PO Box 589Cottage Grove, OR 97424rudys@ordata.com

Getting the Most fromHalf-Wave Sloper Arrays

By Rudy Severns, N6LF

So you want to put up a really big 160-meterdirectional array? Here are some tips.

For those who have a single tallsupport, λ/4 or higher, the half-wave sloper family of antennas

described by K1WA,1 K8UR,2 K3LR3,4

and others can be a relatively simpleway to make an antenna with modestgain, good F/B and an electricallysteerable pattern on 80 or 160 meters.Previous articles have provided muchinformation on this family of anten-nas. But having just come through acycle of building several variations, Ifound that a lot more needed to besaid. Fig 1A shows two different half-wave sloper array element shapesthat I will refer to as the “K1WA” andthe “K8UR,” with the understandingthat many other arrays use theseshapes. Fig 1B shows some other pos-sible element shapes.

This article presents a 160-metervariation of this family of antennasand, more importantly, a discussion ofthe details of how to get such a beastworking really well. You could simplyput up four precut dipoles, with3/8-λ phasing lines à la K1WA and thearray will work with reasonableF/B. However, with extensive model-ing I discovered that fanatical atten-tion to detail and tuning and addinga first-class ground system willgreatly enhance performance.

In the summer of 2000, I put up apair of 150-foot wooden poles placed

east-west along a ridge. I called George,W2VJN, who had been using half-waveslopers for years and asked for his ad-vice. That began a long series of con-versations and experiments. Georgesupplied many key insights while I wasdoing field testing and modeling work.I very quickly learned how difficult itis to actually obtain the performancepredicted from modeling in a real160-meter antenna. The configurationreported here is a bit different from ear-lier versions but is simpler to build and,more importantly, easier to get up andrunning at full performance.

Initial ExperimentsYou can use several slopers spaced

uniformly around the support to pro-duce a steerable pattern. These can besimple λ/2 slopers (K1WA) or dia-mond-shaped (K8UR), with the lowerends brought back to the base of thesupport. The slopers may be driven asa phased array (K8UR) or as a para-sitic array (K1WA and K3LR). It isvery common to drive and/or load thecenter of each element.

There is another possibility, however.You can voltage feed at the lower endsof the elements. This approach, whilecertainly known, has not gotten muchpress. It has some advantages whenK8UR-shaped elements are used.

My experiments began with a2-element version of the K3LR antenna,where the length of the feed line fromthe center of an element to a switch boxis adjusted to tune one element as areflector while the other element isdriven. The non-driven element is open-

Fig 1—Half-wave sloper array elementshapes.

circuited at the switch box. This allowedme to switch the direction of the mainlobe from east to west with a SPDT re-lay, selecting one or the other feed line.I quickly discovered how much the

1Notes to appear on page 80.

Fig 2—Present array at N6LF.

shape of the actual array differs fromthe nice straight-line wires we use inmodeling.

First, there is the sag in the130-foot wire spans on each side of thefeed point where the guy lines used tospread the array are attached (seeFig 1A). I found I had to move the guy-line anchor point much farther awayfrom the support to get enough ten-sion to control sag. This was madeworse by the weight of the roughly114 feet of RG-8X feed line going backto the support.

Testing showed that the F/B was notvery high—a few decibels at most—andthe feed-point impedances were sub-stantially different from predicted,making for a poor match. Furtherchecking with a clip-on RF ammetershowed lots of current on the feed lines.

I then modeled the antenna withthe actual sags in the elements andfeed line I use Nittany Scientific’sGNEC, which implements the NEC-4catenary wire (CW) and insulatingsheath (IS) cards. Guess what? Lotsof RF on the feed lines, lousy F/B andmediocre gain were indicated. I putcommon-mode chokes baluns at thefeed points (more weight, more sag,more loss) and that helped, but only abit. The extra weight also increasedthe tension in the wire and guy line tothe point where wire stretch and sub-sequent detuning became a problem.

I also found that if I wanted to ac-tually tune the elements so that theybehaved as a parasitic array, I had tomake measurements at ground level—at the end of about 200 feet of coax. Ihad to calibrate the coax and thentransform the measurements by thetransmission-line equation to get theactual feed-point impedance.

Then I had to lower the array andtrim each end of the elements. Thiswas doable but what a pain! It wasclear from the modeling and measure-ments that the actual shape of the el-ements and whether or not insulatedwire was used had a significant effecton the behavior of the array.

I groused about all this to George aswe drove up to the Northwest DX con-vention last June (2001) and he said“Why not use voltage feed instead?” Thelight went on. I wanted a parasiticarray in the K8UR configuration, butvoltage-fed at the bottom of the drivenelement. The other elements would beopen, acting as reflectors. This wouldhave some advantages:1. All the coax, baluns, relay boxes, etc,

hanging up in the air are eliminated.That removes a lot of stress on thearray and lowers the expense andthe loss in the cable, even on 160meters. The extent of cable loss was

pointed out in the K3LR articles.2. There is no longer any need for the

elements to assume a symmetricalshape (equal lengths at top and bot-tom) to minimize coupling to thefeed line hanging from the centerpoint. They can have considerabledeviation from symmetry, as shownin Fig 1B.

3. All the measurements, pruning,tuning and switching can be doneat the base of the support, right atground level. Very convenient!

