Sunday, January 14, 2024

C.Crane Twin Coil Ferrite Signal Booster DISCONTINUED!

It's always been in my head to try an actual C.Crane Twin Coil Ferrite Signal Booster. I've used tuned Q-stick devices before with a lot of success. They have sharp nulls and lots of inductive gain. The Crane unit promised more of the same with its 8-inch twin coil ferrite rod.

Checking the Crane website the other day, I was shocked to find that they have discontinued it. Now, if I want to give it a try, I'll have to find one elsewhere - maybe eBay. I see there are a few of them out there yet. I'd advise you to pick up one of these fabulous goodies before they are gone forever.

Wednesday, January 10, 2024

U.S. Broadcast Station Counts 1922-2022

100 years of AM broadcast in the U.S.

Shown below on the graph are the counts of licensed stations in the FCC's AM broadcast service for the years 1922-2022. You will see a steady rise in counts from 1922 to 1990.

I remember listening as a kid in Philadelphia in the very early 1960s. The band was literally alive with stations every night from as far away as St. Louis (KMOX), San Antonio (WOAI), New Orleans (WWL), Minneapolis (WCCO), and many others. Even the Mexican border blasters with the likes of Wolfman Jack were a normal catch every night.

We are in slow decline over the past thirty years and gaining more downward speed in the last ten. When will it end? What decade was the heyday of AM broadcasting? You decide.

Friday, November 24, 2023

Mediumwave Skywave Prediction #6 - Wrapping Things Up

Let's close up by defining a few of the terms used in the formulas from the last post, and finish by talking a bit about diurnal and seasonal effects.


Polarization coupling loss, sometimes depicted as Lp, is the fraction of incident power lost on entry into the ionosphere. Further polarization coupling loss occurs when the wave which emerges from the ionosphere induces a voltage in the receiving antenna. Polarization coupling loss depends to some extent on frequency and angle of incidence at the ionosphere. Polarization coupling losses are low in higher latitudes because the Earth's magnetic field is almost vertical. At the magnetic equator, however, the Earth's field is horizontal and polarization coupling losses on east-west paths are large.

Polarization coupling loss at MF is an important factor in skywave propagation. It arises because the Earth's natural gyromagnetic frequency lies within the frequency band being considered. The gyromagnetic frequency of the Earth's ionosphere varies between 800 kHz in the equatorial regions and 1600 kHz near the magnetic poles. When a linearly polarized mediumwave frequency radio wave enters the ionosphere, it gets split into two waves known as ordinary and extraordinary. At the gyromagnetic frequency the extraordinary wave is so greatly attenuated that it makes a negligible contribution to the received signal. As a consequence, the extraordinary wave can be disregarded within the mediumwave band. The propagation is therefore by the ordinary wave.

To explain further, conventional antennas at mediumwave radiate vertically-polarized waves. At MF, the wave which is accepted by the ionosphere and which will propagate back to Earth usually differs in polarization somewhat - hence the ionosphere may not be excited efficiently by the incident wave. We have decreased coupling efficiency, or polarization coupling loss. The wave which subsequently emerges from the ionosphere is in general elliptically-polarized and in-turn may not excite the receiving antenna efficiently because antennas near the ground are most sensitive to vertical polarization, resulting in additional loss.


For long distance paths (1000 to 6000 km or greater), when the path is over the sea and at least one end of the link is located on or near the sea coast, the phenomenon of sea gain can add from 3 to 10 dB to the predicted field strength. 

Gains peak at the usual single, double, and triple hop distances of 2000 km (8 dB), 4000 km (10 dB), and 6000 km (10 dB). Only about 3 dB is gained at the 1000 km distance. A dip in gain (to about 5 dB) occurs at about the 2500 and 5000 km distances.

A knowledge of the land-sea boundary information is necessary to assess the sea gain phenomena. Generally, in the skywave calculation, the sea gain correction is normally set to 0 dB without this knowledge. To take any advantage of sea gain, one of the terminals (transmitter or receiver) must be within about 10 km from the sea coast. Even at 10 km inland, the penalty is about -4 dB. At 4 km, about -2 dB. At 3 km, only about a -1 dB penalty.


Solar Cycle 25 is well on its way now, having started its general upward trend in sunspot count by late 2020. The daily sunspot count for August 30, 2023, for example, was 104.

Do sunspots effect nighttime skywave propagation at the medium waves? Yes they do, at a small but noticeable level. Here are the details.

