Loop Calculations, Part 2

Continuing the Quest for an Accurate Coil Inductance
             -and The Mysteries of Distributed Capacitance

In Part 1 of this series we began our search for an accurate inductance formula. Accuracy is imperative in order to correctly predict our passive loop's inductance value and thus its tuning range. Passive loops for mediumwave are a special breed of coil animal. They could be termed "very large, very short coils", and they don't fit the common formulas found for calculating coil inductance.

Coils can basically be divided into two groups, long and short. The dividing line seems to be that 0.5 ratio of length/diameter. By coil length we mean the length of the winding as opposed to the diameter of the winding. If a coil's length is greater than half its diameter, it can be considered a long coil. If its length is shorter than half its diameter, it can be considered a short coil. The long coil inductance formulas put forth in the 1920s really didn't work well for short coils, those having a length/diameter ratio less than about 0.4. And the short coil formulas of the day only worked down to a length/diameter ratio of about 0.2, greatly losing accuracy below this. Our passive loop lies well south of 0.2, usually in the range 0.05 to 0.1. And it is usually square - not to our advantage as we swim in a sea of mostly circular coil formulas.

Wheeler's and other long coil formulas of the late 1920s were simple and accurate within the range of coil geometries for which they were intended. Many inductance calculators you find on the web use these formulas, despite the fact that there are far more accurate formulas for short coils. The problem with these calculators is there is no indication of coil geometry limitation, leaving the uninitiated to believe the result as accurate. Even Wheeler's short coil formula of this era, thought to be accurate to within 2%, was in later years revised upwards nearly 10% for some coil geometries!

At 79 years old and fourteen years before his death at age 93, Wheeler published in 1982 his continuous inductance formula, a single encompassing formula which calculates the coil inductance of all cylindrical coils, long and short. Using Grover, Wheeler and others work, and refined by Rosa's corrections and unmentioned scientists Lundin, Nagaoka, Knight and more, we have an accurate formula for predicting the inductance of coils with length/diameter ratios approaching that of a passive loop.

One would think we were done now - simply figure the tuning range of the passive loop using the calculated inductance. We have one more complication, however, and that is the loop's unknown self-capacitance. It must be accounted for in the second formula which calculates the tuning range of the loop.

Now we open that can of worms, that of self-capacitance, or commonly but erroneously known as distributed capacitance. Every coil also has self-capacitance as well as inductance. Self-capacitance is the inherant internal capacitance of the wire-formed coil itself. This spurious capacitance adds extra capacitance to the tuned circuit, changing (in fact further lowering) the resonant frequency. Additionally, this self-capacitance reduces the overall tuning range of the coil because it alters the range of the tuning capacitor. For example, if our common 10-365pF tuning capacitor is used in parallel with a proper loop happening to have 30pF of self-capacitance, the capacitive tuning range in reality is 40-395pF. What may have been a perfect, calculated tuning range of 530-1700 KHz is now altered downward to 500-1450 KHz. So, it is advantageous to design a loop with as little self capacitance as possible, or at least account for it in our design.

As stated, few formulas are commonly found which accurately calculate the inductance of a very large, very short coil like our passive loop antenna, whether it be circular, square, or other polygonal shaped. Virtually none of these account for coil self-capacitance, which, as we have seen, greatly changes the tuned circuit's operating parameters. An accurate self-capacitance figure is necessary to predict an accurate tuning range for our loop. Now we must wrestle with attempting to calculate or measure the loop's self-capacitance, which conceivably may change our tuning range by perhaps an additional 5-10 percent.

Much fact and fiction has been written concerning the cause and calculation of self-capacitance of coils. Once again, a little history is in order. Bear with me as I think you will find it interesting, especially if you like a bit of intrigue.

Little work if any had been done in this area of radio science much before 1920 - that of predicting coil self-capacitance. In 1917, J. C. Hubbard publishes a little-known paper in Physical Review entitled, "On the Effect of Distributed Capacity in Single-layer Solenoids". He measures coils of varying geometry down to a 0.2 length/diameter ratio, some with as few as 35 turns. He ponders that, "There is no evidence that the variation of ratio of pitch to diameter of wire [turns spacing] has a measurable effect on the distributed capacity in the region studied, though some effect is to be expected for coils of a smaller number of turns than those studied here."

S. Butterworth, famous innovator and designer of frequency filtering circuitry, tackles the problem again from 1922 - 1926. He publishes self-capacitance formulas which purport to cover single layer solenoids wound with round wire, the stipulations being that the number of turns have to be large (our long coil again) and well spaced.

In 1934, engineer A. J. Palermo enters with his text, "Distributed Capacity of Single-layer Coils", published in the proceedings of the Institute of Radio Engineers. In that text he presents a formula for calculating the self-capacitance of coils, based on his theory of accumulated inner-winding capacitance of a coil's adjacent turns. The paper is widely accepted by the engineering community of the day in both the scientific and popular press. The premise derived from his theory is that spacing of coil turns plays a major part in self capacitance, in that wider turn spacing lowers self capacitance, and tighter turn spacing increases it. Palermo claims to have found the solution. Has he?

Experimentation in the field continues. General Electric engineer R. J. Medhurst suddenly springs onto the scene in 1947 with his two-part article, "H.F. Resistance and Self-Capacitance of Single-Layer Solenoids" in Wireless Engineer. After exhaustive testing of self-capacitance on some 40 coils, Medhurst summarizes:

"These measurements show a very considerable divergence from the formula of A. J. Palermo though they are in quite good agreement with other previous experimental work [inferring Butterworth]. Self-capacitance of coils of this type is shown to be substantially independent of the spacing of the turns. It is given by an expression of this form:

Cd(picofarads) = H * D

where D(cm) is the mean coil diameter and H depends on the length/diameter. A table of H is given, based on these measurements."

"....to better than 5%, the measured values [of self-capacitance] fit the expression:

Cd(picofarads) = 0.46 * D

"....being independent of the spacing ratio."

Medhurst presents a table of values for H, covering coil geometries down to 0.1 length/diameter ratio. Accuracy below about 0.2 is still in question. It also seems that the most efficient length/diameter ratio causing the lowest self-capacitance in a coil is near 1.0, that is, a coil having a length equal to its diameter.

Medhurst explains further:

"Measurements of self-capacitance of a wide range of single-layer coils were consequently carried out. The results failed to confirm Palermo's claim that the self-capacitance varies steeply with the spacing of turns. They are, instead, in quite good agreement with previous work which had shown the self-capacitance to be very nearly independent of d/s (spacing ratio of diameter/turns)."

"Thus, the capacitance between adjacent turns will be less than that predicted by Palermo. The fact that self-capacitance is substantially independent of spacing of turns suggests that the part of the self-capacitance considered by Palermo is actually negligible."

