Vertical Phased Arrays from Compromised Locations

Transcription

1 Technica Feature May 2017 RadCom Pus Vertica Phased Arrays from Compromised Locations INTRODUCTION Athough my primary interest in amateur radio has aways been biased towards weak signa VHF working, the reduction in activity in the winter months has for many years ed me towards CW DX working on 80 and 160m during this period. The initia impetus to improve my antennas for 80m came when I decided to go US county chasing, but ony on 80m CW. Not too dissimiar from square chasing on 144MHz but at east I coud do it a on CW! Avaiabe iterature on the design and ocating of phased vertica antennas for the LF bands has been we documented over the years, predominanty in pubications from the USA (See Bibiography). When erecting mutipe eement vertica phased arrays with directiona switching using common phasing components, eectrica symmetry of a eements is essentia. If this criteria is not met, good front to back performance wi not be achieved. The forward gain of muti eement arrays is not very critica on phasing, but rear rejection is. These antennas reay want to work, but great care needs to be taken to reaise the fu potentia. So what happens, if ike most UK amateurs, we do not have a 5 hectare fied that aows us to space the verticas perfecty and ay down a perfect 120 radia ground system? I hope that this artice goes some way to address some of these issues and show how the spacing, phasing, and genera performance can be adjusted to suit individua situations. There are, of course, compromises that must be accepted but it is sti possibe to get a system working in a ess than perfect situation. My existing antenna for 80m is a 3-eement in ine phased array that is switched NW-SE and was arranged this way to provide a good forward obe into the USA and ong path ZL whist providing rejection towards Europe. Fortunatey, I have access to some woodand, and the antenna is constructed from wire eements suspended in ta oak trees. The spacing was dictated by, rather than seected by, the position of suitabe oak trees. In my case this was at 3.5MHz. The ground radia system consists of roughy radias per vertica using insuated instrument wire aid directy onto the ground. The Eastery vertica has ess wires to the East as the house is in the way. The measured sef impedances of each vertica, are unfortunatey, not identica. So, this is my compromised phased vertica system for 80m. Later I wi describe what I have done to match and phase this system to perform in both directions. COMPLEX NUMBERS No description of phased antennas can made without reference to compex numbers whether in rectanguar or poar form. A that is required as a reader is a basic understanding. Not wishing to fi this artice with pages of formuae and maths, I have provided a of the cacuations as separate useabe and viewabe ony fies. These are avaiabe to those that want them at the ocation shown in the bibiography. The manipuation of these vaues has been done in Mathcad. Pease see the footnote regarding the use of Mathcad. MUTUAL COUPLING Mutua couping is a factor that must be recognised and measured as it has a arge infuence on the correct design of phased arrays. If two resonant eements are paced in cose proximity to one another, mutua couping wi exist. This has the direct effect of atering the drive point impedances of the array and must be taken into consideration when designing the feed system. Exceent in depth descriptions on this subject can be found written by Forrest Gehrke, K2BT and Roy Lewaen, W7EL. See the Bibiography [1, 2]. ANTENNA MEASUREMENTS In order to correcty design a feed system, the feed point impedances and mutua impedances of the array need to be measured. There are numerous antenna anaysers and VNA s avaiabe today at reasonabe prices that wi accuratey measure the compex feed point impedance of antennas. As an introduction, assume a 2-eement array, first measure the impedance of each of eement with the other one open circuit. This is defined as the eement sef impedance. In an idea word these shoud both be resonant (zero ohms reactance) and both have the same vaue of resistance; achieved by adding ground radias to one so that both have the same sef impedance. To measure the mutua couping, measure one antenna with the other connected to the ground radia