4. With much less weight and wind-age the array is less susceptible todamage. This is particularly impor-tant if you live in an area whereicing is a problem.

5. The loading on the support is muchless. Not a big deal with a guyedtower, but important when using atall wooden pole or other lightsupport.Of course, there are some disadvan-

tages too:1. The switching relay(s) must now be

capable of handling high voltage(>5 kV), mandating vacuum relay(s).

2.A tuning unit is required at the baseof the antenna.

The Array At N6LFFig 2 shows a side view of the ar-

ray presently installed at N6LF. Thishas performed very well this winter(2001-2002). Note that the shape of theindividual elements is not symmetri-cal—the triangle apex is well above themidpoint. In my installation I have an-

other 150-foot pole 300-feet east and ananchor point at 100 feet in a tree400 feet west of the main support. Theseallowed me to raise the apex (corner) ofthe element farther above ground, re-ducing ground losses somewhat.

The elevation pattern for thisarray is shown in Fig 3 at severalpoints across the band. I maximizedgain at 1.830 MHz, where the F/B isabout 7 dB. Below that both the gainand F/B drop off but the gain is stillquite useable. As you go up the bandthe gain falls slowly but the F/B im-proves. At 1.890 MHz the low-angleF/B is very good (about 24 decibel) butif you look at the full rear quadrantthe F/R is only 12 dB, pretty much inline with the expectations from free-space modeling.

Because I almost always use a Bev-erage antenna for receiving I electedto go for maximum gain at 1.830 MHz.You could just as well go for high F/Band sacrifice a half dB or so of gain. Iadjusted the tuner for minimumSWR at 1.830 MHz. This gave an SWRof 1.1:1 at 1.800 MHz and 2:1 at1.970 MHz. It would have been quitepossible to adjust for an SWR < 2:1over the whole band but the gainstarts dropping off above 1.900 MHz.

This antenna has been up sinceAugust 2001 and was used in theARRL, Stew Perry and CQ CW 160-meter contests. It has performed verywell indeed, despite the truly terribleconditions on 160 meters at this partof the sunspot cycle and due to myless-than-ideal location. During the

Fig 3—Elevation radiation patterns at 1.800, 1.830, 1.860 and 1.890MHz for the N6LF two-element array.

Fig 4—Typical maximum free-space gain and F/B for two-elementdiamond-shaped array.

ARRL 160-meter contest George wasoperating on the east coast fromW3BGN’s shack and he compared sig-nals from the west-coast stations.

Of course, K6SE (who was using aballoon vertical over the Salton Seasalt flats) beat us all hands down.Compared to the other big stations,however, my signal was right in there,so the antenna is clearly starting towork well. And there is even more Ican do to improve it. The followingdetails how I achieved my level of per-formance and what could be done toimprove it.

Comparison To Other AntennasEven with the best design and con-

struction, this antenna will not beatout an equally well-designed and in-stalled four square. It will also be out-performed by the Spitfire antennas7

that are similar to this antenna. TheSpitfire uses the supporting tower asthe driven element and the parasiticelements as reflectors and directorsto form a 3-element, rather than a2-element, vertical Yagi with asteerable pattern. However, whendone well, the full-wave sloper familyof antennas is not hopelessly out-classed—and they are far easier andless expensive to build compared to afour-square system if a suitable sup-port is already in place.

In all of the modeling to follow,ground is assumed to have σ =0.005 S/m (conductivity) and ε = 13

(relative dielectric constant). For theradiation patterns, the main axis ofthe array is in the (y, –y) direction (90°to 270°).

Element LengthIn most two-element Yagi designs

the length of the driven element is ad-justed so that the feed-point imped-ance is resistive. The parasitic elementlength is adjusted to perform eitheras a director or a reflector. In low-fre-quency arrays, the size is usuallymuch too large to allow the array tobe physically rotated, and the drivenand parasitic elements must be inter-changed to switch the pattern. Thiscan be accomplished in several ways.The most common is to add or subtractsome length or loading and then in-terchange the element you wish tofeed as the driven element.

There is another possibility that hasnot received much attention. If you taketwo equal-length parallel conductors,spaced on the order of 0.1 to 0.3 λ, oneof which is driven and the other para-sitic and do some free-space modeling,you will find that as you increase thelength of the elements (keeping both thesame length) that the parasitic elementwill first act as a director and then as areflector as both are made longer. Theadvantage of this is that both elementsare identical and there is no change inlength or loading when you changedirection. You simply change whichelement is driven.

This is particularly helpful whenmultiple elements are used and onlyone is driven at a time. For an end-fedelement this makes it very easy tochange directions. You simply use asystem of relays to select which ele-ment is to be driven, leaving the otherelement open to act a reflector. A singletuning network at the base of the an-tenna is required, and it sees an im-pedance that does not change as thepattern direction is changed.

Of course the driven element in thiscase will not be resonant and will ex-hibit some reactance. With a simpleparallel L-C tuner at the base, that isnot a problem. Typically, the reactancewill be equivalent to 5 to 10 pF, whichcan easily be accommodated by adjust-ing the tuning capacitor in the tuner.

Modeling two elements in freespace gives a general idea of how thisworks for K8UR-shaped elements. Thegain and F/B will depend on the over-all height of the diamond (dimension“b” in Fig 2) and the width (dimension“a” in Fig 2). Fig 4 graphs typical free-space gain and F/B for elements vary-ing in height from 130 to 180 feet at1.830 MHz, using #12 bare copperwire. Notice these are the maximumvalues found by fixing the height andadjusting the width in the model.

