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Friday, March 13, 2020

Mediumwave Loop Efficiency For The DXer

Many DXers are aware that an external, passive air core loop antenna can be tuned and coupled inductively to a portable mediumwave radio. Signal enhancement is usually quite good.

DXers may be unaware that an external air core loop antenna can be wired directly to the current corral of DSP radios. It is spelled out right in the manufacturer's data sheet for the Silicon Labs radio chips. It replaces, and is soldered in place of the internal ferrite loop. The document suggests a loop of minimal turns connected to the circuit board through a 1:5 winding (the so-called 25x step-up ferrite core transformer) thus providing the correct coil inductance of 180-450 micro-Henries. It was apparent to me that using a full inductance loop was also possible, bypassing the need for the transformer. This would also result in greater signal gathering ability. Some time ago I did an article called A Hardwired Loop For DSP Radios on this blog.

Loop tuned by a capacitor

Using an air core loop and the signal measuring capabilities of many of these radios we can determine a number of interesting things not possible with other analog or digital superheterodyne radios off the shelf. Today I thought we'd take a look at the mathematics of these loops, both passive and directly-wired. Don't be scared off by the mathematics of it - the toughest thing you will have to wrestle with is multiplication and division, or possibly getting the logarithm of a number from a calculator.

We will answer some interesting questions:

  • How big of a signal can I expect from a passive loop antenna of a certain size?
  • How much better will it be if I increase its size?
  • How much signal voltage is generated at the loop output for a certain field strength?
  • What about the reverse of this - what is the field required to generate that voltage?
  • What is the gain of my loop over the internal ferrite loop or another loop?

EVERYTHING IS PROPORTIONAL

The signal voltage induced in a loop is proportional - increases linearly - with the number of turns, the area of the loop, and the frequency being received. Bigger is better, within certain parameters. We can measure the output of the hard-wired loop in microvolts using the modern DSP receiver. This is indicated by the RSSI "dBµ" figure on the display. We can then use that figure in the same formula to calculate the apparent field strength of the signal.

Small loops, that is, loops where the total length of wire is less than 1/10 wavelength at the operating frequency, are called magnetic loops. They respond to the magnetic component of the passing wave. The loop is a transducer which transforms the electromagnetic wave energy into a usable voltage source. The number of turns in the winding, the physical size or area, and the frequency determines the loop's efficiency at transducing the incoming wave.

S-UNITS, dB, AND MICROVOLTS

First, let's review the following S-unit chart from the article: The Ultralight dBµ Mystery, S-Meters, And Field Strength. This will give us an idea of what dBµV values we might see on our radio's DSP display.

S-unit     µV   dBµV
--------------------
S9+60  50000.0   94
S9+50  15810.0   84
S9+40   5000.0   74
S9+30   1581.0   64
S9+20    500.0   54
S9+10    158.1   44
S9        50.0   34
S8        25.0   28
S7        12.5   22
S6         6.3   16
S5         3.2   10
S4         1.6    4
S3         0.8   -2
S2         0.4   -8
S1         0.2  -14

The modern DSP receivers like the Tecsun PL-380, 310, etc. which employ the Silicon Labs chips, measure and display dBµV as received at the tuned front end across a load. They call it the RSSI indicator. It is measuring the voltage output of the ferrite or air core loop at the radio's input.

dB = decibels of course, simply a way of expressing magnitudes of a value, like voltage, logarithmically.

µV = microvolts, or millionths of a volt.

dBµV is a voltage expressed in dB above (or below) one microvolt. This is measured across a specific load impedance, commonly 50 ohms.

The 'dB' or decibel measurement is a logarithmic ratio as you may know. In terms of voltage, an increase of 6 dB is a doubling of voltage. So, if our little DSP radio receives a signal at 28 dBµ and it increases to 34 dBµ, the received voltage has doubled. Coincidentally, this is also an increase of one S-unit!

Use the following formula to convert dBµV to microvolts, or millionths of a volt:

                    µV = 10 ^ (dBµV/ 20)

To convert microvolts back to its decibel representation:

                    dBµV = 20 * Log(µV)

(Log is the common logarithm, or base 10).

THE TUNED ANOMOLY

One more concept we must address which is rarely mentioned in technical articles: A tuned loop produces higher voltage output levels than an untuned loop. In fact, much higher. When connected to our radio the loop is effectively tuned by the DSP receiver, and the voltage output "at the tuned frequency" is greatly increased from that of the untuned, unterminated loop sitting out in the open. Think of the DSP receiver as a variable capacitor which tunes the loop's inductance. This is true for the ferrite loop as well. Combined with the loop inductance, it forms a tuned circuit that literally concentrates the signal's field causing greater current flow at the tuned frequency.

