Is a resonant antenna inherently more efficient because it couples to free space more efficiently?

Question

I saw an interesting assertion recently, that resonant antennas are more efficient because they provide a better impedance match to free space at the resonant frequency. I believe that to be untrue, and that resonant antennas are just easier to match to the output impedance of a transmitter, which is almost always non-reactive. The consensus opinion of this group, as expressed by the votes on answers to two related questions, is clearly that generally resonant antennas are not more efficient.

What do I mean by "efficient", you ask? I suppose I mean efficient in terms of receiving or transmitting power. I'm talking about just the antenna, and not about any matching network or feed line that might be required to connect a real antenna to a radio.

But maybe I'm wrong, or maybe I'm oversimplifying. (There is a lot more that I don't know than I do know, and oversimplifying is how we humans make sense of the universe.) I investigated the Friis Transmission Formula, which I learned about thanks to this site, but it's no help. It introduces the idea that an antenna has an "effective aperture", which is unrelated to its physical size, but the effective aperture is a theoretical construct that is just a stand-in for the gain of the antenna. The formula isn't helpful here because the equation says nothing about gain, which is what this question is about.

So what about the assertion that the impedance of free space has something to do with the gain of an antenna? "Free space", i.e. vacuum, has an impedance, about 377 Ω, that relates the strength of the electric-field component to the strength of the magnetic-field component of an electromagnetic wave passing through the vacuum. When the electromagnetic wave encounters a conductive object then voltages and currents are induced in the object, which is how radio waves are received. I doubt that how close the impedance of the object is to (377 + 0j) Ω has anything to do with the efficiency of the reception, but I don't have enough Calculus or Physics to pick apart and understand everything about Maxwell's equations, so again I could be wrong.

So, is a resonant antenna inherently more efficient because it couples to free space more efficiently?

Answer 1

You could view an antenna as a two-port device. One port is the feedpoint, and the other port is "free space". The antenna's job is to transform the free space impedance of 377 ohms to the specified feedpoint impedance such as 50 ohms.

Ideally we want an antenna with scattering parameters like so:

$$ \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} $$

In other words, all the power coming in from free space makes it to the feedpoint, and all the power coming from the feedpoint radiates to free space.

If port 1 is the feedpoint and port 2 is free space, then we would say the antenna is a "good match" when $S_{11} = 0$, meaning, no reflected power.

Likewise, we could say the antenna is a "good match to free space" when $S_{22} = 0$, since port 2 is free space.

So the question then becomes: does the antenna being non-resonant prevent $S_{22}$ from being zero?

And the answer is: no. If you can provide a matched termination at the feedpoint then the free space port will also be matched.

How do we determine if an antenna is resonant? We connect port 2 to free space (no choice), and then we measure the impedance looking into port 1. If that impedance has zero reactance, it's resonant. Effectively we are discovering the impedance-transforming properties of the antenna by connecting one port to a matched and known load (free space) and seeing what impedance appears at the other port (the feedpoint).

Assume for now we find that feedpoint impedance to be (50+0j) ohms. We know that if we want to capture the maximum power from free space we should put a 50 ohm resistor across the feedpoint. The antenna, being an impedance transforming network, makes this 50 ohm resistor look like 377 ohms from free space (looking in port 2).

If we instead put a 25 ohm resistor there, looking in port 2 we won't see 377 ohms. Since this doesn't match the impedance of free space it means the antenna will scatter some power rather than absorbing it.

If the antenna isn't resonant, this just means we need some reactive component at the feedpoint in addition to a resistor to achieve a complex conjugate match. So if we measure the feedpoint impedance to be (30+15j) ohms, this means simply we need to place a (30-15j) ohm impedance on the feedpoint if we want the other port to look like 377 ohms.

The problem in practice is real capacitors and inductors which we would use to come up with that reactance at the feedpoint have loss. That means some of the power will be lost in those components before it can make it to the receiver, reducing overall efficiency. Or we can choose to omit the reactive components, in which case some of the power from free space will be scattered by the antenna rather than transferred to the feedpoint.

Answer 2

Not really answering the question but requesting more clarity in terms.

From the IEEE definition of standard terms for antennas: I redraw the diagram of power flow in an antenna, (ignoring the polarisation mismatch branch)

Where:

$P_A$ = power available from the generator
$P_M$ = power to matched transmission line
$P_O$ = power accepted by antenna
$P_R$ = power radiated by antenna
$I$ = radiation intensity

and

$M_1$ = mismatch between generator and line
$M_2$ = mismatch between line and antenna
$G_R$ = realised gain
$G$ = gain
$D$ = directivity
$\eta$ = radiation efficiency

The above "loss" terms on the straight line each have a physical explanation:
Directivity is only affected by the geometry of the antenna; how it concentrates power.
Radiation efficiency is only affected by losses in the metal and the dielectric.

The first part of the question is really about what type of antenna has the highest $\eta$ given real-world materials. I can think of a few but would have to simulate to be sure. A dipole is a good start. A travelling wave antenna like an (unterminated) rhombic or very long dipole might be better, they have smaller standing waves.

The second part of the question, "why", is harder to answer, because it might not be possible to reduce the physics of the antenna to a simple explanation. It will certainly involve $Z_0$ of free space but I don't think there will be a direct relationship between that and antenna impedance.

Answer 3

An antenna can radiate effectively at all sorts of lengths or radiation impedances, as tomnexus wrote. Even the theoretical expression for a thin wire antenna's radiation includes a factor of sqrt(mu / epsilon) or 120 pi or 377, so the radiation impedance is related, but that does not lead to any statement made in the OP question.

The impedance of free space appears more directly and beautifully in the context of aperture antennas, especially those with negligible edge diffraction, like curled edge horn or corrugated horn. Look up those antennas and how they work.

Another context where the free space impedance is important is when designing a radio anechoic chamber. The resistivity of the absorbing material is, of course, directly related to it.

But again, most antennas have a complex and distant relationship with the free space impedance and an even less direct link to their operating efficiency.

The phrase "resonant antenna" is really a jargon of convenience and semantically incorrect. I've already written several answers on that subject.

Answer 4

Another example of an antenna without a connected feed point is a broadcast AM radio enhancer (MF band). A multi-turn loop of wire with a capacitor to tune it can be placed around or near, but electrically disconnected from a small AM pocket radio. The received signal will become stronger when the disconnected loop antenna circuit is tuned to (or very near) the receiver frequency.

Here's an example of one, the Eton AN-200 Tunable Passive AM Radio Antenna Loop: https://www.hamradio.com/detail.cfm?pid=H0-015461 , but there are construction articles on how to build one DIY with just wire and a variable capacitor, similar to making a DIY crystal radio.

Answer 5

Effective coupling can result in either higher gain (into some feed point impedance) or to higher heating losses (due to the antenna's elements own real impedance == resistance). Either way, energy is being removed from the RF field (to maintain conservation of energy).

I hypothesize (needs an NEC model to confirm the current maxima?) that a resistor of some very low value in the middle of a tuned Yagi reflector or director element (close to the same length as the driven element) will get warmer than one in the middle of an antenna element much farther (especially much shorter) from any near resonant lengths. Thus that element must be more efficiently coupled to the RF field to extract that energy, and turn it into heating.

Whether any energy extracted from the RF field can be fed somewhere else is a separate issue.