Propagation Tools – Monitoring Background X-Ray Flux Levels

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The GOES 15 weather satellite (the one that is in geostationary orbit and provides the animated views of the weather over the US that you often see on the TV news) also has a set of sensors that monitor the Sun. One of these measures the x-ray output.

These x-rays are produced by sunspots, as well as by solar flares. The x-ray flux we’re interested in is measured in the 1 to 8 Angstrom range (that is the wavelength) and is the red line on the graph below (the blue line is the 0.5 to 4 Angstrom range, x-rays of a shorter wavelength):
x-ray flux

The URL for this graph is http://www.swpc.noaa.gov/rt_plots/Xray.gif

In addition, there is a graph that updates at a 1 minute rate, located at http://www.swpc.noaa.gov/rt_plots/Xray_1m.gif

x-ray flux 1 minute

X-ray level measurements consist of a letter and number, such as B6.7, representing the x-ray flux in watts/square meter. It is a log scale, much like what is used for earthquakes. A value of C1.0 is ten times as large as B1.0 (and would be equivalent to B10). Values in the A range are low background levels, such as at solar minimum. B values are a moderate background, and C values are either a high background or solar flare conditions. Flares usually result in short bursts of large x-ray levels, in the C, M, or even X range. Remember that this is a log scale, so an M1 flare is 10 times as energetic as a C1 flare, and an X1 flare is 100 times. There is a new Y classification as well, so a flare that would have been say X28 in the past would now be Y2.8.

These x-rays ionize the D layer of the ionosphere, which attenuates radio waves. So high x-ray flux levels increase attenuation of radio waves, especially at lower frequencies. Below is a map of D layer absorption:
http://www.swpc.noaa.gov/drap/Global.png

The x-rays also increase the ionization of the F layer (which is the layer that gives us shortwave propagation), although the effect is less than for the D layer.

The net result is that increased x-ray levels cause more attenuation at lower frequencies, but can also lead to better propagation at higher frequencies. Long periods of high x-ray flux levels (well into the C range) may be a sign of good 10 and 6 meter band conditions. I’ve also found that high (C range) levels seem to “stir the pot” for MW DX, bringing in different stations than usual.

Very high flux levels, such as during a major flare (in the high M or X range) however cause radio blackouts. These occur first as lower frequencies, and as the D layer begins to get more ionized higher frequencies are also affected. Extremely energetic flares (X range) can wipe out all of HF. Note that this is only true for propagation paths on the sunlight side of the Earth. The dark side is not affected. This means that flares can be useful at times, in that they can cause the fadeout of an interfering dominant station on a particular frequency, allowing another station to be heard, providing the geometry of the Earth and Sun are correct such that the path of the interfering station is in the sunlit part of the Earth, while the other station is not.

Solar flares are usually of a short duration, minutes to an hour, although there are “long duration events” that can last for several hours. If you notice suddenly poor conditions, you may want to check the current x-ray flux levels, to see if a flare is the cause. If so, try higher frequencies, as they are less affected.

As we are finally nearing the maximum of Solar Cycle 24 (although it appears it will be a fairly weak maximum) we can expect to see more flares. It can be very handy to continuously monitor the x-ray flux and D layer absorption levels, to see what the current conditions are, and to take advantage of them. One handy way to do this is with DX Toolbox. With DX Toolbox, you can monitor the current conditions, and even get an alert when the x-ray flux exceeds a predetermined alarm value. Some screenshots are below, click on them for a larger image:

DX Toolbox is available for Windows and the Macintosh, you can download a copy at this URL: http://www.blackcatsystems.com/download/dxtoolbox.html

There is also an iOS version available for the iPhone, iPad, and iPod:

Visit this URL for more information:http://www.blackcatsystems.com/iphone/dx_toolbox.html or go directly to the iTunes Store

DX Toolbox also has several propagation prediction windows, to help estimate signal levels for any path you enter, based on solar conditions.

A Day In The Life of 1470 kHz

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This waterfall was recorded from 1840 UTC January 3, 2011 to 1840 UTC January 4, 2011. The beginning of the recording is at the top of the image. It shows the carriers of MW radio stations on 1470 kHz. The width is 100 Hz, so frequencies +/-50 Hz from 1470 kHz are shown.

Click on it to open it full sized.

1470 kHz Waterfall

The red line you see in the center is the carrier of semi-local station WTTR. During the daytime it is the only audible station on 1470, although you can see that carriers for about 8 other stations are always present.

