A recent post on ALPB proposed using a 3-m vertical radiator having an OD of 12 inches, hoping to offer 1% system radiation efficiency at 1700 kHz.
Below is an analysis of such a system, using average to low losses in the base loading coil and r-f ground connection.
The system radiation efficiency for the parameters shown is about 0.2%, rather than about 1%.
As I don't post on ALPB, maybe someone reading this who does could forward this information to the writer there who proposed using a 12" OD wire.
BTW, that 12" OD conductor doesn't need to be a solid wire. Due to skin effect, a thin-wall tube with an OD of about 12" would work just as well, and cost a lot less.
Cross-Forum-Link
Here is a link to the post referred to regarding a 12"-diameter wire
Link to Antenna Outer-Diameter Discussion
In addition, that thread is linked back to here.
Posting and reading responses on different forums is awkward. Would someone please ask davec if he is willing to post this topic on Part15.us, or at least read what I post here, directly? TIA.
DaveC has tried to enlist here, but: "By the way, I tried to join the Part15 group but their CAPTCHA shows an error message for the site owner."
davec posted on ALPB: ... For a Q of 100 we can reduce system loss to 9 ohms (4 ohms for the loading coil and 5 for GND ...
Getting the resistance of an r-f ground connection to 5 Ω or less takes a fairly heroic amount of buried radials, and the work to install them. Probably few operators of Part 15 AM stations have, or want to install such a ground system.
Below is a NEC4.2 analysis of a monopole using a set of 32 buried radials, each 10 meters in length. Even for this set of radials, the conductivity of the earth in which they are buried needs to be about 2 mS/m or better to get the ground loss down to 5 Ω or less.
Using fewer/shorter radials would move that 5 ohm resistance to require higher earth conductivity.
Using just a single, 8' copper ground rod buried vertically directly below the monopole can have an r-f resistance ranging upwards from 50 Ω, depending on earth conductivity and frequency.
davec posted on ALPB today: Yes, for a ground mounted single-wire monopole the radiation efficiency is constrained by physics to relatively low values; 0.3% for a CB whip and 1% for a (very) fat wire operating at the top of the AM BC band. The popular way to obtain relatively high radiation efficiency is to elevate the "antenna" on a mast or building. As we all know, the mast, or ground lead, becomes part of the radiating antenna. ...
Below is a graphic posted here and at other sites in the past, showing the improvement in field intensity due to the radiation from a long ground lead, or mast.
The gist of my ALPB post is that AM antenna radiation efficiency is ultimately limited by bandwidth. Reduce system loss too much (add too many radials) and bandwidth becomes too narrow to pass the higher audio frequencies (the AM sidebands become attenuated). We can design an antenna to meet a target bandwidth and we then have the maximum radiation efficiency possible within the constraints of 15.219. Antenna diameter is one of the best "knobs" to turn and can yield 4X the radiation efficiency that a thin wire can. For practical antennas the maximum radiation efficiencies for Q = 100 are:
- base-loaded, 0.3 - 1.2% thin to thick
- center-loaded, 0.3 - 1.2% thin to thick
The numbers below are approximate and are for illustrative purposes.
Reff = QRr/X and Q =X/Rsys are two formulas that show us how the "knobs" work. We can rearrange them to solve for various unknowns and we can assign some as constants.
Reff is Radiation Efficiency, Rr is radiation resistance, X is the loading coil reactance, Q is X/Rsys
For the two short monopole topogies Rr is:
- Base loaded 0.12 ohms
- Center loaded 0.24 ohms
Q can be set to 100 as that gives a -3dB bandwidth of 17 kHz for a 1700 kHz antenna. X is set by the topology and the antenna diameter.
Given a 3 meter base-loaded monopole X varies from approximately 1000 to 4000 ohms as the antenna diameter goes from a thin wire to 12 inches. X for a center-loaded antenna varies from 2000 to 8000 ohms.
Inserting the Rr values above and Q=100 the radiation efficiency becomes:
- base-loaded 12/X, X from 1000 to 4000 ohms thick to thin
- center-loaded 24/X, X from 2000 to 8000 ohms thick to thin
Solving for Reff we get:
- base-loaded, 0.3 - 1.2% thin to thick
- center-loaded, 0.3 - 1.2% thin to thick
Rearranging Q =X/Rsys as Rsys = X/Q and plugging in the X and Q (100) values we get Rsys:
- base-loaded, 10 to 40 ohms thick to thin
- center-loaded, 20 to 80 ohms thick to thin
The advantage of center loading vs bottom loading is that double the system loss yields the same performance; the ground system can less aggressive.
Rsys = radiation resistance + loading coil RF resistance + ground loss resistance
Ground loss = Rsys - Rr - Rcoil
Assigning loading coil Q of 250 we get this range of minimum ground loss for the two topologies and diameters. Rr is neglected as it is so small:
- base-loaded, 6 to 24 ohms thick to thin
- center-loaded, 12 to 48 ohms thick to thin