Converting electrical degrees to height in meters or feet

Here is one of those things that can often be a head-scratcher for the uninitiated:

The FCC database gives antenna height in electrical degrees when what you really want to know is how tall is that tower.  Never fear, figuring all this out, requires math.  Pretty simple math at that, too.  I prefer to do these calculations in metric, it is easier and the final product can be converted to feet if that is desired.

First of all, radio waves travel at the speed of light, known as “c” in many scientific circles.  Therefore, a quick lookup shows the speed of light is 299,792,458 meters per second (m/s).  That is in a vacuum, in a steel tower, there is a velocity factor, most often calculated as 95%, so we have to reduce the speed of light in a vacuum to the speed of RF in a steel tower.

299,792,458 m/s × .95 = 284,802,835 m/s (speed of a radio wave in a steel tower)

Frequencies for AM radio are often given in KHz, which is 1000 cycles per second.  For example, 1,370 KHz × 1000 = 1,370,000 Hz (or c/s)

Therefore:

284,802,835 m/s ÷ 1,370,000 c/s = 207 meters per cycle.  Therefore the wavelength is 207 meters.

There are 360 degrees per cycle, therefore:

207 meters ÷ 360° = 0.575 meters per degree

If the height of the tower is 90°, then 90° × 0.575 m/° = 51.57 meters.  Add to that the height of the base insulator (if there is one) and the concrete tower base and that is the total tower height.

To convert meters to feet, multiply by 3.2808399.

In the United States, that tower would be 169.78 feet tall.

History of the WGY broadcasting tower

To any who lives in the capital region, the WGY tower near the intersection of I-90 and I-88 in the town of Rotterdam is a familiar site.  It is big, tall, and conspicuously marked with a huge “81 WGY” on the southwest face of the tower.   At night the call letters used to be lit up by a spotlight but that may have been turned off in recent years.

In my time as chief engineer there, I found several file folders of memos and other materials about the building of the tower, which started in 1936.  Prior to that, WGY used a T-top wire antenna, first from the General Electric plant in Schenectady (1922-25) and then from the current tower site in Rotterdam.  Located with WGY were GE’s experimental shortwave stations W2XAF and W2XAD.

When the station increased power to 50,000 watts in 1925, many reports of fading were received from locations 20-50 miles away.  WGY engineers studied the situation by doing a full proof on the antenna.  They found an elliptical-shaped pattern with nulls to the north and south.  This coincided approximately with the T arms of the T top antenna, likely due to the self-resonating effect of the support towers for the ends of the T.

NBC, then owners of WJZ (now WABC) in NYC had studied this problem for years and came up with a new antenna design for Standard Broadcast, the uniform cross-section guyed tower.  Starting in 1935, WGY began to investigate installing such a tower in South Schenectady, as the transmitter site was then known.  One report showed an efficiency gain of 430% over the T top antenna that was in use.  The General Electric construction and engineering department raised several objects to the standard triangular tower then and now commonly used for AM radiators.

Much mechanical planning and effort went into the design of the tower, which is a square tower, a 9-foot face, 625 feet tall.   During the planning phase, KDKA was installing a similar tower, which collapsed when it was being erected in 1936.  An analysis of the failure showed that one of the guy anchor cable sockets pulled out of the concrete (which was improperly poured).  This may also be the reason why the KDKA tower collapsed in 2003, although I never read the engineering report on that failure.   Nevertheless,  GE Engineering felt that forging the members of a triangular tower weakens them and was too risky, thus, a square tower was the solution.

Further, every component of the tower was tested individually.  Often, two of a type were build, with one being tested to destruction.  Two base insulators were made for this specific tower.  The first was tested to destruction at the National Standards and Institutes laboratory in Washington DC.  It was found that the insulator withstood slightly more than 1,200,000 pounds of pressure.  The working load (tower dead weight) of the base insulator is calculated to be about 430,000 pounds, thus almost a 3:1 safety margin.

The wire rope used for the guy wires was also tested to destruction.  The working load on the upper guy is about 24,000 pounds, the wire rope broke at nearly 120,000 pounds.  The concrete, guy anchor sockets, T bars, and all other parts were likewise tested.

Electrically, the tower is 186 degrees (it was 180 degrees on 790 kHz, the former WGY frequency).  It had a 40 X 40 foot ground mat with 120 buried ground radials.  The ground radials were #4 hard drawn stranded copper.  When we investigated the system in 1999, it was complete and unbroken.  The radials, ground screen, strap and all other metal component showed no signs of deterioration.  It helps that the soil surrounding the tower is a sandy loam and well drained.

The tower was fed with 600 ohm open transmission line, 180 degrees long.  Initially, the system had been designed for high power operation up to 500 KW.  However, when the transmitter was replaced in 1980, a new Harris ATU was installed, which can only handle 50 KW.  I recall the base resistance to be 192 ohms with -j85 reactance.

A concrete wall surrounds the base insulator.  This was installed in early 1942 to prevent the base insulator from being shot out by sabbators during WWII.