As in any Yagi, maximum gain andmaximum F/B do not occur for the samedimensions. In general, at the maxi-mum F/B point the gain will be downby about 0.5 dB. There are no surpriseshere—the taller the array, the moregain and F/B you can obtain. However,even at λ/4 (≈ 130 feet), there is usablegain and F/B, even though this is halfthe length (λ/2) of normal Yagi elements.

Notice also from Fig 2 that I set theseparation distance between the topends at 6 feet. This is not a magic num-ber, but the distance between the ends

Fig 5—Vertical,horizontal and totalpattern at 22° elevationfor a single half-wavesloper with the upperend at 150 feet.

Fig 6—Vertical, horizontal and total pattern at 22° elevation for two half-wave slopers. At A, driven in-phase and at B, 180° out of phase,with the upper ends at 150 feet.

of the elements does affect the behav-ior. Spacings of order of 1 to 3 feet eachside away from the support structureseem to work fine, although othersshould work also. Chose a spacing dur-ing the design phase and be careful tostick with it when erecting the array.

Element ShapeBesides the obvious mechanical dif-

ference between the K1WA and K8URelements, there are important radia-tion-pattern differences too. If youstart with a single half-wave sloper,with the top at 150 feet, the radiationpattern in Fig 5 will have a combina-tion of vertical and horizontal radia-tion. That’s no real surprise, since youhave a slanting dipole.

When you combine this into atwo-element array, however, somefunny things start to happen, asshown in Fig 6A for in-phase and Fig6B for 180° out-of-phase excitation.The pattern doesn’t look anything likethe broadside-endfire you expect in a2-element vertical array. The problemis that the vertical and horizontalfields add up differently and the ar-ray does not behave quite as you mightexpect. While 160-meter operatorsgenerally favor vertical polarizationfor transmitting, for receiving the com-bination of vertical and horizontal po-larizations may help. I hasten to saythat this is speculation on my part.

For a four-element half-wave sloperarray, where three of the elements arereflectors, the radiation pattern isshown in Fig 7. The total pattern isquite reasonable but is made up ofvertical and horizontal components

that individually have very differentpatterns. Again, it is not clear if thereare any advantages or disadvantagesto this mixed polarization.

The K8UR-element shape has avery different pattern. Fig 8 shows the

Fig 7—Vertical, horizontal and total pattern at 22°°°°° elevation for afour-element K1WA array, one driven element and threereflectors.

Fig 8—Vertical, horizontal and total pattern at 22°°°°° for a singleK8UR-shaped element.

patterns for a single K8UR element.The horizontal component is muchlower, –12 dB or more, and contributeslittle to the total pattern. This is oneof the reasons that this shape is usu-ally preferred if you are building avertically polarized array.

In the K1WA and K8UR antennamodels, I fed the elements at the cen-ter and I made every effort to keepthings symmetrical to minimize cou-pling to the feed line. However, whenfed from the end there is no necessityto make the element shape symmetri-cal. Fig 1B shows two asymmetricshapes (1 and 2). The advantage ofshape 2 is that the anchor point forthe guy line is much closer to the sup-port. The overall space required for theantenna is greatly reduced. The down-side of shape 2 is that it places a highE-field close to ground for a consider-able distance. This increases groundlosses if an extensive ground system isnot used under the antenna.

Lifting the apex up, as shown inshape 1, reduces the ground loss sig-nificantly but requires a high anchorpoint for the guy lines. In the installa-tion at N6LF these two points wereavailable and the initial design did notuse an extensive ground system. LaterI realized just how much could begained by adding a ground system.With a good ground system the addi-tional loss due to shape 2 can bealmost eliminated and the guy-line

anchor points moved in much closerto the main support.

If two high supports are available,then you can use the Moxon rectangle(shape 3 in Fig 1B). This yields some-what better gain and F/B but doesrequire two supports.

Tuner DesignFig 9 is a schematic of the tuner.

The heart of the tuner is a simple par-allel-resonant L-C circuit, with a tapon the inductor for matching to thefeed line. GNEC predicted a feed-pointimpedance of 5318 – j 1776 Ω and theactual array impedance was within 5%of this. Notice that this is the series-equivalent impedance shown in thesidebar, “Design of the Tuner”).

To design the matching network,

Fig 9—Schematic of control unit andtuner for the N6LF array.

Fig 11—Photograph of the tuner.

the series-equivalent is transformedto the parallel-equivalent circuit. Theparallel equivalent impedance isabout 6 kΩ in parallel with 5 pF. Thenext step is to chose a loaded Q. Typi-cally this would be in the range of 5 to10, so I chose Q = 5 to minimize thesize of the tuning capacitor (C1), whichmust be rated for > 5 kV peak at1.5 kW operation. A lower loaded Qalso reduces the circulating currentand increases the match bandwidthsomewhat.

The downside of a low loaded Q isthat the inductor is larger, as are itslosses. However, as shown in thesidebar, for unloaded coil Q > 200 theloss is less than 0.1 dB. The coil I usedwas 6 inches in diameter by 5 incheslong, with 29 turns of #12 wire. It hada measured unloaded Q higher than400 on an HP 4342A Q-meter. The coilloss is thus quite small.

