## Thursday, December 20, 2012

### Field Strength Calculator One

Field Strength Calculator One is a program which will calculate expected received ground wave signal strength at longwave and mediumwave frequencies.

Click image to enlarge.

To download, see the link at the top of the right sidebar under LATEST PROGRAMS. The sidebar at the top right will have the most current link in case the program is updated. The link will change in the case of an update, so I would avoid copying and pasting it into a forum or other web page. Come to the main page of this blog instead.

DISCUSSION

Being a mediumwave DXer and particularly a daytime mediumwave DXer, I wanted a way to determine a "ballpark" signal strength for various stations not only in my immediate area, but out to 100, 200, or even more miles distant. I was unhappy with virtually all the web-based signal strength calculators found on the internet, as they use the vanilla Inverse-Square-Law to calculate signal attenuation. Fine, if you are in an outer space vacuum or on a perfecting conducting surface, but not even close in accuracy for normal people here on Mother Earth.

The few stand-alone programs out there were either wildly expensive, too complicated to use, inaccessible, or plainly won't work on the Windows platform. I set out to accumulate information, formulas, and data to start writing the field strength calculator program. Investigating the history and ferreting out the pertinent information to arrive at a simplified formula that was reasonably accurate took some time.

The result was and is Field Strength Calculator One. It is based on the work of numerous engineers and mathematicians, who, starting about 1909, spent some 50 years developing the extremely complicated formulas to predict accurate signal strength at mediumwave frequencies. The basic, simplified formula has been known since the 1930s, being slightly modified by various people and agencies since then. It is accurate to within a couple of percent of the big programs that calculate field strength - those using additional input like the transmit and receive array heights above average ground, and the earth's topographic elevation changes along the signal path.

Simplified ground wave electrical field intensity calculations can be made by the introduction of a shadow or diffraction factor in the Sommerfeld-Norton planar earth expression. A mouthful! This simply means that a factor is computed and introduced to account for the additional attenuation caused by wave diffraction out beyond the radio horizon. It permits one to calculate the ground wave E (electrical) field well beyond the geometric and radio horizon, where E field values are close to the atmospheric noise level.

Be sure to read about the history of how this fascinating formula came about in the recent article on RADIO-TIMETRAVELLER: Field Strength Calculations: A History. Many of the terms used in the previous and next paragraphs are explained.

The simplified formula used by Field Strength Calculator One takes into account Sommerfeld's original plane earth theory, modified by diffraction factoring. It uses an exponential function which takes into account the spherical earth diffraction effects, and acts on the planar earth equation even before the radio horizon is reached, so the resultant E field values, as a function of distance produce a continuous curve, thus rounding-in difficult intermediate distances.

The long-accepted concept of "numerical distance" (p0) and "phase angle" (b) are used in all calculations, two variables determined by frequency, distance, and dielectric constants of the ground as a radio conductor. Numerical distance depends not only on frequency and ground constants, but also on the actual distance to the transmitter. Phase angle is the measure of the power factor angle of the earth.

Field Strength Calculator One returns expected received field strength in millivolts per meter and dBu (also known as dBµV/m), based on ground conductivity, earth dielectric and several other input constants. It also displays the distance to the radio horizon and the signal path loss in dB, along with several more technical parameters. The resulting output of Field Strength Calculator One should be accurate in most cases to a couple of percent in the longwave and mediumwave bands. It compares favorably to ITU program GRWAVE and currently available FCC Ground Wave Conductivity graphs.

Field strength calculations by Field Strength Calculator One are based on the works of A.Sommerfeld (1909), B.Rolf (1930), K.A.Norton (1936), H.Bremmer (1949, 1958), NTIA Report 86-203 (1986), ITU-R P.368-7 (1992), and NTIA Report 99-368 (1999).

For further information on how field strength is calculated see the Field Strength Calculations Series previously published on RADIO-TIMETRAVELLER.

INSTALL

Install is simple. Download the .zip file and unzip. Click on the FieldStrengthCalculatorOne.exe file to run. This program makes no registry changes and saves no data to your hard drive. It has been developed and tested in Windows 7. It should work fine in Windows Vista and XP environments, and Windows 8. It is written in the old standby Visual Basic 6.

Included in the .zip is a readme.txt file. Be sure to have a look.

I hope you enjoy this program and find it useful.