At this, J. C. Hubbard remarked, "....we apparently have two quite independent factors [determining the self-capacitance of coils], one predominating greatly in very short coils, the other, in very long coils."

Medhursts's findings are approximate of course, though a rudimentary start to the overall understanding of the self-capacitance of coils. Experimentation continues through the next decades, each overwhelmingly refuting Palermo's theory. However, the myth of accumulated inter-turn capacitance has been cast and continues through the years, propagated through popular writing and idle commentary.

On his exceptional web site Dr. David Knight (G3YNH) delves into great detail concerning loop inductance and self-capacitance, both explaining and expanding upon current knowledge in the field. His articles on the current state of inductance calculation and self-capacitance of coils are well worth the read if you have a mathematical curiosity about such things.

The general thinking in past years has pointed to transmission line theory as being the root driving mechanism of coil self-capacitance. So interesting I find the huge amount of evidence against Palermo's supposition of turns spacing driving coil self-capacitance, I'll reproduce some of David Knight's eloquent analysis here. It makes for very interesting reading.

From David Knight's article, "The Self-Resonance and Self-Capacitance of Solenoid Coils", Version 0.01 (provisional), 9th May 2010, and "From Transmitter to Antenna, Inductors and Transformers: Solenoids, Part 1":

"Attributing self-capacitance to the static turn-to-turn electric field is a fallacy akin to taking the coil apart and trying to find the capacitor....The solution, of course, lies in recognising that the coil is a transmission line; except that the line in question turns out to be a rather complicated one."

"Unfortunately, the electrical literature abounds with articles which claim that the self capacitance of a coil is due to the capacitance between adjacent turns. This hypothesis is easily refuted, because it makes the wholly incorrect prediction that coils which have closely-spaced turns will have much greater self-capacitance than those which do not. The static component of self capacitance is small in single-layer coils, because a wave travelling along the wire does so with its electric vector nearly perpendicular to the coil axis, i.e., the electric field component parallel to the axis is almost negligible in comparison to the radial component. Nevertheless, the static capacitance idea appears to be so intellectually compelling, that there are at least two examples, in the peer-reviewed literature, where researchers have been motivated to fabricate or selectively report experimental evidence in order to support it."

"There is even a school of thought which says that the self-capacitance is due to the capacitance between adjacent turns; and although this is partly true for multi-layer coils, the hypothesis turns out to be a hopeless predictor of the reactance of single-layer coils. Experimentally, it transpires that self-capacitance increases as the spacing between turns increases...."

"Palermo gives a formula based on the hypothesis that the self-capacitance can be deduced by considering the capacitance between adjacent turns. Medhurst, being a meticulous experimenter, soon ran into difficulties with that approach; and so was forced to 'find out whether Palermo's formula did in fact agree with experiment'". He concluded that the data supporting Palermo's theory were suspect; and fell only a little short of accusing Palermo of scientific fraud.....Medhurst was aware that self-capacitance is substantially independent of turn-spacing provided that the coil has plenty of turns. He therefore chose to keep the number of turns per unit length high to eliminate pitch effects."

"A trivial investigation involving a Grid-Dip oscillator and a set of engineer's callipers will confirm that the various resonances exhibited by a disconnected coil are associated with the total conductor length. It is therefore extraordinary that the self-capacitance of single-layer coils is still routinely attributed to the static capacitance which is presumed exist between adjacent turns."

"Palermo reported a total of 19 self-capacitance measurements, 12 of which he carried out himself, and 7 of which were communicated to him by F W Grover of the National Bureau of Standards. It was in the group of measurements performed by Palermo himself that Medhurst found some of the numbers to be unreproducibly large....Medhurst was right to cry foul; but, in fact, the extent of the tampering was even greater than Medhurst had suspected."

"His [Palermo] formula often produces values which are much too large. In such cases, he appears to have adopted the habit of adjusting the calculated value downwards and the measured value upwards in order to obtain plausible agreement. Since he acknowledges the help of F W Grover however, he was evidently not in a position to tamper with the NBS data; and so in that case he confined himself to writing down false calculation results. In the worst instance, his formula gives 27pF, but he reports 12.9pF to confer with an NBS measurement of 12.8pF. There are other sleights of hand for those who wish to pursue the issue, but overall the paper is a travesty."

"That then is the insalubrious basis on which the inter-turn capacitance hypothesis became part of electromagnetic folklore. What Palermo hoped to gain by promoting his defective theory is difficult to guess; but he may have been motivated by inability to accept failure after an early success. His formula was subsequently turned into tables and abacs to 'assist' the radio engineer; and his dogma diffused naturally into the textbooks to lie in wait for the unwary. The 'capacitance between adjacent turns' hypothesis re-emerged in a new guise in 1999, in a paper by Grandi, Kazimierczuk, Massarini and Reggiani. These authors cite Medhurst, only to dismiss his work for being empirical; and make no mention of Palermo despite the strong parallel and Medhurst's barbed discussion."

"In summary, it is fair to say that theories which attempt to attribute the self-capacitance of single-layer solenoids to the inter-turn capacitance are wrong. In Palermo's case, the problem lies firstly in the assumption that a single wire can behave like two wires lying parallel, and secondly that the resulting capacitance should be divided by N [number of coil turns]. Logically, his theory is no better than a guess; which happens to work roughly for some coils, but has no actual predictive power."

How interesting and so anti the commonplace conception we have about self-capacitance so often found in the idle writing of today! We see that number of coil turns and spacing of coil turns matters very little in single-layer solenoid coils of many turns, so-called long coils. It is only when we get to the very short coil that matters begin to get sticky. Passive loop territory, again.

So where does this leave us? Even today, commonly-found formula predictors of self-capacitance still fall short of the mark of accuracy when dealing with in very short coils, coils having less than about 0.2 length/diameter ratio. Their result is often high by a factor of two and sometimes more. Over the years, Medhurst produced not one but several formulas for calculating self-capacitance for different coil geometries. Medhurst's original simple formula of Cd(picofarads) = 0.46 * D seems to give a nearly workable result in the region for very short coils. Two other Medhurst formulas purportedly come even closer in accuracy.

We have one additional way to predict, actually calculate, the self-capacitance of a coil. It is fail-safe in its accuracy. We first wind a test loop, then wire a tuning capacitor with known range to the loop. Using a receiver, we record the lower and upper frequency of the capacitor's tuning range by listening for signal or background noise peak at either extent of its range. Plugging the capacitor's known low and high values and the low and high tuned frequency extent into a simple (okay, maybe not so simple) formula, we can directly calculate the coil's exact inductance and self-capacitance. We then have a basis upon which to refine our calculation and thus the number of loop turns to satisfy our goal of tuning the mediumwave band completely.

