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Why does a minimal SWR NOT indicate antenna resonance? Would SWR 1:1 be required to indicate antenna resonance?

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  • $\begingroup$ I'm certain that this has been asked and thoroughly answered here in the past. Have you tried using this site's search feature? $\endgroup$ Oct 14, 2022 at 17:31

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Why does minimal SWR DOES NOT indicate antenna resonance?

Well, because they're not the same thing.

Would SWR 1:1 be required to indicate antenna resonance?

No. A zero reactance indicates resonance. A given antenna might have an impedance of 25+j0 or 300+j0 ohms at resonance. Clearly neither one will give you a 1:1 SWR relative to 50 ohms, but they're both resonant.

Whether or not the minimum SWR happens exactly at the resonant frequency depends on the exact details of the antenna and how its impedance changes with frequency. Usually the two points will be quite close to each other, because reactance tends to grow quickly away from the resonant frequency, but consider this example: a certain theoretical antenna has an impedance of 40+j0 at 7100 kHz, and 41+j3 at 7110 kHz. The resonant frequency is definitely 7100 kHz, and the SWR relative to 50 ohms is 1.25:1. Meanwhile 7110 is not perfectly resonant, but the SWR is 1.23:1, which is lower.

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The main feature of an antenna at resonance is that the impedance is entirely resistive, that is, has no reactance. This is usually the point of maximum Q but not necessarily. A non-resonant antenna will radiate just as well as a resonant one. In practice, an SWR - actually VSWR - of 1:1 is impossible to achieve. Contrary to popular belief, a low SWR does not improve the performance of an antenna system, and only gives a rather useless clue what to do to improve matters. A half wave dipole, and most other antennas, are resonant only on the fundamental frequency and odd harmonics with diminishing strength. So a 40 meter antenna will be resonant around 7100 kHz and on the third harmonic at 21300 kHz which conveniently falls in the 15 meter band. Basically, any length of wire will radiate on almost any frequency, but the challenge lies in matching it to the feedline and transmitter, especially where high power levels are used. Basic operating principle of a half wave dipole at resonance - assuming a center feedpoint, the feedpoint has the lowest impedance along the length of the antenna (impedance is equal to the ratio of voltage to current. As we move away from the center, the impedance increases because of the current and voltage distribution along the antenna. Voltage and current are 90 degrees out of phase except when the antenna is at resonant frequency, and then voltage and current are in phase, and inductive reactance (XL) and capacitive reactance (XC) cancel each other out, and the antenna then looks like a 50 ohm resistor. Whether the antenna is at resonance or not has no bearing on SWR. SWR depends on an impedance match between two different parts of a circuit or antenna system. SWR is a fictitious thing or mathematical idea. In reality, feedlines and antennas only have impedance, voltage and current. High SWR? Who cares?

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    $\begingroup$ Sparks, your answer has multiple untruths - 1. a resonant antenna has higher output than non-resonant, emission is proportional to the square of antenna current, which is maximum for resonant antennas, this is why everyone wants resonant antennas ! 2. "low SWR does not improve the performance of an antenna" - this is wrong - Low SWR = less reflections in transmission line = higher performance 3. Half wave dipoles are resonant at integer multiples of half wave length, which includes odd and even harmonics, odd = low impedance, even = high impedance. $\endgroup$
    – Andrew
    Oct 20, 2022 at 22:06
  • $\begingroup$ 4. Half wave dipoles are not resonant when C and L cancel out, resonance is mostly determined by the length of the elements compared to frequency of operation. 5. "Voltage and current are 90 degrees out of phase except when the antenna is at resonant" this is wrong - the phase difference between current and voltage of the standing wave on a dipole is a bit less than 90 deg everywhere along the antenna elements, including at the feed point, at resonance at the feed point the amplitude of the out of phase voltage is minimum. $\endgroup$
    – Andrew
    Oct 20, 2022 at 22:06
  • $\begingroup$ 6. "Whether the antenna is at resonance or not has no bearing on SWR" this is wrong, if the feed system is non-reactive, then any reactance in the antenna impedance will make the SWR bad, what you mean is that an antenna can be resonant but not match the transmission line impedance and then the SWR will be bad. $\endgroup$
    – Andrew
    Oct 20, 2022 at 22:06
  • $\begingroup$ RE: "inductive reactance (XL) and capacitive reactance (XC) cancel each other out, and the antenna then looks like a 50 ohm resistor." Recall that at resonance (jX=0) , the REAL term of the feedpoint impedance of an antenna mostly is related to the radiation resistance of that antenna on that frequency — which commonly is different than 50 ohms. For example, a thin-wire, self-resonant, 1/2-wave, center-fed dipole in free space has a radiation resistance of about 68 ohms, and its lowest SWR(50) value at its input terminals would be 68/50 = 1.36:1. $\endgroup$ Oct 21, 2022 at 11:05
  • $\begingroup$ Ham radio operators it seems get confused between a lumped constant series RLC circuit, and a half wave dipole, because the two exhibit some similar characteristics at resonance. But the reasons for resonance for each are completely different. Explain how Fc= 1/2π√LC, the equation which describes resonance for a series RLC circuit in terms of the values of lumped constants L and C, provides for dipole resonance when operated at harmonics ? This formula doesn't apply because wave theory is that which is mostly predominate for antennas, not circuit theory. $\endgroup$
    – Andrew
    Oct 22, 2022 at 0:29
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Minimal VSWR can indicate resonance, but may not be 1:1. Take for example a 1/4λ vertical antenna with a counterpoise that is 90 degrees (or horizontal) in relation to the vertical radiator. The feedpoint impedance of that arrangement is 37 Ohms; so in a 50 Ohm system, that will produce a VSWR of 1.5:1. Similarly with a similar arrangement, but with the counterpoise 180 degrees from the radiator (an arrangement some would incorrectly call a dipole), the feedpoint impedance is ~73 Ohms, and again in a 50 Ohm system, that produces a VSWR of 1.5:1. In either case, the VSWR is not 1:1, but the antenna is resonant. In any case where the antenna element is a multiple of 1/4λ, the antenna is resonant, (see more information about 1/4λ resonance here: https://ham.stackexchange.com/a/21331/18388) whether the feed-point impedance is ideal for your transmission system, is another story. Take the case of an end-fed 1/2λ antenna that has a feed-point impedance of ~3000 Ohms, that antenna is resonant, but your transmitter is not going to do very well with that large mismatch in impedance. It is when an antenna is in-between a 1/4λ multiple, that an antenna is not resonant, and its capacitive reactance is not cancelled out by its inductive reactance, and you have to add either capacitance or inductance to make the antenna resonant. Keep in mind that having excess capacitive or inductive reactance will also cause a high VSWR.

