In the summer of 2013 when I lived in Utah, I applied for a part 5 experimental license for 472-479 kHz (630 meters). I was granted WG2XSV in November of that year and put the following transmitter on the air.
The VFO has foam insulation on three sides of the inside of the case to reduce the frequency excursions due to temperature changes and airflow from the heating and air conditioning system. I plan to set it inside of another enclosure with more insulation and with the shaft coming out the front with a dial.
On low and medium frequencies, vertical antennas with a good ground system are a must!! Unless you have a lot of real estate to work with, the antennas will be very short in comparison to a full quarter wave at the operating frequency. As a result the efficiency and the radiation resistance will be very small. To offset this, some method of top loading is often used to raise both of these parameters. We need to know the radiation resistance in order to be able to calculate the effective isotropic radiated power (EIRP) as required by the FCC.
In LaPort’s book, “Radio Antenna Engineering”, 1952, which is now in the public domain**, he gives the equation I used to find the radiation resistance of my MFJ-2990 aluminum telescoping 42.5 foot vertical.
** http://snulbug.mtview.ca.us/books/RadioAntennaEngineering/ **
This equation works for verticals that are less than 30 degrees of wave length (WL) and are NOT top loaded (farther down this page I describe an example of a top loaded vertical inverted-L). In this equation, G is the height of the vertical in radians (radians = degrees divided by 57.3).
I found the wave length, WL, by dividing 984 by 0.475 MHz = 2071.5 feet. Thus, my vertical is 42.5/2071.5 = 0.0205 WL in height. Next convert that to degrees by multiplying by 360 = 7.38 degrees and then into 0.1288 radians (i.e., I divided by 57.3).
The equation given by LaPort on page 23 of his book is R_{r} = 10G^{2}= 10(0.1288)^{2} = ~0.16616 Ohms of radiation resistance, R_{r}.
Andy, G4JNT, showed me a simpler equation that works. It is Rr = 40(Pi)^{2} times (H/WL)^{2 }where H = the actual height of the vertical, and WL is the wavelength at the operating frequency (MHz) both in feet or both in meters (or in degrees).
Thus, for my 42.5 foot vertical, Rr = 40(9.87)(42.5/2071.5)^{2} = 0.16618 ohms which is almost identical to what I got from LaPort's equation. My thanks to Andy for his help. I modified one of Andy's spreadsheets to calculate Rr. You will find a link to my version of the spreadsheet in a section below called "Finding the radiation resistance of an inverted L".
Calculating EIRP and ERP
When the FCC grants us use of 630 meters, they will state our maximum allowable power as EIRP (effective isotropic radiated power). So, when I measure the RF current at the base of the vertical, I can use it to calculate the EIRP. To find my EIRP, I start with equation 5 from Fritz Raab’s article on calculating ERP from this link: http://www.500kc.com/downloads/RN06-32.pdf
Equation 5 uses PEAK current, but my home made RF ammeter measures AVERAGE current which is 0.637 times I_{peak}. So I divide my measured current at the base of the antenna of 0.4 amperes by 0.637 to get 0.6279 amperes peak current. Then, I compute the Total Radiated Power (TRP, which Fritz refers to as “P_{t}”) which, by equation 5, is TRP = I^{2}R/2 = (0.6279)^{2} times (0.166 ohms)/2 =0.0327 watts.
Recently I was able to acquire a THERMOCOUPLE RF ammeter at a swap meet. It measures true RMS current as verified on the Booton website in a pdf (WTG_RefGuide_F1128_sm_web.pdf) on page 9 of that document:
"The thermocouple is one of the oldest ways of directly measuring low RF power levels. This
is done by measuring its heating effect upon a load, and is still in common use today for the
measurement of “true-RMS” power. Thermocouple RF ammeters have been in use since
before 1930 but were restricted to the lower frequencies. It was not until the 1970s that
thermocouples were developed that allowed their use as sensors in the VHF and Microwave
range." (my emphasis added; Booton is the maker of Fluke measuring instruments).
The relationship between EIRP and TRP is a ratio of 3:1 (or 4.77 dB), thus 0.0327 times 3 yields 0.0981 watts, or about 98 milliwatts EIRP. Furthermore, the relationship between ERP and TRP is a ratio of 1.82 to 1 (or 1.77 dB), thus the ERP for this situation is 1.82 times .0327 = .0595 watts, or about 60 milliwatts.
The experimental licenses that were initially on the 600 meter band were issued grants in ERP units. The new grants to amateur radio licenses for 630 meters will be in EIRP units. (A rough comparison between the two units is this: 5 watts EIRP = 3 watts ERP.)
This is a link to a plot (below) of my antenna pattern that I used to calculate my EIRP
Top loading is needed when the vertical portion of the antenna cannot be increased. An inverted L (or a top wire in the form of a T) can be added to increase the radiation resistance, and hence the EIRP. Here is an example of how to determine the R_{r} of a 40 foot vertical with a 60 foot top wire as an inverted-L antenna for 475 kHz. The wavelength, WL, of 0.475 MHz is 984/0.475 = 2071.5 feet. The total length of the antenna is 100 feet, so the WL of the antenna is 100/2071.5 = ~0.048274 WL.
Since the equation we will be using must have the WL in degrees, the antenna is 360 times 0.048274 = 17.37864 degrees. The "relative" current at the base is equal to the Sine of 17.37864 degrees and is called I_{b} in the following equation.
G_{v} is the degrees of the vertical section, which is 6.95 degrees. The “A” is the “degree-Ampere” area which is to be used in the second equation to finally get the radiation resistance from
Then A = (6.95/2) times (.181/.2987 + 1) = 5.5807 degree-amperes. Using this answer for A in the second equation gives us R_{r} = 0.01215(5.5807)^{2} = ~0.3784 Ohms of radiation resistance.
Assuming the same 0.4 RF amperes into the bottom of the vertical, we calculate the ERP in the same way as in the above example. To find my ERP, I start with equation 5 from Fritz Raab’s article on calculating ERP. Remember that equation 5 uses PEAK current, but my RF ammeter measures AVERAGE current which is 0.637 times I_{peak}. So, again, I divide my measured current at the base of the antenna of 0.4 amperes by 0.637 to get 0.6279 amperes peak current. Then, I compute the Total Radiated Power which, by equation 5, is TRP = I^{2}R/2 = (0.6279)^{2} times (0.3784 ohms)/2 =0.0746 watts.
The relationship between TRP and ERP is a ratio of 1:1.82, thus 0.0746 times 1.82 yields 0.13576 watts, or almost 136 milliwatts ERP. This is about 3.5 dB greater than the example above which had no top loading. (Note: the EIRP would be 3xTRP=.2238 watts, or about 224 mW)
Rudy, N6LF, worked out the Rr for this example on a NEC modeling program using #12 wire and came up with an Rr of 0.3753 ohms, which is a difference of less than 1% from my calculations above. Thanks Rudy.
(These equations are from pages 23 and 24 of LaPort’s “Radio Antenna Engineering” book that was referenced in the section above.)
If you have questions about the above, or would like a link to download the book, you can email me at
w0yse at arrl dot net
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This Excell spreadsheet was developed to calculate the radiation resistance of a short vertical, less than 1/12 of a wavelength ( <30 degrees) at the operating frequency. I started with G4JNT's version and converted it into my own. Thanks to Andy for sharing it with us all.
Radiation Resistance calculator for inverted L or T* verticals
(Feel free to share the spreadsheet with others as long as it remains free)
This SS can be used with a vertical with NO top loading if a zero is entered into the box for the "top wire". Also, if you can measure the RF current going into the base of the vertical (see note on measuring RF current below), it will calculate the radiated power
My formulas for Radiation Resistance, Rr, are based on LaPort's, RADIO ANTENNA ENGINEERING, 1952, pages 23-24, and those for finding the radiated power are based on Fritz Raab's tech note at http://500kc.com/downloads/RN06-32.pdf, page 2, formula (5) and following.
* Rudy, N6LF, used a NEC program to compare the L with the T. In the program he moved the connection at the top of the vertical portion along the top wire and found that the change in Rr was insignificant between the T connection and the inverted L connection points. Note that this is only true for an antenna of less than about 1/12 of a wavelength. This leads me to believe that a top hat of three wires of 15 feet each, spread out in different directions from the top, would give about the same Rr as one wire of 45 feet in a T or inverted L configuration.
* You can read about this in Rudy Severns article on 600m-verticals-part-2 at http://rudys.typepad.com/files/600m-verticals-part-2-1.pdf
Scroll down to page 13 of the PDF. The discussion begins directly under figure 13 and continues thru figure 14 on page 14.