system. Now reverse the measurement with the other eement grounded. They shoud of course be the same (reciproca). Armed with these vaues, the drive point impedance can be cacuated for a given vaue of antenna current magnitude and phase. I have written a Mathcad fie that can crunch these compex numbers. Aternativey, if you have the ARRL pubication Low-Band DXing by ON4UN, it comes with some software that wi do the same cacuations but is DOS based. INTRODUCTION: THE 2-ELEMENT ARRAY By way of an introduction to the theory of phased verticas and a method used to correcty feed them, it is idea to anayse the cassic 2 eement phased array as an exampe. It has eectricay identica eements spaced at /4 and is fed with WEST: 1A 0 EAST: 1A Spaced 90 degrees (1/4 Lambda) j j15 FIGURE 1: An array with antenna 2 current agging antenna, 1 by 90 degrees. 4

2 May 2017 RadCom Pus Technica Feature 2 ELEMENT PHASED ARRAY 2 ELEMENT PHASED ARRAY FREQ. = 3.52MHz Beaming EAST FREQ. = 3.52MHz Beaming EAST DRIVING POINT IMPEDANCES EL1 WEST (0 ) EL2 EAST (-90 ) DRIVING POINT IMPEDANCES j j19.76 EL1 WEST (0 ) EL2 EAST (-90 ) j j19.76 WEST: 1A 0 EAST: 1A -90 WEST: 1A 0 EAST: 1A MUTUAL IMPEDANCE = j MUTUAL IMPEDANCE = j SPACING λ/4 (90 ) SPACING λ/4 (90 ) Vdrive=31.7V Zdrive=24.8 -j19.7ω Vdrive= Zdrive= j19.76ω FIGURE 2: Vaues for 2 -eement array spaced 90 degrees and fed 0 and -90 degrees. identica currents of 1 amp, with one eement phase shifted by 90. Figure 1 shows such an array with antenna 2 current agging antenna, 1 by 90 degrees. Vaues for mutua and drive point impedances are hypothetica but reaistic and are shown in Figure 2. Drive impedance resuts may seem a itte surprising as they are very different from the measured sef impedance of the individua antennas. This is mutua couping at work. A cacuations for evauating the mutua and drive point impedances are shown in a pdf fie (DrivePoint_for 2 Ee Vertica.pdf/) to view, or the Mathcad fie (DrivePoint_for 2 Ee Vertica. mcdx) if you want to change vaues to suit your own measurements. Pease see footnotes regarding this appication. MUTUAL IMPEDANCE CALCULATION One very important point regarding mutua impedance cacuation concerns the sign of the cacuated vaue. Mutua impedance cacuations (Zm) requires the square root extraction of compex numbers giving two possibe soutions, positive or negative. The correct sign is reated to the spacing of the eements and is most simpy decided by reading directy from a graph of spacing versus impedance (R±jx). This graph is ceary shown in the Mathcad fies and compies with the foowing rues between 0 and 1 ambda. Reactance shoud be negative for spacing between 0.15 and 0.7 ambda, otherwise positive. Resistance shoud be positive for spacing from 0 to 0.44 ;ambda and negative from 0.44 to 0.97 ambda. FEEDING THE WRONG WAY The intuitive answer to feed this antenna that requires a 90 phase shift, woud be to make one feeder /4 (90 ) onger than the other to λ/4 λ/4 1 2 Zin= j49ω Zin= j14.4ω Vin= Vin= 50 0 Iin= Iin= FIGURE 3: The antenna ayout with currents, votages and impedances that have been cacuated from resuts obtained earier for driving point impedance and current. provide the required 90 phase shift. A common mistake that wi not provide the expected shift. As the driving point impedance of each eement wi differ consideraby from the characteristic impedance of the coaxia cabe, standing waves wi exist causing impedance, votage, and current, to vary aong the ine. Unike the case in a correcty terminated ine. We can ony pace the two coaxia feeder ines together if the votage magnitude and phase are the same. CORRECT FEEDING AND PHASING Inspection of Figure 3 shows the antenna ayout with currents, votages and impedances that have been cacuated from resuts obtained earier for driving point impedance and current. If each antenna is fed with coaxia cabes having an eectrica ength of /4, we need to know the compex vaues for votage and impedance that exist at the ends. Using the Mathcad fie Coax_Z_V_I_2ee. mcdx a of the votages, currents and 5

