3.7 Effective Radiated Power: System Gains and Losses
Key Takeaways
- Effective radiated power equals transmitter power plus antenna system gain minus feedline and connector losses, with every term handled in decibels before converting once to watts.
- Convert a net decibel figure to a power multiplier with 10 to the power of (net dB divided by 10); +3 dB doubles power, +10 dB multiplies it by ten and -3 dB halves it.
- ERP is referenced to a half-wave dipole and uses dBd, while EIRP is referenced to an isotropic radiator and uses dBi, so EIRP is always 2.15 dB (a factor of 1.64) greater than ERP for the same station.
- A Standard station running 100 W into a 10-element 2 m Yagi through 2.75 dB of line and connector loss radiates about 750 W ERP, equivalent to 1230 W EIRP.
- Radiated power, not transmitter power, drives electromagnetic energy exposure compliance distances, and a few Australian allocations such as 2200 m and 630 m express their limit directly as a maximum EIRP.
3.7 Effective Radiated Power: System Gains and Losses
ACMA Exam Focus: Syllabus item 6.11 — effective radiated power is set by the transmitter power plus the gain of the antenna system minus the losses in the feedline and connectors. Examinable material covers the decibel budget method, the difference between ERP and EIRP with its 2.15 dB offset, and why radiated power rather than transmitter power governs electromagnetic energy exposure assessment and the limits on some Australian bands.
What Effective Radiated Power Actually Measures
Your transmitter's power output is only the starting point. What reaches a distant station depends on how much of that power survives the run of coaxial cable and the connectors, and how much of what survives is concentrated towards the horizon by the antenna. Effective radiated power (ERP) answers a single question: how many watts would I have to feed to a plain half-wave dipole, pointed the right way, to produce the same signal strength in the favoured direction as this whole station actually produces?
The word "effective" is doing real work. A 100 W transmitter with a long-boom beam can put out several hundred watts ERP in one direction while radiating far less than 100 W in every other direction. Nothing is being manufactured; the energy is simply redistributed.
The Decibel Budget Method
Because gains and losses are quoted in decibels, and decibels add and subtract where power ratios would have to be multiplied and divided, the reliable exam technique is to do all the bookkeeping in decibels and convert to watts once, at the very end.
ERP (dBd terms) = Transmitter power + antenna gain in dBd - feedline loss - connector loss
EIRP (dBi terms) = Transmitter power + antenna gain in dBi - feedline loss - connector loss
Then convert the net gain figure to a power multiplier:
Power multiplier = 10 ^ (net dB / 10) and ERP in watts = transmitter watts x multiplier
| Net dB | Power multiplier | Net dB | Power multiplier |
|---|---|---|---|
| -6 | 0.25 | +3 | 2.00 |
| -3 | 0.50 | +6 | 3.98 |
| 0 | 1.00 | +7 | 5.01 |
| +1 | 1.26 | +10 | 10.0 |
| +2.15 | 1.64 | +20 | 100 |
Committing the +3 dB (double), +10 dB (ten times) and -3 dB (half) landmarks to memory lets you sanity-check almost any exam answer in your head.
Where the Losses Come From
Feedline loss is the dominant term for most VK stations, and it climbs steeply with frequency. Indicative matched-line figures:
| Cable | Loss per 100 m at 145 MHz | Loss per 100 m at 435 MHz |
|---|---|---|
| RG-58 | about 17 dB | about 32 dB |
| RG-213 | about 8.5 dB | about 16 dB |
| Low-loss 10 mm foam line | about 5 dB | about 9 dB |
Connector loss is small but real — budget roughly 0.1 dB for each good UHF or N-type connector, and remember that a water-damaged or corroded joint can easily throw away 1 dB or more on its own. Losses inside an antenna tuner, a switch, a duplexer or a poorly matched antenna all belong in the same subtraction column.