I use 7/8-inch CATV cable for thelong runs to the shack. To match the75-Ω feed line, the tap was 4.5 turnsfrom the bottom of the coil. Georgereminded me that this would be a goodplace to use a shielded loop made ofcoax with a series-tuning capacitor.This would give better harmonic sup-pression and provide dc decouplingand some improvement in lightningprotection. It also would provide moreisolation from BC station pickup,which can be a real problem in an an-tenna this large. In my case I wentwith the simpler direct tap and it hasworked well but when I improve(translation: rebuild because I can’tstop fooling with it) the antenna nextsummer I will probably incorporate ashielded coupling loop.

C1 is a vacuum variable, but it couldjust as well be an air variable withwidely spaced plates. The capacitancerequired is only of the order of 80 pFand not all of that needs to be vari-able. You could for example use a fixed50-pF capacitor in parallel with a30-pF air variable, which would berelatively small physically. Keep inmind that these network values arefor a particular design. Other designsmay have somewhat different imped-ances and the component values mustbe selected accordingly.

Relay K1 switches between the eastand west elements in the array toswitch the pattern. I used a surplusRB1H Jennings SPDT vacuum relayrated for 12 kV. The relay coil calledfor 26.5 V but I found that it wouldstart to pull in at 16 V and worked justfine with 20 V or more to activate it.For the dc power source I used a walltransformer power supply rated for18 V, but which actually puts out 22 V.The relay is activated through the feed

line using dc-blocking capacitors (C2and C5) and RF chokes. The controlunit is located in the shack and I sim-ply flip switch S1 to change directions.

If you want to use three or four ele-ments, then more relays will beneeded. Fig 10 shows an arrangementof two relays for three elements. It ispossible to use ac combined with dcand some diodes to control as manyas three relays from the shack throughthe coax, as is done in the AmeritronRCS-4 remote coaxial switches. Ofcourse, a separate control cable can beused also. In my case the distance fromthe shack to the array is > 700 feet, soI opted for feed-line control.

Capacitors C2 and C5 are for dcblocking. They must carry the full RFcurrent, about 5.5 A at 1.5 kW whenthe load is matched to 50 Ω. I chose touse multiple NPO disk ceramic capaci-tors in parallel because they werereadily available and inexpensive.NPO capacitors are larger for a givencapacitance than other ceramic ca-pacitors, but they have lower losses.You may be tempted to use 0.1 µFcapacitors instead of a number of 0.01or 0.02 µF capacitors in parallel, butbe careful. The self-resonant frequen-cies for the larger disk ceramics canapproach 1 MHz and you don’t wantthe capacitor to be operated at orabove its self-resonant frequency. Inaddition, a number of smaller capaci-tors in parallel will have much moresurface area and cool much better,enhancing the current-carrying capa-bility, which is primarily limited bytemperature rise. Arrange the paral-lel capacitors with space betweenthem so each one can cool itself.

There are a few other parts in thebox that deserve some attention. The1-MΩ resistors connected from the endof each element to ground are therefor static discharge. The long wires inthe array can develop high static po-tentials under some conditions. Thatpotential on the free-floating reflectorelement can cause the relay to arcwhen transmitting. I happened to haveon hand a bunch of 2-W, 100-kΩ car-

bon-composition resistors, so I simplybuilt up R1 and R2 using 10 of thesein series.

The 20-W overall power rating wasnot really necessary, but using severalresistors in series increased the volt-age rating. Thus I did not have toworry about arcing the resistors whiletransmitting, when there is a highpotential at the ends of both the drivenand parasitic elements. The loss intro-duced by these resistors is small. I alsoplaced a spark-gap to ground acrossthe drain resistors for lightning pro-tection. A lightning strike anywherewithin a quarter mile of this largeantenna will induce very high voltagesand full-up lightning protection isabsolutely necessary.

The layout of the tuner is shown inFig 11. I chose a plastic container forthe enclosure because they are readilyavailable in a wide variety of sizes andare economical. The use of a plasticenclosure also keeps the coil’s un-loaded Q high by keeping conductingsurfaces away from it. A large metalbox would also work and might havesome advantages. One disadvantageof the plastic box is that ultravioletfrom the sun will degrade it. InOregon that is not a big problem but Ido keep it covered with a shade cloth.

For ground within the box I used a2-inch copper strap, which is broughtout the bottom of the box to realground. It is very important to have agood RF and lightning ground at thispoint. I use a 24-inch diameter by8-foot culvert pipe surrounding thebase of the support pole acting as asocket so that the pole can be removedwith a crane for repair and alterations.This provides an excellent ground. If

Fig 10—Relay connections for athree-element array.

you use a tower, there should be a se-ries of ground rods at the base forlightning grounding in any case andthese can be used as a starting pointfor your RF ground system.

Tuning and AdjustmentOne of the advantages of parasitic

arrays is that the phasing of the ele-ment currents is automatically takencare of by tuning the element lengthsproperly. You can thus avoid the mul-tiple matching networks and feed linesused in a phased array, where everyelement current and amplitude mustbe adjusted.

Unfortunately, the tuning in a para-sitic array is strongly effected by thesize and shape of the elements, whichvary with tension and wire size. Some-time I wonder whether the phase ofthe moon manages to get into the act!

