Thursday, December 7, 2023

Stubs for Attenuating Harmonics - an Experiment

I'll start with a funny story. There were 3 of us doing a M/2 (multi-op, two transmitter) operation in CQ WW CW at the end of November. We kept both seats occupied for almost the entire 48 hours. As you might guess it was a tiring effort when each of us had to put in 32 hours on average. We got into this situation when our fourth operator had to cancel at the last minute.

Sleep deprivation is an occupational hazard for dedicated contesters. We may be able to do it, but not always with good results. It explains what happened to me on Sunday morning when the band opened to Europe on 20 meters and the running began. The run was going quite well when I was perturbed to find that an imposter using my call had come on frequency and began to run stations. The interference was high and I was incensed that some joker was going to mess up a lot of logs.

After a string of expletives that surprised my operating partners, I QSY'd a few kilohertz and resumed running. I made a mental note about the letter I ought to write to the contest committee describing the incident.

Two days later, one of us (VE3KI) did a log analysis. He remembered the incident and pulled up the time interval in the log. I think I turned a little red when he shared what he found.

The data was right in front of me on the screen, but I didn't look. That's what sleep deprivation will do to you!

The incident had me thinking about harmonics and how much more I can do to reduce their intensity. I am using low power BPF on both stations, and nothing else to prevent inter-station interference. The BPF are good but they cannot suppress the harmonics generated by the amplifiers. That requires high power filters after the amplifier.

Low power BPF are not the ultimate solution for SO2R and multi-op contesting. I selected them well aware of the limitations. I understood that I might eventually require high power BPF or stubs, or both. I can avoid the harmonics very easily when operating SO2R, but it is not so easy to coordinate with others in a multi-op. That takes communication and vigilance, or perhaps software to flag the risk.

High power BPF are expensive and the insertion loss typically ranges from -0.2 to -0.6 db. For low power BPF you can compensate for insertion loss by increasing the amplifier drive by 5 to 10 watts. Not so with high power BPF. The dissipated power can be quite high and may require fans to vent the heat. Can stubs do an effective job of attenuating amplifier harmonics, and let the low power BPF take care of transmitter spurious emissions? I have tube amplifiers which generally suppress harmonics well, due to the tuned pi output network. When I switch to solid state amps, as planned, the amplifier-generated harmonics will almost certainly increase.

I decided that it was time to do an experiment. I wanted to see for myself how well a stub can suppress harmonics and (hopefully) not otherwise interfere with station performance. I have the necessary equipment so an experiment was easy to arrange.

Before delving into the experiment, it is worth taking a moment to consider what it is that we want to accomplish. The following are the concerns I identified at the start of my quest:

  • Which harmonics are potentially deleterious, and which are benign
  • Which harmonics can be effectively attenuated
  • Bandwidth and depth of the harmonic notches
  • Impact of the stub on the fundamental band of operation (insertion loss and SWR)
  • Effect of the load (antenna) impedance on stub performance

It should not be a surprise that questions about stubs overlap with those of filters in general because a stub is a filter. Fixed components (capacitors and inductors) have been replaced by a network with strongly correlated L and C components due to the structure of transmission lines. You trade flexibility of filter design in return for simplicity. We will see that, as always, there is no free lunch. 

For the purpose of the experiment I went into the basement and looked over my inventory of new and used coax. I chose an ancient length of Amphenol brand RG8, about 16' (5 meters) long that had N connectors on both ends. I have no recollection of where it came from, how old it is or what use I made of it in the distant past. It was therefore important to assess its quality before proceeding. I connected it between the ports of my recently calibrated VNWA3 and swept it from 160 to 6 meters.

It measured better than I expected. The impedance is good and the insertion loss is only a little worse than the specification for new RG8. For example, at the (randomly set) 33.5 MHz marker the loss is -0.24 db. That's only -0.055 db worse than the -0.185 db spec. However, its random length doesn't correspond to any amateur band. I only knew that, from its length, it would be effective within the HF spectrum. I declared the cable adequate for the experiment.