Our last problem now is predicting the inductance of a very short, very large diameter polygonal coil to a high degree of accuracy. We will take our best shot with Wheeler's Continuous inductance formula and Nagaoka's formula for circular coils, using Rosa's corrections for both, and then interpolate for a polygonal loop. This, because we know that inductance varies very nearly proportionally with the area of the loop. Two other formulas we will use for comparison are Grover's old formulas for polygonal loops.

Next up in Part 3: The Inductance Calculator Program - Loop Calculator One

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Bibliography and of Interest:

Frederick W. Grover "Additions to Inductance Formulas", Scientific Paper #320, Bulletin of the Bureau of Standards 14, pp. 555-570 (1918).

Frederick W. Grover "Tables for the Calculation of the Inductance of Circular Coils of Rectangular Cross Section", Scientific Paper #455, Scientific Papers of the Bureau of Standards 18, pp. 451-487 (1922).

Frederick W. Grover "Formulas and Tables for the Calculation of the Inductance of Coils of Polygonal Form", Scientific Paper #468, Scientific Papers of the Bureau of Standards 18, pp. 737-762 (1922).

Frederick W. Grover "The Calculation of the Inductance of Single-Layer Coils and Spirals Wound with Wire of Large Cross Section", Proceedings of the Institute of Radio Engineers (1929).

Frederick W. Grover "Inductance Calculations: Working Formulas and Tables", (Van Nostrand, 1946 and Dover, 1962 and 2004).

Harold A. Wheeler "Simple Inductance Formulas for Radio Coils", Proceedings of the Institute of Radio Engineers, Vol. 16, No. 10, October 1928.

A. J. Palermo. "Distributed Capacity of Single-layer Coils", Proceedings of the Institute of Radio Engineers, Vol. 22, pp. 897 (1934).

H. Nagaoka, "The Inductance Coefficients of Solenoids", Tokyo, Vol. 27, No. 6, (1909).

E. B. Rosa, "The Self and Mutual Inductances of Linear Conductors", BBS Vol. 4, No. 2, (1908).

E. B. Rosa, Bulletin of the Bureau of Standards, Vol. 2, pp. 161-187 (1906).

E. B. Rosa and F. W. Grover, "Formulas and Tables for the Calculation of Mutual and Self Induction", [Revised], Bulletin of the Bureau of Standards, Vol. 8, No. 1, p. 122 (1911).

R. G. Medhurst, "H.F. Resistance and Self-Capacitance of Single-Layer Solenoids", Wireless Engineer, Feb. 1947, pp. 35-43 & Mar. 1947 pp. 80-92.

J. C. Hubbard, "On the Effect of Distributed Capacity in Single-layer Solenoids", Physical Review, 1917, Vol. 9, p. 529.

R. Lundin, "A Handbook Formula for the Inductance of a Single-Layer Circular Coil", Proceedings IEEE, Vol. 73, No. 9, pp. 1428-1429 (1985).

David W. Knight, G3YNH, "From Transmitter to Antenna, Inductors and Transformers: Solenoids, Part 1"

David W. Knight, G3YNH, "The Self-Resonance and Self-Capacitance of Solenoid Coils", Version 0.01 (provisional), 9th May 2010.

Loop Calculations, Part 1

The Search for an Accurate Inductance Formula

Mediumwave DXers routinely use passive antenna devices to enhance signal pickup to a portable or handheld AM radio. Many of these are multi-turn loop antennas wound on a frame, usually square, some as small as 12 inches across. Tuned to resonance with a variable capacitor, the passive loop is placed in the near-field of the radio, coupling the enhanced signal to the radio's ferrite loopstick antenna.

Within 1/10 wavelength, the loop antenna is actually more sensitive to the magnetic field of signals, not the electric field. It outputs a voltage proportional to that field. Antenna performance is influenced by the number of turns and the area of the loop. For an air core loop, the bigger the loop, the bigger the signal voltage.

For the beginner or experimentalist wanting to construct a passive, air core loop, the question often arises: "How many turns of wire are required to tune the mediumwave broadcast band for a (_fill_in_the_blank_) sized frame?". Numerous formulas on numerous web sites can be found on the Internet. Some pages even include a Javascript or server-side calculator allowing different values to be plugged in and tried out. Results are generally close enough to get you in the ballpark, but can often be off as much as 20-30%. What gives?

How do these calculators work? Quite simply, they start by using one formula to calculate the inductance of the loop coil itself based on its side length (square coils), or diameter (circular coils), and number of turns. A second formula then takes this inductance value and the capacitance range of the tuning capacitor paired with the loop, then calculates the resonant frequency range (see The Simplified Frequency Formula) which the capacitor and loop combination will tune. Sounds simple, doesn't it. But there are complications. Oh, are there ever complications.

First we must calculate that crucial value of coil inductance. Accuracy is important if we are to have meaningful results. Over the last 180 years, a number of people have worked on the problem of inductance, and of finding an accurate inductance formula for coils, both small (in diameter) coils of various types, and the large air core coil - the passive loop which we mediumwave DXers use. It's been a long road. Here are the highlights:

In 1831, English chemist and physicist Michael Faraday, pictured at right, shows that changing currents in one circuit induce currents in a neighboring circuit, thus discovering induction. Over the next several years he performs hundreds of experiments and shows that they can all be explained by the idea of changing magnetic flux.

From 1856 through 1873, Scottish physicist and mathematician James Clerk Maxwell, pictured just below at left, develops the laws of electromagnetism, beginning with Michael Faraday's concept of a field of lines of force. Maxwell's calculations show that electromagnetic waves in a vacuum travel at the same speed as light; he correctly concludes that light is a form of electromagnetic wave, boldly predicting the rest of the electromagnetic spectrum. The time of America's Civil War, 1860-1865, is especially known for the advances Maxwell makes in the fields of electricity and magnetism.

He examines the nature of both electric and magnetic fields in his two-part paper on physical lines of force, published in 1861, in which he provides a conceptual model for electromagnetic induction, consisting of tiny spinning cells of magnetic flux. In 1873, he publishes his seminal work, Electricity and Magnetism.

Maxwell is considered by some to be the third greatest physicist of all time, behind only Isaac Newton and Albert Einstein. Great physicists are known for uniting theories into a single unified theory, and Maxwell did this with his formulation of classical electromagnetic theory. It leads to radio.

Finally, the twentieth century dawns and radio has been born. Engineers yearn for accurate formulas to calculate the inductance of coils. In the early part of the century, three names stand out prominently from the field of science as contributors to the art of inductance calculation.

