Radiation Resistance and Efficiency
When RF power flows from your transmitter into an antenna, not all of it gets radiated as electromagnetic waves. Some is converted to heat in the antenna conductor, some is lost in the ground, and some may be absorbed by nearby objects. The fraction that actually gets radiated — the antenna efficiency — can range from nearly 100% for a well-designed full-size antenna to less than 1% for some severely compromised shortened antennas. Understanding radiation resistance and efficiency gives you a quantitative grip on how good your antenna actually is, and helps you make informed decisions about antenna design and installation.
An antenna's feedpoint resistance is the sum of its radiation resistance (power usefully radiated) and its loss resistance (power wasted as heat).
View LargerWhat Is Radiation Resistance?
Imagine connecting a resistor to your transmitter instead of an antenna. The resistor would absorb exactly as much power as you fed it and convert every watt to heat — none would be radiated. Now replace the resistor with an antenna. The antenna also absorbs power from the transmitter, but instead of converting everything to heat, it converts some of it to electromagnetic radiation. The question is: from the transmitter's perspective, what does the antenna look like electrically?
The transmitter sees the antenna as a load with a certain impedance. For a resonant half-wave dipole, that impedance is approximately 73 ohms, purely resistive. But that 73 ohms is not a real resistor in the usual sense — it is a combination of two things: the radiation resistance (which represents the power actually radiated as electromagnetic waves) and the loss resistance (which represents power lost as heat in the antenna conductor and surrounding lossy materials). For a well-made half-wave dipole in the clear, the loss resistance is very small — perhaps 0.5 to 1 ohm — so the 73-ohm feedpoint resistance is almost entirely radiation resistance.
More precisely: radiation resistance (Rrad) is defined as the equivalent resistance that, when carrying the same current as the antenna's feedpoint current, would dissipate the same power as the antenna radiates. If the antenna feedpoint current is I amperes and the antenna radiates P_rad watts, then:
Rrad = Prad / I2
where Prad is the total radiated power in watts and I is the feedpoint current in amperes RMS.
This definition means that radiation resistance is not a physical resistor inside the antenna — it is a mathematical way of expressing how much power the antenna radiates in terms of the feedpoint current. It is as if the antenna's ability to radiate is represented by a resistance that dissipates power (in this case, radiates it into space) at the same rate as the antenna.
The value of radiation resistance depends heavily on the antenna's geometry, particularly on the current distribution. For a half-wave dipole, the current distribution is sinusoidal with maximum at the feedpoint. The theoretical radiation resistance at the feedpoint of an ideal half-wave dipole in free space is approximately 73.1 ohms. For a quarter-wave monopole over a perfect ground plane (which creates an image that makes it look like a half-wave dipole to the feed), the radiation resistance is approximately half that — about 36.5 ohms.
Loss Resistance
Loss resistance (Rloss) represents all of the power that goes into the antenna and its environment but does not get radiated. It includes:
- Conductor resistance: The RF resistance of the antenna wire itself. At radio frequencies, current flows only in a thin skin on the conductor surface (the skin effect), so the RF resistance is much higher than the DC resistance. For a typical copper wire antenna at HF, this might be 0.1 to 1 ohm.
- Dielectric losses: If the antenna uses insulating supports or traps that have dielectric losses at RF, these add to Rloss. High-quality insulators (ceramic, PTFE/Teflon) have very low loss. Poor-quality plastic insulators can be surprisingly lossy at HF.
- Ground losses: For vertical antennas, the earth acts as a conductor for return currents, but it is not a perfect conductor. Power flowing through lossy soil (especially dry soil) is converted to heat. Ground losses can easily be the largest single loss mechanism in a vertical antenna system.
- Loading coil losses: When a shortened antenna uses a loading coil, the coil has a finite Q (quality factor) and therefore a finite series resistance. This resistance is part of Rloss and can be a major efficiency killer for mobile and compact antennas.
- Nearby lossy objects: Metal objects, masonry walls, and wet organic material near the antenna can absorb energy from the near field. These are sometimes grouped as "proximity losses."
The total feedpoint resistance of a resonant antenna is approximately: Rfeedpoint ≈ Rrad + Rloss. (This is a simplification that holds well for most practical antenna configurations; the exact relationship involves the current distribution at the feedpoint compared to the current distribution at the point where losses occur.)
Antenna Efficiency
Antenna efficiency is the fraction of the input power that gets radiated as electromagnetic waves. It is expressed either as a percentage or in decibels:
η = Rrad / (Rrad + Rloss)
Efficiency in dB = 10 × log10(η)
where η is the efficiency as a fraction (0 to 1).
If Rrad >> Rloss, the efficiency approaches 1 (100%) and nearly all the input power is radiated. If Rrad << Rloss, the efficiency is very poor and most of the input power goes to heat. The goal in antenna design is always to maximize Rrad and minimize Rloss.