I inserted a BNC T between the VNA port leads and, with the help of adaptors, connected the coax to the T. The other end, with more adaptors, is terminated with a BNC short from a VNA calibration kit.

The length of the coax is 16'-8½", which is 16.7' or 5.1 m. The length is measured from the through-line centre of the T to the short cap at the far end. 

Assuming the nominal VF (velocity factor) of 0.66 for RG8, without compensation for the VF of the adaptors, the cable's electrical length is 1λ at 38.8 MHz.

The test setup was then swept from below the predicted fundamental frequency of 9.7 MHz (where the stub is ¼λ long) to beyond the fourth harmonic. The first predicted notch is at 19.4 MHz (second harmonic) where the stub length is ½λ; the second predicted notch at 38.8 MHz is where the stub length is 1λ. Markers were placed inside the notches and bracketing the fundamental frequency. [Note: the frequencies are not exact multiples due to the limited number of discrete points sampled by the VNA.]

Were this a proper stub the fundamental and the harmonic notch would be within amateur bands. However, this test is sufficient to the requirements of the experiment. It is straight forward to scale the measurements to nearby amateur bands.

As you can see, the predictions were accurate. In practice you should cut your stubs long and trim them until they resonate where you want, just like you would to adjust a wire dipole. Coax has manufacturing variations that can render an accurately cut stub too short for its design frequency. The only recourse is to toss it aside and try again.

I plotted a variety of S11 curves to illustrate how the notch behaves and works as a filter. Around the stub resonance the real component of the impedance approaches 0 Ω; that is, a dead short. This is an important factor for understanding how the stub work, that will be discussed further below.

The stub is not transparent away from its resonant notches. The presence of the stub adds reactance into the transmission line that can be highly disruptive across the spectrum of interest. It is only at the fundamental frequency that the reactances cancel and the stub effectively disappears. Markers 1 and 2 are placed at the SWR 1.1 points surrounding the fundamental frequency of 9.7 MHz since I consider those to be the boundaries of the stub's usable pass band.

Notice the depth of the notches: -27.7 db at 19.4 MHz (second harmonic) and -24.3 at 38.9 MHz (fourth harmonic). The notches can be deeper with better coax because loss reduces notch depth. That is also why the upper notch is a few decibels less. 

The reason coax loss matters is because for total cancellation of the incident and reflected wave the amplitudes must be equal and of opposite polarity. It is not enough for the phase difference to be 180°. To achieve a -20 db notch the amplitudes must match to within 1%. For a -30 db notch the amplitude match must be 0.1%. 

To illustrate the impact I tested a short length of LMR400 as a shorted stub. It was similarly equipped with N connectors and adaptors, and attached to the T connector between the VNA ports.

We've improved the notch a few decibels. Because the stub is short the harmonic notch is at 74.1 MHz. Since loss is (roughly) proportional to frequency and length, the results are applicable to HF stubs. 

It is possible to achieve deeper notches with hard line like Heliax. However, notch depth is not the only important parameter. 

The above plot is restricted to HF and the markers have been placed for a discussion about bandwidth. I want to know the widths of the pass band and stop band. Their definitions are not rigid so I chose my own bandwidth definitions: SWR better than 1.1 for the pass band into a 50 Ω load (matched antenna); and second harmonic suppression better than -20 db. You are free to choose your own definitions if you don't like mine.

The pass band width is 13% for both the 19.4 MHz RG8 stub and the 74.1 MHz LMR400 stub. That appears to be consistent with all or most 50 Ω coax. That is far wider than the HF band segments that are relevant to contesting; the worst case is 8.6% between 3.5 and 3.8 MHz. It is fair to conclude that a coaxial stub filter designed to suppress harmonics from operation on any HF band contest segment will not affect performance on that band. That's good news.