LOOP EFFICIENCY

Let's talk about loop efficiency. The efficiency of the loop determines the sensitivity of the loop. How is one loop better or worse than another? We can calculate a loop's efficiency if we know its area, number of turns, and the wavelength we wish to receive on it. Once that is known we can make comparisons to other loops.

An 18 inch untuned loop

Our efficiency factor here is often called the "effective height" H, in meters.

Effective height of an 18 inch loop of 12 turns:

                    H = (2 * pi * N * A) / wavelength

                         pi = 3.14159
                         N = number of turns
                         A = area of the loop in square meters
                         wavelength = wavelength of the frequency, in meters.

Effective height, in meters, is what the popular articles call it, sometimes referred to as He. That's a bit of a misnomer. It is actually a ratio or percentage of the wavelength, 0 - 1, since its value is derived by division by wavelength of the received signal.

Referencing the formula above, wavelength is easily calculated. It is the speed of light in meters/second (299,792,458) divided by the frequency in Hertz (Hz).

Wavelength example for 640 KHz:

     299792458 / 640000 = 468.425 meters.

Next, area of the loop in square meters. In the US we commonly use imperial measure, feet. Area conversion to meters is easily done. One square meter = 10.7639 sq ft. Length of a meter is 3.28084 ft. We square this, as such:

     1 sq meter = 10.7639 sq ft. =  3.28084 ft. * 3.28084 ft.

Area, for practical example:

     Area of 48 inch loop = (4ft * 4ft) / 10.7639 = 1.486 sq. meters
     Area of 18 inch loop = (1.5ft * 1.5ft) / 10.7639 = 0.209 sq. meters
     Area of 12 inch loop = (1ft * 1ft) / 10.7639 = 0.093 sq. meters
     Area of 9 inch loop = (.75ft * .75ft) / 10.7639 = 0.052 sq. meters

So, plugging in the values for our 18 inch loop, assuming a frequency of 640 KHz:

     Effective height H = (2 * 3.14159 * 12turns * 0.209area) / 468.425wavelength = 0.03364

Our loop's effective height H is 0.03364.

If we double the number of turns to 24 the effective height is doubled to 0.06728.

If we double the area to 0.418 sq. meters the effective height is doubled to 0.06728.

If we double the received frequency to 1280 KHz the effective height is doubled to 0.06728. Aha! More signal output as we go higher in the band!

The loop's voltage output will be directly related to its efficiency, or effective height. As you can see, efficiency increases linearly with the number of turns, the area of the loop, and the frequency. Voltage output will track right along with that too.

SIGNAL MEASUREMENTS

Let's measure the voltage output of our loop. We find the loop's voltage output by converting the RSSI value right off the display of our DSP receiver, marked "dBµ" (which is actually dBµV).

63 dBµV from a station on 1040 KHz

Here's an example. In western Arizona, at mid-day we'll tune to Los Angeles station KFI-640, a 50 KW outlet. At 240 miles, it's a fairly weak signal (about 17 dBµV) using the radio's ferrite loop. However by removing the ferrite and hard-wiring an 18 inch square loop in its place it generates a commendable 42 dBµV at the receiver.

Our conversion formula again is:

                    µV = (10 ^ (dBµV/ 20))

Substituting values:

                    125.89(µV) = 10 ^ (42/ 20)

We have a loop output of 125.89 microvolts.

Now that we know the loop's effective height H and the voltage output of our loop we can calculate the received signal's field strength. Be aware, there is a slight hitch here. The calculated E field is the "apparent" E field, not the actual one. Follow along and I'll explain further.

Let's calculate the apparent electric field E required to produce that loop output. The formula becomes simple at this point:

                    Erms(V/m) = Vrms / H

Vrms is the loop output V in Volts or mV or µV
Erms is the electric field E in V/m or mV/m or µV/m (volts, millivolts, or microvolts per meter)

Be sure to use the same factors in the formula: microvolts to microvolts, millivolts to millivolts, and volts to volts. If we use microvolts in the equation we will have the answer in microvolts, as such:

Substituting values:

                    E(µV/m) = 125.89 / .03364
   
                    3742.27(µV/m) = 125.89 / .03364

Our E field is 3742.27 µV/m (microvolts per meter). This is equivalent to 3.74227 mV/m (in millivolts per meter).