A 20-meter dipole (14 MHz) made of AWG 12 copper wire is installed at 10 meters height with good insulators. Estimated values: Rrad ≈ 73 Ω, Rloss (conductor + insulators) ≈ 0.5 Ω.
Efficiency η = 73 / (73 + 0.5) = 73 / 73.5 = 0.993
Efficiency = 99.3% — approximately −0.03 dB loss. This is excellent. The half-wave dipole at HF in good condition is a very efficient radiator. Almost nothing is wasted.
A 1/4-wave equivalent 40-meter mobile antenna on a car is 2 meters long (instead of the required 10 meters), using a large center-loaded coil. The coil Q is 150 (a reasonably good loading coil).
For a severely shortened antenna like this, the radiation resistance drops dramatically — typical values are around 1–5 Ω for a mobile antenna on 40 meters. Let's say Rrad ≈ 3 Ω.
The loading coil reactance needed to resonate the short antenna might be XL ≈ 500 Ω. The coil loss resistance: Rloss(coil) = XL / Q = 500 / 150 = 3.3 Ω. Add conductor and ground losses: Rloss(total) ≈ 5 Ω.
Efficiency η = 3 / (3 + 5) = 3/8 = 0.375 = 37.5% = −4.3 dB.
Result: A typical 40-meter mobile antenna with a loading coil is about 37% efficient — you lose more than 4 dB, equivalent to reducing your 100-watt signal to about 37 watts. This is why mobile HF operation is inherently at a disadvantage compared to a base station with a full-size antenna.
Typical Values for Ham Radio Antennas
| Antenna Type | Typical Rrad (ohms) | Typical Rloss (ohms) | Typical Efficiency | Notes |
|---|---|---|---|---|
| Half-wave dipole, 14 MHz, good wire | 73 | 0.5–1 | 98–99% | Very efficient; standard reference antenna |
| Quarter-wave vertical, 14 MHz, 4 elevated radials | 36 | 5–15 | 71–88% | Ground losses dominate; more radials improve efficiency |
| Quarter-wave vertical, 14 MHz, 32 buried radials | 36 | 1–3 | 92–97% | Good radial system greatly reduces ground loss |
| Mobile whip, 40 meters, center-loaded | 2–5 | 4–10 | 20–55% | Highly variable; coil Q and length are critical |
| Shortened dipole, 10% of λ/2 | ~0.5 | 1–3 | 14–33% | Very small Rrad makes any loss catastrophic |
| Small transmitting loop, 1m diameter, 14 MHz | ~0.1 | 0.05–0.2 | 33–67% | Very low Rrad but also very low Rloss if well made |
| Full-wave loop, 14 MHz | ~100 | 1–2 | 98–99% | Slightly higher Rrad than dipole; excellent efficiency |
Why Short Antennas Are Less Efficient
The radiation resistance of an antenna depends on how well the current distribution in the antenna matches the optimal pattern for radiation. As an antenna is made shorter than its resonant length, the current distribution changes. Where a half-wave dipole has a nicely peaked sinusoidal current, a very short dipole (much shorter than λ/2) has current that is nearly uniform along its length but very small in magnitude for a given feedpoint voltage.
Theoretical analysis shows that for a short dipole of length L (where L << λ), the radiation resistance scales as (L/λ)². This is a quadratic dependence — halving the antenna length quarters the radiation resistance. As the antenna gets shorter and shorter, Rrad drops catastrophically, while the loss resistance stays roughly constant or may even increase (because you need a more complex loading structure to resonate the antenna).
At 3.5 MHz (80 meters), a full half-wave dipole is about 40 meters long and has Rrad ≈ 73 Ω.
Shorten the dipole to half its resonant length (20 meters, now L/λ ≈ 0.117): Rrad drops to roughly 73 × (0.5)² ≈ 18 Ω.
Shorten it to one-quarter of resonant length (10 meters, L/λ ≈ 0.058): Rrad ≈ 73 × (0.25)² ≈ 4.6 Ω.
Shorten it to one-tenth (4 meters, L/λ ≈ 0.023): Rrad ≈ 73 × (0.1)² ≈ 0.73 Ω.
Now if loss resistance is just 1 ohm (conductor + loading coil), the efficiency of the 4-meter antenna on 80 meters is: 0.73 / (0.73 + 1) = 42%. And this assumes a loss resistance as low as 1 ohm, which requires a very high-Q loading coil.
The lesson from this analysis is that every additional length you take away from a resonant antenna pushes you toward an exponentially worse efficiency penalty. The first 20% reduction in antenna length might cost you just 1–2 dB. The last 20% reduction (from 20% of resonant length down to near zero) costs you many dB. This is why experienced antenna builders always use as much wire as they possibly can and only compromise when absolutely forced to by space constraints.
Ground Losses
For vertical antennas — monopoles that use the ground as their electrical mirror image — ground losses can be the single largest factor in efficiency. The RF return current from the antenna does not flow in a wire back to the transmitter; it flows through the earth below the antenna. Soil conductivity varies enormously, from very good (sea water, at 4 siemens per meter) to very poor (dry sand or rock, at less than 0.001 S/m). Poor soil can have effectively hundreds of ohms of loss resistance in the ground path.