Update January 2018:
The Spreadsheet calculations assume that the top loading wires are HORIZONTAL but my top load wires are the upper part of my guying system. I know that the Rr of my antenna has to be between that of a "topless" vertical and one with perfectly horizontal wires. I assume, since those wires are at a 45 degree angle to the vertical section, that the actual Rr is somewhere between those two values. I further assume that it is probably near the "arithmetic average" of those two values.
Ralph Hartwell, w5jgv, has a simple way to make an ammeter to measure RF. You can find it at http://w5jgv.com/rfa-2/rfa-2.htm
The meter is inserted at the base of the vertical, between the vertical and the loading coil. Be sure to use the Schottky diodes that he mentions and then check the calibration against a good multimeter. Rudy contributed this comment: "the older RF ammeters, which are so common at flea markets, used a bimetal junction (a thermocouple) the output of which is determined by it's temperature. The meters show true RMS. The thermocouple does not respond lineally, that's why the non-linear scales on the meters." That's good to know because, if you are using one of these RMS meters, you will need to divide by 0.707 in the examples where I divided by 0.637 to find ERP. (Rudy's comment is corroborated by Booton, maker of Fluke meters. You can see this in my paragraph above called " Effective Isotropic Radiated Power (EIRP)".
Here is an interesting site about thermocouple type meters that is worth looking at....
http://k4che.com/GO-9%20Transmitter/RF%20Ammeters/RF%20Ammeters.htm
To find out the total resistance of my antenna system, which includes the radiation resistance, the resistance of the loading coil (which will be LARGE compared to any other part of the system), and the ground losses, I used a MFJ-259b Antenna Analyzer. I did the 630 meter modification similar to KL7UW's mod on his MFJ269. Ed's mod can be found at http://www.kl7uw.com/mfjmod.htm. The schematic is the same as my "259b".
To measure R(total) I un-grounded the bottom of my coil and connected the analyzer between the coil and my ground system. After bringing the system back into resonance by tuning for the lowest reactance (x), I read the R value from the meter and got 23 ohms. I then was able to determine the radiation efficiency for my vertical without top loading as R(rad)/R(total) or 0.166/23 = .0072 (or 0.72%) and for the inverted-L above as 0.3784/23 = 0.01645 (or 1.645%), which is pretty low, but this is typical for an antenna that is extremely short compared to a full quarter wavelength of almost 500 feet for 475 kHz. (My thanks go to Pat Hamel, W5THT, for teaching me this trick)
With this circuit I am able to get my reflected power down to virtually zero for an SWR of 1.0 to 1. It helps to pre-tune it with an antenna analyzer such as the MFJ-259B which I modified to work down to a little below 470 kHz. The variometer can adjust the main coil to between about 300 to 400 uH and the left side of the coil adds enough turns and taps to be able to bring the antenna to resonance at 475 kHz. Both "arrows" (below) are adjusted to bring the SWR to minimum. The coils and capacitor are mounted right outside my shack window in a rectangular storage tub to keep everything dry. The variable capacitor is a 3 gang from an old TRF type receiver that has about 600 pF per section. (updated 6 July 2015)
I used the free demo version of EZnec 6.0 to generate data and graphs of my 40 foot vertical antenna for 630 meters. It is top loaded with 3 sloping wires of 25 feet each. The "FF PLOT" of the far field signal strength shows that the maximum "gain" of the antenna is -16.47 dBi at an angle of elevation of about 23 to 24 degrees. I was able to calculate my EIRP for 100 watts into the antenna. My EIRP is about 2.25 watts as explained below the picture.
I solved this formula for P1:
10 Log(P1/P2) = -16.47, where P2 is 100 watts
Note: The antenna gain is heavily based on the total antenna system resistance.
My R(tot) is 17 ohms
The following item is just an example of what 50 milliwatts of ERP (effective radiated power)
can do on the 630 meter band....
on December 29, 2013
With 50 milliwatts ERP to a 44 foot vertical antenna, base loaded.
Timestamp | Call | MHz | SNR | Drift | Grid | Pwr | Reporter | RGrid | km | az |
2013-12-29 10:24 | WG2XSV | 0.475712 | -30 | 0 | DN41ac | 0.05 | WE2XPQ | BP51ip | 3373 | 325 |