But wait, there's more. 3.742 mV/m seems awfully much for KFI Los Angeles at 240 miles. Its groundwave field strength on computed charts is only 0.209 mV/m. What's going on here?

Recall above I said a tuned loop produces higher voltage output levels than an untuned loop. Remember that the tuned loop literally concentrates the signal's field, the same as a ferrite loop does. This concentration results in an apparent increase in the E field, or a "gain" if you will. The Erms field we just calculated includes the literal "gain" of the loop as well. The gain of the tuned 18 inch loop makes the apparent field equivalent to 3.742 mV/m! This is a ratio increase of 3.742 / .209 or 17.904.

This is a hard concept to wrap your head around. The "efficiency", or effective height formula, does not tell the whole story of how we get from actual field strength - the E field passing our loop - to signal strength - the loop's output. There is also gain involved, plus a little thing called Antenna Factor.

In the previous article Decoding Antenna Factor In Ferrite Loops on this blog, we dived into antenna factor. Antenna factor applies to all kinds of antennas, not just ferrite loops. Since we're here let's calculate the antenna factor of our 18 inch loop.

From a chart, KFI-640 will produce an actual E field here of .209 mV/m, or 46.4 dBµV/m.

You might recall from the The dBµ vs. dBu Mystery: Signal Strength vs. Field Strength? article on this blog the conversion formula to get from millivolts per meter to dBµV/m, also known as dBu, or engineer's dBu.

                    dBµV/m = 20 * Log(mV/m * 1000)        ...a.k.a. dBu (lowercase 'u')

Substituting values:

                    46.4(dBµV/m) = 20 * Log(.209 * 1000)

We are receiving KFI at 42 dBµV on the receiver's RSSI display for our 18 inch loop. Since we are dealing with decibels on both sides of the equation, we can use simple subtraction to arrive at our antenna factor. Antenna factor of our 18 inch loop is then 4.4 dB (46.4 - 42).

9 inch Helper Loop

I have a little 9 inch loop I built which I call my "Helper Loop". The side length is exactly half of the 18 inch loop, so the area is one-fourth that of the 18 inch. Thus, we should see about one-fourth the signal output. Let's compare it to the 18 inch. First we calculate the efficiency, or effective height again.

Plugging in the values for our 9 inch loop, assuming a frequency of 640 KHz again:

     Effective height H = (2 * 3.14159 * 24turns * 0.052area) / 468.425wavelength = 0.01674

Our 9 inch loop's effective height H is 0.01674.

Directly-wired to the DSP radio, we tune to KFI-640 again at mid-day and see an RSSI dBµV of 30.

Substituting values again:

                    31.62(µV) = 10 ^ (30/ 20)

We have a loop output of 31.62 microvolts.

Now we'll calculate the apparent electric field E again:

                    Erms(V/m) = Vrms / H

Substituting values:

                    E(µV/m) = 31.62 / .01674
 
                    1888.88(µV/m) = 31.62 / .01674

Our apparent E field is 1888.88 µV/m (microvolts per meter). This is equivalent to 1.88888 mV/m (in millivolts per meter).

Back to our measured RSSI outputs again. Our 9 inch loop's output is 31.62 µV. Our 18 inch loop's output was 125.89 µV. That's virtually four times the output of our 9 inch loop which is one-fourth its area. In dB (voltage), exactly +12 dB greater signal output is generated by the 18 inch loop which of course is 4 times the output as well. Remember, 6 dB is a doubling of the voltage, and another 6 dB doubles it again.

The gain of the tuned 9 inch loop makes the apparent field equivalent to 1.888 mV/m. This is a ratio increase of 1.888 / .209 or 9.033.

Wrapping up, using simple subtraction again to arrive at our antenna factor for the 9 inch loop, (46.4 - 30) = 16.4 dB Antenna Factor. This, again, is a 12 dB difference.

Here's a slightly different way to express our original  formula:

The induced voltage V of an untuned loop (the loop's output) is:

                    V(µV) = ((2 * pi * N * A) / wavelength) * E(µV/m) * Cos(theta)

                    Remember, our effective height, H, is this part:  ((2 * pi * N * A) / wavelength)

                    V = H * E * cos(theta)
                    E * cos(theta) = V / H

                         V is in µV (loop output)
                         H is the loop effective height
                         E is the field strength of the passing wave in µV/m
                         Cos(theta) is the cosine of the angle between the antenna and the transmitter

For untuned loops, the calculated E field is the actual passing field. Tuned, the calculated E field is the apparent passing field. Think of it this way: tuning a loop does not change the loop's core efficiency H which is determined by turns, size, and impressed wavelength, but it will indeed change the loop's output V.