When you use insulated wire for theelements, the insulation material it-self has a considerable effect. For atypical 20-meter array made with alu-minum tubing, dimensions derivedfrom modeling are usually very closeand any adjustments needed aremerely for matching. For a large160-meter wire array with an arbi-trary element shape that is not thecase. The elements must be carefullytuned in the field for full performance.

What I elected to do was to designthe array in GNEC with the elementshapes as close to reality as possible,including insulation, sag, etc. When Ioptimized the array, I modeled oneelement alone and determined its self-resonant frequency. In the field I thenerected one element at a time and ad-justed it to be resonant at the samefrequency as the model. I used solid#12 THHN insulated wire because itwas much more economical than bare#12 (for some strange reason) andavailable in 2500-foot reels at a retailoutlet near me.

Besides cost, I prefer to avoid thesurface oxidation normal in bare wire.As I showed in my QEX article,5

insulation in reasonable condition in-troduces very little loss, while an oxi-dized surface introduces significantloss, at least in low-impedance arrays.However, the insulation significantlychanges the resonant frequency of anelement and it increases the weight,requiring more tension to maintainthe shape.

For the first pass I erected an ele-ment with the shape shown in Fig 2.The upper dimension for this first trywas 113 feet and the lower section153 feet. With bare wire, the resonantfrequency was 1.838 MHz and with in-sulated wire the resonant frequencydropped to 1.789 MHz. That’s a shift

of almost 3%—no big deal in a dipolebut bad news for a Yagi element. I ex-perimented with other wires andinsulations that had even larger fre-quency shifts.

So I went back to GNEC and mod-eled the resonant frequency with barewire and with two different types ofinsulation. The insulation on THHNwire is listed as having a dielectric con-stant in the range of 3 to 4, so I used avalue of 4. Back in the field I erectedelements using bare wire and the twodifferent insulations. The correlationbetween the GNEC insulating sheath(IS card) calculation and the actualmeasurements in the field was verygood. It was better than 0.1%, so longas I kept sufficient tension onthe element. I did repeated measure-ments as a check.

For tensioning I used a filled2.5-gallon water jug, approximately25 lbs, on the halyard for hoisting theupper end of the element. Higher ten-sion had very little effect on elementresonant frequency. However, reduc-ing the tension below about 15 lbsallowed the sag to visibly increase andthe resonant frequency dropped bynearly 60 kHz. These two effects com-bined were more than sufficient toseriously mistune the element.

By trimming the length of the lowersection to resonate the individual ele-ments (one at a time, with the otherelement not present) and maintaininga constant tension, I was able to getthe array to work very well. Testing ofF/B in the ARRL, Stew Perry and CQ160-meter contests when numerousstations were available showed thatthe antenna had a F/B of 8 to 10 dB.This was just about where it shouldhave been and the performance wasall I could ask for.

One problem I encountered washow to measure the resonant fre-quency of an end-fed element. For asingle element, the feed-point imped-ance is approximately 6 kΩ at reso-nance. This is out of the range of mostamateur impedance bridges. You coulduse a more professional bridge, suchas a General Radio 916 or 1606A, butagain the impedance is outside of thenormal range and some range-extend-ing tricks have to be used.

I tried using a dip meter, with verypoor results. The frequency calibrationis very poor in most dip meters andthere is considerable frequency pullingat resonance. Even using a frequencycounter to track the dip meter was nottotally satisfactory because of the effectof the meter itself and the fact thathand capacitance altered the resonantfrequency. The resonant frequency ofthe elements is very sensitive to small

amounts (a few pF) of capacitive load-ing at the ends—right where you aretrying to make the measurement.

Another problem with the dip meterand with other ham test gear can comefrom broadcast-band (BC) signals. Inmy case there is a 1-kW BC station afew miles away. At the station frequencyI get induced voltages of a volt or moreat the open end of an element undertest, and almost 100 mV on the trans-mission line back in the shack. I usedan MFJ-249 SWR analyzer and theAEA complex-impedance analyzer tocheck the match at the tap point. Bothinstruments go bonkers in the presenceof a large BC signal.

I could make the measurementwith these instruments if I placed aBC high-pass filter between the in-strument and the tap, but that doesn’thelp with the resonant frequency mea-surement. I found the use of a Birddirectional wattmeter to be more sat-isfactory for SWR adjustment andused a Boonton 250A RX meter for theresonance check. It may be possible toadapt a noise bridge with a tuned de-tector to make direct measurementson the antenna but I did not try that.

Indeed, I am very fortunate to havemy old Boonton 250A RX meter. Thisis a vacuum-tube instrument thatseems to shrug off the BC signal. TheRX meter measures parallel imped-ance up to 100 kΩ and proved idealfor these measurements. I picked upmine for $35 at a corporate surplussale many years ago and recentlybought another for $46 on eBay. Forlow-band antenna enthusiasts this isa very nice instrument to have. Keepan eye out at flea markets and on eBay.

The frequency calibration is notadequate in the 250A but I fixedthat with an inexpensive externalfrequency counter to monitor theinternal generator frequency. I alsocalibrated the RX meter using 1% filmresistors to further improve the accu-racy. These are inexpensive andreadily available.

