# ATTEMPT TO ESTIMATE ANTENNA EFFICIENCY

Although it's very hard to calculate the effective efficiency of my LF antenna, I've tried an indirect evaluation, with the aid of the german station DCF39, transmitting on 139 kHz, and starting with a careful calculation of my single-turn receiving loop (see pictures).

Fig. 1

Fig. 2
The first step has been the definition of the parameters of the single-turn alone, supposed in the free space, subsequently, using the Mininec method, it was modeled in its operative position accounting for the presence of the building and for the surrounding heavy urbanized terrain. Remember that, in the layout at right, T1 is the toroidal transformer, 2 / 18 t., located at the base of the loop, L is the coaxial line, C the tuning condenser, A the safety relais, T2 the output transformer and O the output connector.
The parameters of the loop itself, calculated at 139 kHz result: Diameter = 1.5 m
Conductor diameter = 8 mm, aluminium
Radiation resistance = 4.49 x 10 ^ - 9 ohm
Loop RF resistance = .0236 ohm
Loop reactance = 4.374 ohm
Effective height = .00515 m
Free space efficiency = - 65.43 dBi

With the Mininec I've found about the same efficiency in free space and, over ground, values ranging from - 61 to - 59.5 dBi at some degrees of elevation with a strange peak of - 45.5 dBi at 42 degrees. These values are obviously approximate, being very difficult to reproduce exactly the real conditions of operation, particularly the strange peak at 42 degrees appears suspicious.

Separately has been evaluated the gain of the amplifier:
Input impedance = 220000 ohm
Load impedance = 50 ohm (actual input impedance of RX)
Output voltage = 78% of the input voltage
Gain = 34.27 dB

The loaded Q measured at points 1, 2 (see layout), results = 76, so the whole loop, considering the turn-ratio of the toroidal transformer and the gain of the amplifier, shows a total efficiency of - 38.13 dBi in free space and, following the results of Mininec calculation (excluding the strange peak at 42 degrees), from - 33.7 to - 33.2 dBi in its operative position.

These values seem to be roughly confirmed by the signal level of the german station DCF39 transmitting from Burg, about 950 km away, with an ERP of 40 kW = 76 dBm. This level varies daily between - 70 and - 40 dBm, reaching frequently - 35 dBm. A careful calculation of the ground wave gives a field strength around 100 µV/m, an estimation of space wave gives around 180 µV/m, supposing zero losses in the ionosphere, the space wave could reach 360 µV/m. Adding this last value to the 100 µV/m of the ground wave (supposing both waves arriving in phase), and relating the resulting field strength with the level of - 35 dBm, read on my receiver, the efficiency of the loop would be around - 28 dBi, probably a too high value, so seems to be more realistic suppose a further increase of the space wave due to a concentration in the reflection of the ionosphere, and confirm the efficiency of the loop around - 33 - 34 dBi.

At this point, comparing the signal received by the loop with the signal received by the antenna, this last appears in substantial parity with dry weather and about 2 dB lower with wet weather. So, averaging, the efficiency of the antenna can be estimated around - 34 - 35 dBi, meaning an EIRP of roughly 80 - 60 mW with 200 W applied power.

This value appears well higher in respect to the 20 - 30 mW estimated before, but really there has been a noticeable improvement, after the last modifications made in the antenna circuitry, as confirm the very good reports received from DX stations.

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