# WG2XSV EXPERIMENTAL STATION

### FINDING THE EIRP AND RADIATION RESISTANCE

To arrive at a calculation of EIRP for a short vertical antenna, such as one for 630 meters or 2200 meters, I needed know the RADIATION RESISTANCE and to be able to measure the RF antenna current at the base of the vertical, above the base loading coil.

I constructed a simple RF ammeter using a DC ammeter whose full deflection current was about 300 mA. It was turned into an AC ammeter by using 4 Schottky, 5 ampere diodes in a bridge rectifier configuration (NTE 573). This idea came from Ralph Hartwell, w5jgv.com. Ralph said it is a good idea to place an RF bypass capacitor directly across the meter's DC terminals. This is suggested because as the RF frequency increases, the coil of the meter movement will exhibit rising impedance to the rectified RF pulses, and will cause a drop in the apparent meter reading at higher frequencies. He found that a value between 0.01 and 0.2 uF works well. Use a low inductance capacitor, such as a Polypropylene capacitor, or any good RF rated capacitor.

I then used a digital test meter to calibrate the shunt needed so as to enable my meter to read above my maximum expected antenna current. A meter of this type will read AVERAGE current rather than RMS (RMS will be 1.11 times the AVERAGE value).  If you have access to a thermocouple type RF ammeter, it will probably read in RMS units.

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Next we need to find the RADIATION RESISTANCE, Rr, of the vertical antenna. This can be done with published graphs or a simple formula, if the vertical has no top loading.

Rr = 160π^2(He / λ)^2  which is approximately equal to 1579(He / λ)^2

where He is the effective height of the vertical which is ½ of the total height due to the fact that the current at the top of the antenna is zero with no top loading. The denominator, λ, is one wave length at the frequency in question. The numerator and denominator must be in the same units of measure, be it feet or meters or degrees. For example, if the height of the antenna is 43 feet, then the effective height is 21.5 feet, since there is no top loading (as yet). The wave length at 475 kHz is 2071.6 feet. Thus the fraction (He / λ) is 21.5/2071.6 = 0.010378 which, when squared and then multiplied by 1579 equals a radiation resistance of ~0.17 ohms. This can be verified in several texts with the graphs that are printed therein.

However, if the antenna is top loaded as an inverted L, or a T top hat, then the calculations are a bit more involved. I have simplified the process by generating an Excel spreadsheet to do this. The calculations in the spreadsheet are based upon those given in Radio Antenna Engineering, 1952 by LaPort (page 23-24).

The spreadsheet can be found in my Dropbox antenna files HERE.

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Now, to find the Total Radiated Power, TRP = I^2*R where I is the RMS value of the antenna current. Let’s suppose we measured it to be 1.40 amperes RMS. Then TRP = (1.40)^2 times 0.17 ohms = ~.333 watts, or 333 milliwatts. Since EIRP is 3 times TRP, the EIRP = 999 mW or about 1 watt.

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### THIS ANTENNA WAS AN ALUMINUM TELESCOPING VERTICAL AT 42.5 FEET(At my former QTH in Utah) <==

This was

my first

tuning

system

for

630m

(The antenna setup that I NOW have in Vancouver Washington is almost the same. It is 45 ft vertically with a top hat of three 25 foot wires that also serve as the guying for the vertical. The insulators at the ends of each top loading wire connect to black UV cord two of which continue to anchors near ground level. The third top load wire spans across part of the roof of the house and anchors to the roof peak. I also changed my feed point system to the loading coils as can be seen in the schematic circuit that is at the bottom of the first page of this website.) ### The following is amap of all those spotting my wspr beacon overnight on February 11-12, 2015with 1 watt ERP (1.64w EIRP) ### *********************************************************************************

I will be moving and/or copying stuff to this website from my WG2XSV PAGE at http://w0yse.webs.com

(For example: Calculations for the Radiation Resistance, Rr, of an inverted-L can be found there

as well as pictures of my QRPp 630 meter transmitter)