3 Technica Feature May 2017 RadCom Pus impedances aong the coax ines are cacuated and dispayed. If you ony wish to ook at the workings it can be seen as a pdf fie Coax_Z_V_I_2ee.pdf. Vaues shown in Figure 3 are taken from this. It is very interesting to note that the phase of current at each coax output, ags the votage phase at the input by 90. This occurs regardess of the terminating impedance and is one of the magica properties of /4 ines. See [2]. With the antenna drive currents shown in Figure 3, there wi be 50 vots with a phase ange of 90 degrees (50V 90 ) at the input to antenna 1 and 50 vots with a phase ange of 0 degrees (50V 0 ) at the input to antenna 2 There is now 50V 90 at the input to antenna 1 and 50 vots with a phase ange of 0 degrees (50V 0 ) at the input to antenna 2. We know from the earier statement, that simpy adding a /4 ine wi not provide the correct phasing as the compex votages woud not be the same. So, how ong must the additiona coaxia cabe be to provide the correct votage and 90 phase shift, to enabes the feeders to be joined in parae? THE CORRECT PHASING LINE Referring back to the Mathcad (or pdf) fie Coax_Z_V_I_2ee we need to find a votage match of 50V 90 for antenna 2 so that it can be connected in parae with the feeder for antenna 1. Scanning down the cacuated resuts for Votage input to coaxia cabe 2, it can be seen that at 158 degrees from the oad, (antenna 2) the votage is 51.16V This is a cose enough match to aow the feeders to be joined together and shows that the additiona ength of coax to achieve this is not 90 degrees but 68 degrees, (158-90). Figure 4 shows the feeder ayout and vaues. REVERSING AND MATCHING The setup shown in Figure 4 depicts antenna 2 with the agging phase and thus the direction of 2 ELEMENT PHASED ARRAY VALUES FREQ. = 3.52MHz fire. To reverse this, a that needs to be done is to swap the 68 degree feeder across to antenna 1 feeder and apart from fina matching is job done. At the end of the fie Coax_Z_V_I_2ee there is a simpe cacuation to provide the combined compex impedance of both antennas and aso cacuate vaues for a simpe L-C match and a 50 ohm feed-point. The ony input required is the impedance at the input to the Beaming λ/4 (90 ) λ/4 (90 ) 1 2 Zin= j49ω Zin= j14.4ω Vin= Vin= 50 0 Iin= Iin= FIGURE 4: The feeder ayout and vaues. Z tota = j13 Zin= j15.6ω Vin= Degrees 0.188λ additiona 68 degree feeder. In the exampe j15.6. A Christman, K3LC (ex KB8I) describes this method in Ham Radio magazine, May 1985 using coaxia cabes to provide the matching of a 2-eement array. This requires the same drive point impedance information and the inspection of votage ampitude and phase aong each feeder unti a suitabe match is found. It is both simpe to expedite and very effective. This reative simpicity highights the big advantage of making both antennas symmetrica, but at the same time, begs the question posed earier in the introduction, what if we are unabe to and are forced to make a compromise due to ocation. A 3 ELEMENT IN LINE PHASED ARRAY The genera principes for a 2-eement array have been described that works very we. If constructed for 20m the eements ony require a spacing of around 5 metres. I used just such an arrangement for many years on 80m unti I decided to try a 3-eement in ine phased array. As mentioned at the start, the eements were going to have to be wires, and they woud need to be suspended in arge oak trees. A good ook at my options forced me into wondering whether this was a good idea! The position of the house woud restrict radias on the East antenna and the positioning of the oak trees restricted the eement spacing to about 14 metres, Direction was good. The first stage was to ook at what might be achieved using this spacing and what woud be the most suitabe phase for the drive current. The 3-eement in ine uses a binomia or current distribution and is ideay suited to 4 feed ines using current forcing. This method is described by Roy Lewaen, W7EL in the ARRL Antenna Book. It uses a feed ine to the centre eement that is /4 ong and haf the impedance of feeders to the outer eements forcing doube the current to the centre eement. MODELING THE 3 ELEMENT ARRAY In order to find the most suitabe phasing for my compromised spacing of I modeed the antenna using EZNEC [8] over rea ground. Each vertica eement was resonant and /4 ong. The end resut was to use a current phase cose to ±135 degrees referenced to the centre eement, 6

