# Does a resonant antenna work better than a non-resonant antenna?

Some books on antenna fundamentals i've read recently say that, for a half wave resonant dipole when transmitting for example, the traveling wave of movement of charges reflected back from the ends of the antenna constructively adds to the incident waveform emanating from the feed point, resulting in the standing wave of current having the maximum amplitude for a given input. And since the electric field intensity (according to the ARRL handbook) is proportional to antenna current, this means at resonance the antenna produces the most output for a given input.

The books also say that at resonance for transmit ignoring resistive losses an antenna converts all of the applied energy to electromagnetic radiation, and conversely that when there is reactance present some of the applied energy is wasted in 'circulating' (for want of a better word) currents due to the reactance.

In addition to this, a resonant antenna apparently has the desirable effect of reducing the ratio of out of band interference to wanted signals that are within the frequency band of interest.

Is resonance for an antenna something that should be aimed for in the interests of improved antenna performance ? or doesn't it make much difference ...

• "Not important" is an opinion. I'm not sure, especially without more context about who is stating this opinion and why, this is a question that can be effectively addressed here. – Phil Frost - W8II Jun 10 at 18:58
• @PhilFrost-W8II Agreed, i changed the question heading. – Andrew Jun 10 at 23:50

You are probably familiar with impedance. It is a complex number, made of the sum of a real and imaginary number. The real part is called resistance, and the imaginary part reactance.

You've probably seen some equation like this to describe the power dissipated by a current through a resistor:

$$P = I^2 R$$

But what happens when the load can have reactance? Without going into the math, it should be obvious that if the load can be a complex number, than power can also be a complex number.

When power is represented as a complex number, it's called (uncreatively) complex power. It is the sum of active power, which is the real part, and reactive power which is the imaginary part.

Plotting complex power on the complex plane is called the power triangle:

$$S$$ is complex power, $$P$$ active power, and $$Q$$ reactive power.

As with impedance, thinking of this complex number in polar form yields some intuition. The angle to the real axis, $$\varphi$$, is the phase difference between current and voltage, just like impedance. And the magnitude $$|S|$$ is called apparent power: it's RMS voltage multiplied by RMS current.

This is all relevant because only the active power does work. One way to demonstrate this: build a circuit of any impedance with resistors, inductors, and capacitors, and apply an AC power source to it. The resistors get hot, whereas the capacitors and inductors do not (except to the extent they have non-ideal resistance).

The reactive power does no work. Consider a tank circuit of an ideal inductor and capacitor. The energy in the inductor and capacitor oscillate, but the total energy remains the same. No work is performed.

That works for ideal components, but real inductor and a real capacitor would have to be connected by a real wire. A real wire has resistance, and the wire will do work by converting electrical energy to heat according to $$P = I^2 R$$.

Antennas are no exception. A lot of antennas have feedlines. Feedlines have resistance. Refer to the power triangle above, and note that $$|S|$$ is a little bit longer than $$P$$. The former is proportional to the current in the feedline, whereas the latter is proportional to the work done by the antenna (radiating, if it's an efficient antenna). More reactance means higher apparent power, and thus higher current, and thus higher feedline losses for a given active power.

Is resonance for an antenna something that should be aimed for in the interests of improved antenna performance ?

The answer, as with most engineering, is "it depends". Some people will get pedantic and argue that even if the antenna is highly reactive, it radiates just as effectively. That may be true, but a device must be usable to be performant. If the antenna is too reactive, there's simply no way to efficiently couple active power into it: all the available energy will go into overcoming losses due to the reactive power.

That said, if you look at the power triangle again, you'll notice that as long as the reactive power is small compared to the active power, $$|S|$$ isn't that much greater than $$P$$. Meaning, RMS current, and thus resistive losses, won't be substantially increased. It's certainly possible to imagine antenna designs where accepting a reasonable reactance enables an improvement in some other respect which works out to a net improvement.

It's also relevant to consider that resonance implies zero reactive power, but not necessarily a good match to the feedline. Resonance is in some cases close to the points of minimum VSWR, but that is not generally true for all possible antennas and feedlines. A VSWR above 1:1 is also associated with voltage and current in excess of the useful work performed. While any zero-reactance impedance could theoretically be matched by some feedline, such a feedline may not be practical or available. As such, it's important to not only consider reactive power, but also feedline match and the capabilities of the receiver and/or transmitter in optimizing a radio system.

