Optimizing Inductors

While intended mainly for antenna loading coils, the text below also applies to other resonant systems, such as amplifier tank circuits. 

Related pages:

Inductor spice model

Mobile and loaded verticals

Optimum form factor of any inductor depends heavily on the actual end use of the component. Current through and voltage across an inductor as well as the required reactance influences both materials and form factor of an inductor. In high impedance systems, optimum form factor becomes longer with a smaller diameter. Even the best insulation materials will have a deleterious effect on component Q when impedances are high, and dielectric constant often becomes more important than dissipation factor in insulating materials. With low impedances, optimum form factors become more square and insulation has a much less noticeable effect.     

Weight, size, and cost often require use of less-than-ideal materials and construction, but careful design generally results in a compromise that doesn't noticeably compromise 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 current must proportionally decrease. This isn't true in reactive systems, where voltage and current are not exactly in-phase or 180-degrees out-of-phase.  

It is relatively common for programs and formulas to greatly overestimate maximum obtainable inductor Q. Confirming measurements are often flawed, either being made far from the operating frequency or with inadequate methods or equipment. This is especially true in high impedance high frequency systems. 

Worse of all, antenna manufacturers and builders tend to seriously understate or estimate loss in other forms of loading, specifically linear-loading. 

There are five common errors we should avoid:

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!    

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: 

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:

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) 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

The underlying reason for change in optimum form factor with external circuit impedance rests almost entirely on inductor stray capacitance and mutual coupling between turns.

With high external capacitance, any reasonable amount of internal stray capacitance shunting the inductor causes a very small change in circulating current in the inductor. The external circuit, in effect, determines circulating currents. In this case, inductor Q is set mostly by flux leakage and conductor resistance in the inductor. 

In such a system designers can place turns closer together, increasing mutual coupling or flux linkage from turn-to-turn. Since external capacitance causes most of the circulating currents, any increase in inductor distributed capacitance has little effect on the system. It becomes most important 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.

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. 

If inductor design or location is poor, and if system impedances are high, current can actually vary significantly along the length of an inductor. In properly designed systems, this will not occur.

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.           

Inductor Modeling Programs

Many inductor modeling programs fail to consider two important effects:

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.   

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 and loaded antennas 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 and Loaded Antennas 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:

As I measure inductors in the future, I'll include pictures and impedance data here.

Final Comments 

We should keep the following in mind: