Basic antenna parameters: radiation resistance, gain, beamwidth, efficiency; effective radiated power (ERP) and effective isotropic radiated power (EIRP)
Drill results are kept in this browser. Log in to keep them on your account and get a study plan.
Why An isotropic radiator is a mathematical fiction: a lossless point source that spreads power equally in every direction in three dimensions, so its pattern is a perfect sphere. No real antenna can do this, but it makes a clean reference for comparing gain, which is why gain figures carried as dBi are 'decibels over isotropic'. For example, a half-wave dipole in free space has about 2.15 dBi of gain because it concentrates power into a doughnut shape rather than a sphere.
Watch out The choices describing a calibrated physical antenna used for field measurements are wrong because an isotropic radiator cannot be built; real reference antennas are dipoles or standard gain horns, whose gain is itself stated relative to isotropic.
Isotropic = imaginary perfect sphere of radiation. dBi means 'gain over that fiction'; a dipole is 2.15 dBi.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
What is the effective radiated power (ERP) of a repeater station with 150 watts transmitter power output, 2 dB feed line loss, 2.2 dB duplexer loss, and 7 dBd antenna gain?
Why ERP is transmitter power multiplied by the net system gain, where gain is in dBd (referenced to a dipole). Add the gains and subtract the losses in decibels first: 7 dBd - 2 dB - 2.2 dB = 2.8 dB net gain. Then convert: 150 W x 10^(2.8/10) = 150 x 1.905, which is about 286 watts.
Watch out The 469 watt answer comes from using only the 7 dBi/dBd gain (or ignoring one of the losses); you must subtract both the feed line and duplexer losses before converting.
Do all the dB math first, then one power conversion: P x 10^(dB/10). Net +3 dB roughly doubles the power.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
What term describing total radiated power takes into account all gains and losses?
Why Effective radiated power is the transmitter output power adjusted by every gain and loss in the system: feedline loss, connector and duplexer or filter losses, and the antenna's gain referenced to a dipole. You convert everything to decibels, add the gains and subtract the losses, then apply that net dB figure to the transmitter power. ERP is what a half-wave dipole would need to be fed to produce the same signal in the antenna's favored direction; EIRP is the same idea referenced to an isotropic radiator, which is 2.15 dB higher.
Watch out Power factor and apparent power are AC power terms describing the phase relationship between voltage and current in a reactive circuit, and half-power bandwidth describes the width of a resonant response between its -3 dB points. None of them relate to radiated signal strength.
ERP = TX power + antenna gain - feedline and component losses, all in dB. EIRP is ERP plus 2.15 dB.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
Which of the following factors affect the feed point impedance of an antenna?
Why Feed point impedance is set by the antenna's own geometry and its electromagnetic surroundings. Height above ground is a big factor because ground reflections couple back into the antenna, so a horizontal dipole's feed point impedance swings well above and below the free-space value of roughly 70 ohms as height changes, converging near that value at a wavelength or more up. Nearby objects and the antenna's length and diameter matter for the same reason.
Watch out Transmission line length and tuner settings change the impedance seen at the transmitter end of the system, not the impedance actually present at the antenna's feed point; power level is irrelevant because the antenna is a linear, passive load.
Feed point impedance is set at the antenna, by its surroundings. Anything back in the shack only changes what you see, not what's there.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
Why Ground gain is the extra signal strength that comes from the ground acting as a reflector. Energy radiated downward bounces off the earth and, at certain elevation angles, arrives in phase with the direct wave, adding to it. Over a perfect reflecting surface this addition can theoretically reach 6 dB, and over real earth or salt water HF antennas commonly see roughly 3 to 6 dB at low takeoff angles. Nothing about the antenna itself changed; the environment supplied the gain.
Watch out The choice about grounding the antenna confuses ground gain with a DC or safety ground connection. Ground gain has nothing to do with wiring the antenna to earth; it is purely a reflection effect, which is why height above ground and ground conductivity matter so much on HF.
Ground gain = free bonus from the mirror below you, up to 6 dB when the reflection adds in phase.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
What is the effective radiated power (ERP) of a repeater station with 200 watts transmitter power output, 4 dB feed line loss, 3.2 dB duplexer loss, 0.8 dB circulator loss, and 10 dBd antenna gain?
Why ERP is transmitter power adjusted by the net gain in dB along the path to the antenna. Add the losses: 4 + 3.2 + 0.8 = 8 dB, and subtract from the 10 dBd antenna gain, leaving +2 dB net. A gain of 2 dB is a power ratio of 10^(2/10) = 1.58, so 200 W x 1.58 = about 317 watts. Because the gain is given in dBd (referenced to a dipole), the result is ERP rather than EIRP.
Watch out The choice of 126 watts comes from getting the sign backwards and taking a net loss of 2 dB instead of a net gain; 2,000 watts would be a full 10 dB gain with the losses ignored.
Sum the losses, subtract from gain, then ratio = 10^(dB/10). Remember 2 dB = 1.58x, 3 dB = 2x.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
What is the effective isotropic radiated power (EIRP) of a repeater station with 200 watts transmitter power output, 2 dB feed line loss, 2.8 dB duplexer loss, 1.2 dB circulator loss, and 7 dBi antenna gain?
Why Work the whole chain in decibels, then convert once. Losses total 2 + 2.8 + 1.2 = 6 dB, and the antenna adds 7 dBi, so the net gain is +1 dB. A gain of 1 dB is a power ratio of about 1.26, so 200 W x 1.26 = 252 W. Because the antenna gain is given in dBi (referenced to an isotropic radiator), the result is EIRP directly, with no 2.15 dB correction needed.
Watch out The choice near 159 watts is what you get if you treat the net as -1 dB, that is, if you subtract the gain and add the losses backwards; watch the sign of each term.
Add gains, subtract losses in dB first, convert last. dBi in means EIRP out; dBd in means ERP out.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
Which frequency band has the smallest first Fresnel zone?
Why The first Fresnel zone is the ellipsoid around the line-of-sight path where the bulk of the signal energy travels, and its radius grows with wavelength: r1 = 17.31 * sqrt(D / (4f)) meters, with D in km and f in GHz. Radius varies as 1/sqrt(f), so the highest frequency listed has the smallest zone. At 5.8 GHz the wavelength is only about 5 cm, so the zone is narrower than at any of the lower bands and clears obstacles more easily for a given path.
Watch out 900 MHz is the tempting pick if you reason that a lower frequency 'bends around' obstacles better, but that is diffraction, not zone size; its long wavelength actually makes the Fresnel zone the largest of the group.
Fresnel zone size follows wavelength: highest frequency, smallest zone. Pick the biggest GHz number.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
Why Antenna current flows through two kinds of resistance: radiation resistance, which represents power actually launched as radio waves, and loss resistance from conductor resistance, ground losses, loading coil losses and nearby lossy objects. Efficiency is the fraction of input power that becomes radiation, so it equals radiation resistance divided by total resistance (radiation plus loss), usually expressed as a percent. A short 160 meter vertical might have 5 ohms radiation resistance and 15 ohms of loss, giving 5/20 = 25 percent efficiency.
Watch out The choice comparing effective radiated power to transmitter output is not efficiency because ERP already includes antenna gain over a dipole and feed line loss, so a high-gain array can show ERP far above transmitter output. Dividing total resistance by radiation resistance just inverts the formula and would give a number greater than 1.
Efficiency is a fraction less than 1, so the smaller piece (radiation resistance) goes on top of the total.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
Which of the following improves the efficiency of a ground-mounted quarter-wave vertical antenna?
Why A ground-mounted quarter-wave vertical uses the earth as the other half of the dipole, so the return currents flow through lossy soil. Efficiency is radiation resistance divided by the total of radiation resistance plus loss resistance, and poor ground can add many ohms of loss to a feedpoint resistance of only about 36 ohms. Laying down a system of buried or elevated radial wires gives those currents a low-resistance metallic path instead of dirt, cutting the loss term and raising efficiency.
Watch out Shortening the radiating element makes things worse: it lowers radiation resistance, so the fixed ground and coil losses eat a larger share of the power. Isolating the coax shield from ground affects common-mode current and feedline radiation, not ground-loss efficiency.
Efficiency = Rrad / (Rrad + Rloss). Radials shrink Rloss; more radials, more efficiency.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
Which of the following determines ground losses for a ground-mounted vertical antenna operating on HF?
Why A ground-mounted vertical works against the earth, so return currents flow through the soil near the base and dissipate power as heat. How much is lost depends on how well the soil conducts, which is set by soil conductivity (and moisture/mineral content). Poor, dry, sandy soil has high loss; salt marsh or seawater is nearly lossless, which is why adding many buried radials helps by carrying the return current in copper instead of dirt.
Watch out Take-off angle is tempting because ground quality does affect the far-field pattern and low-angle radiation, but that is a pattern effect, not what creates the I-squared-R loss at the antenna base. SWR just describes the impedance match on the feed line and can even look better when losses are worse.
Ground loss lives in the dirt: conductivity rules. Bad soil? Bury more radials.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
How much gain does an antenna have compared to a half-wavelength dipole if it has 6 dB gain over an isotropic radiator?
Why Antenna gain can be referenced either to an isotropic radiator (dBi) or to a half-wave dipole (dBd). A half-wave dipole itself has 2.15 dB of gain over an isotropic radiator, so dBd = dBi - 2.15. Here 6.0 dBi - 2.15 dB = 3.85 dBd.
Watch out The choice that says 8.15 dB comes from adding 2.15 instead of subtracting it, which is the conversion the other direction (dBd to dBi). The choice that says 6.0 dB ignores the reference change entirely.
Remember 2.15: dBi minus 2.15 equals dBd. The dipole already beats isotropic, so the dBd number is always smaller.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.