I’ve annotated several events with UTC times.

At about 2213 UTC you can see a sudden reduction in received signal strength, and the start of a drift in frequency. This is most likely due to a station switching to nighttime power levels. The change in transmitter power causes a change in temperature inside the transmitter, causing drift in the frequency. My suspicion is that it is WLOA from Farrel, PA, since they are supposed to switch at 2215 UTC.

At about 2252 UTC a carrier suddenly disappears. It is possible that this is KMAL from Malden, MO. They are supposed to shut down at 2300 UTC.

Note that these are hunches of mine, I am not 100% certain that these are the identified stations. These events do suggest that it may be possible to identify and DX stations based on carrier transients, if the actual times that the stations make the changes are known.

At 0400 UTC a carrier suddenly disappears. I am not sure who this could be. This would be 11 PM EST. The station started to fade in around 2300 UTC (6 PM EST). That suggests to me a station in the central US. I’m not sure why they would be shutting down at this late time of the evening, vs around sunset. Perhaps some more experienced MW DXers have some theories / candidates?

There’s also some transients in the morning.

First at around 1200 UTC (7 AM local time) you can see the received signal strengths of the distant carriers decrease. The Sun is rising, and the D Layer is forming again, attenuating MW skywave signals.

At 1230 UTC one of the carriers suddenly disappears. At 1251 a carrier appears.

At 1326, it looks like a a transmitter is changing power levels.

At 1406 UTC there is another transient on another carrier.

There’s also noticeable differences in the frequency regulation of transmitter carriers. Several of the carriers have a periodic cycling to the frequency. I thought is this is due to some temperature cycling in the transmitter.

The 1610 Zoo

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Below is a waterfall centered around 1610 kHz in the extended MW (AM) Band, 100 Hz Wide (click on it to see an enlarged image): 1610 waterfall

1610 kHz is used by only two broadcast stations, both in Canada: CJWI in Montreal, and CHHA in Toronto. It is also, however, used by many TIS (Travelers Information Stations) stations, which broadcast traffic reports, weather, etc. These are low power stations, typically in the 10 watt range.

Locally, the dominant station on 1610 kHz is a TIS that relays NOAA weather transmissions, and is located somewhere in south central PA. I’ve never heard an ID.

This recording was made between about 2100 and 1700 UTC, you can see the increase in signal (and background) levels overnight, and then the weakening of the signals as the Sun rises and the D Layer reforms, attenuating distant stations. Looking at the waterfall, you can see dozens of carriers, each a different radio station. It’s interesting to note how many radio station signals are present, even during the daytime.

The horizontal lines are due to static bursts, and there’s some changes in the signal level due to the wind blowing around the antenna.

Some of the wandering of carriers you see that is in unison is due to drift of the A/D clock in the SDR. Other drift you see is due to the carriers themselves. Note that each major division at the top of the waterfall is only 10 Hz (and the entire width is 100 Hz) so there’s really only a few Hz total drift. Eventually I’ll get a more stable reference clock for the SDR, and receiver drift should go away.

Let’s have a contest. How many carriers can you count?

Measuring The Speed of Light Using a Shortwave Radio

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I thought it would be interesting to see whether or not it was possible to crudely measure the speed of light using a shortwave radio and a time station.

Various time stations transmit precise time on several shortwave frequencies. Here in the USA, we have WWV in Ft. Collins, Colorado, which transmits on 2.5, 5, 10, 15, and 20 MHz. We also have WWVH in Kekaha, Hawaii, which transmits on 2.5, 5, 10, and 15 MHz. These stations transmit an audio “tick” at exactly each UTC second.

One way to measure the speed of radio waves (and light) would be to measure how long it takes for the tick to travel a fixed distance. Divide the distance by the time, and we have the speed of light. However, that requires knowing the exact UTC time locally. While this can be done with a GPS unit that outputs a 1 PPS (pulse per second) signal, I thought it would be more interesting to do it using just a shortwave radio without any extra hardware, other than a computer to record the audio.

Both WWV and WWVH transmit on several of the international time frequencies. And it turns out that at certain times of the day, it is possible to receive both of them on the same frequency. The following recording was made on 15 MHz at 1821 UTC on January 1, 2011: Recording of WWV and WWVH

You can hear the time announcement for WWVH first, by a woman, followed by a man giving the WWV time announcement.