ERP Versus EIRP
The two radiated-power terms differ only in the reference antenna used:
- ERP is referenced to a half-wave dipole, so it is calculated using antenna gain expressed in dBd.
- EIRP, or equivalent isotropically radiated power, is referenced to an isotropic radiator, so it is calculated using gain expressed in dBi.
Since a dipole has 2.15 dBi of gain of its own, the same station always has an EIRP figure that is 2.15 dB higher than its ERP figure:
EIRP (dBW) = ERP (dBW) + 2.15 and EIRP (watts) = ERP (watts) x 1.64
Going the other way, ERP = EIRP / 1.64 = 0.61 x EIRP. Mixing the two references is the single most common arithmetic error in this part of the syllabus.
Worked Examples for Typical VK Stations
Example 1 — 2 m weak-signal station. A VK3 operator runs the Standard limit of 100 W into 30 m of RG-213 on 145 MHz, through two connectors, feeding a 10-element Yagi rated at 11.5 dBd.
- Feedline loss: 30 m at 8.5 dB per 100 m = 2.55 dB.
- Connectors: 2 x 0.1 dB = 0.2 dB.
- Net gain over a dipole: 11.5 - 2.55 - 0.2 = +8.75 dBd.
- Multiplier: 10 ^ 0.875 = 7.50.
- ERP = 100 x 7.50 = 750 W.
- EIRP = 750 x 1.64 = 1230 W (check: 8.75 + 2.15 = 10.9 dBi, and 10 ^ 1.09 = 12.3, so 100 x 12.3 = 1230 W).
Example 2 — 70 cm repeater access. A station runs 50 W on 435 MHz through 20 m of low-loss cable (1.8 dB) plus 0.2 dB of connectors into an 8 dBd collinear.
- Net gain: 8 - 1.8 - 0.2 = +6 dBd, a multiplier of 3.98.
- ERP = 50 x 3.98 = 199 W, near enough to 200 W.
- EIRP = 199 x 1.64 = 326 W.
Example 3 — catalogue figures in dBi. An HF beam is advertised at 9.15 dBi and is fed with 100 W through 3 dB of total line and connector loss. Convert the gain first: 9.15 - 2.15 = 7 dBd. Net gain = 7 - 3 = +4 dBd, a multiplier of 2.51, so ERP = 251 W and EIRP = 251 x 1.64 = 412 W.
Notice what Example 3 shows: 3 dB of feeder loss threw away half the transmitter power before the antenna ever saw it. Fixing a lossy feedline is usually cheaper and always more legal than reaching for more transmitter power.
Why ERP Matters in Australia
Electromagnetic energy (EME) exposure. Human exposure limits published by ARPANSA and enforced through the ACMA's arrangements are expressed as field strength or power density at a distance. Those quantities depend on what is radiated in the direction of people, not on what the transmitter dial says. A Standard station running 100 W into a 13 dBd beam is radiating close to 2 kW ERP along the boresight, and its compliance distance is calculated from that figure — which is exactly why height, beam heading and ERP all feature in a station EME assessment.
Licence limits. Australian amateur qualifications cap the transmitter power: 10 W peak envelope power for Foundation, 100 W peak envelope power for Standard, and 400 W for Advanced. Antenna gain sits on top of that limit legally, but a few allocations — notably the LF and MF amateur bands at 2200 m and 630 m — are written instead as a maximum EIRP of a few watts, so on those bands you must work backwards from the permitted radiated power, subtracting antenna gain and adding back feeder loss, to find the transmitter power you are allowed to run. Always check the current class licence conditions for the band you intend to use.
A transmitter delivers 100 W into a feedline and connector run with 2 dB of total loss, feeding an antenna with 9 dBd of gain. What is the effective radiated power?
How are ERP and EIRP related for one and the same transmitting station?
A 25 W transmitter feeds a total of 3 dB of feedline and connector loss into an antenna rated at 5.15 dBi. What is the station's effective radiated power?