Concerning medium wave, sunspots and the increasing solar flux are relevant to skywave field strength and are accounted for in most modern (nighttime) skywave prediction methods. In general, mediumwave skywave field strength is slightly better during low or zero sunspot periods, at the bottom of the solar cycle. The calculation of the additional path loss in dB is dependent on location.

Greater consideration is given to paths within North America and Europe (nearer to the north geomagnetic pole), and Australia (nearer to the south geomagnetic pole). The North American loss factor is 4 times that of Europe and Australia, and rises for all as we get to the higher latitudes. Longer paths, those between North America and Europe are usually interpolated.

The ITU skywave prediction method is one such method which incorporates these added loss factors due to sunspots and solar flux. Figures below have been extracted from that prediction method.

Below are increased single hop skywave loss factors in dB as the sunspot count goes up.

Paths within North America:

Sunspot count = 0 a net added loss of zero
Sunspot count = 7 an additional loss of 0.28 dB
Sunspot count = 25 an additional loss of 1 dB
Sunspot count = 50 an additional loss of 2 dB
Sunspot count = 100 an additional loss of 4 dB

Paths within Europe:

Sunspot count = 0 a net added loss of zero
Sunspot count = 7 an additional loss of 0.07 dB
Sunspot count = 25 an additional loss of 0.25 dB
Sunspot count = 50 an additional loss of 0.5 dB
Sunspot count = 100 an additional loss of 1 dB

Paths between North America and Europe:

Sunspot count = 0 a net added loss of zero
Sunspot count = 7 an additional loss of 0.175 dB
Sunspot count = 25 an additional loss of 0.625 dB
Sunspot count = 50 an additional loss of 1.25 dB
Sunspot count = 100 an additional loss of 2.5 dB

Admittedly, these extra losses are small but important enough that they are factored in for skywave calculations. Be aware that 3 or 4 dB can make a difference logging a station or not. A single S-unit is 6 dB.


The final determination which really completes our skywave field strength calculation must include three more tweaks:

1. Diurnal hourly losses/gains
2. Sunrise and sunset enhancements
3. Seasonally-driven losses/gains

The D-layer of the ionosphere is characterized as having a strong dependence on frequency, but this is present only during the daytime. The E-layer is the dominant contributor to LF and MF propagation at night and is only mildly dependent on frequency, so the effects of frequency of this layer can be neglected for most practical purposes.

Although daytime ionospheric propagation is relatively unimportant, it cannot be entirely disregarded at the upper end of the band, since ionospheric attenuation decreases with the square of the frequency. Nor can it be entirely disregarded at the lower end of the band, where partial reflection from the lower edge of the D region may occur, especially in winter at temperate latitudes.

The critical frequency of the normal E layer is about 1500 kHz at sunset, but it then falls rapidly as a result of electron-ion recombination and will assume a value of about 500 kHz late at night. Skywaves may be reflected from the E layer, or they may penetrate the E layer and be reflected from the F layer, depending on the frequency, path length, and time of night. Simultaneous reflection by both layers is also possible in some circumstances. 

Upper MW band diurnal (or daily) morning enhancement can show effect as late as 3 hours after sunrise. The start of the pre-sunset afternoon enhancement is delayed a little to about 2 hours before sunset, gradually building to sunset. The lower part of the band shows little of this effect, morning or night.

The diurnal enhancement described in the last paragraph is not to be confused with the short sunrise and sunset enhancements on extreme DX due to what is called "greyline effect", the signal traveling along, or partly along, the sunrise/sunset terminator.

Skywave propagation does indeed exist during the daytime hours, and its strength varies greatly, seasonally.

Daytime, noon-hour skywave is generally pegged at approximately 30 dB lower than the nighttime field-strength prediction, and this will vary considerably seasonally. An ionospheric transition period occurs immediately surrounding sunset and lasts till approximately four hours after sunset, and another occurs during the period from 2 hours before sunrise until sunrise where the field strength goes through this 30 dB change with a very steep slope. The shapes of the curves are not symmetrical for the transition from day-to-night and night-to-day.


In this series I have attempted to present to you first a little history skywave propagation analysis, who developed the formulas and how they are geographically dependent, and the formulas themselves. I hope it has brought some perspective to the process and you have enjoyed it.