I am roughly at a location of 77W and 40N. WWV is located at roughly 105W and 41N, and is about 2,372 km away. WWVH is located at roughly 160W and 22N, about 7,883 km away. The actual path the radio waves takes to reach me is longer, due to the fact that they reflect off the ionosphere, a few hundred km high. We’ll neglect that for now.

The difference in distance between WWV and WWVH is 7883 – 2372 = 5510 km.

The following is a display of the waveform from the above recording, centered around one of the second ticks. You can see the stronger WWV second tick centered at about 19.086 seconds into the recording. You can also see the weaker WWVH second tick centered at about 19.105 seconds: wwv and wwvh

The other waveforms you see before and after the second ticks are the audio that each station always transmits.

If we subtract the time markers for the two ticks, we get 19.105 – 19.086 = 0.019 seconds (19 milliseconds). That’s the time delay between the two ticks. Next, performing our division, 5510 km / 0.019 seconds = 290,000 km/second. The generally accepted value for the speed of light is 299,792 km/second. That’s pretty close!

In all fairness, the time resolution is not that good, and I had to eyeball the readings. Plus, a one millisecond difference in the time delay would have resulted in about a 15,000 km/sec difference in the speed of light. So a slight difference in eyeballing these broad time ticks would result in a large error in our estimate of the speed of light.

If you listened carefully to the recording, you no doubt heard a fluttery or watery quality to the sound. This is often indicative of multipath, where the radio waves take two (or more) paths between the transmitter and receiver.

Here’s another waveform from the recording, centered at 27 seconds into the recording: wwv and wwvh long path

In this case, we can clearly see the second tick from WWVH. But there’s no second tick from WWVH, just silence. Where is it?

Looking further into the recording, we see another second tick delayed much further. Eyeballing it, the delayed tick is at about 27.187 seconds into the recording. And the first tick, which we believe is from WWV is at about 27.087 seconds. The difference between the two is 0.100 seconds. Using the accepted speed of light, this difference in time could be due to a distance of 299,792 km/sec * 0.100 sec = 29,972 km. What could account for this delay?

One possibility is that during this time period, the signal from WWVH was not taking the normal or short path to my location, but was instead travelling around the other side of the Earth, taking the long path.

The circumference of the Earth is about 40,075 km (the exact value depends on which path around the Earth you take, as the Earth is not a perfect sphere). We know the short path is 7,883 km, so the long path is about 40075 – 7883 = 32192 km. There is still the delay due to the time it takes the radio waves to get from WWV to my location, that path is 2,372 km. The net difference between the two is 32192 – 2372= 29820 km.

We can divide that distance by the speed of light to see what the time delay should be: 29820 km / 299792 km/sec = 0.099 seconds. This is extremely close to our measured period of 0.100 seconds, and suggests that the long delayed second tick really is from the WWVH signal taking the long path around the Earth to reach us.

The following map, generated with the DX ToolBox Radio Propagation Forecasting Program, shows both the short path (white line) and long path (gray line) between my location and WWVH: WWVH Path

Comments appreciated!

Beating Carriers

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You’ve probably heard the low frequency beat that occurs when two closely spaced carriers are present, like in this recording.

Here’s what it looks like in a waterfall, taken with a netSDR:
beating carriers

The two bright greenish lines are the carriers, one at about 1620.0076 kHz and the other around 1620.0095 kHz (and wandering around). The result of the two carriers mixing is the difference frequency, 1620.0095-1620.0076=0.0019 kHz or 1.9 Hz. The higher and wandering carrier is the local college station (it’s actually about 12 miles away), the other station is probably WDND from South Bend, IN.

In case you’re wondering, the netSDR settings were a 200 kHz bandwidth (250 kHz output rate), and a 2,097,152 FFT with a resolution of 0.12 Hz.

An Interesting Example of a Station Going Long

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A fairly active pirate station the past week or so has been the “Fruitcake” station, which plays songs and sound clips related to, well, fruitcake. Hence the name. On December 20, 2011 at 2300 UTC I recorded a transmission of this station with my netSDR. What I ended up capturing was a very interesting and educational example of a station going long.

Here is a graph of the received signal strength:
Signal Strength in dBm

An S9 signal is -73 dBm, right about the received signal level at the beginning of the broadcast. There is some fading up and down, typical with shortwave radio. What’s interesting is that the change in signal strength seems to have a definite period, rising and falling every few seconds. After a few minutes, the period starts to become longer, and the amplitude of the variation also increases. About half way through the transmission, the amplitude becomes quite large. There is then one deep fade, one large increase in signal strength, and then the signal almost fades out, going down to about -95 dBm (about S4). Notice that 10 minutes ago it was S9.

