# Inductors

 Loading Inductors   ### Optimizing Inductors

###### While intended mainly for antenna loading coils the text below also applies to other resonant systems, such as amplifier tank circuits. Before doing anything with information in this article or any other article related to loss and efficiency in antennas, please read the radiation resistance article on this site!  Related pages:

Inductor spice model

Mobile and loaded verticals

Optimum

form
(length to diameter and turns spacing)
of any inductor
depends heavily on
the end-use of the
inductor. Current through
and voltage across
an inductor, as well as the operating reactance,
determine optimum physical
attributes.

Current
and operating frequency mainly determines
minimum conductor
size, although turn-to-turn spacing, spacing to surrounding objects, and thermal
characteristics also affect minimum conductor size.

Voltage
across the inductor, as well as voltage from the inductor to surrounding
objects, establishes minimum conductor
spacing and
insulation
requirements.

Environmental conditions
determine some
aspects of construction, including turns spacing, insulation, form type, and
requirements for weatherproofing.

Operating reactance influences both material choice and optimum physical form of
the inductor.

Making the matter
more complex,
a seemingly simple change
inside an inductor often
interacts in very esoteric ways. For
example, if we add
insulation to
weatherproof an
inductor, the insulation will
reduce high frequency Q. Part of
the Q reduction is
from dielectric
losses, and part of
the Q reduction is
from increasing
stray capacitance
across the inductor and stray capacitance to the outside world.
The question is
always if the change
will be noticeable; the answer is
“it depends on
the reactance and
the system the
inductor is used in”
.

Some things are
very
counterintuitive.
For example, we assume narrow bandwidth is a sign of low loss (high efficiency).
unwanted shunt
capacitance across
an inductor, counter intuitively, can
decrease system
bandwidth

while increasing loss!
If we measure Q
externally by
looking at a plot of
3 dB voltage points
as frequency is
varied, increased shunt
capacitance or
turn-to-turn
capacitance will
actually decrease
system bandwidth while
simultaneously
increasing losses in
the inductor. We
cannot always rely on bandwidth
as a measure of
efficiency.

## High Impedance Systems

In higher impedance
systems,
optimum form factor
(length -to-diameter) leans towards a longer
inductor with a smaller
diameter. This is
because a longer
inductor with
smaller diameter has
less stray
capacitance from
end-to-end. A
smaller diameter
and shorter coil can have less
stray capacitance to
the outside world,
since current isn’t
shunted out of the
coil through
displacement
currents.

Even the best insulation materials have a deleterious effect on
component Q when impedances are high.
This is because
insulating materials
increase stray
capacitance. Dielectric constant
can become more
important than dissipation factor in
choosing insulating materials,
but the ideal
dielectric would
have the lowest
dissipation factor
and lowest
dielectric constant.

There is no clear
boundary between
high and low
impedance systems,
but generally high
impedance systems
would include
electrically short
mobile antennas, or
any other system,
where more than one
thousand ohms or so
of inductor
reactance is
required. is a good example of
why high-reactance
should be longer and
narrower than
inductors used in
low-impedance
systems. This
near the bottom of a
43-foot tall
vertical. The top of
the coil directly
bonds to the upper
vertical section
with a jumper wire
(hidden) on the far
side of the plastic
insulator.

Shiny streamer marks on the surface of the plastic show where the
intense electric field has caused corona or “streamers”. This vertical
was operated at a kilowatt. Voltage was so high the edge of the metal washer
produced corona streamers that etched the plastic!

Even when the black plastic was replaced with Teflon, the corona ate into the
Teflon!

The long form
factor,
6:1 (length six times diameter), minimizes
capacitance and
maximizes voltage
rating from
end-to-end of the
loading coil. It prevents arcing across areas of the coil, and makes the
inductor less sensitive to moisture changes.

## Low Impedance Systems

With low impedances,
optimum form factors become more
“square”.
“Square” meaning the
length to diameter
ratio is unity. Optimum
length in low
impedance
applications is short
when
compared to diameter
because stray C has
very little effect. The
resistance from the
external circuit
dominates the system
current when the
impedance of the
inductor is low at
the operating
frequency.
Insulation has very
little effect
because any change
in stray
capacitance, even if
a large percentage
of the air
dielectric
capacitance of the
coil, is very small
compared to the
fixed external
capacitance.

Two cases where
an inductor might be
a low
impedance are
antenna traps and
amplifier tank coils. In
these cases
intentional external
low reactance
capacitances often
shunt the inductor,
and the inductive
reactance is often
hundreds of ohms or
less. The internal
winding turn-to-turn
capacitance, and the
stray capacitance of
the inductor to the
outside world, is
small compared to
the desired or
necessary
external
capacitances. The edge wound
inductor on the left
is mostly suitable
for tank circuits or
systems where there
is considerable
external capacitance
involved, or where
the required
inductive reactance
is low. This edge
wound inductor has a
form factor of 1.3 :
1 (length to
diameter).