The solution is a radial system — an array of wires laid on or buried in the soil beneath the antenna. These wires provide a low-resistance return path for the RF current, bypassing the lossy soil. The more radials, the better. FCC broadcast tower standards call for 120 radials at 0.4 wavelengths each — at that point, ground losses approach the theoretical minimum. For ham radio operators, even 4 to 8 radials produce a significant improvement over no radials, and 32 buried radials bring performance to within a few dB of the 120-radial standard.
Elevated radials are particularly effective because they avoid soil entirely. A quarter-wave vertical with just 4 elevated quarter-wave radials, positioned a few meters above ground, can achieve a ground-loss resistance of just 1–2 ohms — far better than a simple ground rod, and competitive with an extensive buried radial system. The radials need to be separated (ideally at 90-degree spacing) and mounted horizontally at the base of the antenna.
Practical Implications
Radiation resistance and efficiency concepts have direct practical value for antenna decisions:
Use full-size antennas whenever possible. On 40 meters and below, full-size antennas are often impractical due to space constraints, but on 10, 15, 20, and sometimes 40 meters, a full-size dipole or vertical is entirely practical. A full-size antenna is almost always more efficient than a shortened equivalent.
For vertical antennas, invest in the radial system. Adding radials is the single most cost-effective improvement to most vertical antenna installations. Going from zero radials (just a ground rod) to 32 buried radials can improve effective radiated power by 5–10 dB or more — equivalent to multiplying your transmitter output by 3 to 10 times. Wire is cheap. Hours of effort are worthwhile for that kind of improvement.
Evaluate loading coil quality.} For any shortened antenna using a loading coil, the coil Q is critical. Higher Q means lower loss resistance. Commercially wound mobile antenna coils often have Q values of 100–200. Home-wound coils with optimized wire gauge, pitch, and core material can achieve Q values of 300–500, dramatically improving efficiency. The difference between a Q=100 coil and a Q=400 coil on a 40-meter mobile antenna can be 3–5 dB of additional signal.
Treat efficiency losses in dB. The efficiency in dB directly affects your effective radiated power. If your antenna is 50% efficient (−3 dB), your 100-watt transmitter effectively puts out only 50 watts of radiated power. If it is 10% efficient (−10 dB), you effectively have 10 watts. These losses stack on top of feedline losses, so a poor antenna combined with a long run of RG-58 can easily represent 6–10 dB of total loss — the equivalent of reducing your legal 100-watt signal to 10 watts or less before it even leaves the ground.
- Radiation resistance (Rrad) represents the power radiated as electromagnetic waves, expressed as an equivalent feedpoint resistance.
- Loss resistance (Rloss) represents all power lost as heat — conductor, loading coil, and ground losses.
- Antenna efficiency η = Rrad / (Rrad + Rloss). A 73-ohm dipole with 0.5 ohm loss is 99% efficient.
- Radiation resistance scales as (L/λ)² for short antennas — halving antenna length quarters Rrad.
- Ground losses dominate vertical antenna efficiency; an extensive radial system is the best investment.
- Loading coil Q determines coil loss resistance: Rloss(coil) = XL/Q.
Frequently Asked Questions
If a dipole is 99% efficient, why do people say antennas vary by 10 dB or more?
A full-size dipole in the clear at a good height is indeed close to 100% efficient — antenna losses are tiny. But real-world antennas often differ from that ideal in ways that compound: they may be shorter than resonant (needing a tuner and associated losses), they may be mounted close to buildings (proximity losses), they may use a poor feedline (coax loss), or they may be oriented unfavorably for the desired path (pattern issues). The large performance differences between stations are usually the result of these compounded factors, not just the antenna's inherent radiation efficiency.
Does radiation resistance change with frequency?
Yes, significantly. For a fixed physical antenna, the radiation resistance changes as you move away from resonant frequency. For a dipole, Rrad is about 73 ohms at the fundamental resonant frequency (λ/2). At other frequencies, the impedance (and therefore Rrad) changes, and reactance also appears. Multi-band operation using a tuner works, but the efficiency depends on whether Rrad remains significantly higher than Rloss at all operating frequencies. Some antenna designs optimize Rrad across a range of frequencies (broadband antennas); others work best at one frequency.
Can I measure radiation resistance directly with my antenna analyzer?
An antenna analyzer measures the total feedpoint impedance, which is the combination of Rrad and Rloss, plus any reactance. You cannot separate Rrad from Rloss with a simple impedance measurement because they both appear as a real (resistive) part of the feedpoint impedance. To measure efficiency, you would need to compare the antenna's measured gain against the theoretical gain of a lossless version of the same antenna — typically done with antenna modeling software or in a controlled test range. Practically, you estimate efficiency by modeling the antenna and its loss mechanisms.
Test Your Knowledge
Answer the questions below to check your understanding. Every answer can be found in the lesson above.