Furthermore, feedline losses can largely be mitigated with the addition of a matching network at the feedpoint. The reactive power doesn't go away, but the associated increased voltage and current is then restricted to just the matching network rather than the entire feedline. If the losses in the matching network are less than they would have been in the feedline, losses can be reduced.

In addition to this, a resonant antenna apparently has the desirable effect of reducing the ratio of out of band interference to wanted signals that are within the frequency band of interest.

Yeah, somewhat. To some out of band signals, the antenna will appear reactive and thus they will experience higher loss.

But also consider many antennas that are resonant on frequency $$f$$ are also resonant on all odd harmonics: $$3f$$, $$5f$$, etc. At the same time, these odd harmonics are very much the ones you might want to attenuate.

• This answer confuses resonance with reactance. It's quite possible to have a resonant length of wire that is highly reactive at the feed point. (Off-center or side loaded, etc.) Given a fixed mismatched or "bad" reactance, is a resonant length or geometry better (lower radiation resistance, better pattern, etc.), than non resonant? That is how I interpret the (current?) question. – hotpaw2 Jun 13 at 15:58
• @hotpaw2 I bet someone will model it for us: ham.stackexchange.com/questions/16827/… – Phil Frost - W8II Jun 13 at 17:01
• @hotpaw2 That's true, but resonance is defined as zero reactance, and implies nothing about the match to the feedline. That said, I think I see what you are getting at and I'll try to add a little bit about that point without going too far off on a tangent. – Phil Frost - W8II Jun 13 at 19:37
• @Andrew An ideal resistor has a 0 Q-factor. Since it can't store energy, it can't be resonant. Anyway, if you don't believe my definition, here's another source: antenna-theory.com/definitions/resonant.php Of course there are other possible definitions, and en.wikipedia.org/wiki/Resonance even has some examples where the same RLC circuit can have different resonant frequencies, depending on your definition. But in the context of antennas, it's conventionally understood that "resonant" means "zero reactance". – Phil Frost - W8II Jun 22 at 14:34
• @Andrew So what if the transmission line is driven by a current source? If impedance is cause divided by effect, and the cause is a current source, then the effect must be voltage. So impedance = current / voltage? We're well beyond the scope of comments here -- if you want to discuss this further, perhaps a new question. – Phil Frost - W8II Jun 24 at 4:00

From a system point of view, an antenna's feedpoint impedance is important only inasmuch as it can be efficiently matched to the feedline, maximizing the transfer of power from the generator. While the feedpoint of some antennas reflects other aspects of its behavior, this is not generally true. For example, a center-fed length of wire - e.g., a "20-meter half-wave dipole" that resonates at a particular frequency exhibits less than 1-dB variation in field strength over an octave of frequency:

This results from the fact that the current distribution over the antenna's length is substantially the same:

Considerable gain results at approximately twice the frequency of the antenna's half-wave resonance:

where the antenna comprises two half-waves in phase. But, the feedpoint impedance is 3958-j1531 ohms, a very difficult match to any conventional feedline.

• @Andrew Your OP asked, "...why do some amateur radio operators insist that resonance isn't important ?" To "insist" that something "isn't important" frequently ignores the plethora of other related issues that go into engineering an effective station. One could flip the script and say that, "Resonance is important primarily insofar as it provides a low-loss match to a commonly available feedline." Otherwise, as shown in the examples, "resonance" doesn't bear any special relationship to antenna performance. – Brian K1LI Jun 10 at 14:09
• @BrianK1LI I think that you should edit your answer to include "Resonance is important primarily insofar as it provides a low-loss match to a commonly available feedline." – rclocher3 Jun 10 at 17:41
• @Andrew It's difficult to respond to a moving target. Your question has morphed considerably since I posed my answer. My graphs are "facts," not my opinion, inasmuch as they are the product of calculations. Out of courtesy to we who spend considerable time trying to help, please refrain from editing your questions on-the-fly as answers trickle in. – Brian K1LI Jun 11 at 13:11
• @Andrew Brian has a point. You have edited your question 10 times. – Mike Waters Jun 11 at 14:13
• @BrianK1LI you are confusing impedance matching with resonance. My question asks "Does a resonant antenna work better than a non-resonant antenna" and you replied with "From a system point of view, an antenna's feed point impedance is important only inasmuch as it can be efficiently matched to the feed line, maximizing the transfer of power from the generator." The question doesn't ask about the feed point impedance. – Andrew Jun 13 at 23:34

A short answer, in two parts:

1. Irrespective of their natural "resonance," ALL non-zero electrical lengths of the conductors of a "standing wave" antenna radiate virtually ALL of the r-f energy that flows along them, as electromagnetic waves into space.