4 May 2017 RadCom Pus Technica Feature FIGURE 5: Azimuth and eevation pots using EZNEC. with the current ampitude fixed at the required ratio. Designing for a good rear pattern is the most important and most difficut aspect of endfire array design. Getting the perfect cardioid pattern with its deep rear notch is ony possibe under some circumstances but 30dB shoud be readiy achievabe with care in a compromised set-up. Forward gain, as mentioned earier, is far more toerant of ampitude and phase errors. This arrangement with the fixed oak tree spacing provides a good compromise in my set of circumstances. Azimuth and eevation pots using EZNEC with current distribution and a phase ange of ±135 degrees referenced to the centre eement are shown in Figure 5. Eement spacing does not have to be at a fixed text book vaue but can be what is convenient if you do not have the uxury of choice. However, it does come with some caveats. As the eement spacing is reduced the drive point impedance wi decrease, eement current wi increase eading to higher oss, matching difficuty and reduced radiation efficiency. Where possibe, it is advisabe to try and keep the spacing above 0.125, 10.7 metres at 3.5MHz. ELEMENT SYMMETRY Wires for the 3-eement array were aunched in the appropriate oak trees and as many radias as I coud manage to insta through the brambes and bushes were aid down. This amounted to between 20 and 30 for each vertica with a sma gap in the East vertica as the house was in the way! For those dubious regarding the effectiveness of verticas in trees, especiay at LF, may I bring your attention to the piece in Forrest Gehrke s (K2BT) artice [1] in part he states, In commenting on vertica phased arrays, severa writers have cautioned against pacing arrays near trees. The apparent assumption is that trees represent resonant oss eements or somehow disturb the fied so that the radiated pattern wi be changed. I remain unconvinced. And so do I. Every pubication, without exception, regarding the use of phased verticas in the amateur word paces eement symmetry at the heart of every good design. The reasons for this are obvious, if the antenna is to be switched in more than one direction (using common phasing networks) the phasing woud be wrong in directions other than for which it is designed. Despite much effort, I was unabe to reach this idea goa of symmetry. The most recent measurements for sef impedance for the 3 eements are shown in Tabe 1. To the vertica phased array purist, these resuts woud demand many more hours of work, panting more radias, cutting and trimming. Admittedy, these resuts are not as good as when I first instaed the antennas but rabbits squirres and other widife digging up my hard work has not heped over the past few of years. The eements are a resonant at around 3.6MHz and the vaues shown are for 3.515MHz which is why they a show a capacitive reactance. These are the numbers that wi be used to design the system at 3.515MHz. But what about the ack of symmetry? If this array was to be used in a singe direction, the phasing coud be arranged such that it provides the required performance as shown in the pots of Figure 5. However, if the direction of fire was reversed the phasing woud be wrong due to the ack of antenna and drive symmetry. Athough more compex, my answer was to provide two phasing networks, one for firing East and another for firing West. It does require additiona components and more crunching of compex numbers, but is done reativey easiy with the Mathcad fies provided. DRIVE IMPEDANCE: CRUNCHING THE NUMBERS The measurements taken to enabe mutua impedance to be cacuated are shown in Tabe 2. You wi observe that two measurements have been made for each pair, ie West (1) with Centre TABLE 1: Measured vaues for sef Impedance j j Sef Impedance of Antenna A [West No 1] Sef Impedance of Antenna B [Centre No 2] Sef Impedance of Antenna C [East No 3] TABLE 2: Measurement of antennas used to cacuate mutua impedance j j j j j j7.9 Impedance of Antenna 1: West, with 2: Centre, Grounded Impedance of Antenna 1: West, with 3: East, Grounded Impedance of Antenna 2: Centre, with 1: West, Grounded Impedance of Antenna 2: Centre, with 3: East, Grounded Impedance of Antenna 3: East, with 1: West, Grounded Impedance of Antenna 3: East, with 2: Centre, Grounded grounded and Centre with West (1) grounded. These vaues shoud, of course, be identica, but there are sma measurement differences and I prefer to take both and use the average of the two measurements