Frederick W. Grover is perhaps the most prominent. Few photographs exist of this American physicist and electrical engineer. Grover worked as a physicist at the National Bureau of Standards starting in 1902, then side-tracked to study with Arnold Sommerfeld at the Ludwig Maximilians University of Munich in 1907. He was awarded his doctorate in 1908, and his thesis dealt with precision measurements and theory of eddy currents to determine a new method for finding the conductivity of metals. Upon receipt of his doctorate, he returned to the National Bureau of Standards. Grover's formulas, scientific papers and articles on induction form the basis of what we know today concerning the calculation of the inductance of a coil in its various forms. His book, Inductance Calculations (1946), is Grover's monograph for engineers and scientists engaged in the accurate calculation of self and mutual inductance. The book is based on the work carried out by Grover and E. B. Rosa during their distinguished careers at the National Bureau of Standards during the first half of the 20th Century.

Refining Grover's formulas was Edward Bennett Rosa, pictured at left. In 1901, Rosa was called to the newly-organized National Bureau of Standards, at Washington. There, as physicist, and later on, as chief physicist, he continued through the remainder of his life. When Dr. Rosa began his work in the Electrical Division of the National Bureau of Standards it was his ambition to determine a number of the fundamental electrical constants to a degree of accuracy far exceeding all previous determinations. One of these determinations was the ratio of the electromagnetic and the electrostatic units. This work was started early in 1907 and resulted in the most accurate determination yet made of this constant. Rosa, chief physicist, died suddenly while engaged in work in his office at the National Bureau of Standards on May 17, 1921.

Harold A. Wheeler also figures prominently, pictured with radios at right. During his university education in the early 1920s he worked part-time at the National Bureau of Standards Radio Laboratory. In 1924, Wheeler joined the Hazeltine Corporation, becoming head of its Bayside Laboratory by 1930. Under its auspices, he invented the automatic volume control for radio receivers, patented in 1932. Hazeltine spent the 1920s and 1930s working on various aspects of radio and TV technology. Wheeler enjoyed figuring out simple formulas for engineering questions: computing the inductance of a conductor, formulas for strip lines, transmission-line impedance curves. His formulas continue to be used today.

Most of the early inductance formulas developed were for small, round coils, that is, solenoid-wound, circular coils having a small diameter, with length that exceeds at least half the diameter (length/diameter ratio of 0.5 or more). These kinds of coils are more often found in radio circuitry. Our passive loop coil does not meet these specifications. It is usually larger by an order of magnitude or more, normally square or at least non-circular (polygonal in shape), and very short - with a length/diameter ratio approaching 0.1 or less.

Grover and others continued to work on the inductance riddle for years, eventually developing equations which approximately fit. I say "approximately" because as the length/diameter ratio approaches zero, the inductance curve becomes skewed and non-linear. A single equation would not fit the curve for all possibilities in this region of coil geometry where the length/diameter ratio edged below 0.5, the region of the "short coil".

Complications abound. Loop diameter, number of coil turns, wire spacing (also called pitch, or spacing between coil turns), and in some cases wire diameter all alter the final inductance of the coil, changing the resonant frequency range of the coil/tuning capacitor combination of our passive loop antenna.

Are we done? Hardly. A new complication arises. It is called self-capacitance, or distributed capacitance, which further changes the tuning parameters of our passive loop. It is an interesting and controversial subject, adding mystery to our loop calculation, as you will see.

Next up: Loop Calculations, Part 2: Continuing the Quest for an Accurate Coil Inductance

The Simplified Frequency Formula

When I was a kid getting into radio and electronics, the only formula I knew to calculate the tuned frequency of an inductor and capacitor wired in combination was the tried and true formula dating back to the dawn of radio:

The result f is the frequency in Hertz of the tuned circuit (logically called cycles per second back in the day), L is the inductance in Henries, and C is the capacitance in Farads. Farads? Henries? Capacitors in the Farads range are huge, like railroad boxcars, they used to say. Coils in the Henries range are heavy (remember those 5U4GB tubed power supply filter chokes?). Conversely, inductance at mediumwave broadcast frequencies is measured in micro henries (millionths of a Henry, or µH) and capacitance is measured in pico farads (millionths of a millionth of a Farad, years ago noted as µµF). Wow, that's a mouthful.

Let's apply this old formula to a commonly-seen tuned circuit, a 240 µH inductor and a 365 pF capacitor wired in parallel. How confusing is this?

f = 1 / (2 * pi * Sqrt(.000240 * .000000000365))   [Sqrt = square root]

Now how many zeros am I supposed to add ahead of the 365 pF capacitor? The inductor?

I remember trying to work this formula before electronic calculators. Lots of zeros. Remember the time before electronic calculators? Okay, well, maybe you don't. Too many zeros to keep track of, in fact, too many zeros to keep track of even if working with a calculator. Oh, use scientific notation? Times ten to the minus what? Please show me (simply), at what frequency a 240 µH inductor and a 365 pf capacitor resonate?

Then one day, years later, I came upon the formula:

L * C * f * f = 25330

In the formula above, f is the frequency in megahertz, C the capacitance in pico farads, L the inductance in micro henries. 25330 will always be the same in every calculation. Inductance times capacitance times frequency times frequency will always equal 25330. Magic. Okay, now we're talking simplicity.

Using this formula, it's also very easy to change the operands around to calculate any one of the values, when the others are known.

Solving for Inductance (in µH):

       L = 25330 / (C * f * f)

Solving for Capacitance (in pF):

       C = 25330 / (L * f * f)

Solving for Frequency (in MHz):

       f = Sqrt(25330 / (L * C))

A few examples:

1. Find the resonant frequency of a 240 µH inductor and a 365 pF capacitor:

       .537 MHz = Sqrt(25330 / (240 * 365))

2. Find the inductance required to resonate at 530 KHz using a 365 pF capacitor:

       247.05 µH = 25330 / (365 * .53 * .53)

3. Find the capacitance required to resonate at 1700 KHz using a 247.05 µH inductor:

       35.47 pF = 25330 / (247.05 * 1.7 * 1.7)

Henry Thoreau said, "Simplify, simplify, simplify!". In this formula we have done that.

Can we make the original formula of old more workable to find frequency? Yes we can. Using our simple whole units of micro henries and pico farads, we use a multiplier at the end to get our result in KHz or MHz.

       f(MHz) = (1 / (2 * pi * Sqrt(240 * 365)) * 1000

       f(KHz) = (1 / (2 * pi * Sqrt(240 * 365)) * 1000000

That's a little easier to manage than the original without all the zeros. Should we rearrange the formula to calculate for inductance or capacitance? Well, we could. But why bother now that we have the simplified formula, L * C * f * f = 25330!

Now, why would we be wanting to calculate the resonant frequency of an inductor and capacitor? Let's say you plan to build a passive loop and want it to tune the mediumwave band. You've decided on a two foot square loop of 11 turns. Your loop calculator widget (or LCR inductance tester for those who can afford one) shows this loop to have a certain inductance. Pair that with your trusty old 365 pF broadcast tuning capacitor and using the frequency formula you can calculate the tuning range of the loop. Or roughly so.