There are other impedance-measur-ing instruments on the used marketthat appear regularly on eBay and atflea markets. A more modern instru-ment that is fairly common is theHP 4815A vector impedance meter.These also go up to 100 kΩ but sufferfrom much greater sensitivity to BC in-terference than the Boonton 250A.While the HP 4815A is relatively inex-pensive on the used market, you haveto be very careful to get one with a func-tioning probe. The probes are easilydamaged and prohibitively expensive tohave repaired.

In making the actual measurements,I was very careful to keep the layout as

The tuner is a simple parallel-tuned L-C network, witha tap on the inductor to match to the feed line, as shownin Fig 6 in the main article. The task at hand it to deter-mine the values for L1 and C1.

An equivalent circuit for the tuner and the antenna isgiven in Fig A1A. The antenna is represented by Ra andXa in series and the tuner by the parallel combination ofL1, C1 and R1, where R1 represents the loss in the L-Cnetwork, almost entirely due to the finite unloaded Q ofL1.

The values for aR and Xa are determined using model-ing and confirmed by measurements on the completedarray:

aR = 5318 Ω and Xa = –1776 W (capacitive reactance)The next step is to convert the series-equivalent circuit

for the antenna to a parallel equivalent, as shown inFigure A1B using the following expressions:

0.1120.334Q

0.3345318

1776

R

XQ

22a

a

aa

==

=−

==

Parallel equivalents of aR and aX are:

[ ] [ ]

Ω176330.112

111776

Q

11XX

Ω59140.11215318Q1RR

2a

aP

2aap

=+×−=+×=

=+×=+×=

PX is the impedance at 1.830 MHz for a shunt capaci-tance of 4.9 pF.

Selection of L1 and C1The next step is to choose a loaded LQ for the tuned

circuit when the antenna is connected. A LQ in the rangeof 2 to 10 would be typical. Smaller LQ means a smallercapacitor and a larger inductor, along with somewhatwider matching bandwidth. The problem is that a largerinductor will have greater loss. I chose LQ = 5, whichworks out very well, with minimal coil loss. For:

pF73.4101031.833.144

1

Lfπ4

1C

µH10351.833.142

5914

Qfπ2

RLmeaning

X

RQ

Lfπ2X

5Q

6221

220

L

p1

L

pL

1L

L

=××××

==

=×××

===

=

=

−

Design of the Tuner

0C is the capacitance needed to resonate at 1.830MHz with 1L .

pF68.54.973.4CCC1 p0 =−=−=

Loss Due to L1R1 represents the loss in L1 and depends on the

unloaded 1Q of L1:

( ) dB0.070.01671log10RatioLoss

0.0167355000

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This is pretty small, and you can ignore the coil lossas long as 1Q > 200. Coil Qs of 400 or more are notvery difficult to obtain with a little care in construction.

Fig A1—Equivalent circuits for the antenna and tuner.

close as possible to the final one. I posi-tioned the Boonton 250A in the samelocation the tuning unit would occupy.I then brought a 2-inch ground strapup to the same point it would be in thetuner and connected the strap to the“low” terminal of the 250A. I broughtthe end of the element down to wherethe tuner would be with a 12-inch pig-

tail from the insulator at the lower endof the element.

I zeroed the meter and then con-nected the pigtail to the “high” termi-nal of the 250A. Yes, all of this fussingaround is necessary to get accuratemeasurements! An important check isto see if placing your hands on the testgear has any effect on the readings.

There should be none. If there is, thenyou have to work on your layout, mostlikely the grounding. You should alsotry to keep away from the bottom of theelement. Holding a hand near the ele-ment will shift the resonant frequency.

In the end the array has worked verywell, but at the low end of the band theF/B appears to be higher than

predicted. I suspect that the final ar-ray is tuned a bit low in frequency dueto stray capacitance loading at the bot-tom of the array, probably caused by thetuner and the final layout. Of course inan 80-meter array this effect could beexploited by switching in a smallamount of capacitance to shift downfrom 3.790 to 3.510 MHz.

Ground SystemOne of the underlying assumptions

for this family of antennas has beenthat since they use full-size half-wavedipoles, fed at the center, no groundsystem is required. It is true that theantennas will work reasonably wellwithout the extensive ground systemtypical of a λ/4 vertical. However, thelower ends of the elements have a veryhigh potential to ground. Using GNECto plot the near-field electric (E) andmagnetic (H) field intensities showsthat the E field intensities are>800 V/m for 1.5 kW at ground levelbeneath the ends of the elements. Thistranslates into high ground losses in thenear field.

The K3LR articles mention the useof four elevated radials to improve per-formance somewhat, but that is aboutall that has been said on the subject. Ibegan by modeling the fields under thearray to get a feeling for ground lossesand then modeled the array with 60buried radials of progressively longerlength out to 0.3 λ. The result was asteady increase in peak gain due tolower ground loss. The gain increaseamounted to 0.6 to 1.5 dB, dependingto some extent on the modeling ap-proach. Even at the low end of thisrange, this is a very worthwhile im-provement.

In the present N6LF array there isa ground screen made from 2-inch meshchicken wire with a radius of 50 feet.From there, I go out another 150 feetwith #12 insulated radials lying on thesurface of the ground. Because I useonly two elements at present, the fieldintensities are not uniform in all direc-tions around the array, being higherunder the elements and lower off to thesides. I therefore have placed more cop-per and ground screen in the high-fieldregions. With three or four elements thefield intensities are much more uniformas you go around the array and stan-dard symmetrical radial systems wouldbe more appropriate. The ground sys-tem is not yet complete but already itappears to make a difference. Certainlythe modeling says it should.

