of a
loading inductor.
Radiation comes
solely from charge
acceleration or
current over spatial
(in line)
distance. 

If any loading
inductor shows
substantial decrease
in current over the
length of the
inductor, it is an
absolute certainty
that the inductor is
poorly designed and
that the system
above the loading
inductor is not
contributing to
system efficiency.
The reason for this
is very simple and
straight forward.
Any two-terminal
component (even
considering wire as
a
“component”
applies) MUST have
equal charges
flowing into and out
of each terminal.
Voltages to other
reference points can
be different, but
for every charge
moving into one
terminal a like
number of charges
MUST move out of the
other terminal.
Radiation, induction
fields, and loss
resistances have no
influence on this
rule.

In order to have
any change in
current, there must
be an additional
path or paths for
charges. This path
can be through
leakage resistances,
or through
fictitious currents
called displacement
currents. Whatever
the path, the total
charge movements
must be
reconcilable. We
simply can not have
current
“disappear”.

The normal path
upsetting
“unbalancing”
current into and out
of each terminal in
an inductor is
provided by
displacement
currents through
electric fields. As
with any system, the
amount of current
flow is proportional
to  potential
difference and
impedance of the
path. In order to
shunt a substantial
current out of an
inductor, the
potential difference
between the ends of
the path has to be
high compared to the
impedance of the
path. The impedance
of the stray path
must also be
reasonably low
compared to the
normal desired path.

Current diversion
is problematic in
very large inductors
operated at (or very
near) internal self
resonance, when the
self resonance is
what we typically
refer to as a
“series-resonant”
condition. This
condition is common
in plate chokes used
in vacuum tube power
amplifiers, where
the system operates
over many octaves of
frequency range.

“Series
resonances”
inside components
occur when
distributed
inductance forms a
pair (or multiples
of  pairs) of
“L”
networks. The large
series inductance
from each end of a
winding reacts with
the small stray
capacitance at the
center, and forms a
very high impedance
transformation L
network. The
electrical potential
at the center of the
system becomes
extremely high, and
even the smallest
amount of
capacitance to
surrounding objects
will carry a
substantial
displacement
current. The large
displacement
currents cause the
terminal impedances
to drop, and allow
considerable current
to concentrate in
small areas of the
component. At the
same time,
considerable voltage
can be present. The
normal result is
arcing or
destruction of the
component, or
failure of the
system depending on
the choke to
operate.   

Series resonance
always occurs at a
frequency higher
than the self parallel
resonant frequency
of the component. A
loading coil
operating under such
conditions would be
required to have
serious design
errors to fall into
this category, since
the end termination
capacitances should
always be
substantially higher
than stray
capacitance
throughout the
component. Failure
to follow this rule
would result in
needless loss and
reduced SWR
bandwidth in an
antenna.     

The speculation
or supposition that
the first few turns
of a loading coil
carry most of the
current is clearly
untrue. In order to
shunt current off,
high series
impedances would
have to exist along
with high stray
shunting capacitance
to areas removed
from the radiator.
Additionally, the
remaining coil area
connected to the top
area of the antenna
above the loading
coil would have to
present a high
impedance to the
area where current
reduction occurs.
This would never be
the case, unless the
top area of the
antenna and loading
coil are not
resonant near the
operating frequency.

A reasonable test
for proper inductor
and system design
would be to remove
the antenna above
the loading coil,
measuring system
resonance. If
resonance does not
change
substantially, the
area above the coil
is not correctly
terminating the
system. First-order
self resonance of
the inductor
(parallel
resonance), when
removed from the
system, should also
be far above the
operating frequency
of the system. If
self-resonance comes
within three or four
times the operating
frequency range, the
loading coil almost
certainly will have
needless performance
shortfalls.

Conclusion

A normally
functioning inductor
has essentially
equal currents
throughout the
inductor, loading
coils are no
exception. Any
current difference
requires “missing current” 
flow through
undesired stray
capacitances (displacement current) or leakage currents.

In a reasonably
well-designed
system, current into
and out of the
loading inductor
should be
substantially equal.
Large differences in
current would
indicate excessive
and problematic
undesired stray
capacitance in the
loading coil or antenna system
design.

Reduced
sensitivity to coil
Q is primarily a
function of
additional losses in
the system, not
reduction of current
through the coil.

Also see Loading Inductors

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has had
visits
since February 11,
2004.