 Potomac FIM-71 Field Strength Meter

## Sunday, December 16, 2012

### Field Strength Calculations: A History

A previous three-part series on RADIO-TIMETRAVELLER delved into Field Strength Calculations. It covered ground conductivity's effects on signal strength, measurements quantifying signal intensity, and how to use the FCC Groundwave Conductivity Graphs to calculate expected received signal strength. Mathematical formulas, somewhere, produced those graphs. What is their history? Might we use a simplified formula to calculate expected received signal strength for our DX purposes?

Let's continue with the story behind Field Strength Calculations and explore the 50 year quest for accuracy in calculating signal strength by mathematical formula. It is an interesting tale. We will finish with a handy field strength calculator program I wrote using a simplified formula.

When we talk about field strength, we are really talking about radio propagation - the behavior of radio waves when they are transmitted or propagated from one point on the earth to another, or into various parts of the atmosphere. In our formula quest, we will mostly be concerned with those signals that hug the ground, or "ground wave". It may surprise many who are new to the hobby of mediumwave DXing that daytime ground wave range for a mediumwave signal might extend out to as much as several hundred, and in extreme cases, nearly 1000 miles!

Accurate formulas for calculating expected signal strength at mediumwave and longwave frequencies took many years to develop. Radio originally inhabited the longwaves in its infancy. Many of Marconi's early broadcasts, including his 1905-1906 transatlantic tests, were sub-100 KHz. The trend would be decidedly upward in frequency and downward in wavelength.

At the end of World War I, a fierce battle ensued between the US government and the Department of the Navy over control of the airwaves. The Department of Commerce eventually won and became master of the air and the regulatory agency for commercial radio. They started by establishing two broadcast frequencies: 833 KHz (360 meters) and 619 KHz (485 meters). The Federal Radio Commission took charge in 1926, lasting until 1934 when the current Federal Communications Commission was formed.

Throughout the early years of radio, interest mounted to quantitatively determine the service area of broadcast stations. Engineers redoubled their efforts to derive an accurate attenuation formula. The radio world was focused on accuracy of measurements at broadcast frequencies.

"Accuracy" is the key word here. The Inverse-Square Law, as applied to physics, had been commonly known since Isaac Newton's day in the 1600s. Applied to radio, it stated that the power density of the wave is proportional to the inverse of the square of the distance from a point source. In other words, doubling the distance from a transmitter means that the power density of the radiated wave at that new location is reduced to one-quarter of its previous value. But did it apply?

"Free-space" formulas calculating signal loss in the vacuum of space or "perfectly conducting earth" using the so-called inverse-square law are indeed accurate for those environments. But the Earth is not a perfect conductor, nor does it represent perfect-world conditions. Free-space formulas alone are not usable for our purposes. You will find many of them on the web, even calculators, purporting to deliver a signal strength solution for a given transmitter-to-receiver distance. They can be ignored as inaccurate. In fact, they are not even close.

 Arnold Sommerfeld, 1868-1951

Mathematicians started with a "plane earth" (flat earth) theory when they first envisioned a signal attenuation formula. Brilliant, German-born genius Arnold Sommerfeld, nominated a record 81 times for the Nobel Prize during his lifetime, solved the plane earth general problem by 1909, publishing signal attenuation graphs in 1911. Bruno Rolf, basing his work on Sommerfeld's findings, published more attenuation graphs in 1930, some 21 years later. From this information, the Federal Radio Commission compiled formulas and curves, published in 1931. They were used in hearings and allocation matters at least until 1933. It was just the beginning.

In the intervening years from 1909 to 1930, four more scientists obtained independent solutions of the Sommerfeld problem which agreed with the 1909 solution. That is, except for one difference - an inverted mathematical sign. Apparently none of these authors noticed this discrepancy until the FCC's K.A. Norton, in a letter to the editor of "Nature" in 1935, pointed it out and showed that it was responsible for the anomalies in propagation predicted by the Sommerfeld-Rolf graphs. Norton in 1936 was able to construct a universal curve for prediction of field strength at relatively short distances.

Focusing on the plane earth theory, Sommerfeld expected that the surface or ground wave would be only slightly affected by the curvature of the earth since it is guided around the earth's curve in much the same manner as an electric field can follow around the bend in a wire with a comparatively small loss of energy. This explains the general success of the Sommerfeld plane earth formula at distances far beyond the line of sight. However, two major roadblocks to accuracy still existed.

The first, and most important, was "diffraction". The other, "intermediate distance".

Out beyond what is called the "radio horizon", radio signals undergo atmospheric and ionospheric diffraction, that is, refraction and scattering caused by atmospheric irregularities. This enables AM radio signals in low-noise environments to be received well after the transmitting antenna has dropped below the horizon. It has been shown theoretically that the ground wave attenuation factor at mediumwave frequencies is very little affected by diffraction at distances less than about 55 miles, the approximate "radio horizon" for mediumwave.