As more reactance
is required, the
coil’s optimum form
factor progressively
increases. The air
wound inductor on
the right has a form
factor slightly over
2 : 1.

Optimum turns
spacing is about one
wire diameter.
Although neither of
these inductors meet
that criteria, they
both avoid any
insulation or
dielectric in the
gap between turns or
insulation covering
or coating the
conductor.

Insulation, even
the best insulation,
will decrease
inductor Q.
This does not mean we should never insulate a coil, that Q reduction is always
measureable or noticeable, or that insulated coils are “bad”. Even where
insulation reduces Q a measureable amount, we sometimes must compromise Q for
reliability, life, weather immunity, and/or cost. Insulation is
sometimes necessary to prevent
short circuits or
arcing, although it is a
good idea to avoid
insulating conductors or the area around conductors when reasonably possible.

## How can we tell if the coil design is critical?

The transition between
critical and
non-critical
systems is somewhat wide and difficult to define. Design is a
complicated blur of
many factors. For
example, working
hard to push
inductor equivalent
series resistance
(ESR) very low when
the effective series resistance of
the inductor is low,
compared to the loss
resistances of the
system outside the
inductor, doesn’t
make sense. The same is true for power losses. If the system outside the
inductor is very lossy, loss in the inductor becomes much less important. One
example might be an inductor loaded Marconi antenna with very poor ground
system. If we apply 400 watts of transmitter power and ground system losses are
200 watts, doubling inductor Q might only change system efficiency a fraction of
a decibel. Other
than temperature
rise in the
inductor, who cares
if a system with 200-watts of ground loss wastes an
or an additional 4 watts in the
inductor?

This is why very large mobile antenna loading coils generally offer marginal
improvement over smaller inductors.

One way to
roughly determine
the quality of an
inductor without
fancy test equipment
is to compare
out-of-circuit
self-resonant
frequency (SRF) of
an open inductor
(do not short the
ends together) to
the expected
operating frequency.
A good inductor will
be self-resonant a
minimum of four or
more times the
operating frequency.
A simple Grid Dip
Oscillator is all
that is needed, but
be sure you use a
real
GDO.
Antenna analyzers
make very poor GDO’s!

The best general idea
is to make an
air-core inductor as
close to a 1:1 form
factor as possible,
while keeping the
SRF as far above the
operating frequency
as possible.

It is possible to
test an inductor or
compare power loss
between different
inductors by
enclosing the
inductor in a
Styrofoam box and
measuring
temperature rise
with a known applied
current, although
the ability to
measure loss
resistance and
reactance at the
operating frequency
is certainly much
faster.

## Overall Design Compromises

Weight, size, and cost often require use of less-than-ideal materials and
construction, but careful design generally results in a compromise that
won’t
noticeably affect system performance.

As a further complication, very simple systems might work quite differently than we
intuitively believe. Many experimenters fail to consider what the inductor does
in the system, and how the inductor behaves internally. For example many people
assume, with a fixed amount of applied power, as voltage increases
at different points
along a coil current
in the coil must be must
proportionally decreasing.
The logic or
intuition is based
on the fact power is
I times E.

That doesn’t
apply to reactive systems
because there can be
power factor
involved. Voltage and
current are not exactly in-phase or 180-degrees out-of-phase,
so the simple
product of E*I will
not equal the
applied power.
Because of the phase
difference, we would
have consider the
phase relationship.

### Errors

I’ve noticed programs and formulas
often over-estimate maximum obtainable
inductor Q. I’m not
sure why this
occurs, but it seems
to be somewhat common.
Sometimes the
estimated Q is well
beyond any real
world Q that is
obtainable. I’ve
also seen Q measurements
the actual operating frequency, or
marginal equipment. This is
especially common in high impedance high frequency systems.

Worse of all,
antenna
manufacturers and
antenna builders tend to
under-state
or under-estimate loss in
other forms of
specifically
Because of the very
poor form factor,
systems have Q’s in
the double digits.
provides wide
bandwidth, it also
resistive losses. It
is not “lossless
some have claimed.

I’ve found it
difficult here to
get perfectly
repeatable
measurements even
using expensive
laboratory
equipment. For
example I use a

HP-4191A Impedance
Analyzer.

I
still cross check
inductors by placing
them in a large
copper-lined box and
tune them to
resonance with
vacuum variables
(Q>50,000). By
measuring inductor
current and voltage
across the vacuum
variable, or
measuring the series
or parallel RF
resistance, I can
determine Q or ESR.

The highest Q I
have found is around
1000 or just over
1000 when
determining Q by
using  X / ESR
= Q .