Next, here is a waterfall of the recorded transmission:
Waterfall

A waterfall is a color coded representation of the signal strength of a band of frequencies over time. In this case, it shows us the signal strength from about 2300 to 2310 UTC, over a frequency range of 6900 to 6950 kHz. The blue background represents the weak background noise that is always present, in this case about -97 dBm. The brighter colors towards green represent stronger signals. We can see the station’s carrier at 6924 kHz, and the sidebands containing the audio modulation (this is an AM signal).

The change in bandwidth of the received signal about a minute and a half into the transmission is due to the audio that was transmitted, one song ended, and another sound clip, with wider audio, began.

This is an extremely educational image. We can see several things happening here:

1. The short choppy fades at the beginning of the transmission are evident.

2. As time goes on, the fades become more prominent, and we can see the increase in their period.

3. We can see the background noise levels increasing in amplitude. Look just outside the passband of the station itself, and you can see waves of increasing and decreasing background noise.

4. The fades all start at a higher frequency, and drift down to lower frequencies over time. This is a type of phenomena called selective fading, which you may have read about.

So, what is the cause of the selective fading? There are several possibilities.

One is when both ground wave and sky wave signals are being received. If there are phase differences between the two signals, they cancel out, reducing the received signal strength. Likewise, if they are in phase, they support each other, and add together, increasing the signal strength. One common example of this is with medium wave (AM broadcast) stations. When you are close to the station, the ground wave signal is extremely strong, and the sky wave is relatively weak, resulting in excellent reception with no fading. At a long distance away from the station, the ground wave is extremely weak or nonexistent, resulting in only a sky wave. Reception is weaker than the first example, but often reliable for stronger stations. This is why you can pick up AM stations over long distances at night. However, if you are at an intermediate distance, you can receive both the sky wave and ground wave. As the relative phase between them changes, you get fades. I’ve noticed this with a semi-local AM station. It has excellent reception in the daytime, but once evening approaches, reception gets very choppy. This is even before other stations begin to roll in.

I don’t think this is the cause in this case, as there should be little or no ground wave. And if there was, I would still be able to pick up the station after the band went long, since the ground wave was present. (Being HF instead of MW, the ground wave does not travel very far anyway)

Another possibility is due to propagation via both the E and F layers. In this case, it is again relative phase differences that cause the fading. I’m not sold on this scenario either, because I don’t believe the E layer would support propagation of 7 MHz signals. (E layer propagation should not be confused with sporadic E layer propagation that often causes VHF skip)

Next up, and the idea I am presently sold on, is propagation via both the F1 and F2 layers. During the daytime, when ionization is strongest, the F layer splits into two layers, the F1 at about 150-220 km and the F2 at 220-800 km. At night, the F1 layer merges with the F2 layer.

Perhaps, during the daytime, only one layer is responsible for NVIS propagation. My thought is that the F1 layer is providing the propagation, as it is the lower layer, and the first one the radio waves would interact with. Then, in the evening, when the band is going long and the F1 layer starts to dissipate allowing some radio waves to reach the F2 layer, propagation is occurring via both layers. Relative phase differences between the signals propagated by each layer cause the selective fading effects. Once the F1 layer completely dissipates, only the F2 layer is left, but it is unable to support NVIS propagation at 7 MHz.

Comments welcome and appreciated!

A comparison of three low power AM shortwave pirate transmitters

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Recently shortwave free radio station Channel Z Radio conducted test broadcasts using three different transmitters, all on the same frequency with the same antenna, a half-wave horizontal dipole cut for 6925 kHz, mounted about 40 feet high. As described in a recent article, this setup should be ideal for NVIS or regional operation.

It was interesting to see how closely theory predicted real world performance for signal intelligibility and propagation. For background information, see the September 2011 articles “Signal to Noise Ratios” for which simulations were run, and the related article “How many watts do you need?”

These recordings were made with a netSDR receiver, and a 635 ft sky loop antenna. The I/Q data was recorded to disk, and later demodulated with my own SDR software, which is based on the cuteSDR code. If you hear any glitches in the audio, that’s my fault, the code is still under development.

In all cases, I used a 4 kHz wide filter on the demodulated signal. I chose 4 kHz because examining the waterfall of the received signal, that seemed to encompass the entire transmitted audio.

