WEBVTT NOTE Antenna Parameters, Computed 1 00:00:00.000 --> 00:00:01.721 The reference antennas. 2 00:00:01.721 --> 00:00:06.441 Question. What is an isotropic radiator? 3 00:00:07.341 --> 00:00:18.824 Answer. A hypothetical, lossless antenna having equal radiation intensity in all directions used as a reference for antenna gain. 4 00:00:19.424 --> 00:00:43.919 Hypothetical, it cannot exist, which is exactly why it is useful as a reference. Every direction equal, no losses, a perfect sphere of radiation. Two references, and the 2.15 dB between them: dBi equals dBd plus 2.15 5 00:00:43.919 --> 00:00:54.263 Question. How much gain does an antenna have compared to a half-wavelength dipole if it has 6 dB gain over an isotropic radiator? 6 00:00:55.163 --> 00:00:59.603 Answer. 3.85 dB. 7 00:01:00.203 --> 00:01:19.003 6 − 2.15 = 3.85 dBd. The dipole itself has 2.15 dBi, so referencing to it always reads 2.15 dB lower. 8 00:01:25.003 --> 00:01:40.630 The 2.15 is not a convention or a measurement. It is the directivity of a half-wave dipole, and it is computable in closed form. A half-wave dipole carries a standing current the formula in the text. 9 00:01:40.630 --> 00:01:52.017 Integrating that current distribution against the free-space Green's function gives a far-field pattern, which is written out in the lesson text. 10 00:01:52.017 --> 00:02:07.565 Directivity is peak radiation intensity over the average, so with F normalised to 1 at theta equals pi divided by 2: The formula for this is written out in the lesson text. That integral has a name. 11 00:02:07.565 --> 00:02:22.250 It is the formula in the text, where Cin is the entire cosine integral, and it evaluates to a value written out in the lesson text. The formula for this is written out in the lesson text. 12 00:02:22.250 --> 00:02:36.934 And the same integral gives the feed impedance. Radiation resistance is defined by the formula in the text, and working it through: The formula for this is written out in the lesson text. 13 00:02:36.934 --> 00:02:51.384 So the two numbers every antenna discussion opens with, 2.15 dB of gain and 73 ohms, are the same integral read two ways. Neither is a rule of thumb. Two things worth taking from this. 14 00:02:51.384 --> 00:03:01.828 First, the 2.15 dB is small: a dipole is barely directive, and its "gain" is almost entirely the absence of radiation along the wire. 15 00:03:01.828 --> 00:03:17.926 Second, 73 Ω is why 50 Ω cable is a compromise rather than a match, the mismatch is 73/50 = 1.46:1, which is why a dipole fed with 50 Ω coax reads about 1.5:1 at resonance and that is correct, not a fault. 16 00:03:17.926 --> 00:03:32.806 Both figures, and the closed form, are recomputed in scripts/tests/test_rf_numbers.py on every test run. ERP and EIRP. 17 00:03:32.806 --> 00:03:41.126 Question. What term describing total radiated power takes into account all gains and losses? 18 00:03:42.026 --> 00:03:46.346 Answer. Effective radiated power. 19 00:03:46.946 --> 00:04:06.183 P ERP equals P tx times 10 to the power of (G minus L) divided by 10 Sum the losses in decibels, subtract from the gain, apply the net as a power ratio. 20 00:04:06.183 --> 00:04:31.621 ERP uses dBd; EIRP uses dBi, and the question tells you which by naming the gain's reference. Three worked answers, exactly as the pool asks them: 150 W, 2 dB feed line, 2.2 dB duplexer, 7 dBd antenna. 21 00:04:31.621 --> 00:04:55.794 Losses 4.2 dB; net 7 − 4.2 = +2.8 dB. 150 times 10^0.28 = 150 times 1.905 = 286 watts ERP. 200 W, 4 dB feed line, 3.2 dB duplexer, 0.8 dB circulator, 10 dBd antenna. Losses 8.0 dB; net +2 dB. 22 00:04:55.794 --> 00:05:21.612 200 times 10^0.2 = 200 times 1.585 = 317 watts ERP. 200 W, 2 dB feed line, 2.8 dB duplexer, 1.2 dB circulator, 7 dBi antenna. Losses 6.0 dB; net +1 dB. 200 times 10^0.1 = 200 times 1.259 = 252 watts EIRP. 23 00:05:21.612 --> 00:05:45.026 The method never changes. Add up losses, subtract from gain, one power ratio. The only thing to watch is that every loss goes in, repeater questions deliberately list three. Efficiency. 24 00:05:45.026 --> 00:05:49.186 Question. What is antenna efficiency? 25 00:05:50.086 --> 00:05:55.937 Answer. Radiation resistance divided by total resistance. 