# For an antenna when used for transmittiing, what is the optimum radiation resistance?

For a 100 % efficient antenna, the real part of the impedance is equal to the radiation resistance.

If the antenna were a dead short with zero impedance then the radiation resistance would be zero.

And at the other end of the scale an antenna with an infinite impedance (ie: no antenna) and so infinite radiation resistance also probably won't work that well.

So somewhere in between those two extremes there must be an optimal radiation resistance.

Assuming a matched transmission line and transmitter, and ignoring the transmission line impedance values available (eg: 50, 75, 300 ohms), and all other things equal, what is that optimum radiation resistance for an antenna ?

• An open connection (e.g. a capacitor) would have a very high shunt resistance, but a very low radiation resistance. Impedance would depend on the size of the capacitance. – hotpaw2 Dec 17 '19 at 0:45
• @hotpaw2 is that true ? i thought the radiation resistance equals the real part of the impedance ... – Andrew Dec 17 '19 at 0:49
• Power dissipates either though heat or EM waves. Without coupling to free space, it (resistive loss) mostly becomes heat (infrared or black body radiation, not EM radiation). e.g. your toaster. – hotpaw2 Dec 17 '19 at 0:53
• @hotpaw2 an open connection isn't the same thing as a capacitor however in the ideal cases both have an infinite real impedance which equals zero radiation ... – Andrew Dec 17 '19 at 1:18
• How about giving an explanation for the minus votes ? Subtracting votes with no explanation doesn't help anyone ! This is a perfectly reasonable question, don't see how it deserves minus votes ... – Andrew Dec 17 '19 at 21:55

Any non-zero radiation resistance will do. What matters is not the radiation resistance, but the ratio of energy radiated to energy lost to other means, such as ohmic losses in the feedline, antenna, or soil.

If the antenna system is made of ideal, lossless components, then any nonzero radiation resistance is 100% efficient. While somewhat counterintuitive it's easy to prove: the antenna must be 100% efficient because by definition there is no loss, so by the law of conservation of energy 100% of the energy must go to radiation.

There is this equation:

$$\text{efficiency} = {R_\text{radiation} \over R_\text{radiation} + R_\text{loss}}$$

which would suggest that higher radiation resistance means higher efficiency. But it is important when using this equation to pick a single point to measure radiation resistance and loss resistance, and normalize all values to that point.

Consider that a typical antenna system consists of numerous devices which transform impedances. They may be simple transformers, but also transmission lines and even antennas themselves (which are effectively transformers between the feedpoint impedance and the impedance of free space) do transformer impedances. So a resistance of a particular value may appear to have a different value when viewed from another perspective.

For example, a folded dipole has 4x the impedance of a similar not-folded dipole, and thus 4x the radiation efficiency if your definition for radiation resistance is to measure it at the feedpoint. (There are other definitions!) But that does not mean a folded dipole is 4x as efficient, because the ohmic losses in the antenna conductors are also 4x bigger. And if this folded dipole is fed with coax it will be a poor match, and the antenna system is subject to additional SWR loss as well.

• Does this mean tho that for antennas which have low loss and are almost 100 % efficient the effect of radiation resistance is negligible, but for antennas which do have a high loss due to resistance such as a small loop that the higher the radiation resistance the better ? – Andrew Dec 17 '19 at 5:13
• @Andrew yes, though usually you have more control over the loss resistance than the radiation resistance, because if you have an antenna with a low radiation resistance it's probably because you need a small antenna: making it bigger would increase the radiation resistance but you can't make it bigger. So it's more about minimizing loss: for example with a small transmitting loop you want to use very thick conductors, soldered connections, and get a variable capacitor without a sliding contact. – Phil Frost - W8II Dec 17 '19 at 17:58

No. What matters is if the radiation resistance (or do you mean feedpoint impedance?) of the antenna is matched to the feedline.

• I answered this based on the original title "For transmit, antenna radation resistance of zero ohms means zero radiation, does that mean the higher the radiation resistance the better?" which you changed while I was typing this answer. – Mike Waters Dec 16 '19 at 23:54
• no probs apologies for that. I don't think it would matter if you changed your answer ? – Andrew Dec 17 '19 at 0:06
• I'd say the second paragraph only holds as long as the feedline is still matched, or if the feedline is short. A folded dipole (absent any matching device) is not more efficient than a similar, not-folded dipole, especially when the latter is a better match to coax. – Phil Frost - W8II Dec 17 '19 at 4:21
• @PhilFrost-W8II You're right. I didn't think of that. – Mike Waters Dec 18 '19 at 2:38