When I worked there, the station had a Harris MW-50B transmitter.  This unit was in slightly better shape than its counterpart at WPTR across town.  I did find some of the same quirky things with it, however.  Our consulting engineer had a good line, “Harris, where no economy is spared…”

The site had a FEMA owned backup generator installed in the 60’s.  This was an Onan 225 KW diesel powered unit.  225KW is likely a conservative estimate as those units were way overbuilt.  The original fuel tank was buried out behind the building.  FEMA contracted for it’s removal in 1995 because of concerns of leaks and soil contamination.  When they dug it up, the primer was still on the tank.  After getting the tank out of the ground, the contractor cut a large hole in it and lowered a person into the tank to clean it out.  Something that should be profiled on the Dirties Jobs TV show.

The new tank was installed in the old outdoor transformer vault.  It is a 5000 gallon double walled above ground tank with monitoring system.

It has been several years since I have been to this site.  I know they installed a Harris DX-50 sometime in 2001 or so.  They also may have replaced the open transmission line.  WGY now transmits in HD radio, which they are able to do because the tower was well designed and installed.

Partly for my own edification, partly just because, here is some information about AM antenna systems and their bandwidth. An AM tower is a radiator that, simply by the physical constraints of the tower structure itself, is pretty narrow-banded, even under the best conditions. Add to that, antenna tuning units, transmission line phasing, antenna phasing units, diplexing units, and things can get very squished outside of the immediate carrier frequency. This seems to be a particular problem with directional antennas, which most AM stations employ.

As an engineer, you can get some idea of how narrow an antenna system’s bandwidth is by looking at the base impedance measurement.  Every AM station is required to keep the latest impedance measurement on file.  When looking at these measurements, there will be one curve that indicates base resistance (R) and another curve that indicates reactance ( X, although often noted as + or -j).  If the resistance and or reactance curve is slopped steeply at the carrier frequency and out to 20-30 kHz, it is a narrow tower.  Add to that the different phase shifts of an ATU and or Phasor and things will be compounded.  That is why it takes a professional to design and tune up these things, a poor design will never sound right.

Another way to get some idea of bandwidth requires a field strength meter.  Modulate the transmitter with a 10 kHz tone at 50% modulation.  Then, away from the near field, measure the carrier and 10 kHz +/- the carrier frequency on the log scale.  The sidebands should be symmetrical and about 1/4 the carrier level.

Generally speaking, antenna systems need to be designed for low VSWR across the entire side band range (+/- 10 kHz from the carrier) as well as symmetrical distribution of radiated energy across the lower and upper sidebands.  Several factors influence these conditions:

1. Electrical tower height is perhaps the hardest thing to change once a tower is constructed.  Short towers (less than 80 electrical degrees), or very tall towers, (taller than 200 electrical degrees) present problems.  If one were constructing an AM station and could choose any tower height, something between 120 to 190 electrical degrees would be ideal.  Existing towers can be top-loaded to add electrical height for an additional 30 degrees or so.  Beyond 30 degrees it becomes difficult to physically attain and therefore impractical in most situations.  Top loading and bottom loading of a tower can reduce bandwidth if done improperly.   Bottom loading an AM tower is almost never done due to the very high voltage and current as the electrical length approaches 180°.
2. Antenna matching networks can greatly improve or degrade bandwidth, depending on how they are designed.  A T-matching network has more parts and is more expensive, however, it allows for optimum control over the R and jX phasing.  This becomes much more difficult with directional antenna where phase considerations are a part of the station’s antenna field pattern development.
3. Phasors present the biggest challenge, particularly in the power divider sections.  A tank circuit power divider is the worst choice, and a shunt circuit power divider is the best bandwidth choice, however, it is the hardest to conceptualize.

Obviously, the more complicated the antenna system, the harder it will be to keep the bandwidth open over 20 kHz of spectrum.  This is especially true on lower-frequency AM signals, where the bandwidth is a much larger percentage of the frequency.   Multiple patterns, multiple tower DAs are a nightmare.  Single-tower non-directional stations are the easiest to modify.

As far as the circuit itself, higher Q circuits have smaller bandwidths.  Simply stated, in an alternating current circuit, Q=X/R.  The better the reduction of X, which also has a lot to do with the relationship of the current and voltage phasing, the better the Q will be.  This is why a T network is the best design for an ATU.  With a 90° or 180° tower, this is relatively straightforward.  In towers that are shorter or taller than that, it becomes more difficult as the value of R becomes less friendly.

In most cases, some sort of L/C network can be deployed to decrease the Q of an antenna system at the base of the tower.  Directional stations also need to have the phasing equipment looked at, because, as noted above, certain designs can create bandwidth bottlenecks.  All in all, it is usually an expensive proposition for a multi-tower directional station to broadband its antenna system.  This is another reason why IBOC on AM is destined to fail, many AM towers cannot pass the extended sidebands adequately.