First up, he used a Corsette transmitter, putting out 1.1 watts:
Corsette transmitter
The average received signal strength was -90.9 dBm. This is about an S6.
This recording was made starting at 1949 UTC

Next he used a Grenade transmitter, putting out 14 watts:
Grenade transmitter
The average received signal strength was -77.0 dBm. This is about an S8 signal.
This recording was made starting at 2010 UTC

Finally he used a Commando transmitter, putting out 25 watts:
Commando Transmitter
The average received signal strength was -73.4 dBm. This is almost exactly an “official” S9 signal.
This recording was made starting at 2028 UTC

The playlists for the three transmissions included several of the same songs, so I recorded the same song for these comparisons, to be as fair as possible. Listen for yourself to decide what the differences are.

It’s also interesting to compare the received signal levels to theory. A 10 dB increase in the received signal level is expected for a 10x increase in transmitter power. In the case of the 1.1 watt Corsette and 14 watt Grenade, we have a power ratio of 14 / 1.1 = 12.7, which is 11 dB. So we expect an 11 dB difference in received signal strength. We actually had a 90.9 – 77.0 = 13.9 dB.

In the case of the Grenade vs Commando, we had a power ratio of 25 / 14 = 1.79, or 2.5 dB. We had a received power difference of 77.0 – 73.4 = 3.6 dB, very close.

Comparing the Commando and Corsette, we had a power ratio of 25 / 1.1 = 22.7, or 13.6 dB. We had a received power difference of 90.9 – 73.4 = 17.5 dB.

I went back and measured the background noise levels during each transmission, on an adjacent (unoccupied) frequency, with the same 4 kHz bandwidth. During the Corsette transmission it was -98.1 dBm. During the Grenade transmission, it was -97.8 dBm. And during the Commando transmission, it was -95.9 dBm.

So it seems the background noise levels went up as time went on, possibly due to changes (for the better) in propagation. This might explain why the measured power differences were larger than we expected from theory – propagation was getting better.

Still, it’s nice to see how close our results are to theory.

Speaking of theory, I am ran some predictions of the expected signal levels using DX ToolBox. Obviously I have no idea where Channel Z is located, nor do I want to speculate. But since this is NVIS operation, selecting any location in a several hundred mile radius produces about the same results (I played around with various locations). So I selected Buffalo, because I like chicken wings. Here are the results:

1 Watt Corsette Prediction:
1 watt calculated signal level

14 Watt Grenade Prediction:
14 watt calculated signal level

25 Watt Commando Prediction:
25 watt calculated signal level

Ignore the box drawn around the 1700z prediction, that was the time today that I ran the software. You can see that for the 1 watt case, it predicts S5, for 14 watts between S6 and S7, and for 25 watts about S7. Numbers lower but in line with what I experienced. Note that my setup uses a 635 ft sky loop antenna, which likely produces stronger received signals than estimated.

You also see that the signal strength curves upwards as time goes on, showing an increasing signal. This is also what I experienced with the increasing background noise levels, and suspected increase in received signal from Channel Z from the first to last transmission. As it got later, the signal increased. This is something I have experienced with NVIS – the signal improves, until the band suddenly closes, and the signal level suddenly drops.

My thanks to Channel Z for running these tests on three of his transmitters, I believe the results are very interesting, and shed some light on how well signals with different transmitter power levels get out, under the same conditions.

Comments welcome and appreciated!

NVIS Near Vertical Incident Sky Wave

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   PSK31     
   iPad app to decode PSK31     

While shortwave radio is commonly thought of as being used for long distance communications, it also functions for local and medium distance links. This is accomplished by a method known as NVIS, or Near Vertical Incident Sky Wave, and is in fact what most US pirate operators are using, even if they have never heard of it before.

I touched on NVIS in my previous post Going Long, which readers may wish to read before continuing.

To summarize, the ability of HF radio waves to get from the transmitter to target location depends on the ionosphere being able to refract (or reflect) them back to the Earth. The stronger the ionization level, the higher the frequency that can be refracted back, as most radio enthusiasts know. This is why during periods of high solar activity, the higher bands (up to 30 MHz and even beyond) are useful for long distance communications during much or even all of the day. Whereas when solar activity is low (as it has been until recently) the higher frequencies are often dead, and lower frequencies must be used.