Monday, September 11, 2023

Mediumwave Skywave Prediction #5 - Dissecting The Formulas

We'll get to the actual skywave prediction formulas shortly, but first let's talk about how to calculate the geomagnetic midpoint of our signal path. To get this, we'll need the latitude and longitude of both the transmitter and receiver sites. We'll also need the latitude and longitude of geomagnetic north, which moves by small increments each year. A nice chart can be found at:

The following geomagnetic north pole coordinates are accurate for 2023:

    dipoleN = 80.8° latitude (actual)
    dipoleW = 72.7° longitude (actual) -use a positive number in the final mid-point formula

Note: dipoleN and dipoleW are the geomagnetic north pole, NOT the magnetic north pole. There is a difference. To reiterate from the previous post, 'geomagnetic poles (dipole poles) are the intersections of the Earth's surface and the axis of a bar magnet hypothetically placed at the center the Earth by which we approximate the geomagnetic field. They differ greatly from the magnetic poles, which are the points at which magnetic needles become vertical. The magnetic poles are what has been "wandering", a subject in the news lately, but they drag the geomagnetic poles with them too, albeit at a lesser rate.'

First we'll calculate the actual geographic mid-point latitude and longitude between transmitter and receiver. The Movable-Type scripts website has our formula to do that:

Many websites have geographic mid-point calculators as well. Those familiar with Javascript can use the formula below or convert it to a different language if you wish to do the calculation yourself.

lat1 = transmitter latitude in degrees
lon1 = transmitter longitude in degrees
lat2 = receiver latitude in degrees
lon2 = receiver longitude in degrees

double dLon = Math.toRadians(lon2 - lon1);

    //convert to radians
    lat1 = Math.toRadians(lat1);
    lat2 = Math.toRadians(lat2);
    lon1 = Math.toRadians(lon1);

    double Bx = Math.cos(lat2) * Math.cos(dLon);
    double By = Math.cos(lat2) * Math.sin(dLon);
    double lat3 = Math.atan2(Math.sin(lat1) + Math.sin(lat2), Math.sqrt((Math.cos(lat1) + Bx) * (Math.cos(lat1) + Bx) + By * By));
    double lon3 = lon1 + Math.atan2(By, Math.cos(lat1) + Bx);

    //answer in degrees
    mid_lat = Math.toDegrees(lat3);
    mid_lon = Math.toDegrees(lon3);

mid_lat and mid_lon is the actual geographic mid-point of our path.

Now, we'll use a separate formula to translate the actual mid-point latitude-longitude to geomagnetic latitude:

    ThetaM(radians) = 
        Asin(Sin(mid_lat) * Sin(dipoleN) + Cos(mid_lat) * Cos(dipoleN) * Cos(dipoleW + mid_lon))

ThetaM will be in radians and must be converted to degrees. To do so:

    ThetaM(degrees) = (ThetaM(radians) * 180) / Pi

ThetaM is the geomagnetic latitude in degrees.

Let's dive right into the skywave prediction formulas. We know slant distance, geomagnetic latitude of the path mid-point, and we have everything we need to calculate Kr, the aggregated ionospheric losses. Take note that the skywave prediction normally is the prediction for the local midnight hour, equidistant between sunset and sunrise, commonly referred to as SS+6, or sunset + 6 hours.


The Wang method is the only method which offers good to excellent results for short and long paths alike at all frequencies in the LF/MF bands, at all latitudes, and in all regions. It has been demonstrated that the Wang method is the only method that can be considered a true worldwide method.

The Wang expression for field strength is:

Note: FS(dBu), is also known as dBµV/m.

Where: FS(dBu) is the field strength in dBµV/m, V is the transmitter cymomotive force above the reference 300 mV in dB (better known as our effective radiated power (ERP) referenced to 1 KW in the direction of interest). ThetaM is the mid-point transmitter and receiver geomagnetic latitude, Dslant is the slant distance in km. Kr, or generalized ionospheric losses, are described below.

In the Wang method, the 107 (dB) factor is used for most of the world. New Zealand and Australia use 110 dB, giving that part of the world a 3 dB field strength improvement (half an S-unit).

To convert FS(dBu) back to millivolts per meter: mV/m = 10 ^ (FS(dBu) / 20) / 1000

The generalized ionospheric losses are found in Wang's Kr factor. Both Wang and the FCC method calculate Kr in this manner:

Kr is the loss factor in dB, to include ionospheric absorption, focusing and terminal losses, losses between hops, geomagnetic latitude influence, and basic polarization coupling loss.

Where: ThetaM is the geomagnetic latitude defined previously. Dslant, the slant distance, will modify Kr accordingly.

Wang recommends that the geomagnetic mid-point latitude, ThetaM, be between -60 (south) and +60 degrees (north). When compared to the ITU expression, Wang's expression is symmetrical about zero degrees latitude and is not dependent on frequency.