2. Other things equal, the natural resonance of such radiating conductors enables more efficient transfer of the r-f energy from the transmitter to flow along the antenna conductors, increasing its useful radiation of e-m waves.

• How precisely do you define "r-f energy"? It's certainly possible to put a lot of RF current or voltage into some conductor, and yet not radiate much of anything. Pretty huge potential for miscommunication here, I'd say. – Phil Frost - W8II Jun 15 at 14:19
• Energy has the ability to do work, which in this case is "unlikely" unless BOTH r-f current AND r-f voltage are present simultaneously along conductors expected to radiate e-m waves into space. – Richard Fry Jun 15 at 15:39
• I think you need to be more specific still. Work is done when a capacitor is charged, or discharged. But rapidly charging and discharging a capacitor at high frequencies doesn't result in much RF radiation. – Phil Frost - W8II Jun 15 at 16:51
• Work is done by accelerating a change along some non-zero distance. So if the capacitor is big enough to require significant (non-cancelling) distances to charge it... – hotpaw2 Jun 15 at 17:12
• @hotpaw2 The capacitor does indeed radiate some non-zero energy, but the energy radiated is very small in proportion of the work done to charge it. We all know that capacitors make for terrible antennas: my point is the statement "radiate virtually ALL of the r-f energy that flows" can be misinterpreted all kinds of ways since "a flow of r-f energy" hasn't really been clearly defined. – Phil Frost - W8II Jun 15 at 18:23

resulting in the standing wave of current having the maximum amplitude for a given input. And since the electric field intensity (according to the ARRL handbook) is proportional to antenna current, this means at resonance the antenna produces the most output for a given input.

Only if the impedance feeding the antenna is purely real! In general, you get maximum power transfer when the load impedance is the complex conjugate of the source impedance, which includes the case of a reactive (non-resonant) antenna and a reactive source (e.g. a matching network).

The books also say that at resonance for transmit ignoring resistive losses an antenna converts all of the applied energy to electromagnetic radiation, and conversely that when there is reactance present some of the applied energy is wasted in 'circulating' (for want of a better word) currents due to the reactance.

This is somewhat true, but in many cases the losses are acceptably small, or a valid trade for some other aspect of the design (like size, or frequency agility). Especially on lower bands, the loss due to standing-wave currents is relatively insignificant.

In addition to this, a resonant antenna apparently has the desirable effect of reducing the ratio of out of band interference to wanted signals that are within the frequency band of interest.

This isn't a function of the resonant frequency of the antenna, it's a function of the resonant frequency of the antenna system including any matching. See the first point about maximum power transfer.

• Hobbs, I think you're getting resonance and impedance matching mixed up. My question asks about antenna resonance, it doesn't ask about matching the antenna feed point and transmission line impedance. – Andrew Jun 12 at 1:54
• @Andrew no, no, no, and no. – hobbs - KC2G Jun 12 at 2:12
• Yes. An off-center or otherwise imbalanced, but exactly resonant length antenna, is likely not matched to a purely real feed line. This answer is thus incomplete. – hotpaw2 Jun 13 at 16:00
• Optimal for receiving might also imply minimum power transfer for out-of-band signals, or some other parameter related to S/N. – hotpaw2 Jun 13 at 16:05
• Your first comment which suggests that the amplitude of the standing wave of current in the antenna is greatest only when the feed line impedance is real is incorrect. Even though resonance for an antenna results in the impedance presented at the feed point containing zero reactance, which allows matching to a transmission line to be easier (or in fact possible), the fundamental condition of antenna resonance occurs regardless of the impedance of the transmission line and whether or not the antenna impedance is a complex conjugate of the source impedance or not. – Andrew Jun 13 at 23:46