A note on angle theta: Theta is the angle that the plane of the loop makes to the station's passing field. Our desired angle is almost always zero, pointed directly at the station, for max signal pickup. Since the cosine of 0 = 1, we can leave that factor out of the equation. Note that if you rotate the loop 30 degrees away from the station you have reduced the signal pickup by Cos(30), or 0.866. 60 degrees, Cos(60), or 0.5, half!

A 42 inch tuned loop

Above, a 42 inch loop tuned with a variable capacitor. Remove the capacitor and directly-wire this loop to a DSP radio after removing the radio's ferrite. You will see results! Watch out for overload!

LOOP FACTS

Some interesting facts about loops, both passive and directly-wired:

1. A 48 inch loop gathers 16 times more signal than the 12 inch loop because it has 16 times the area of the 12 inch loop. A 9 foot loop gathers 81 times more signal than the 12 inch loop! Loop area is the determining factor here.

2. Halving the received frequency (let's say from 1200 KHz to 600 KHz) results in half the induced voltage given the field strengths at 1200 KHz and 600 KHz are equal at the reception point.

3. More turns are better. Pack as many turns as you can into your loop. Additionally for passive tuned loops: weigh turns over capacitance when calculating tuning parameters. For SiLabs DSP type radios, try to keep your loop inductance at the upper end of the range, 450 micro-Henries.

4. Be sure the plane of your loop is aligned at 0 degrees to the station. Rotating the loop 30 degrees off the station reduces the maximum induced voltage to 86.6%, because cosine(30) = 0.866. Rotating 60 degrees off the station reduces it to 50%, because cosine(60) = 0.5. Rotating 90 degrees to the station reduces it to 0%. The total null is a theoretical value of course, and not attainable in actual practice as there is no perfectly nulling loop.

5. Remember that tuned loops generate lots more signal than untuned loops.

Saturday, February 1, 2020

2020 US-Canadian Mediumwave Pattern Reference Is Here

The 2020 US-Canadian Mediumwave Pattern Reference for all stations is now available. Find the download link at upper right. Remember, the links change each time a new set is uploaded. Always look to this RADIO-TIMETRAVELLER site for the current link. Download is 52 MB.

DOWNLOAD LINK

Media Fire link here.

When downloading from the Media Fire link, be sure to click the DOWNLOAD button.


The Media Fire site is ad-supported and has several ad links on the page and will also issue an ad pop-under. Just ignore these.

A mirror link for the 2020 files has not been established yet.

INSTALLING

The maps are HTML-based, so no regular install is necessary. Simply unzip the downloaded file and click on the individual map file to run. The map will open up in your web browser. They are self-contained, with image icons embedded right into the code. You must have an internet connection to view the maps.

IMPROVEMENTS FOR 2020

January 21, 2020:

1. Much of the summer and fall of 2019 has been spent bug fixing and tweaking the skywave formulas for accuracy. A slight tweak to the groundwave formula has brought the predicted groundwave strengths more in line with V-Soft (https://www.v-soft.com/on-line-based-software/zipsignal). Skywave values now more reflect actual received signal strengths as measured. Consequently the mV/m threshold was upped this year to 0.1 mV/m (40 dBu). If signal overlap is a problem, simply turn off all plots and select the ones you want.

Additionally, a rather lengthy skywave overhaul now permits skywave calculations for any date and time of the year, accurate to the solar latitude of the chosen location. In order to show a median skywave calculation value, the date of November 5 has been chosen, exactly halfway between the Autumnal equinox of September 21 and the Winter solstice of December 21, the dates of the most extreme deviation from the median.

The nighttime skywave calculation is based on midnight Central Standard Time (SS+6). The daytime groundwave calculation is based on noon Central Standard Time (SR+6).

Los Angeles station KABC-790 was missed in last years maps due to an error in the FCC's database archiving its license to cover. It has been patched in this year, as the FCC has not corrected the problem.

Daytime Franklin, VA station KJZU-1250 is missing this year due to errors in its tower record.

Missing Canadian Nova Scotia and Newfoundland stations have been added. In previous years an error in RDMW's filtering had bypassed them.