Let's do a Kr loss example for a 1500 km slant path and see what our ionospheric losses are.

Here are the results for a single hop, 1500 kilometer (932 miles) slant distance for various mid-point locations. Using this Wang formula, I've prepared a chart showing the additional losses, in dB, caused by geomagnetic latitude influence.

Basic Loss  Deviation  Geo-Lat Mid-Point (actual location of)
---------- ----------- ------- ------------------------------
7.854 dB      0          9.19   0°N, over the equator
8.347 dB     +0.493dB   18.15  10°N, over Venezuela
10.637 dB    +2.783dB   34.86  25°N, over south Florida
11.778 dB    +3.924dB   39.37  30°N, over north Florida
14.553 dB    +6.669dB   46.76  38°N, over Richmond VA
17.889 dB   +10.035dB   52.36  43°N, over Rochester NY
18.767 dB   +10.913dB   53.50  45°N, over Minneapolis MN
21.233 dB   +13.379dB   56.21  48°N, over Grand Forks ND

Basic Loss = the basic loss on this 1500 km path. The first entry has its mid-point (reflection point) over the equator.
Deviation = additional loss incurred as latitudes increase using the basic equator loss as the base.
Geo-Lat = the adjusted geomagnetic latitude of the reflection mid-point.
Mid-Point = the actual geographic location of the reflection midpoint.

As you can see, we have lost over 13 dB in field strength when the reflection point is at 48° actual latitude!

Here is an example of how geomagnetic positioning of the signal path affects the final field strength result. Reception of KFAB (1110 kHz), Omaha, Nebraska (41.23°N, 96.0°W) here in Rochester, NY, places the mid-point of our ionospheric reflection at a geomagnetic latitude of 51.355 degrees. The slant distance is 1548 km. An overall Kr loss of 17.45 dB gives an additional geomagnetic position penalty of some extra 9.596 dB over tropical paths!

Now, let's calculate an expected skywave field strength value for 50 KW KFAB-1110 here in Rochester, NY. From above, we already know our slant distance is 1548 km. Our Kr loss factor from the example above is 17.45 dB.

FS(dBu) = V(-18.739) + 107 - 20 * Log10(1548) - 17.45

FS(dBu) = 7.01

Converting to millivolts per meter:

mV/m = 10 ^ (FS(dBu) / 20) / 1000 ...convert dBu back to mV/m, or:

.00224 = 10 ^ (7.01 / 20) / 1000

.00224 mV/m is a weak signal indeed.

Why such a weak signal from a 50 KW powerhouse station at only ~1500 km? We are placed perfectly in KFAB's deep cardioid pattern notch at 76 degrees azimuth and a 4 degree takeoff angle. Facing us at those angles is a theoretical and nearly-microscopic 12.72 watts ERP. This is a primary lesson we learn from tower array pattern analysis, both skywave and groundwave. One will naturally think, "Well, it's a 50 KW station, and only a mere 960 miles distant. I should be getting a pretty good signal". Not necessarily so. If you are in a deep notch of a pattern, you may only be "seeing" a few watts facing you.

Take a look at the graphic below. You will see the deep cardioid notch of KFAB's nighttime pattern. Stations to the east suffer a great signal loss.

KFAB Nighttime Pattern. Click for larger image.

Where did the V(-18.739) figure come from, you ask? That is KFAB's facing 12.72 watts aimed at us, referenced to 1 KW, in dBW. It is 18.739 dB down from 1 KW. How did we get this and the 12.72 watts figure? The FCC has some rather serious formulas which will calculate power and mV/m levels delivered at any azimuth and elevation angle for any tower array. The FCC website for the station also provides a basic chart for each compass degree around the tower array, listing mV/m levels. This is the easiest to use, although it is calculated for 0 degrees takeoff elevation.


The FCC method has close resemblance to the Wang method. The FCC expression for field strength is:

Note: FS(dBu), is also known as dBµV/m (normalized to 100 mV/m, in dBµV/m per 100 mV/m).

Where: FS(dBu) is the field strength in dBµV/m, ThetaM is the mid-point transmitter and receiver geomagnetic latitude, Dslant is the slant distance in km. Kr, or generalized ionospheric losses, are described below.

