# Interpretation of radiation resistance in receiving mode

Assume we have an antenna in receiving mode, connected to a matched load. The equivalent circuit is a voltage source in series with the antenna feedpoint impedance and the load impedance. As we know, the feedpoint impedance is made up of a reactive component, an ohmic resistance and a radiation resistance. Now, since the load is matched, half of the intercepted power will be delivered to the load, while the other half will be delivered to the ohmic and radiation resistances respectively. The power delivered to the ohmic resistance will be converted into heat, but how to interpret the power delivered to the radiation resistance? Is this part of the total power reflected by the antenna?

• Where does the reactive component come from? Dec 6, 2015 at 22:29
• @Andyaka I'm not an antenna expert, but it is my understanding that all antennas produce a field comprised of a radiative part and a reactive part, where only the former is present in the far zone. The direction of the Poynting vector (power density) for the radiative part is constant in time, while it for the reactive part is oscillating back and forth. Across the feedpoint, this translates into a resistance and reactance respectively. Dec 7, 2015 at 21:11
• No, an antenna, if matched to its optimal frequency will look resistive. Sure, if it's not tuned exactly then it will present a complex impedance. This is why I asked because it seemed you were taking an obscure line with the question. For instance a half wave dipole is 70 ohms + 42 ohms but if the length is reduced to 0.48 it becomes 70 ohms resistive. Dec 7, 2015 at 21:45
• The fields up close are complex and non-coherent regards a proper EM wave but, if the antenna is tuned it will produce a radiating power that makes its input impedance (and o/p impedance when receiving) purely resistive. Dec 7, 2015 at 21:46
• You are right, wrong on my part to say anything general about shape of near field. I wonder, however, whether a perfectly tuned antenna will store and retrieve energy from it's near field or only a nontuned antenna will do this? Dec 8, 2015 at 13:15

The equivalent circuit model for the receiving antenna, as referred to above, sounds correct (see for instance Collin & Zucker). However, what is not correct is to estimate the power dissipated (or re-radiated) by the impedance of that circuit. Indeed, that circuit corresponds to an equivalent Thevenin model; and the equivalence only holds with respect to what is connected to that circuit; for instance a receiver, whose first stage usually is a low-noise amplifier. That equivalent circuit does not hold from the perspective of what happens IN the circuit. Having said that, some antennas scatter, other don't. Generally speaking, the equivalent circuit of the receiving antenna does not inform about the amount of scattered power.

• Makes sense, thank you! Apr 6, 2023 at 9:00

No, in general, there is no such effect as reradiation. This heavily depends on the antenna type. The radiation resistance is a model for the radiation. Due to reciprocity, one should still match to this resistance in the receive case, but the simple model as you describe it (a voltage source in series with the antenna feedpoint impedance) is not valid in the receive case.

Generally, all power accepted by the antenna (described, e.g., by the effective aperture size) is received. Any other amount can be scattered by the antenna, but this is related to geometrical features of the antenna and, in the matched case, by no means always 50% of the power, but a rather arbitrary value.

• This is not correct, there will always be reradiation. The effective area $A_e$ multiplied by the power density yields the available power available at the antenna terminals. This power can be delivered to a load by a complex conjugate match. However, an equal amount of the power is delivered to the combination of antenna loss resistance (dissipation) and antenna radiation resistance (reradiation). Check the first chapter of Balanis' book Antenna Theory and Design, 4th edition. Mar 19, 2020 at 11:26
• @TroelsFolke I will check the Balanis book. However, the radiation resistance is not causing any reradiation since it is a model for transmit operation. Reradiation is a (unfortunately very common) misconception. It is very easy to construct synthetic / ideal antennas which do not have any reradiation. Mar 19, 2020 at 18:00
• Of course, for some kinds of antennas (e.g. dipoles), reradiation exits. Mar 19, 2020 at 18:00
• @TroelsFolke I did check the Balanis book now. I do not agree with his point of view. For me, it seems impossible that reradiation is a fixed amount of 50%. Think of a reflector antenna, if the incident wave comes from behind, 100% is scattered/reradiated by the antenna structure and nothing is received. Mar 27, 2020 at 19:18
• And a simple example with a very small amount of reradiation would be an open-ended waveguide with (infinitely thin) PEC top walls and PMC side walls. If an incident plane wave comes aligned with the aperture, the oewg "swallows" the incident field. There might happen some scattering at the back of the oewg, but this can be suppressed by absorbers or a suitable geometry. The real question is now (which just comes into my mind), what does Balanis mean by reradiation? I am not so sure right now... Mar 27, 2020 at 19:22

Yes, it is effectively radiated back by the antenna. If the antenna is receiving from a point source, but its radiation pattern is not pointing only at the source (e.g. is isotropic), this radiation will go in 'all' directions. Thus the antenna will redirect (reflect) the incoming signal back in a broader beam.