L-network for Stacked Yagis

An important component of switching stacks of yagis is an impedance matching network. When yagis are connected together their impedances are in parallel. Two 50 Ω yagis present a 25 Ω load to the transmission line. The parallel impedance should be transformed to 50 Ω to lower transmission line loss and to keep the transmitter happy. The network is switched out of circuit when only one of the yagis in the stack is selected.

The network is 2:1 for a two yagi stack and higher ratios should be used for 3 or more yagis. More than one network may be needed if a variable number of yagis can be selected in stacks with 3 or more antennas. The 15 and 20 meter stacks I am building have two yagis each so that is the antenna system I will primarily address in this article.

The simplified schematic shows the topology of a stack switch for two yagis. The options are upper, lower or both in phase (BIP). Switches for both out of phase (BOP) and 3 or more yagis are similar but more complex. I am sticking with the simplest version since it helps with the explanation and is what is needed for the 15 and 20 meter stacks I am building. 'N' is the matching network.

Most stack switches I've looked at typically have all yagis connected and in phase, therefore the network is in line by default. When only one of a two yagi stack is selected the network is bypassed and that yagi is connected to the input port. The basic two yagi circuit requires 4 SPDT relays rated for the RF power. The diodes isolate the control lines from each other since both must power K1 and K2.

The unused yagi(s) can be left connected to the network under the assumption that the yagis are far enough apart that their mutual impedance is low. This is a fair assumption since otherwise the network would require customization to accommodate impedances that are neither 50 Ω individually nor 25 Ω for two together.

With DC injectors, reverse polarity for one the selections and several diodes the transmission line can be used in lieu of separate control lines (3 wires for the above circuit). For the design of my station it is more convenient to use a dedicated control cable. With a common DC ground a total of 5 wires are required for the 15 and 20 meter stack switches (they are on the same tower).

There are a variety of networks that can be used for the impedance transformation. The most popular for HF are:

• Broadband transformer: Typically a transmission line transformer with trifilar windings on a ferrite toroid.
  
• Transmission line section: ¼λ transmission line to transform the 50 Ω of each yagi to a higher value so that the parallel impedance is 50 Ω or, alternatively, to transform the parallel impedance to 50 Ω.
• LC network: An L-network or similar network comprise of discrete inductors and capacitors.

Commercial products are almost all of the first type (example). These can be made to work on all bands from 80 through 10 meters with high efficiency and so a single product can suit many applications. Many home brew networks for mono-band stacks use the second type with 70 Ω coax (e.g. RG11) switched into both yagi ports. In all cases the electrical lengths of 50 Ω coax from the switch to each yagi must be equal to phase the yagi feed points for maximum gain.

Although they look simple enough building your own broadband transformer is not without its challenges. These are not conventional transformers but transmission line transformers. These are variations of the excellent design to be found in Sevick's Transmission Line Transformers book. Modern versions use Fair-Rite 61 mix 2.4" OD ferrite toroids.

The number and arrangement of the trifilar windings has a significant effect on efficiency, optimum port impedance and impedance ratio. Get it wrong and the heat generated at maximum legal limit, especially on 10 meters, can destroy the transformer. Compensation for stray capacitance at the highest bands may be required. When properly designed and built they perform very well, with a loss better than -0.1 db (20 watts dissipation for a 1000 watt transmitter) from 80 through 10 meters.

The transformer, and any matching network for that matter, can exhibit different behaviour with high Q yagis (e.g. most tri-band yagis) at the band edges where the SWR is high. Deviations of the impedance ratio and efficiency in these situations can become a serious problem with high power. Regardless of the matching network and SWR it is important that the yagi impedances are near equal at all frequencies of operation to achieve equal power division. Special design considerations for stacking dissimilar antennas are beyond the scope of this article.

For a multi-band yagi a broadband transformer is the best choice since the others have a narrower bandwidth and are only suitable for a mono-band stack, with narrow exceptions as we'll see. Since most stacks are mono-band the narrow band choices deserve a close look. I plan to build my own stack switching systems since they are not complex and I can put the money saved into other projects. The learning experience is another benefit. But I would like to keep it simple, hence the motivation for this article.

Since transmission line sections require more extensive switching systems and I don't have a ready supply of RG11 I pivoted to L-networks. Both can be very efficient for the broadband yagis I've built since the impedance is close to the ideal 50 + j0 Ω across the band. TLW produced the following design (with a low pass network topology) of a 15 meter L-network for a 2-yagi stack.