But there’s a second factor as well – the angle that the radio waves strike the ionosphere. For a given ionization level, the lowest maximum frequency that can be reflected occurs when the radio waves are directed straight up. In this case, they would be reflected right down, for local reception. As the radio waves strike the ionosphere at more shallow angles (as would be the case for waves that are going to reach the Earth further away), higher frequencies will be reflected.

critical angle

In the above picture, paths A and B are at shallow enough angles that the radio waves get reflected back to the Earth. For path C, the angle is too steep, and the radio waves are not reflected, but pass into space.

The maximum frequency that will be reflected straight back is called the foF2 frequency. It is continuously varying, based on solar activity, and what part of the Earth the Sun is over. You can find a real time map at this URL: http://www.spacew.com/www/fof2.gif

http://www.spacew.com/www/fof2.gif

During the daytime, it lately has been reaching 10 or 12 MHz over the USA. At night, it drops down to 3 or 4 MHz.

The angle that the radio waves strike the ionosphere depends on the distance between the transmitter and receiver, and the height of the ionosphere, which unfortunately also varies. This is called the hmF2, and there’s a real time map of it also: http://www.spacew.com/www/hmf2.gif

The Maximum Usable Frequency (MUF) can be found by:
MUF = foF2 * sqrt( 1+ [D/(2*hmF2)]^2) where D is the distance in km.

Obviously, if the foF2 frequency is above your transmitter frequency, you don’t need to worry, you’ll be able to operate NVIS and be heard (assuming you have enough power to overcome noise, of course)

Once foF2 drops below your operating frequency, radio waves directed straight up keep going into space. Waves at more shallow angles (reaching the earth some distance away) could still be reflected, depending on the geometry. This creates what is referred to as the skip zone, the distance around the transmitter where the signal cannot be received.

For example, assuming a hmF2 height of 300 km (fairly average) here’s the skip zone distance for several different foF2 values, for a transmitter frequency of 7 MHz:
3 MHz 1270 km
4 MHz 860 km
5 MHz 580 km
6 MHz 360 km

As I type this at 0030Z on December 15, 2011, foF2 has dropped to 5 MHz over the northeast US. This leaves an approximately 350 mile diameter skip zone around the transmitter, where the broadcast cannot be received.

For good NVIS operation, an operator wants most of the transmitted RF to go straight up. This suggests the use of simple antennas like dipoles at low heights, which as it turns out is what most operators are doing anyway. A 43 meter band dipole at 30 feet up has radiation patterns like this:
http://www.hfunderpants.com/mypics/6.9_dipole_above_ground.png

The graph on the left is the pattern around the points of the compass, and the one on the right is the elevation. As you can see from the graph on the right, most of the RF energy is going up. This is bad for long distance DX, but good for NVIS operation.

The key point to remember is that when the band closes for NVIS, you will lose your local audience, where local could mean a radius of several hundred miles around your station. Dropping to a lower frequency (like 5, or even 3 MHz which operators have used in the past) regains your local audience. There’s a reason WBCQ uses 5110 kHz. Absorption losses increase as you go down in frequency, however, roughly inversely to the square of the frequency. So the absorption losses at 3 MHz are four times that at 6 MHz, and about 5.4 times that at 7 MHz. Operating earlier in the evening, before the band closes for NVIS, is another solution.

An AD8307 Based RF Meter

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The AD8307 IC is advertised as being a “Low Cost, DC to 500 MHz, 92 dB Logarithmic Amplifier”. This is a block diagram:
AD8307 Block Diagram

From the AD8307 datasheet: The essential purpose
of a log amp is not to amplify, though amplification is utilized to
achieve the function. Rather, it is to compress a signal of wide
dynamic range to its decibel equivalent. It is thus a measurement
device. A better term may be logarithmic converter, because its
basic function is the conversion of a signal from one domain of
representation to another via a precise nonlinear transformation.

And here’s a basic AD8307 circuit, mine is similar:
AD8307 Circuit

In my case, I have an LC filter on the incoming DC power, as well as the outgoing DC signal level, to reduce noise pickup. My meter is built into a small paint can, on the underside of the lid, which works as an excellent ground plane:
RF Meter

And here is the top of the lid, mounted on the can:
RF Meter
The toggle switch isn’t being used. I was going to power the meter off of a 9 volt battery to further reduce noise, but comparison tests between the battery and DC power supply showed no difference.

The output of the meter is a voltage proportional to the input power, measured in dBm. Zero volts is output for −84 dBm,
corresponding to a sine amplitude of 20 μV. There is a noise floor, and the specified range of the AD8307 is −74 dBm to +16 dBm. The output voltage increases by 25 mV for each dBm increase in RF input.