Norton, also in 1936, provided curves for greater distances in the diffraction region. These curves, however, were based on an incompletely developed theory. Mathematical solutions were being developed in Europe, and were two years away from completion. Europeans van der Pol and Bremmer published their paper in 1938, offering a more complete solution of the radio diffraction problem for propagation. Never-the-less, the calculation of field strength beyond the radio horizon still proved troublesome, though Norton's remarkable work clarified Sommerfeld's ground wave propagation theory.

The radio horizon at the longer wavelengths, including mediumwave, can be calculated quite simply.

For example, the radio horizon for a station transmitting on 600 KHz is about 59 miles.

By 1940 the FCC, through the work of K. A. Norton, had developed a practical method for constructing curves approximately representing the theoretical predictions. The method used the flat earth theory of Sommerfeld out to a distance of about 80 kilometers, and the diffraction theory of van der Pol and Bremmer at relatively great distances, those in excess of 200-300 kilometers depending on frequency and ground constants.

The gap in the curve was still intermediate distances. The Watson transformation, a theory originally described in 1918 by English mathematician G.N. Watson, was an attempt to connect the two. How to incorporate it into the general theory, to calculate the intermediate distances, was still the final problem. In the curves published in 1940, the gap was simply sketched in by a draftsman.

In 1952, George A. Hufford of the National Telecommunications and Information Administration provided a basis for unifying the ground wave prediction methods of Sommerfeld with Watson's diffraction transformation. It had been 43 years since Sommerfeld's 1909 thesis. There was finally light at the end of the tunnel. New curves were added in 1954 for very low conductivity. These were quite accurate, although freehand drawing was still necessary to join the Sommerfeld curve segment to the curve segment calculated for the diffraction field at relatively great distances.

Then in 1958, Hendricus Bremmer, the same Bremmer who in 1938 brought the general solution to the diffraction problem, provided correction terms which completed the search for the practical formula. Engineers could finally calculate ground wave field strength with accuracy. It had been 50 years in the making. The formula was born.

The FCC curves were considered satisfactory for regulatory purposes until it became necessary to convert to metric units toward the end of the 1970s. In a 1979 FCC report, it was recommended that a computer program be written for recalculating the curves using the methods in Bremmer's 1949 book. The program was subsequently used to produce new FCC curves in 1985 which agree within 1 to 2 decibels with the previous curves. However, the 1979 computer program was mathematically deficient in its ability to cover all the range of intermediate distances, and the great distance values it computed were shifted upward to force a match in the middle. FCC curves drawn for the X-band, 1605-1705 KHz, are the most recent. They are the result of precise calculations of field strength over the full range of distances of interest, including the previously troublesome intermediate distances.

And thus we have the short version of the history to achieve accuracy in field strength formulas. Stay tuned for the next installment, a program to calculate field strength, based on a simplified formula.

Next up: Field Strength Calculator One

 Original measured vs. calculated f/s values for KOA, Denver, 1934

## Wednesday, December 12, 2012

### Cross Country DX, Fall 2012

Greetings from the great southwest!

It's been awhile. Had a good trip across country during the last three weeks of October. Been busy getting life back in order the last few weeks, so apologies for no posting. Had some good DXing moments while crossing the mid-section of the country which I'd like to relate. Long distance daytime reception along the I-70 route from Columbus, OH to Denver, CO was good.

All reception on the road using 2006 Ford Ranger truck radio with 24 inch extension to whip antenna.

October 10.

WSM-650, Nashville, TN (50KW) hung in there from Ohio clear into central Missouri at mile marker 154, near Kingdom City, a distance of 346 miles. Final reception was at 13:30L. Very weak at the end, with long fades.

The next day, traveling through eastern Kansas on I-70, the following were heard with positive ID. All daylight hours, mid-morning, 9:00-10:00L. Sunrise was 06:35L.

October 11.

KOA-850, Denver, CO (50KW) at mile marker 343 (476 miles) Weak.
KKOB-770, Albuquerque, NM (50KW) at mile marker 336 (643 miles). Weak but steady.
KGAB-650, Cheyenne, WY (8.5KW) at mile marker 286 (444 miles). Very weak.
KHOW-630, Denver, CO (5KW) at mile marker 272 (416 miles). Weak.

KKOB-770, Albuquerque was the real surprise, with exceptional distance for the time of day.

More coming soon! An article on field strength calculations is in the works, plus a field strength calculator program for mediumwave. Stay tuned.