# What is the advantage of making an antenna resonant?

I am constructing a small loop antenna; apprx 4' diameter, will be used with an antenna tuner (mounted at the feedpoint) and 100W transmitter, and hope to use it on 20m, 40m, and maybe other bands if possible. I can add a tuning capacitor to make it resonate on one of the bands but cannot help wondering... what does that get me?

Is a resonant antenna more efficient? I would assume so, but seem to recall that the increased efficiency is not really all that much.

The Question What is an antenna tuner? Why bother with resonant antennas in the first place? seems to address what I am asking, but the answer is still unclear.

In case it matters, it is not a continuous loop, there is a break opposite the feed point (where the tuning capacitor would be placed). The antenna uses a gamma match to better align the feed point impedance to the line impedance. The main purpose is to learn what to expect from these sorts of loops as I plan to build a much larger one and would prefer to make my mistakes on a small scale first.

• It will help the answerers to make a clear A/B question out of this - it's not a hypothetical discussion about the merits of resonance. So... Should Chris A) bother to "resonate" the small loop with a capacitor at the gap in the loop, or simply B) take a cable down to the ATU and let it do the matching. Why would A or B be more efficient for transmitting? Any other gotchas? Dec 30, 2018 at 12:26
• @tomnexus I took your suggestion and added this analysis to my answer. Dec 31, 2018 at 12:55

Resonance or non-resonance does not have a direct effect on the efficiency or gain of the antenna. A resonant antenna is one that has only resistance without any reactance (capacitive or inductance) at its feedpoint.

To transfer the maximum available (or rated) power from a transmitter to its load (the antenna system in this case), the impedance of the antenna system must match the specified load impedance of the transmitter. Most transmitters specify a 50 ohm load without any reactance. If the antenna system has reactance (i.e. it is not resonant) the transmitter will not be able to put out its rated power. This is the primary reason we tend to try to "resonate" the antenna.

Imagine if transmitter manufacturers specified a 50 ohm resistive with 23 ohms of inductive reactance (50+j23) as the required load impedance. We would all be working to "non-resonate" our antenna systems to meet this specification in order to put out the rated power!

It is important to note that most antennas, even when resonant, do not have a 50 ohm impedance. It is therefore often required to add some type of matching network to the antenna system to transform the impedance to 50 ohms so that the transmitter can put out its rated power. The matching circuit may be designed to cancel out any reactance in addition to transforming the resistive component of the antenna system to 50 ohms.

One more point about non-resonant antennas. We generally consider a 1/2 wavelength dipole to be essentially resonant. When we extend its length to 10/8 of a wavelength long, it is no longer a resonant antenna. Yet this length of a dipole has the highest gain of any dipole configuration. Clearly antenna resonance and gain bear no direct relationship.

The Small Loop Resonance Question

The small loop the OP referenced, without any matching network, will have a feedpoint impedance with a very low radiation resistance (<<1 ohm on 40 meters) and a very high inductive reactance (>>500 ohms). To put this in perspective, this amounts to an SWR50>5,000:1 - well out of bounds for a typical antenna tuner.

If such an impedance were connected to the end of a piece of 50 ohm coax cable that is connected to a transmitter rated for a 50 ohm load, there would be high losses in the cable due to the high SWR and the transmitter would put out a fraction of its power (if it doesn't shut down all together) due to the load being far from 50 ohms resistive. A well designed small loop antenna will have a gain of < -15 dBi. The coax and transmitter losses under this scenario could easily attribute another 20 dB of loss rendering the station communications ability very ineffective. So a matching network is generally required.

The matching network in a typical small loop consists of the feedline connected to a smaller loop that magnetically couples to the larger loop. This portion of the matching circuit effectively acts as a transformer that raises the low radiation resistance of the larger loop to close to 50 ohms in the smaller loop. The other part of the matching network is a variable capacitor across a break in the larger loop. This capacitor is adjusted such that it largely cancels out the inductive reactance present in the large loop with an equal, but opposite, capacitive reactance. The net result is typically an SWR50 of <2:1. Due to the high Q of a small loop antenna, the capacitor will require adjustment for relatively small changes in the operating frequency.

It should be noted that the small loop matching network described does not appreciably change the gain of the small loop. The gain of the small loop is largely constrained by its relatively small dimension compared to the wavelength involved and due to its very low radiation resistance that lowers its efficiency. The matching circuit loss is negligible compared to the latter so there is no practical change in efficiency, and thus gain, of the antenna. As explained earlier, the real advantage of the matching circuit is to allow the transmitter to output its rated power and for the losses in the coax to be minimized. The math related to efficiency and gain are given in my answer to the SE question that the OP referenced earlier.