26 00:05:56.537 --> 00:06:16.351 eta equals (R radiation ) divided by (R total ) An antenna's feed point resistance has two parts: radiation resistance, which represents power that leaves as radio waves, and loss resistance, which represents power that becomes heat. 27 00:06:16.351 --> 00:06:24.770 Both look identical to the transmitter. This is the number that explains the loaded mobile antenna. 28 00:06:24.770 --> 00:06:39.057 A short whip may have 2 ohms of radiation resistance and 8 ohms of loss, 20% efficient, and 80% of your power warming a coil, while the SWR meter reads a contented 1:1. 29 00:06:39.057 --> 00:06:47.911 Question. Which of the following improves the efficiency of a ground-mounted quarter-wave vertical antenna? 30 00:06:48.811 --> 00:06:52.706 Answer. Installing a ground radial system. 31 00:06:53.306 --> 00:07:02.786 Question. Which of the following determines ground losses for a ground-mounted vertical antenna operating on HF? 32 00:07:03.686 --> 00:07:07.046 Answer. Soil conductivity. 33 00:07:07.646 --> 00:07:23.308 A ground-mounted vertical returns its current through the earth, and earth is a poor conductor. Radials give that current a metal path instead, cutting the loss resistance and raising efficiency. 34 00:07:23.308 --> 00:07:38.086 Soil conductivity is why the same antenna performs differently in salt marsh and in dry sand, and it is not something you can change, which is why you add radials instead. Ground gain. 35 00:07:38.086 --> 00:07:42.995 Question. What does the term "ground gain" mean? 36 00:07:43.895 --> 00:07:50.719 Answer. An increase in signal strength from ground reflections in the environment of the antenna. 37 00:07:51.319 --> 00:08:03.841 The ground reflects, and at low elevation angles the reflected wave can arrive in phase with the direct one, adding up to 6 dB over free space in that direction. 38 00:08:03.841 --> 00:08:19.319 It is genuinely free gain, and it is why antenna height is the single most effective HF investment: height sets the elevation angle at which the reflection reinforces, and low angles are where DX is. 39 00:08:19.319 --> 00:08:25.953 Question. Which of the following factors affect the feed point impedance of an antenna? 40 00:08:26.853 --> 00:08:29.533 Answer. Antenna height. 41 00:08:30.133 --> 00:08:47.013 The same coupling to ground that produces ground gain also changes feed point impedance, which is the General-level observation that a dipole's impedance falls as you lower it, now with the mechanism. Two more terms. 42 00:08:47.013 --> 00:08:59.016 Question. What is the difference in radiated power between a lossless antenna with gain and an isotropic radiator driven by the same power? 43 00:08:59.916 --> 00:09:03.076 Answer. They are the same. 44 00:09:03.676 --> 00:09:16.027 A lossless antenna radiates all the power it is given, exactly as an isotropic radiator would. Gain redistributes that power; it does not create any. 45 00:09:16.027 --> 00:09:24.814 This is the "gain is not amplification" point from the Technician track, stated as a total-power identity. 46 00:09:24.814 --> 00:09:30.894 Question. Which frequency band has the smallest first Fresnel zone? 47 00:09:31.794 --> 00:09:35.619 Answer. 5.8 GHz. 48 00:09:36.219 --> 00:09:45.906 The Fresnel zone is the ellipsoidal region around a line-of-sight path that must be kept clear of obstructions. 49 00:09:45.906 --> 00:10:01.265 Its radius shrinks with wavelength, so the highest frequency has the smallest zone, which is why microwave links tolerate a narrower cleared path than VHF ones. Check yourself. 50 00:10:01.265 --> 00:10:18.108 A repeater: 100 W out, 3 dB feed line loss, 1 dB duplexer loss, 6 dBd antenna. ERP? Your vertical has 3 ohms radiation resistance and 12 ohms of loss. Efficiency? An antenna is quoted at 9 dBi. 51 00:10:18.108 --> 00:10:23.868 What is that in dBd, and which figure would a manufacturer prefer? 52 00:10:29.868 --> 00:10:52.597 Losses 4 dB, net +2 dB. 100 times 10^0.2 = 158 watts ERP. 3 / (3 + 12) = 20%. Four-fifths of your power becomes heat. 9 − 2.15 = 6.85 dBd. 53 00:10:52.597 --> 00:11:06.268 The manufacturer prefers dBi, because it is the bigger number for the same antenna.