We will have more on the topic of passive loop frequency calculations in a future article, including a custom loop calculator program. Stay tuned.

On the Road Again

"On the road again...." Actually I have been "on the road again" since before I wrote last, and have completed the annual road trip west from New York to Arizona by way of Denver. The last of the Mediumwave Along the Erie Canal series was posted while enroute, from Fraser, Colorado on October 9th, while sitting in six inches of snow in the high Rockies.

Had a good trip. Saw some new mediumwave towers in Kansas and Colorado and photographed them. Am settled now in the southwestern desert an hour north of Old Mexico, just east of the Colorado River, and am back to contemplating our radio hobby and DXing again.

Check back soon for some new posts!

Mediumwave Along the Erie Canal, Part 3

Continuing with our exploration of mediumwave station sites along the Erie Canal.

We are walking the Erie Canal path in the Rochester, New York area, headed west from Lock 33. Within a one mile stretch there are three mediumwave stations lining the canal. In the last part of this series we passed within sight of WHTK-1280.

Hiking along the canal past WHTK-1280 perhaps another half mile brings us to the Clinton Ave. overpass, situated just shy of the four-lane I-390 overpass. Poking above the trees to the north are the four equal height towers of WROC-950, and shown in the photo just below. Three are in direct alignment and the fourth sits off some distance broadside to the northeast. They are each .193 wavelength in height. Take the side path off the canal to the north about 50 yards and you have a good view of the tower site. WROC-950 is one of Rochester's oldest AM radio outlets. Both daytime and nighttime powers are set at 1KW.

The tower configuration at WROC is a bit curious. Three towers are used at night, those three in direct row alignment, broadcasting with a main lobe at 353 degrees, and a very minor lobe at 173 degrees. Gain in the favored direction, north towards the main population center, is 6.2dB.

Daytime coverage is bi-directional, using two towers, tower #3 from the aligned row and tower #4, the tower broadside to the northeast. The main lobes are at 343 degrees and 163 degrees, generating about 4.8 dB gain each.

WROC-AM's call sign is a reference to WROC-TV. While the stations are not and have never been co-owned, WROC-AM has an agreement with WROC-TV to provide local news coverage, and the borrowing of the WROC call signs from WROC-TV is included in this agreement. Coincidentally, the WROC-AM call sign was previously held at WHTK-1280 from 1961 into the 1970s, and was co-owned with WROC-TV while at that location.

WROC-950 began broadcasting in 1947 under the call sign WARC. It was an early affiliate of the ABC radio network, but later changed to a locally programmed, personality-driven popular music station. It was purchased by the B. Forman regional department store chain in 1953 and changed its call letters to WBBF, the last three letters of which stood for "Buy B. Forman". In 1966 it was sold to LIN Broadcasting for what was then a market record of over $2 million, but retained its popular music format and personality lineup until the early 1980s.

As WBBF, 950 AM was a popular Top 40 music station in Rochester, often leading the market in ratings surveys from the 1950s through the early 1970s, and ranking among the city's top stations through the late 1970s even after strong format competition arrived in 1972 from WAXC-1460 and later on the FM band from WPXY. Consistent success was achieved although as a relative latecomer to the AM band in the postwar era, WBBF's coverage area had to be restricted to the east and west to prevent interference with other stations on the same channel. In 1982, as hit music radio listeners were migrating to FM, the station evolved into a talk format. WBBF served a short stint as WEZO from 1998 to 2002, then adopting the WROC call sign. The WBBF calls are now in use in Buffalo, New York.

In September of 2004, WROC signed on with the liberal Air America network, having previously carried conservative talk. In September of 2008, WROC became an ESPN affiliate. The format is closely affiliated with Buffalo sister station WGR-550.

Shown below is WROC-950's nighttime pattern plot. On the plot are shown various co-channel stations around the region and where they fall into WROC's pattern.

This concludes this series. Hope you have enjoyed it.

Mediumwave Along the Erie Canal, Part 2

Continuing with our exploration of mediumwave station sites along the Erie Canal.

We are walking the Erie Canal path in the Rochester, New York area, headed west from Lock 33. Within a one mile stretch there are three mediumwave stations lining the canal. In the last part of this series we passed within sight of WXXI-1370.

Walking just a little further along the canal path, coming into view is the four tower array of WHTK-1280 protruding above the Winton Rd. overpass, and shown in the photo just below. Its equal height .339 wavelength towers stand in a perfectly-aligned row at the northwest corner of Winton Rd. and Henrietta-Townline Rd. behind an industrial park, and just across the canal to the south. Passing under the overpass and walking about 100 yards further we get a great view of WHTK's towers.

WHTK-1280, also known as Sportsradio 1280, obviously airs a sports radio format. It is fully simulcast on WHTK-FM (107.3). WHTK is a Clear Channel Communications affiliate and is owned by Citicasters, Inc., featuring programing from Fox Sports Radio and Westwood One as well as New York Yankees, Rochester Americans and Rochester Red Wings games among other local and national sports. It transmits in AM-HD (IBOC). Both daytime and nighttime powers are set at 5KW.

Daytime coverage is omni-directional, using only one tower. The four tower array in use at night broadcasts with a main lobe at 346 degrees, and a minor lobe at 166 degrees. Gain in the favored direction, north again towards the main population center, is a respectable 7.5dB, pushing an effective 28.3KW towards Rochester.

The station was first known as WVET, signing on in 1947 under ownership of a group of returning World War II veterans calling themselves Veterans' Broadcasting Company. It operated successfully for many years with a personality full service adult popular music format. It changed callsign from WVET to WROC when Veterans bought WROC-TV from Transcontinent Television Corporation in 1961. Simultaneously an FM sister station, WROC-FM, signed on, first playing classical music and later automated jazz and pop standards. Veterans Broadcasting sold all the WROC stations in the mid-1970s. The AM station continued with its full service format until late in the 1970s, when it tried an all-news format first as WROC and then as WPXN (AM). It would later simulcast its FM sister station, by the early 1980s known as WPXY (FM) amd airing the personality contemporary hit music format which it still runs today. Late in the 80s, after changes in ownership, it would migrate to pop standards and then to mostly syndicated "hot talk", a lineup of talk and sports programming meant to appeal to young adult men. At that time it adopted the WHTK callsign (the "HTK" meant to stand for "hot talk") which it still uses today.

Shown below is WHTK-1280's nighttime pattern plot. On the plot are shown various co-channel stations around the region and where they fall into WHTK's pattern.

Stay tuned for Part 3 of this series.

Mediumwave Along the Erie Canal, Part 1

Let's explore some mediumwave stations whose transmitter sites line the Erie Canal at Rochester, New York. Three sites are in such close proximity to the canal that their ground radials almost dangle in its waters.