There are five common errors we should avoid:

• Building for excessive Q, when the reduced ESR will not noticeably improve
system
efficiency
• In antennas, considering inductor ESR directly as a portion of loss resistance at the point
where radiation resistance is taken, rather than normalizing ESR to the point where
radiation resistance is taken
• Believing programs or articles predicting Q’s in the range of 1000 or more
for inductors
• Thinking one optimum form factor (L to D ratio) always provides optimum
performance
• Misapplying radiation or loss resistance formulas
provides lower loss than well-designed lumped loading

### Range of Inductor Form Factor

There are two critical form factor dimensions, diameter and length. The ratio
of diameter to length has two limits. The first limit occurs when the inductor
occupies only one wire diameter as the length. The other limit occurs when the
inductor is one wire diameter in diameter. The first condition would be met by a single layer pancake coil, the second
by a linear conductor such as the inductance of a single wire transmission line.
Optimum form factor occurs between these two extremes, and varies with the exact
application.

Length-to-diameter ratio is important for two reasons:

• Shorter lengths and larger diameters increase capacitance across the inductor. Capacitance
across any inductor carrying time-varying current increases circulating
currents in the inductor, increasing loss while simultaneously reducing
system bandwidth.
• Longer lengths and smaller coil diameters reduce mutual coupling between
turns and increase leakage flux. This results in use of increased conductor
length for a given inductance, increasing wire resistance.

These two situations are obviously in direct conflict, a balance must be
achieved. Optimum balance between conflicting L/D effects listed above depend
heavily on external circuit capacitance and operating frequency.

There is actually only one nearly constant parameter in design of high-Q RF
solenoid inductors, turn-to-turn spacing. Optimum turn-to-turn spacing occurs when the
spacing or gap between turns is about the same diameter as the wire. If the
turn-to-turn gap is filled (even partially) with insulation, optimum conductor spacing
increases.

For the purposes of this article, the following terms are used:

• D=diameter
• d=turn diameter
• L=coil length

As a general rule, Q in a RF inductor peaks with a form factor (L/D) between 1 and 4.

The size and shape of the conductor used in the coil sets the optimum
diameter, larger conductors require larger diameters.

Lower optimum L/D ratios (near unity) appear in systems where higher amounts
of external capacitance load the system. Two examples would be amplifier tank circuits or large
antennas with considerable loading capacitance beyond the coil. Another way to
view this is by resonant frequencies. Form factor moves closer to 1:1 when an
inductor is operated far below its natural self-resonant frequency.

Higher optimum L/D ratios (up to 4:1
or more) occur when capacitance values external
to the coil are reduced. Small mobile antennas without hats, especially
top-loaded antennas, require longer form factors. Such systems operate the
inductor closer to its self (parallel) resonant frequency.

### The Reason Optimum Form Factors Vary

As mentioned
earlier, the underlying reason for change in optimum form factor
in systems with
different external circuit
impedances rests almost entirely
in the inductor stray capacitance and
the mutual
coupling between turns.

With high external capacitance, any reasonable amount of internal
stray capacitance shunting the inductor
only causes a very
small change in
circulating current
in the inductor. The
low-impedance
external circuit can
almost exclusively determine current
in the inductor. In this case, inductor Q is set mostly by conductor
resistance in the inductor,
so anything we do to
minimize the copper
path resistance will
help. This would
include closely
packed turns that
increase mutual
coupling between
turns.

In a low
impedance system designers can place turns closer together, increasing mutual
coupling or flux linkage
from turn-to-turn. Since external capacitance
generally is large, any increase in inductor distributed capacitance
will have very little effect on
the system. The most
important goal is to reduce wire resistance by minimizing
wire length. Dielectrics around the conductors have little effect on Q, because
increases in capacitance caused by replacing air with a dielectric has little
effect on the overall circulating currents.
The type of form
(solid core or air)
and materials used
in the form or
insulation on the
wire are far from
critical because the
electric field
around the coil is
very small.

For example I
measured a number 8
gauge 13.5 uH
air-core inductor
with a diameter of 1
inch and length of
3.5 inches on 4 MHz.

339 ohms
reactance

2.26 ohms
resistance

150 Q

fitting solid Delrin
core, Q dropped to
145. Changing the
Delrin to Teflon
produced an
identical Q of 145.
All three Q’s are
within measurement
error of the Agilent
Network Analyzer
used. We should
consider them all
equal.

As the system’s external capacitance is reduced, circulating currents inside
an inductor become increasingly influenced by stray capacitance. This includes
capacitance within the inductor as well as capacitance between the inductor and
objects surrounding the inductor.

When external capacitance is reduced, the coil ends must be increasingly
separated from each other. The form factor chosen must reduce coil
diameter while increasing length. In high impedance (reactance) systems,
reducing capacitance improves component Q in spite of the
resistance penalty resulting from increased conductor length required in long
form factors.

