Is there a radio engineer in the house?

I would like guidance on whether I have the math right. This is a gross oversimplification ignoring antenna gain, non free space signal loss, directional antennas, etc – just distance, transmitter ERP and frequency to derive theoretical receiver dBm


Do those calculations look right? The FCC protects signals until th dBm reaches -60 dBm, I think. The station may or may not be heard further depending on the sensitivity of the receiver.

Am I on the right track?

If you want to play along at home,

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10 Responses to Is there a radio engineer in the house?

  1. Art Stone says:

    Other related bits of info… Things I think I understand…

    FM is purely line of sight – the curvature of the earth limits the signal even if the dBm would have a strong enough signal. Obviously hills and other things can also block line of sight and the receiver being higher in elevation would extend the range.

    AM propagation is based on ground waves that curve with the earth (ignoring ionosphere reflection) but also dependent on ground wave conductivity which can’t be known without measurement – my AM signal numbers look wrong (not enough signal loss) I’m guessing the groundwave loss needs to be in this and isn’t

    Different FM classes have different contour protections even if the signal reaches further. The key is the signal can’t overlap someone else’s contour

  2. Art Stone says:

    Turns out the math of AM groundwave propagation is very complex. If there are any calculus geeks out there, enjoy!

  3. TheChairman says:

    Wave propagation and signal theory wasn’t my strength. 😉 Sorry, couldn’t resist…

    The operative word in the title of that FCC document is smooth, since many other factors (variables) come into play ‘in the field’: topo, geology, climate, lat/long, etc.

    I think you need a ground attenuation factor. Interesting as it may be, doing integral calculus and implementing the numerical computation algorithm would be overkill.

    A better option might be to look at the following PDF from the Australians. It pretty much eschews the integral calc theory (Maxwell’s equations, etal) and provides some practical ‘plug-n-chug’ examples for computing various aspects of broadcast planning.

    There’s also a ham radio website/blog (can’t recall the name right now) which has a page with algebraic ‘rule of thumb’ formulae, including useful correction parameters.

    • Art Stone says:

      My first take looking through the document – my math education ends at calculus so I understand just enough to be dangerous… Is the FORTRAN program has an early branch of “is this over a long distance?”. Presumably the purpose of the analysis of expanding the medium wave band was European concern that 1605-1705 kHz signals would reach Europe. Short range (less than a hundred miles) can skip all the differential equations.

      The wild card is the groundwave conductivity – which ranges from 0.5 millisiemens in Long Island to 30.0 in South Dakota. Using differential equations to get very precise answers is like cutting diamonds using a sledgehammer. It’s pointless to calculate 3 decimals when every 50 feet the conductivity is changing, and may be different tomorrow if it rains.

      Even if that is necessary, it seems to me it could be precomputed once and stored in a database. The main thing I don’t understand is the “dialectric coefficient” that is a required input.

      The FCC says basically if you don’t know, 15 millisiemens/m is a good guess. Here the official FCC shows 2 or 4… I really doubt that the tiny 500 watt class D radio stations hire an engineer to run around on a regular basic taking field strength measurements. One station I was looking at today got caught in 2000 running at only 40% power. Looking in Google Earth, I’m pretty sure they tore down their tower, but the FCC renewed the license. They checked the check box saying “yep, we’re still on the air!”

      • TheChairman says:

        The dielectric coefficient you cited is probably to adjust for meteorological factors in the medium (i.e. air), and will also affect those Diff EQ’s you mentioned…and are wise to avoid.

        The coefficient will change with air pressure, temperature, humidity, particulates, etc. E.g. The dry dusty air over Phoenix in June will have different coefficients (atmospheric refraction and permittivity) as compared to Denver or San Francisco.

        Likewise for influences on ground conductivity/attenuation by the predominant surface material. e.g sand vs granite vs water.

        That data should be available in a useful format (database).

        I assume you know about the following link…

        • Art Stone says:

          I pull a lot of data already from the FCC

          Being at the crawling stage, I’m willing to assume the FCC default of 15 millisiemens/m for the whole country

          The official FCC wild ass guess map is here

          It has a link there to a M3 dataset, but I didn’t see a format. That’s the next step maybe. The groundwave can be broken into segments (the Australian documents go into that) where you can apply different groundwave conductivity to portions of the path and add them up to get a total. I would be inclined to use the FCC data at the transmitter and apply it for the entire distance. Not accurate, but close enough. The 50kw stations like KDKA reach only a hundred or so miles during the daytime. Stations in Chicago mostly fade out before you reach Detroit, etc

          Assuming the dialectric constant as 1.00 is probably equally reasonable.

          Part of this is to see if anyone wants to talk about anything other than ISIS.

  4. Art Stone says:

    So it seems unlikely it is as simple as my first experiment

    MariaDB [fcc]> select * from fcc.m3 where (-80.84 between lon1 and lon2) and (35.23 between lat1 and lat2) limit 50;
    | Seq | Lat1 | Lon1 | Lat2 | Lon2 | Gc1 | Gc2 |
    | 7544 | 35.140000 | -80.980000 | 35.320000 | -80.770000 | 4.000000 | 2.000000 |
    1 row in set (0.00 sec)

    MariaDB [fcc]> describe m3;
    | Field | Type | Null | Key | Default | Extra |
    | Seq | int(11) | NO | | NULL | |
    | Lat1 | decimal(10,6) | NO | | NULL | |
    | Lon1 | decimal(10,6) | NO | | NULL | |
    | Lat2 | decimal(10,6) | NO | | NULL | |
    | Lon2 | decimal(10,6) | NO | | NULL | |
    | Gc1 | decimal(10,6) | NO | | NULL | |
    | Gc2 | decimal(10,6) | NO | | NULL | |
    7 rows in set (0.01 sec)

    The coordinates are uptown Charlotte. The “line” of difference forms a rectangle (ignoring I’m on a sphere and not flat earth!). Since I’m North of the line (or am I?) , gC1 applies, hence my groundwave coefficient is 4.0 (matching the map)

    Maybe I’ll just be a punk and average GC1 and GC2 and say 3.0 😉

    Where can I sign up for the flat Earth Society?

  5. Art Stone says:

    Battle plans don’t survive the first contact 😉

    However, in this case the AM coverage prediction looks close to perfect. The only mistake was my understanding of what the final number means. Checking it in the car with a non directional antenna, if the rx dBm > 0.00, I appear to be inside the 60 dB contour. The signal is solid and no adjacent channel interference (“you should be able to hear it”).

    In general, the station with the highest rx signal strength < 0.0 is the station the radio hears unless one of the stations is directional, unless it is drowned out by the very loud station on the next channel - hence the concept of adjacent channel selectivity, another measure of the good expensive receivers. Car radios are typically average since they don't get rx gain by being able to point the antenna

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