The Erie Canal is a waterway that runs about 363 miles from Albany, New York, on the Hudson River to Buffalo, New York, at Lake Erie, completing a navigable water route from the Atlantic Ocean to the Great Lakes. The canal contains 36 locks with a total elevation differential of about 565 ft. It was first proposed in 1807, and remained under construction from 1817 to 1825.

The canal was the first transportation system between the eastern seaboard (New York City) and the western interior (Great Lakes) of the United States that did not require portage. It was much faster than carts pulled by draft animals, and cut transportation costs from $100 per ton to $10 per ton. The canal fostered a population surge in western New York state, opened regions farther west to settlement, and helped New York City become the chief U.S. port. It was enlarged between 1834 and 1862. In 1918, the enlarged canal was replaced by the larger New York State Barge Canal.

Canal boats were pulled by horses and mules along a towpath which ran alongside the canal. In modern days, the old towpath has been turned into a walkway for hiking and biking in many places. A one mile section along the Erie Canal through Rochester, New York plays host to no less than three mediumwave stations. Walking the canal, one passes within 500 yards of stations WXXI-1370 (5KW), WHTK-1280 (5KW), and WROC-950 (1KW).

Let's take a walk along the canal in this area and I'll describe what we see, radio-wise.

Pictured just below is the tower array of WXXI-1370. Starting at Lock 33 on Edgewood Ave. and proceeding west, after a few hundred yards we see WXXI-1370 off to the north about 500 yards and behind an apartment building just off of French Rd. WXXI's four towers stand in a rectangular trapezoidal-shaped array. Both daytime and nighttime powers are set at 5KW.

Daytime coverage is omni-directional, using only one tower. The four tower array in use at night broadcasts with a main lobe at 354 degrees, and a minor lobe at 157 degrees. Gain in the favored direction, north towards the main population center of Rochester, is just over 5dB. WXXI is one of those rare stations that reference all towers in their orientation, spacing, and phasing to a non-primary tower: Tower 2.

WXXI is Rochester's National Public Radio outlet on the AM band. It also broadcasts in HD on the FM band. WXXI dates its origins to July 2, 1984, when it signed on with a mix of NPR news programming, local news and talk, and public affairs programming geared to serve adult listeners in the six-county Rochester metropolitan area. The station is the successor to WSAY, a facility founded and built by the late Gordon P. Brown in 1936 as a small local area station with a 250 watt signal on 1210 kHz. It moved to 1240 kHz in 1941. In the pre-war era WSAY became best known as the home of local music programs at a time when its network-affiliated competitors were airing a mix of local news and sports with national drama, comedy and music/variety shows supplied by the NBC and CBS networks. WSAY also was the first station to hire an African-American announcer for a regular shift.

Following World War II WSAY received FCC permission to improve its signal by moving to the regional 1370 kHz frequency. It relocated its transmitter from a downtown Rochester building with rooftop antenna to a modern four-tower plant in suburban Brighton. It increased power first to 1000 watts and shortly afterward to 5000 watts full time. Over the next three decades WSAY operated under a number of formats, from pop standards to top 40 to progressive rock to country. Gordon Brown owned WSAY until his death in 1979, and his estate sold it to the Dickey family. The Dickeys operated it from 1980 to 1984, also under a variety of formats from personality adult contemporary to country to talk, eventually changing its callsign to WRTK. The license and facility was eventually sold to the WXXI Public Broadcasting Council, and briefly taken dark before its summer 1984 relaunch as WXXI-1370 with a round-the-clock non-commercial format of news, talk and public affairs. The WXXI news and public affairs department produces local newscasts seven days a week and local talk programming every weekday, along with NPR news programming and locally produced documentary and specialty offerings. It currently operates from modern digital studios in the downtown Public Broadcasting Center, and upgraded transmitting facilities at the Brighton location first brought on line by Gordon Brown in 1946.

Over the past 25 years WXXI-1370 has achieved success in attracting a sizable audience for its news and public affairs programming, consistently ranking second in audience size among the Rochester market's AM signals and second among stations on either AM or FM with spoken-word (news, talk, or sports) formats according to Arbitron quarterly audience measurements. It has also won numerous local, state and national awards for its program offerings.

Shown below is WXXI-1370's nighttime pattern plot. On the plot are shown various co-channel stations around the region and where they fall into WXXI's pattern.

Stay tuned for Part 2 of this series.

Mexican Governmental Mediumwave List Updated

About a month ago, the Mexican government finally updated their official mediumwave station list, now dated June 30, 2011. Updates to this list do not come very often, perhaps every year or so. The previous list was dated December 31, 2009, 18 months ago. It's been a long time coming.

The list, in .PDF format, documents station location (city and state), owner, call sign, frequency, daytime and nighttime powers, and license expiration date or status. It is unfortunate that actual latitude and longitude coordinates of transmitter sites are not included. However, latitude and longitude can be extracted from the matching entry in the US FCC database if you look carefully and wade through the huge number of redundant and outdated Mexican records to find the right one. I am working on creating a combined list using my Radio Data MW program. That will allow the creation of a list in many forms, sorted at will by call sign, frequency, power, location, signal strength, etc.

To my knowledge, Mexico does not maintain an internet downloadable, official database in file form like the FCC or Industry Canada does. It would be nice if they did.

Mediumwave DX Meets the eReader

We have seen how to create personalized station lists at no cost in the first installment of this series. We can even create a file system of antenna pattern plots. But, as stated, who wants to print all of this and haul it around, not to mention the expense of all the paper and ink?

A couple of ideas come to mind. Save the desired station lists and pattern plots to a flash drive, then take it and our laptop to the field where we will have access to the information. But even a laptop is cumbersome to haul around when you are already carrying radios, headphones, loop antennas, wire, etc. And a laptop generally only has a battery life of a couple of hours before it is dead.

A number of years ago I toyed with the idea of loading text files on a PDA (Personal Data Assistant) device, like a Palm Pilot. There were ways to do this at the time, and you had to be a bit of a geek to figure it out. My idea was to load station lists and other textual documents for reference in the field. But upon further examination, it seemed like reading text on such a tiny device with poor screen resolution was not the way to go. I resisted, waiting for technology to advance. It did.

The dedicated ereader device appeared. At first they were cumbersome to use, and extremely proprietary - having almost no support for anything but books. Finally a couple of years ago the market shifted directions. Manufacturers had at last gotten the word that the public wanted some versatility in their ereader. Text files and .PDF files became compatible and well-supported, along with a host of other common file types like HTML, images, and video.