We also must avoid using dielectrics near or in the inductor,
especially any dielectric coating or between turns. Dielectrics other than air
or vacuum, even low dissipation factor
dielectrics,
increase stray capacitance. Anything that increases capacitance
will reduce component Q, and ALL dielectrics (other than air or  vacuum)
increase capacitance. The most noticeable effects in high reactance systems
often come from dielectrics increasing capacitance, rather than actual dielectric losses!

The increase in loss can be directly proportional to the increase in
capacitance, even when required turns are reduced. Low-loss Teflon or Polyethylene dielectrics
can be nearly as detrimental as higher
dissipation factor materials like fiberglass or Delrin.

In very high
impedance systems,
such as a physically
inductor with a very
small “stinger” just
above the inductor, current can actually vary significantly along the length of an inductor.
This is because
displacement
currents can flow
out of the coil
through the stray
capacitance to the
outside world. In
properly designed or
well thought-out systems, this will not occur
to any significant
extent. If it
does occur, it might
be time to
re-examine the basic
design.  This
again has the effect
of reducing
bandwidth while
increasing losses.

### Inductor Modeling Programs

Many inductor modeling programs fail to consider two important effects:

• They ignore capacitance across the inductor
• They ignore “current pushing” or bunching caused by strong magnetic fields

The first effect causes Q to peak well below the self-resonant frequency
of the inductor. The second effect causes a decrease in Q as
frequency is increased or as turns are brought closer together. The second effect
occurs because current flows
in a smaller and smaller cross section of conductor with increasing frequency.

If a model, prediction, or estimate does not show Q dropping drastically as
first order (parallel) self-resonance is approached, the results almost certainly contain
significant Q errors.

I’ve corresponded with some program writers who claim to have verifying measurements, and found their test equipment doesn’t reliably operate
(or operate at all) at the operating frequency of the inductors! Verifying inductor
Q at frequencies far below the operating frequency in the model does NOT provide
any assurance the model or predictions are correct. We
have to measure at
the operating
frequency.

### Optimum Q

There is a strong tendency to overkill the size of inductors, in an effort to
reach unrealistic Q factors. Examples are commonly found in high-performance
mobile antenna systems, where ground loss and other system resistances dominate the system.
We often find high performance inductors with Q’s in the several hundreds (at
the upper practical limit of Q) and very low ESR’s used in systems where overall loss resistances normalized to the
feedpoint are very high.

Even though electrical problems are NOT created when using the
highest possible Q, there is a point where the end improvement in signal level
does not justify the physical size and cost to obtain “excessive”
Q.

One example can be found in my Trap Measurements
article, where differences in trap Rp (parallel resistance) when #10 AWG and
copper tubing are compared, with unnoticeable changes in
performance.

Another example appears in my mobile
article.

### Inductor Placement in Antennas

The optimum location of an inductor varies with ground resistance and overall
length of the antenna. Fortunately efficiency changes are smooth and gradual
changes. Minor errors in
placement generally do not result in noticeable efficiency changes.

Radiation Resistance and Mobile
articles on
this site give some perspective of how load placement affects radiation
resistance.

### Q Ranges

The highest Q HF inductors I have measured, at least when operated away from
self-resonance, are copper tubing coils and edge-wound inductors, such as those
commonly used in high power tank coils. The highest Q I have measured in very large inductors
of optimum form factor in the HF range has been near 1000.

Miniductor-type coils have a surprising amount of Q for the wire size, and
maintain Q better as self-resonance is approached than larger
coils.

These are the typical ranges of peak Q I have measured:

 HF Q Peak Q at 80% of self-resonant freq Copper Tubing Coils 600-1100 400-600 Edge-wound inductors 600-900 400-600 #8 miniductors 500-700 300-500 #12 miniductors 300-500 200-400 #16 miniductors 250-350 200-300 Large #2 mix iron on 1.8MHz 500-600 enameled wire close-wound 200 100

We should keep the following in mind:

• Optimum form factor varies with application.
• Q peaks at some frequency significantly lower than self-resonant
frequency, at self-resonance Q is zero (the coil appears as a pure
resistance to any external circuit). Above that frequency inductor becomes
the electrical equivalent of a low-Q capacitor.
• Linear Loading is really nothing other than a poor form-factor inductor.
resistance of the antenna except as the effective position of the load might
change from the direction of fold. In all cases, a proper form-factor
inductor would have less loss, and provide the same radiation resistance.
• Most inductor Q calculation programs overestimate Q.
• Any metal around an inductor decreases Q. Copper or steel, it often has nearly the
same effect.
• Any dielectric (even
a low dissipation
factor dielectric) decreases Q because the
dielectric increases shunt capacitance. This increases circulating currents.
The effect is most pronounced as self-resonance is approached.