The bandwidth of the notches is not as good according to my criteria. The -20 db second harmonic stop band between 19.11 and 19.69 MHz is 3%. It is narrower yet for the fourth harmonic. For lower loss coax the stop band is wider, but not by much; it's also near 3% for the 74.1 MHz notch of the LMR400 stub. The stop band is wide enough to cover most but not all of the contesting segments of the HF bands from 7 MHz and up.

  • 3.5 to 3.6 MHz: 2.9%; 3.6 to 3.8 MHz: 5.6%; 3.5 to 3.8 MHz: 8%
  • 7.0 to 7.2 MHz: 2.9%; and 7.0 to 7.3 MHz: 4.3%
  • 14.0 to 14.35 MHz: 2.5%
  • 21.0 to 21.45: 2.1%
  • 28.0 to 29.0: 3.6%

The low band figures are not as daunting as they appear. First, 160 meters is not discussed since we are only interested in the pass band and not the stop band because it's the lowest of the 6 contest bands. Second, harmonic filters for 15 and 10 meter are not needed since there are no higher HF contest bands to interfere with. Third, phone contests are less plagued by harmonics because, due to the higher frequencies of those segments, it is usually adequate to tune the stubs for the CW and RTTY segments. For example, the harmonics of 3.7 MHz are 7.4 MHz, 14.8 MHz, 21.2 MHz, etc. That sixth harmonic on 15 meters is usually so weak that it requires no additional suppression. Harmonics from operation on 160 meters is similarly of limited concern for most contesters.

The third harmonic of 7 MHz can be notched with an open stub. However, the insertion loss and SWR on the fundamental are less than ideal because the optimum pass band for an open stub does not coincide with ⅓ the frequency of the available notches. For the length of RG8 measured above, when it is employed as an open stub, for the best correspondence of a notch and operating frequency, the insertion loss is -0.34 db and the SWR is 1.75. Those are not acceptable. [Note: VNA plots not included.]

That aside, it is arguably sufficient to have harmonic stubs for 80, 40 and 20 meters since the harmonics for 160, 15 and 10 meters are not a significant interference risk. The 80 meter stub deal with harmonics on 40 and 20 meters; the 40 meter stub for 20 and 10 meters; and the 20 meter stub for 10 meters. Since a shorted stub can only suppress even harmonics, we can't use one for the 40 meter third harmonic on 15 meters.

At this point it is worthwhile to step back and ask a rhetorical question: is a coax stub sufficient to attenuate harmonics to an acceptable level? I hope that you'll agree that the answer is no. Lowering the harmonic by -30 db is good but not great. It depends on the unattenuated strength of the harmonic. Since we're discussing this in the context of amplifiers, we'll set 1 kW as the baseline.

If the second harmonic specification of the amplifier is -50 dbC (-50 db relative to the fundamental carrier) the harmonic power is 10 mW. That's a lot, although context matters. A coax stub will further knock it down to -80 dbC. A well-designed BPF will do even better. Two coax stubs in series can perform as well as a BPF. It is equivalent to increasing the order of a traditional filter. 

A BPF attenuates all out of band energy and not just the even harmonics. Its pass band insertion is typically -0.2 to -0.6 db depending on the filter design and the frequency. High power BPF often need fans to exhaust the dissipated power.

Stubs are more commonly used in conjunction with low power BPF since the BPF can't suppress harmonics generated by the amplifier. Certainly they attenuate harmonics generated by the transmitter, so that the amplifier doesn't amplify them, but the amplifier has its own non-linearity that generates harmonics regardless of what appears at the input. Amplifiers with tuned inputs attenuate transmitter harmonics regardless of whether a BPF is placed between the transmitter and amplifier.