And with that direction change came the Kindle 3 by Amazon and the Nook Color by Barnes and Noble. I bought a Nook Color. It cost $250. Natively, it will display text files and HTML files, as well as .JPEGs and other image formats. It has a marvelous .PDF viewer. Most of these modes have zoom capability, making viewing easier. Amazon's Kindle 3 ereader device has similar features, though getting .PDFs and text across to them is a little quirky. Tablet computers also abound today, like Apple's iPad2 and the Samsung Galaxy. Virtually all have the ability to handle these same file types.

So, we are set. What we will do is load our saved station reference files to our ereader device. The 7-inch Nook Color ereader is small, the size of a paperback book, and thin, hardly 1/2 inch thick. It is ultimately portable, and can be carried easily wherever we want to go.

The ereader with its 8 gigabyte memory can hold the entire US mediumwave station reference if we choose, and many times over. And that includes the antenna pattern plots if we elect to save them too. No paper, no ink. It can be carried anywhere. Its battery life can be 8 hours (Nook Color, LCD display) to almost a month with one hour per day of reading (Kindle 3 or Barnes and Noble Simple Touch, both e-ink displays). Files are usually searchable. This means that you can locate a frequency or station call sign or format or whatever you are searching for quickly. Not as easy with a 500+ page paper volume.

The only requirement is that we come up with some sort of way to arrange our mediumwave files in an organized fashion so we can have quick access to them. Easily done.

Some ideas on file arranging:

1. Create folders named by frequency or by frequency block (range) to hold station files.
2. Create folders by state name to hold station files from that state.
3. Create folders by city name to hold station files from that city area.
4. Name the files themselves to include call sign and frequency to aid in recognition.

Our master copy folder and file scheme can be created on the laptop and housed there for safe keeping. It will be a simple matter of transferring the master database over to the ereader by dragging and dropping files or folders from one unit to the other when the ereader is cabled to the laptop through the USB port.

For those that have tablet computing devices instead of dedicated ereaders, the procedure would be similar. I am convinced the ereader or tablet device is the way to go for taking mediumwave station lists to the field. Give it some thought.

Also see: Mediumwave DX Meets The Tablet Computer

Mediumwave Station Reference Lists

I DX a lot outside, whether on the road in a vehicle or just to be outside and away from the extreme household noise that we find today. Whether you be a mediumwave DXer, shortwave DXer, or DXer of another kind, the problem in DXing away from home has always been the lack of ready DX reference materials nearby. You have to pack and carry all that stuff. And I like to travel light. My outdoor DXing is often casual and spur of the moment, with a ULR or portable. Who might that weak station be under KHOW-630? I need a station reference.

At minimum, a reference guide of stations helps you to know what to look for and what to expect, so it is important to have one close by. In recent years there were two common radio DXer guides in bound-book form, the World Radio TV Handbook (WRTH) and Passport to Worldband Radio. I used to buy them faithfully every year. Passport had a great radio review section, but its station reference only covered the shortwave bands. Passport also folded last year and ceased publication. It was a great shortwave guide.

WRTH covers longwave to 30 MHz and also FM and TV, listing nearly every broadcast radio and TV station a country has. Unfortunately, its US mediumwave coverage is not complete, in that it doesn't cover many lower powered and graveyard stations. The information is scant, basically only station addresses, power, and antenna type. The recent list price: $35.00 per issue, though it can be had at a discount later in the year. That's a lot of dollars for a little bit of usable information if you are just interested in mediumwave.

The National Radio Club publishes its AM Radio Log every year, and it's a winner. The current, 32nd edition of the log contains some 300 pages in 8.5 x 11 inch size, 3-hole punched, in U.S. loose leaf format. Current cost is $20 for members and $26 for non-members.

The NRC also publishes an Antenna Pattern Book, helpful in determining which direction stations are favoring in their broadcast pattern. The current, 6th edition (late 2005 data) is 238 pages containing both daytime and nightime patterns for stations in the US, Canada and parts of Mexico. It is in the same format as the AM Radio Log, and is designed to be used as a companion to it. The "book" fits in a 1 inch three ring binder. The current cost: $17 for members and $23 for non-members.

We are starting to accumulate a lot of paper (500+ pages so far). And the cost is going up. As you can see, reference guides can be expensive to buy. They also go out of date quickly. Thirdly, they can be heavy and take up a lot of space. We are back to the packing and carrying problem.

In the article, Radio Station Databases 101, we explored several countries' mediumwave databases which might help us in creating our own lists of mediumwave stations to aid us in our DX quests.

However, database information is not generally in a readable format. In most cases it is hundreds or thousands of lines of incomprehensible textual data. It is mainly useful to the software hobbyist who might want to write a database program or create an XCEL (.XLS) file to display station information in various sorted forms. This is obviously a highly technical and tedious endeavor which most people are not equipped or trained to do. My own project in this area is the Radio Data MW program. I will write more on this project at a later date.

Thankfully, a number of web sites exist which have done much of the work for us, tabulating this data and presenting it in one form or another which can be useful as a reference. These web pages, or in some cases, files, can simply be printed and placed into a binder of some sort, then used in your shack or carried to an outside DX location and used there. We have at least saved cost, though not paper.

Let's explore what's available for free on the web.

Pre-eminate in the field, the FCC maintains an AM Query web page that utilizes and searches its standard database for all US stations - AM, FM, and TV, as well as Travelers Information (TIS) stations. I have found the FCC information for US stations to be highly accurate. Be wary of Canadian and Mexican information. Much of it is either redundant or out of date. Properly used, the FCC AM Query will output a large text file of all MW stations.

Opening the web page and selecting the dropdown boxes, "Authorization type: Licensed Records Only (Daytime + Nighttime" and "Output-- AM Short List (or AM List)", then clicking the Submit Data button returns a huge list of active stations. Save this to a file, print it, and you have the entire US mediumwave listing. But it is huge, some 8 megabytes in some cases. You can also search by frequency or state, thus you can create customized lists, saving and printing them.

The FCC also makes antenna pattern plots available. Virtually all stations with multiple towers have directional patterns and the FCC makes this plot available in PDF form. Once displayed in your browser, this PDF can be saved to a file for future reference. Pull up the page for the station of interest to get to the pattern link. Example: WWKB-1520 facility and WWKB-1520 pattern.

radio-locator.com, a favorite site of mine, also has an advanced station search page. Many of us think of radio-locator only as the site that shows us mediumwave antenna pattern plots. The great thing about their page is you can also plug in parameters to filter stations by frequency or state. You can even search by broadcast format. Results are returned in formatted HTML pages. Save the resultant pages to file, print them, and create your own database of stations.

As just stated, radio-locator.com is another site which produces antenna pattern plots. These particular plots depict the expected signal coverage area of the mediumwave station over a map. The pattern plot is displayed as a GIF image. Once displayed in your browser, this GIF can be also saved to a file for future reference. Example: WWKB-1520 pattern.

am-dx.com is a simple textual site that tallies all US stations by frequency. Canada and Mexico are also available. Pick a frequency, display the list, save it, then print it.