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    $\begingroup$ ...and that is why amateur radio exams( in USA ) are multiple choice.Why does minimal SWR DOES NOT indicate antenna resonance? false - it does.Would SWR 1:1 be required to indicate antenna resonance? No. $\endgroup$
    – Jan Hus
    Oct 15, 2022 at 23:46
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Jan.

SWR or Voltage Standing Wave Ratio is a measure of impedance mismatch in an antenna system and generally applies for transmitting.

Usually a mismatch will be present at the junction between transmission line and antenna, but can also occur at the radio / transmission line junction.

If for example there is a difference in impedance between the coax and antenna, during TX, there will be a reflection of RF energy at that junction which interferes with the original outgoing signal from the radio. This results in an interference pattern known as a Standing Wave to appear along the transmission line.

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The standing wave looks like a sine wave and oscillates in time at the frequency of the RF signal from the transmitter. VSWR is a measure of the difference between maximum and minimum values of the voltage of the standing wave, and is the same everywhere along the length of the transmission line. If there are no impedance mis-matches, then there will be no standing wave and SWR will be 1:1.

The condition of resonance for a center series fed (split in the middle) dipole antenna occurs when the ends of the elements are that distance away from the center feed points which allows for each cycle of applied RF to be in phase with the current reflected from the ends of the elements, the effect being that the applied RF reinforces the antenna current to produce a larger output.

When this condition occurs, reactance in the feed point impedance is zero, because the RMS amplitude of the voltage of the standing wave at the feed points, which is 90 deg out of phase with the current of the applied RF, is zero.

To reiterate further, the driven element in a yagi antenna could be 5 % longer than the resonant length at the desired operating frequency, but a gamma match can be used to provide series capacitance to cancel out the added inductance of the antenna which is too long. In this case the antenna is not resonant, but the gamma match acts as a lumped constant antenna tuner which cancels out the reactance resulting in a 1:1 SWR.

When an antenna is resonant, there is no reactance present in the impedance seen across the feed point terminals, but resonance does not mean the SWR will be good. The frequencies at which resonance occurs are mostly determined by the length of the antenna elements, and the feed point impedance is determined mostly by the physical dimensions of the antenna and the impedance of free space. If a center series fed half wave dipole is operated at its resonant frequency, then the impedance seen between the two feed point terminals will be purely resistive and will contain zero reactance. Then, if the transmission line has the same resistive impedance, it is matched and no reflections occur, there will be no standing wave on the coax, and the SWR will be 1:1.

However, if the antenna is being operated at it's resonance frequency or a harmonic, and the impedance across the feed point terminals is not the same as that of the coax, then the antenna is still resonant but the impedance of antenna and coax don't match and there will be reflection, a standing wave and bad SWR.

To complicate things further, there can be a situation where an antenna is not resonant and has a reactive impedance across it's feed point terminals, but the radio has a reactive impedance of opposite polarity, and in this case the two reactances can cancel and still give a 1:1 SWR even though the antenna is not resonant. This is in fact partly how an antenna tuner works.

Different antennas have different values of impedance across the feed point terminals at resonance, and for a given antenna the impedance changes depending on the frequency of operation .

In contrast, transmission lines have a characteristic impedance which is fixed regardless of the operating frequency and is usually 50 or 75 ohms.

Hope that makes sense !

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There seems to be some confusion which has led the subject away from the original question. Here's a situation that would illustrate one reason why minimum SWR (VSWR) does not necessarily indicate antenna resonance. And to clarify one area of confusion, VSWR can be present at many points in an antenna system. So let's take an example whereby we feed a half wave dipole at the center with 50 ohm coax. When the antenna is resonant, the feedpoint is seeing an impedance mismatch of approximately 1.5:1. So in this case we can't determine if the antenna is on resonance or not by looking at the SWR meter in the radio. If on the other hand we feed the antenna with 72 or 75 ohm coax, there will be no mismatch indicated but as far as the antenna is concerned, nothing has changed. And, an antenna does not have to be resonant to radiate well, and there will be situations where it radiates better when not at resonance. The ARRL Handbook (any edition) has excellent material on this subject. One moral of this story is not to obsess over VSWR because it in large part beside the point and may result in less than idea feedline and antenna system design and construction.

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