There is another place where harmonics can be attenuated: the antenna. Dipoles and yagis made of dipole elements present a high impedance to even numbered harmonics, assuming the elements are not loaded. If the elements are loaded, the third harmonic may also be attenuated. I used that to good effect when designing my 3-element 40 meter yagi to eliminate the resonance within the 15 meter band. Of course a multi-band yagi may not attenuate harmonics at all. For example, the second harmonic of 20 meters and a tri-band yagi.

The presence of a mismatch at the antenna may not be enough. Any harmonic energy that reaches the feed point has to go somewhere. If the antenna presents a poor match (high SWR) our best hope is that it is reflected. If the coax outer surface presents a more favourable impedance, the harmonic energy will "leak" around the feed point and become common mode current on the coax shield. It can then radiate and/or return to ground by some circuitous route. CMC (common mode chokes) help prevent harmonic leakage if designed to be effective at the frequencies of the harmonics. Often CMC are optimized for the fundamental frequency.

Assuming we have well-designed high power BPF and coax stubs, should we care what happens to harmonics at the antenna? Perhaps not, although there is a valid concern when the antenna is not a close match to 50 Ω. All filters, and that includes BPF and stubs, only work as designed for specific port impedances. When there is a mismatch at the antenna or a fault due to poor coax or switching equipment, the filter may not perform as intended.

For this reason I did a further set of tests. I created a mismatch on the load side of the stub and measured the effects with the VNA. These were simple tests to probe the parameter space rather than a comprehensive analysis. I am not an expert and there was a risk that I would not design the experiment to get a broadly applicable result.

On the left I placed a 50 Ω resistor in parallel with the transmission line between the stub and the load (right VNA port). On the right I substituted a 100 pf parallel capacitor. In both cases I am using the original RG8 stub that has its fundamental frequency at 9.7 MHz. I skipped trying this with series elements since they would have taken more time to set up. Let's look at these two cases in turn.

With the parallel resistor the notches didn't change. Not surprisingly the SWR at the 9.7 MHz rose to 2 and there is an insertion loss due to the use of a real resistor rather than radiating one as found in an antenna. This is a good result. Unfortunately it is unrealistic since it is rare for a mismatch to be purely resistive. Thus we come to the second case.

The notch position and performance are unchanged. What has changed is the behaviour within the pass band. The SWR at 9.7 MHz has increased to approximately 1.4. This is also a good result because, despite the imperfect load the coax stub continues to perform well. That might not be case with a much higher SWR. Although it is an interesting question, it is not one I'm too concerned about since I design my antennas to have a low SWR over the band segments of interest. Not always, it is true, but it is true enough for my purposes most of the time. I am not aiming for perfection.

One of the reasons why I did the mismatch test was that I have seen it reported that due to the varying R and X values along a mismatched transmission line, the placement of the stub affects its performance. I now doubt whether that is true. Further testing may be called for, but not now. I can explore it in greater depth another time if I feel so inclined. I'm supplementing my mismatch experiment with a simple diagram. [Too simple, but I didn't want to spend the time making it complete and complex; it is only intended as a guide while following the text.]

After the transmission starts, the wavefront splits at the T connector, half going each way (blue & red). It takes a fraction of a microsecond for the signal to travel down and up the coax stub where it interferes with the signal from the transmitter. In this case it is in phase at the fundamental frequency and out of phase at the even harmonics. 

The fundamental wavefront continues toward the antenna at full power (half + half). The even harmonics go no further because the signal from the transmitter and exiting the stub are equal and opposite and travelling the same direction. Other than a small residual energy that is not cancelled (orange), the antenna behaviour at the harmonic frequencies becomes irrelevant.

Harmonics exiting the stub also travel in the reverse direction, towards the generator (amplifier). It is not cancelled, and the reflection causes extreme standing waves between the stub and amplifier. That is seen by the amplifier as a high SWR at those frequencies. The power in the harmonics is very low so the operating parameters of the amp are unaffected.