• A matching network isn't strictly necessary if the receiver is designed to have a very low input impedance. For example: lz1aq.signacor.com/docs/wsml/… Dec 31, 2018 at 20:01
• @PhilFrost-W8II Although arguably that is an active, receive only, matching network (not a receiver at all). The author calls it a "wideband active small loop amplifier". Dec 31, 2018 at 21:28
• I'm sure you realize the referenced amplifier could just as easily be a receiver front-end. If you're going to count such active electronics as "matching networks" I think it bears mentioning in the answer, because as written it's reasonable to assume by matching networks you mean high-Q, passive networks like the capacitor mentioned in the question which would preclude the existence of any functional, wideband short loop antenna. Jan 1, 2019 at 21:44

# Bandwidth

Non-resonant antennas typically have a high input reactance $$X_\text{in}$$. This results in a higher loaded $$Q$$ and, by consequence, a reduced bandwidth $$BW$$.

$${Q_\text{loaded}\uparrow}\equiv\frac{X_\text{in}\uparrow}{R_\text{in}+R_\text{source}}\quad\textrm{and}\quad Q_\text{loaded}=\frac{f_\text{res}}{BW}\quad\Rightarrow\quad{BW\downarrow}\,=\frac{f_\text{res}}{Q_\text{loaded}\uparrow}$$

However, for extremely short, active receiving antennas this does not matter as these are matched against an extremely high load impedance of a MOSFET RF amplifier. In this case, the loaded $$Q$$ hardly changes.

$${Q_\text{loaded}}\equiv\frac{X_\text{in}\uparrow\uparrow}{R_\text{in}+R_\text{load}\uparrow\uparrow}$$

Resonant off-center fed dipole (OCFD) antennas exploit this effect by being fed at a higher input resistance $$R_\text{in}$$ from a source with a higher internal resistance $$R_\text{source}$$. Consequently, OCFDs achieve much broader bandwidths at their fundamental resonant frequency than their center-fed counterparts.

$${Q_\text{loaded}\downarrow}\equiv\frac{X_\text{in}}{R_\text{in}\uparrow+R_\text{source}\uparrow}\quad\textrm{and}\quad Q_\text{loaded}=\frac{f_\text{res}}{BW}\quad\Rightarrow\quad{BW\uparrow}\,=\frac{f_\text{res}}{Q_\text{loaded}\downarrow}$$

For example, here is a graph of the 80m VSWR bandwidth of my multiband CL-OCFD. I carry a resonant end fed half wave monoband antenna with matching stub (window line) for portable operations. Its huge advantage is that I need not carry an antenna tuner. One less piece of electronics to carry along, one less point of fail, one less thing to break or get lost. It works for me.

End fed antennas are also easy to deploy. I usually work 20 meters, a good daytime band. I don't do portable at night. It can hang easily from a tree or some other support.

As long as a near-conjugate match to the antenna feedpoint impedance is achieved, resonance and/or non-resonance doesn't matter at all. Let's assume we have antenna1 with 50 ohms of radiation resistance and no reactance at the feedpoint vs antenna2 with 100 ohms of radiation resistance and +j100 ohms of reactance at the feedpoint, (assuming negligible losses in the antenna).

For antenna1, we adjust our transmitter output to get 1.414 amps of current flowing through the 50 ohms radiation resistance. For antenna2, we adjust our antenna tuner to get 1.0 amps of current flowing through the 100 ohms of radiation resistance. Which antenna is more efficient and which will radiate the most power?

The power radiated by antenna1 is 50(1.414)^2 = 100 watts

The power radiated by antenna2 is 100(1.0)^2 = 100 watts

The power radiated by the resonant antenna1 is identical to the power radiated by the non-resonant antenna2. When are we going to lay that old XYL's tale to rest? The very basic purpose of an antenna tuner is to maximize the current flowing through the radiation resistance of the antenna. When it maximizes the current flowing through the radiation resistance of the antenna, it necessarily must accomplish a near-conjugate match not only at the antenna feedpoint but also at the transmitter output thus satisfying the maximum power transfer theorem's requirement of a conjugate match at every point in a conjugately matched system.

In a low-loss system, when we tune our antenna tuners for a 50 ohm Z0-match at the tuner input, we have tuned to a near conjugate match both at the tuner output AND also at the antenna feedpoint. The things that keeps those near conjugate matches from being perfect conjugate matches are the (hopefully) minor losses in the tuner and feedline.

• I could only Accept 1 answer but this is credible and easy to understand. In my case, the feedpoint impedance is 9-46i ohms at 28MHz (copper pipe, loss is negligible i assume; very little is turning into heat). I plugged my numbers into your equation and came to the same conclusion you did. Dec 31, 2018 at 15:21