The AM Logbook by Lee Freshwater is another interesting site that lists stations in a myriad of ways. Frequency, call sign, state, city, sites (transmitter), slogan, etc. Again, select your preference, display the list, save it, then print it. US and Canadian stations are represented.

AM Logbook also provides its current AM database in spreadsheet (XCEL) format. You must of course have an XCEL (.XLS) viewer. You'll find the link on the Updates page.

Topaz Designs is a basic textual site with search box, returning results by frequency, state, power cutoff (100W), and broadcast format. US and Canadian stations are represented.

Mediumwave List is a comprehensive site that offers a lot of information, including transmitter mapping, logbooks of users, and station news. Worldwide mediumwave stations are represented, including of course North America - Canada, Mexico, Cuba, the Caribbean, etc. To create your station list, login if you are a member or click "Continue as guest". This site will also allow you to download files from their huge database of stations, by region or country. The output is in PDF form. Registration is required for certain information beyond the basic.

Outside of the US, the Mexican government provides a very nice list of their mediumwave service in PDF form. Australia provides a list of their mediumwave service in XCEL form. Using the Industry Canada site, you can search the Canadian mediumwave service and create various lists in text, HTML, and XCEL form.

Note that most of these sites return station lists in a web page (HTML format) versus a simple text page. Lists can be saved as a web page by the Save As function in your browser. But there is also another way. It is possible to select the important data on the web page, copy it to the Windows clipboard (CTRL+C), then paste it into a text editor (CTRL-V). The text can then be saved as a text file, which may require a little editing. Sometimes it is easier to read this way. If you go this route, be sure to use a text editor that supports Unicode text format, like Window's Wordpad, Notepad++, etc. Window's Notepad does not, and you may get a jumble of text with no line breaks.

So, we have several options available for saving and/or printing station lists. We have two options available for saving and/or printing antenna pattern plots. If you choose to print some or all of these and place the pages in a binder of some sort, all well and good. But a comprehensive list of the entire US database is still a lot of paper to store, pack, and carry around. Of course we could just save all these files to a laptop and take the laptop with us. There is also one another option.

Next up: Mediumwave DX Meets the eReader

Also see: Mediumwave DX Meets The Tablet Computer

The Field Strength Machine

What do professional broadcasters and the FCC use to measure the field strength of a mediumwave station? Let me assure you they don't use charts and graphs like we hobbyists do. Let's find out.

What appears to be the premium device on the market today for field strength measuring is the Potomac Instruments PI-4100 Medium Wave Field Strength Meter, available from Potomac Instruments of Frederick, MD, and shown in the photo just above. It is Potomac's "third generation of precision survey instrumentation intended for the direct measurement of electromagnetic field strength in the 520 KHz to 5.1 MHz frequency spectrum."

This meter has a laboratory quality radio frequency voltmeter, a calibrated, Balanced Loop antenna, an internal GPS receiver, an internal calibration source, and data acquisition hardware and software. The unit weighs in at about 5.5 lbs. It is the successor to the previous industry standard, the FIM-41 meter, also by Potomac.

Also included in the 4100 is a spectrum display. Sensitivity is phenomenal, from 22 µV/m (microvolts per meter) to 50,000 mV/m (millivolts per meter). And there is no "meter" as with old units; everything is indicated digitally and calibrated automatically. The on-board GPS indicates your current coordinates as well as the distance and bearing to the station. It even includes a "wet" compass. For more information, see the Radio World product survey.

Oh, what I wouldn't give to spend a day with one of these. What is the price, you ask?

A cool $14,975. You can pick up a used one for about $13,000. Or, you might be able to buy a second-hand FIM-41 for about $5,000, or rent such an older unit for $595 per week. I can only dream.

The older, Potomac Industries FIM-41 unit:

The Perfectly-Spaced Passive Loop

Let's build a passive loop with perfectly spaced coil turns.

One of the problems I've always encountered in constructing passive loops is keeping the coil turns evenly spaced and perfectly parallel to each other. Regardless if you form a loop support in the form of a cross or a square, you must devise a way to space the turns evenly at each corner. Traditionally I would make the support of wood (usually 1 x 2 lumber) and file notches in the corners for the wire to sit into, or pound many tiny nails in a row to hold the wire apart. It's tough to file evenly-spaced notches very close together and tedious to pound a lot of tiny nails.

I tend to use light gauge insulated, solid copper wire for my loops. Stripped-out four conductor telephone wire is cheap and easy, usually running about 24 gauge. It's nice and light, flexible, and holds its shape. Have a walk around a hardware store and you will find many other items that might be used in the construction of antenna devices. One day, I came across some short plastic pipe nipples, generally used in sprinkling system work. These were 3/4 inch pipe size (3/4 inside diameter) and 1.5 inches long. They are threaded the entire way across, with thread spacing at 14 threads per inch (0.0714") apart - perfect thread spacing for this sized wire. The thread notch is just deep enough to accommodate most small sized wire. It would be difficult to file notches or drive tiny nails this precisely together. 1/2 inch diameter pipe nipples could also be used, as the thread spacing is the same.

I built a square frame for this loop, 24 inches on a side, again out of 1 x 2 inch wood, commonly called "furring strip". At each corner and at the center of each side I screwed a 2 inch screw (8 screws total) to hang the plastic pipe nipples on. One could probably use wooden pegs to avoid the metal screws being near the loop wires, but I have not found it a problem as it's a small amount of metal, and at 90 degrees to the wires. I placed a plastic nipple on each screw. The screws don't actually fasten the nipples down, but the nipples sort of pivot on each screw and move with the wire, settling where they need and taking up the wire tension. Use a screw with a wide enough head to capture the nipple so it doesn't slip off the screw.

The loop requires about 90 feet of wire, 11 full turns in all. I mounted a 365pf variable capacitor for tuning near one corner. Drive two very small nails into the frame at the same corner as the variable capacitor to secure the start and end of the coil. Fasten the wire to start and begin winding the loop, making sure the wire sits into each nipple thread from the thread closest to the frame and working towards the outside. Run the last leg of the final coil turn back to the ending nail and fasten there. Solder the start and end of the loop to the capacitor. Install a knob on the capacitor and you are done. This loop tunes precisely between 530 KHz and 1700 KHz.

PVC could be adapted to use as a frame, and I considered this before using the wood. A 3-legged, 3/4 inch PVC corner tee is available which has a female pipe thread at the center leg. The nipples would be screwed into this leg of each tee to form the corners of the loop like we did with the wooden frame. A PVC frame would be totally portable, as it could be disassembled very easily.

I find a loop with perfectly spaced turns to have sharper nulls and more precise (sharper) tuning. Try this loop sometime.