Wire IssuesConductor loss, using #12 solid cop-

per wire, is about 0.5 dB, which is rea-sonable but it could be reduced. Using

a larger-diameter copper wire wouldhelp but also increases the weight of theelement. Aluminum wire, although ithas a lower conductivity than copper,can provide less resistance for the sameweight. For example, a #7 aluminumwire will weigh about the same as a #12copper wire, but will have a loss about40% lower (taking into account skin ef-fect, where resistance varies with thesquare root of conductivity). Of course,it will have more windage and the lossimprovement is only a fraction of a deci-bel, so going to large aluminum wiremay be a bit too picky.

Whether you decide to use copper oraluminum wire, stretching of the wireis a concern because it detunes the ar-ray. I tried a simple experiment: I tooka 100-foot piece of copper wire, anchoredone end and yanked really hard on theother end. It stretched a bit, about6 inches (≈ 1/2%). Conventional wisdomsays that stretching the wire this waywill increase its resistance by work-hardening the copper and also by re-ducing the diameter. I measured thewire resistance very carefully beforeand after stretching, using a Kelvinbridge good to a fraction of a milliohm.The dc resistance increase was right inline with the increase in length, ≈ 1/2%.

Work hardening and diameterreduction effects were too small to de-tect. For this reason I pre-stretched myelements and then trimmed them tolength because it was more importantto have the element correctly tunedthan worry about a very small loss ef-fect. This winter I had a lot of strongwinds push the array around but noicing, which is very rare in any case. Sofar the pre-stretched elements havebeen stable. If you live in an area whereicing is a problem, then you probablyneed to use either Copperweld orAlumoweld wire, both of which aremuch stronger but real pains to workwith.

Another problem that caught me bysurprise was the simple act of accu-rately measuring the length of a longpiece of wire. I began by pulling the wireoff the reel simultaneously with a longtape measure, both held in my hand.Every time I tried it I got a differentfinal length—by a foot or more. Theproblem is that the wire slips withreference to the tape. So next I tried an-choring the end of the tape and stretch-ing it out on the ground beforehand andthen pulling the wire out and ten-sioning both the wire and the tape.

This was much more accurate andrepeatable, but it also was a lot oftrouble and requires a clear space ofnearly 300 feet. George showed me hissolution: a wire-length meter6 like yousee in hardware stores. It measures

wire length to an inch in 300 feet with-out having to go out in the cold andwet. (It has been known to rain occa-sionally in Oregon.) It does the jobquickly and easily and I was particu-larly glad I bought my own when Istarted to cut the numerous radials forthe ground system. You have to builda simple 2×4 frame to hold the meterand a reel of wire but that’s not diffi-cult. If you want to do it right you canalso buy an adjustable reel for the wireyou cut off. That makes handling thelong lengths much easier, especiallywhen cutting numerous long radials.

Safety IssueWhile end feeding the elements has

many advantages, it presents a safetyhazard because the fed ends are soclose to ground level, where someonemight be able to touch them. The volt-ages on the lower ends of the wiresare very high while transmitting athigh power. Some form of guard fenceor safety screen is advisable if thereis any likelihood of people or animalscoming in contact with the wires.

Modeling CommentsThroughout this discussion I have

emphasized the need for careful mod-eling. In my case I have no tower inthe middle of things but most installa-tions are likely to have one with HFYagis attached. I began modeling atower by obtaining an antenna file fromAl Christman, K3LC (ex-KB8I), for aRohn 55 tower, which models essen-tially every strut in the tower. Thenormal thing to do is to calculate theself-resonant frequency of the towerand then model it using a single wirewith a diameter that results in thesame resonant frequency. You can thenuse the simpler model in the overall an-tenna model. I found that I could findsuch an equivalent wire but the varia-tion in feed-point impedance aroundresonance was not the same as for thetower. I got a better match in imped-ance characteristics by adjusting boththe diameter and the height.

Using this equivalent model I thenmodeled George’s antenna system. Ifound that his tower did not interactvery much with his array. However,that represents a sample of one. It isperfectly possible that another tower,with a different collection of HF Yagison it, might interact strongly andgreatly modify the behavior. This hasto be dealt with on a case-by-case ba-sis for each installation.

The W2VJN AntennaW2VJN has built a number of

K1WA arrays over the years. WhenGeorge was living in New Jersey, he

had used a K1WA configuration on80 meters with very good results. Hebegan with a one-element sloper, thenadded another element and finallywent to four elements. After movingout to the wilderness in Oregon heerected a 150-foot Rohn 55 tower withan array of HF Yagis on it. About 21/2

years ago he put two elements on160 meters and then a year lateradded two more elements. The arraydrives one element at a time, with theremaining three acting as reflectors.

The original K1WA array used λ/2elements, with the length of the coaxcable going to the switch box tuned tomake the element a reflector when notdriven. The result is that the matchat the drive element is not all thatgood for a 50-Ω line—SWR is typicallyon the order of 1.8:1 or so. George hasa variation that improves the match.The elements are cut for 1.850 MHz(by calculation, L=492/ MHzf ). Withthree elements open and acting as re-flectors, the apparent resonant fre-quency measured at the switch box is1.770 MHz. This means that at1.830 MHz there is an inductive reac-tance at the feed point in the switchbox. This is tuned out with a 1200 pFcapacitor, resulting in a much bettermatch, close to 1:1 at 1.830 MHz.