Missing Canadian station CHHA-1610 (Toronto) has been added. The Industry Canada database is missing a class identifier for this station, so I have placed it in Class C which I believe to be correct. I have written to IC about this omission, but they have not responded.

New on the maps this year are the Canadian low power stations, which generally run 20-40 watts. Due to the low power, they generally will not generate a skywave pattern, but the daytime pattern should be substituted. They may be receivable at distance, however, don't give up!

Again for 2020, the following parametrics are considered in the skywave calculation:

   * Hourly transitional loss variance from sunset to sunrise.
   * Seasonal gain or loss, January - December.
   * Diurnal enhancement at the sunrise and sunset period.
   * Winter daytime skywave enhancement (only on maps created for times during the day).
   * Daily seasonal nighttime skywave enhancement.
   * Take off angle variances for stations at relatively close distances (experimental).

2. Colored plot (yellow), again, for groundwave 1.0 mV/m level.

3. Small changes made to the map's title bar heading. Signal dBu (dBµV/m) is now displayed instead of millivolts per meter. Also the map's day of year (DOY) and GMT time "z" are displayed.

4. Unlimited, Daytime, and Critical Hours plots are at the 1.0 (60 dBu) and 0.1 mV/m (40 dBu) levels. Skywave is set at the 0.1 mV/m level. Levels have been chosen to minimize pattern overlap yet still attempt to show what you can accurately hear during the day and night.

ABOUT THE MAPS

Included is a complete set of GoogleMap-based, HTML-driven maps which show the most current pattern plots of all licensed US and Canadian mediumwave broadcast stations from 530 - 1700 KHz. The set includes all frequencies for the indicated services: Unlimited, Daytime, Nighttime, and Critical Hours. Individual maps are grouped by channel frequency: 540, 550, 560, .. 1700 KHz, etc. Data for the plots in this offering is based on the current FCC and Industry Canada databases available at the time of its creation (January 21, 2020).

The daytime map series, in two parts, shows expected groundwave coverage patterns for Unlimited and Daytime (part 1), and Critical Hours (part 2) operations. Daytime signal patterns represent groundwave coverage at two levels, out to the 1.0 and 0.1 millivolts per meter contours (60 dBu and 40 dBu respectively). The choice of these levels is made in order to more closely match those which might be helpful to the mediumwave DXer. Note that daytime reception of signals out to and beyond the depicted 0.1 mV/m pattern is very possible, and in fact likely for the DXer. The contour line represents a signal strength at the station's extreme fringe distance, a level usually received on a sensitive portable radio with a low ambient local-noise level. I have chosen this signal level to give a good representation of what can be received by most DXers during sunlight hours.

The nighttime map series shows expected skywave coverage patterns for Unlimited and Nighttime operations. Nighttime signal patterns represent the standard SS+6 (sunset plus 6 hours, or approximately midnight Central Standard Time), 50% signal probability at 0.1 millivolts per meter (40 dBu). Note also that nighttime reception of signals out to and beyond the depicted pattern is very possible, and in fact quite likely for a skywave signal. The maps represent a signal strength at the fringe level. I have chosen this signal level to give a good representation of what is possibly received by most DXers on an average evening. The nighttime signal probability of 50% means that the signal will be received at this level approximately 50% of the time at Central Standard Time.

HOW THEY ARE PRODUCED

Using the actual FCC database files, Radio Data MW will auto-generate an interactive HTML pattern map, showing the pattern plots for all stations included at the discretion of the user. A complete set of mediumwave pattern maps can be generated in about eight hours of processing time. Processing time had increased by nearly two hours by 2019 due to enhanced skywave calculations and other upgrades.

For daytime signal maps, Radio Data MW generates a real pattern plot based on transmitter power, antenna array efficiency and directivity, ground conductivity and ground dielectric constant of the path to the receiver. Increased conductivity of water paths over the Great Lakes are also accounted for. It displays actual (but approximate of course) signal level boundaries for Local, Distant, Fringe, Extreme mV/m levels, or any custom mV/m level chosen by the user.

For skywave signal maps, predicted signal levels are calculated in accordance with current FCC or ITU methods of recent years (1999 onward). A number of parametrics are now analyzed and accounted for in the calculation, namely diurnal and seasonal changes, and daily sunrise and sunset enhancements to the signal. The process is rather complicated.