The L and C values are easily attainable. For stability the capacitor should be one that is not temperature sensitive and must have a low ESR (equivalent series resistance) for high efficiency and large enough to safely dissipate the heat. The coil will be physically small and with an easily attainable Q of 400 will only shed 3 watts at a power level of 1000 watts. Efficiency is worse for large deviations from 50 + j0 Ω so design the network accordingly.

While this is a simple and efficient way to match the stack parallel impedance there are a few issues to be considered:

• Tuning: Unlike a broadband transformer the L and C values must be carefully adjusted. A small variable capacitor with a rating of at least 1000 volts in parallel with a similar fixed capacitor is a good choice. The coil can be tapped and once the correct value is found the tap can be permanently bonded.
• Bandwidth: The design is for a single frequency near band centre. The network must work across the entire band and behave well when the yagi SWR is high. Yagis optimized for gain can have a high Q and therefore high SWR at the band edges.
• Field management: Within a metal box the value of a coil is different due to the field intersecting the enclosure, either increasing (steel) or decreasing (aluminum). Toroidal coils are mostly immune to this effect. Variable capacitors, the coil and wiring will exhibit stray capacitance with each other and the enclosure walls.

On the positive side the network is cheap and efficient and easy to adapt to bigger stacks by switching in one or more capacitors. For a 3-stack C is 210 pf and 260 pf for a 4-stack, while L decreases very little and can be left alone. An intermediate capacitor value can give a good match to 2 or 3 yagis in the stack without the need for switching.

The tuning process is not too demanding. To deal with enclosure effects simply cover the box after each adjustment. Broadband transformers and transmission line sections have similar issues that, although smaller, can be more difficult to compensate.

For me the critical issue is whether the L-network is broadband enough to use across the typical amateur band without additional tuning elements that must be dynamically switched. To test the concept I used EZNEC to model the L-network. As a first step I simulated the 2-stack 25 Ω parallel impedance with a long lossy transmission line. I have found that this is a good technique to emulate a resistive load in EZNEC. Although only virtual wires are needed the model requires a real wire so I specified one but didn't use it.

That's excellent. The match is even broader than the 15 meter band. I developed similar L-networks for 20 and 40 meters and achieved the same result. L-networks for a 3-stack and 4-stack were equally good across the entire band despite the higher transformation ratio.

Real antennas do not have a perfect 50 Ω impedance across the entire band. I did not explore the L-network's performance with high SWRs since my 15 and 20 meter yagis have low SWR (below 1.5) across each band. Besides, the other impedance matching alternatives would fare no better. With EZNEC I stacked the 5-element 15 meter yagis at 100' and 150' (close to the actual heights of my antennas), including the gamma matches previously modelled.

The match is perfect, barely deviating from the SWR curve for an individual yagi. The lengths of the phasing harnesses are nominal and close to the actuality but would only have a significant effect on the match were the SWR high, which it isn't in this case. To be fair the match is also very good for the broadband transformer despite its 22.25 Ω antenna port impedance (shown below). It is common for the same transformer to be used in a 3-stack, with 2 or 3 yagis selected, since the SWR is moderately good for a 17 Ω parallel impedance.

Having reached this point there is one important question to be explored: does a real L-network live up to the promise of the theory and model? Happily enough the answer is yes. I bread boarded the 15 meter L-network with little regard to good layout. The many sources of stray L and C tune out during adjustment of the network. The yagis are simulated by two parallel 51 Ω carbon composition resistors.

I measured the same excellent result with the L-network tuned for 20 meters. The only difficulty with the tuning was moving the coil tap with this fragile setup. Squeezing and spreading the coil turns does not allow a wide enough adjustment range.

To give an idea of how far the network can be pushed I modelled a L-network centred midway between our two closest (by percent) HF contest bands: 10 and 15 meters.

Although it does reasonably well it is marginal. It certainly cannot be used for a stack of tri-band yagis or for any other pair of adjacent bands. To test the model I measure the SWR of the 15 meter L-network prototype from 14 to 30 MHz. It does better than I expected for 20 meters but is unacceptable on 10. There may be unexplored loss in the network at the frequency extremes that damp the measured SWR and therefore overstate its actual performance.

Building it

The upper 15 meter yagi was raised last week. I'll have more to say about it in a forthcoming article. Once the yagi is in position at the top of the mast and the phasing harness installed I will build a stack switch using the L-network discussed in this article. If all goes well I will do the same for the 20 meter stack. The upper 20 meter yagi will not be raised before late summer.

Sometimes it feels like progress on the station is glacial. That is unavoidable since I do most of the work myself and rely on friends to help out with the big jobs. But I would not experience the same sense of accomplishment by hiring out the work and only using commercial products.

If all goes well I am going to have a lot of fun during the upcoming winter contest season.