The initial leading edge of harmonic energy, having gotten ahead of the signal transitting the stub, will in most cases reflect back from the antenna's high impedance at that frequency, as discussed earlier. It, too, encounters the stub and the same thing happens in the reverse direction as it did in the forward direction. It will eventually dissipate through attenuation and (some) radiation.

The fundamental and harmonic signals can be individually followed and analyzed. They do add in superposition but the harmonics are too weak to measurably affect the total system. From this brief analysis I suspect that K9YC is incorrect about the importance of stub placement on the transmission line.

Stubs are not the only way to attenuate amplifier harmonics, as already mentioned. Let's recap the alternatives:

  • Coax ½λ shorted stub (relative to the second harmonic): With low loss coax the second harmonic can be attenuated by at least -20 db across the higher band, often better than -25 db, with low insertion loss. The third harmonic cannot be attenuated. The fourth harmonic is attenuated only a few decibels less than the second. Filters can be ganged in series for greater harmonic attenuation.
  • High power BPF: All harmonics are attenuated. Depending on filter design, the second harmonic can be attenuated by -40 db or better, and higher order harmonics are often attenuated better than -50 db.
  • High power LPF: Low pass filters filter all harmonics. They are not as complex as BPF but neither can they work as well below fifth order for the second harmonic. The Elsie model below is an example of a fifth order Chebyshev 40 meter LPF. The marker is at 14.2 MHz. Insertion loss is better than a BPF for a similar or lower component count and can be cheaper if you build it yourself.

How much harmonic attenuation is enough? In the story at the start of this article the second harmonic was S9+, so it was loud but not louder than a great many signals on 20 meters that morning. That helps explain why I mistook it for another station. Let's see what Acom has to say about their amplifiers. I'll quote from their specs for the Acom 2000a:

"Classical Pi-L network, all-air coils (no ferrite), and carefully designed layout of the output tank offer typical harmonic emissions as low as - 55 dBc (second) and below - 70 dBc (third and above)."

And for Acom 1500 that I own:

  • 1.8-21.5 MHz - better than 50 dB below rated output;
  • 24-54 MHz - better than 66 dB below rated output;

That is about as good as it gets since tetrodes in a well-designed amplifier exhibit very linear performance. Grounded grid triodes do a little worse and solid state amp typically do worse yet. It is good practice to choose a solid state amp that has lots of headroom at your intended operating power to ensure maximum linearity. The rollout of DPD (digital pre-distortion) may play a role in removing the harmonics generated by solid state amplifiers by improving system linearity.

I can't do much better for harmonic levels with amplifiers other than the ones I own -- Acom 1500 and Drake L7 -- yet I have problems with harmonics. It won't get better because it is likely that I will eventually transition to solid state amps to allow rapid and reliable band and antenna switching. Based on my experience I will wither have to switch to high power BPF, as almost all the best contest stations have done, or use stubs. The wait for broad deployment of DPD in the shack could be a long one.

VA6AM makes excellent high power BPF that are used by many contesters of my acquaintance. There are other products of similar quality available. But high power BPF are expensive and in most stations will require heat management and custom switching.

The time has come to try coax stubs in my station. I will start small, and if it is successful I can expand their use. For my antenna switching architecture it is easiest to make a stub for either 80 or 40 meters. The reason is that there is no switching required. My antennas for those bands have auxiliary switches connected to single ports on the 2 × 8 antenna switch where the stub can be conveniently attached. Better, it will be outdoors and out of sight. 

I have an ample supply of short lengths of Heliax and connectors from which to make low loss coax stubs. They can finally be put to good use. Assuming all goes well, I can do the same for 160 meters. For 20 meters they will need to be switched, per station, since there are several antennas distributed across several switch ports. As previously discussed, stubs are superfluous on 15 and 10 meters.

I'll try to get the first one done in time for the ARRL DX contests later this winter if I can fit it into my schedule. I may have to make it easily removable between contests because I currently use the 40 and 80 meter antennas on 30, 17 and 12 meters (the WARC bands). The stubs are incompatible with that.

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