The online Google Maps API is used to generate and plot each station on a map of the US. An accurate flag pin is placed at each transmitter location, and in satellite view may be zoomed in to see the actual transmitter site. Map flags are color-coded to indicate Unlimited (light red), Daytime (yellow), Nighttime (black), and Critical Hours (grey) services. Each flag has a tooltip-type note, and when hovered over with the mouse will display a note on the station.

A pattern plot for each station is generated and displayed. Each pattern can be calculated using standard formulas used by the FCC or ITU to compute the base values at one kilometer, and field strength formulas at distance based on the works of many people over the years. See Field Strength Calculations: A History and Field Strength Calculator One, previously posted on RADIO-TIMETRAVELLER. See the RADIO-TIMETRAVELLER blog at: http://radio-timetraveller.blogspot.com/

An accurate ray path can be drawn from all transmitters to a user-specified receiving location by inputting latitude-longitude coordinates on the heading bar at the top of the map. Super-imposed on the pattern plots, the ray paths show the listener where he or she falls on each station's pattern, a handy guide to knowing where you stand.

Individual station plots can be turned on or off by a checkbox. Click the station flag and you will see the option in a pop-up balloon. Check or uncheck the box, then click the ReDraw button. The entire plot set can also be turned on or off by buttons at the top of the map.

Included in each station's flag tooltip are FCC facility ID, engineering (application) ID, and distance of the station from the home latitude-longitude. Of interest to the DXer, by setting the home location latitude-longitude to your location and redrawing the map, each flag tooltip will have the distance from your location to the station.

ON PATTERN OVERLAP AND PLOT SWITCHING

A varying amount of pattern overlap exists on the maps, some extreme, as it does in real life. For the Daytime and Critical Hours plots, the outer 0.1 mV/m signal level ring represents an extreme groundwave fringe distance where a station can be heard. At that level, there may be some minimal overlap with co-channel stations.

Pattern overlap is of course much more severe for skywave on the nighttime plots. A level of 0.1 mV/m was chosen to represent the fringe distance a station is heard at night about 50% of the time. This may seem low to many, why not increase it to lessen the overlap? Unfortunately, increasing it even to 0.15 mV/m results in no skywave plot at all for many stations under 1500 watts as their skywave signal never reaches the 0.15 mV/m threshold at points around the compass. This is particularly bothersome in the northern latitudes above 40 degrees north where signals are weaker.

The unusual case exists on the graveyard channels (1230, 1240, 1340, 1400, 1450, 1490 KHz). The plots are a massive overlay of signals (as it is in real life!). There is no real good way to display a graveyard channel for station-to-station comparison but to throw them all in there and then allow you to choose which ones to compare. Virtually 99% of all graveyarders run 1 KW power to a single tower. The technical reality is that a one kilowatt station does not produce a skywave signal in any direction above a level of about 3 mV/m. Raising the plot mV/m level to reduce the chaos unfortunately results in no plot at all for most stations.

The solution to the graveyard confusion (all, really) is simple, and one of the enhancements added in 2016. You can turn plots on or off individually, or all at once. Turn all plots off and simply check the plots you wish to see.

SPECIAL NOTE ON SKYWAVE PLOTS

As of 2019, the skywave calculation has been totally overhauled and enhanced to more reflect actual signal expectations across the U.S. at night. The fact of life is that pattern overlay occurs on many frequencies. Simply select the plots you want to analyze. Check the No Plots checkbox then ReDraw to turn off all plots. Click any station flag and check the box to plot that station then ReDraw.

You will occasionally see a skywave plot which looks much smaller than surrounding plots. This is a case where the station's skywave signal did not meet the mV/m threshold (0.1 mV/m). The groundwave plot level is substituted in this case. The station does in fact have a skywave component, however small, it will be measurably less than the 0.1 mV/m level (very weak). It may be receivable!

The darker line defining the outer edge of the skywave plot shows the location of the 0.1 mV/m signal point at all compass points. Be aware that skywave signal strength does not decrease linearly with distance from the station. From the station outward, the signal strength will generally increase to a point usually 200-400 kilometers distant where it will peak, then decrease somewhat linearly from there.

Also note that the atmospheric background noise level on the mediumwave band is generally considered to be approximately 36 dBu (dBu in this case = dBµV/m), equivalent to 0.063 mV/m. Signals below that level will not be heard unless they fade up above the noise. A gain or directional antenna can be used to increase signal strength while limiting or even reducing the overall atmospheric background noise level.

Image below is an example of the 1040 KHz skywave map.

Hope you enjoy.