George’s array can be switched infour different directions and he usesit for receiving as well as transmitting.He has found that selecting the rightdirection can make a considerable dif-ference in some cases. He has foundhis antenna to be very effective onreceive despite (or perhaps becauseof) the mix of vertical and horizontalpolarization.

Future Improvements at N6LFWhile the present array works very

well, there is more that I can do. Oneidea is to add directors. At N6LF I havethree tall poles in a row that wouldallow me to hang director elements forincreased gain. I have already donethis accidentally. After finishing withthe 160-meter array I put up an80-meter dipole on the east side of the160-meter array, suspended betweenthe poles that support the 160-meterarray, as shown in Fig 12.

I checked to see if the 80-meter di-pole had any effect on the 160-meterarray by modeling the combination. Itcertainly did have an effect! With the80-meter feed line grounded, the80-meter dipole acted like a reflectorand killed my gain to the east. Addinga coax common-mode choke balunturned the dipole into a director andthis increased the gain to the east. Thedipole is not a very reliable director,however, because as the wind blew it

moved up and down, changing its char-acteristics. One minute it might be adirector but a reflector at another. Fornow I drop the 80-meter dipole for con-tests or if I think there is the possibil-ity of an opening to Europe. Nextsummer I plan to make other arrange-ments for the 80-meter antenna sothat it does not interact with the160-meter array.

And of course a three-element Yagiwould have more gain and better F/Bthan a two-element Yagi. Next sum-mer I will expand the array to threeelements. I had originally planned tosuspend the directors between theother available poles but after look-ing at the Spitfire antenna7 I changedmy mind. Since I already have an ex-tensive ground system in place, itmakes more sense for me to simplyhoist a wire up along the supportingpole and use it as a driven element,and then use the other two elementsas director/reflectors. I could even sus-pend a second director between thesupports and go to a four-element (oreven five-element) Yagi on 160-meters.Of course, the beamwidth will narrowand I would have to go to at least four-direction switching for the pattern tohave reasonable coverage.

Although I use only two elementsthat allow me to switch the patternfrom east to west, the present arrayhas been very useful. Going to threeelements (one driven and two reflec-tors) would be worthwhile. The gainis changed very little by having tworeflectors but there is some improve-ment in F/B. The real improvementwould be the ability to slew the pat-tern in three different directionsrather than two. It is possible to havetwo driven elements and have one asa reflector. This in combination withone driven and two reflectors wouldgive six headings for the pattern. I amnot convinced that this would be worththe trouble, however.

AcknowledgementsMuch of the progress I made in this

project was the result of endless dis-cussions with George Cutsogeorge,

W2VJN. He was a tremendous help. Iwould also like to thank Dean Straw,N6BV, for putting me onto the antennafile for the Rohn tower and to AlChristman, K3LC, for sending it to me.This was very helpful in evaluatingthe effect of the tower on George’s ar-ray and sloper arrays in general.

I have referenced only a few of themultitude of articles on sloper anten-nas. George told me to go to Google. comand enter “sloper arrays”. I got over 500references, about two thirds of whichwere for sloper antennas! No doubt ev-erything said here has already beensaid many times but perhaps this fo-rum will reach a wider audience.

John Devoldere’s Low-Band DXing8

is another great reference source. Atthe last moment in preparing this ar-ticle John, EI7BA, made me aware ofa particularly good article by TonyPreedy, G3LNP.9 It deals with bentverticals less than λ/2wavelength longand arrays made from them, which arevery much like the arrays in this ar-ticle. This is also a “must read” article.

References1D. Pietraszewski, K1WA, The ARRL An-

tenna Book, 16th Ed. (Newington: ARRL,1988), pp 4-12 to 4-14.

2D. C. Mitchell, K8UR, “The K8UR Low-BandVertical Array,” CQ Magazine, Dec 1989,pp 42-45.

3Christman, Duffy and Breakall, “The 160-Meter Sloper System at K3LR,” QST, Dec1994, pp 36-38.

4Christman, Duffy and Breakall, “The 160-Meter Sloper System at K3LR,” The ARRLAntenna Compendium, Vol 4, (Newington:ARRL, 1995), pp 9-17.

5R. Severns, N6LF, “Conductors for HF An-tennas,” QEX, Nov/Dec 2000, pp 20-29.

6HYKON model 1410 wire-length meter,HYKON Manufacturing; 1-800-458-1480;www.hykon.com.

7Kaufmann, W1FV, and Hopengarten,K1VR, “The FVR Spitfire Array,” DaytonHamfest presentation, 1998. Copies ofthis can be found on the Yankee ClipperContest Club Web site; www.4CCC.org/Articles/Spitfire/spitfire.html.

8J. Devoldere, Low-Band DXing, 3rd Ed.(Newington, ARRL: 1999).

9T. Preedy, G3LNP, “Single Support Direc-tional Wires,” RADCOM, Aug and Sep1997.

Fig 12—Combination of the N6LF array and an 80-meter dipole for modeling.

!!