The FCC formula would appear to not include any system gain, referred previously as "transmitter cymomotive force above the reference 300 mV in dB". The field strength predicted is normalized to 100 mV/m (in dBµV/m per 100 mV/m). We must convert this back to the actual mV/m value by multiplying by the number of 100 mV/m "portions" we have in the total mV/m measurement at 1 km. The total mV/m measurement is calculated and published by the FCC for each compass degree. This figure also contains our tower array gain - our effective radiated power (ERP) referenced to 1 KW from a quarterwave monopole.

Converting to millivolts per meter, again:

mV100 = 10 ^ (FS(dBu) / 20) / 1000 ...convert dBu back to mV/m

mV/m = mV100 * (measured_mVm@1km / 100) ...corrected to actual mV/m 

The FCC formula uses Wang's identical Kr factor. The generalized ionospheric losses are again found in it:

Refer to the previous discussion of Kr, above, in the Wang equation. Their usage is identical.

Wang again recommends that the geomagnetic mid-point latitude, ThetaM, be between -60 (south) and +60 degrees (north). It is not dependent on frequency.


The ITU expression for field strength is:

Note: FS(dBu), is also known as dBµV/m.

Where: FS(dBu) is the field strength in dBµV/m, V is the transmitter cymomotive force above (or below) the reference 300 mV in dB, Gs is the sea gain correction in dB, Lp is the excess polarization coupling loss in dB (defined graphically in ITU Recommendation 435-7), ThetaM is the mid-point transmitter and receiver geomagnetic latitude, Dslant is the slant distance in km. Kr, or generalized ionospheric losses, are described below.

Converting to millivolts per meter, again:

mV/m = 10 ^ (FS(dBu) / 20) / 1000 ...convert dBu back to mV/m

The ITU formula applies the basic path loss elements, the slant distance and the mid-point geomagnetic latitude influence. It also attempts to quantify some of the additional ionospheric losses I alluded to in an earlier post:

1. Sea gains (separately, as Gs)
2. Excess polarization coupling losses (separately, as Lp)
3. Sunspot influence (specified within Kr, as R)
4. Regional loss due to solar activity (calculated within Kr, as bsa * R)

The generalized ionospheric losses are found in the ITU's Kr factor:

Kr is the loss factor in dB, to include ionospheric absorption, focusing and terminal losses, and losses between hops, geomagnetic latitude factor, and basic polarization coupling loss. Unlike the Wang and FCC formulas, the ITU formula incorporates a sunspot factor and a frequency factor as well.

Where: f is the frequency in kHz, and ThetaM is the geomagnetic latitude defined previously. ThetaM must not exceed 60 degrees north or -60 degrees south. For paths shorter than 3000 km, the ITU suggests simply using the geographic mid-point between transmitter and receiver. Note: this, on average, skews results about 6 dB higher for North America.

Where: R is the twelve-month smoothed international relative sunspot number, bsa is the regional solar activity factor (bsa=0 for LF band; bsa=4 for MF band for North American paths, 1 for Europe and Australia, and 0 elsewhere). For paths where the terminals are in different regions we use the average value of bsa, for example: Europe to the USA, 2.5.

Note that we have a frequency correction, a geomagnetic latitude (ThetaM) correction, a regional correction in bsa (North America has the highest absorption), and a sunspot count correction.

The sharp analyst will notice that the ITU's frequency correction results in greater loss at higher frequencies, something perhaps theoretically sound, but not observed in North America (shown by measurements). The ITU suggests that for North America, a fixed frequency of 1000 kHz should be used.

Sea gain (Gs) is included in the ITU formula, but is usually set to zero and not accounted for since the transmitting or receiving station must be very close to a coastal point, generally within ten kilometers, and having a path length of thousands of kilometers. Lp, excess polarization coupling loss, is also included. This is an attempt to compensate for Lp differences in the generalized Kr part of the formula. We generally leave this at zero.


The modern day formula for the Cairo curve, adapted to Region 2, is presented for informational purposes. The resultant field strength should be further modified by subtracting ionospheric absorption losses (Kr), and adding any antenna gain.

The Cairo Curve, Revised for North America, Region 2

Where D is the overland great circle distance in kilometers between transmitter and receiver.

Again, we find our result in dBu per 100 mV/m (NTIA Report 99-368). It must be converted back to actual mV/m, as does the FCC formula.

mV100 = 10 ^ (FS(dBu) / 20) / 1000 ...convert dBu back to mV/m

mV/m = mV100 * (measured_mVm@1km / 100) ...corrected to actual mV/m

In the final part of this series on skywave prediction we will wrap up by discussing polarization coupling loss, sea gain, solar cycle losses, and diurnal and seasonal effects on mediumwave propagation.