in the cacuation for driving point impedance. Cacuations for finding the eement drive point impedances, votages and current from measured antenna data can be found in the Mathcad fie East_DrivePoint3EL_135deg. mcdx and may be changed to suit persona measurements. There is aso a viewabe ony fie East_DrivePoint3EL_135deg.pdf. This configuration represents the array beaming towards antenna 3 (East), the eement with agging current phase. The ayout of the array with the associated drive votages and impedances cacuated from the fie are shown in Figure 6. Transformation of votage and current at the coaxia phasing ines input are considered next. COAXIAL PHASING LINES With /4 coaxia current forcing feeders in 7

5 Technica Feature May 2017 RadCom Pus 3 Eement Phased Array beaming to Antenna 3: East TABLE 3: Input required to cacuate V and Z aong coaxia feeders. FREQ. = 3.515MHz Beaming EAST DRIVING POINT IMPEDANCES EL1 WEST j EL2 CENTRE j EL3 EAST j WEST: 1A +135 CENTRE: 2A O EAST: 1A Antenna 1 (W) beaming towards antenna 3 (E) Zo := 50 + j 0 Zant := j 15.2 Fr := Ld := 90 Ima := Repeat for Centre and antenna 3. ENTER: Coax characteristic Impedance ENTER: Ant. Load (drive point Impedance) ENTER: Frequency in MHz ENTER: Cabe Length in Degrees ENTER: Magnitude & Phase of Antenna Current j j j V V V λ/4 λ/4 λ/4 λ/ A A A V (+225 ) 50V V j43.04 Ω j10.1ω j87.67 Ω FIGURE 6: The ayout of the array with the associated drive votages and impedances. pace, the transformed vaues of impedance and votage must be defined. This cacuation must be repeated for each antenna feeder in the array and for both directions of fire. The fie used to make these cacuations is COAXZ_V_I_3ee. mcdx or the viewabe ony fie COAXZ_V_I_3ee. pdf. In order to define the vaues at the feed-ine inputs just enter the vaues aready generated for drive point and feeder characteristic impedance pus the antenna current, see Tabe 3 for antenna 1 (West) beaming to antenna 3 (East) and highighted in yeow. Leave the format exacty as it is given and ony change the vaues and sign. The resutant compex vaues for votage impedance and current, firing towards antenna 3 are shown in Figure 6. Under norma circumstances, and with a system that possesses perfect symmetry, these resuts for the phasing ines woud be compete. However, as a consequence of the compromises being made, this array is being treated as a separate design for each direction and so we need to cacuate a vaues when the antenna is switched towards antenna 1, the reverse direction. The reason for this is down to the differing drive point impedance presented by the ack of symmetry. This wi be done after competing the phasing networks required for the system described and shown in Figure 6. PHASE SHIFTERS - LINE STRETCHERS Looking at Figure 6, it can be seen that the votage phases at the phasing ine inputs are a different. In the expanation for the 2-eement array it was shown that these votages must be made the same ampitude and phase before the feeders can be connected together. The centre antenna coaxia feed point votage of 50V 90 is used as the reference, and the outer antenna feeds wi be phase matched to this, so ony two are needed. When this criteria is satisfied, the feeders can be connected in parae, matched, and connected to a singe feed-ine. Line stretchers or constant impedance phase shift networks are an effective way to do this and cacuation for these networks are more convenienty made into a purey resistive termination. A cacuations for these networks and the shunt components required to cance the reactive part of the oad impedance are done in Mathcad fie: Line_stretch_Pi_T.mcdx or the read ony fie Line_stretch_Pi-T.pdf. As shown, the cacuation is for antenna 3 beaming towards antenna 3 (East). The ony user input data required, is phase in, phase out, frequency and oad impedance. A choice of Tee or Pi network wi then be presented aong with the appropriate vaues and the component type to cance the oad reactance at the input to the coaxia phasing ine. Additionay, vaues are cacuated for a simpe L network to match the combined array impedance to 50 ohms. Figure 7 shows the computed data with phase shift network vaues for the compete 3-eement array when it is beaming towards antenna 3, in this instance towards the East. This woud compete the design if no directiona switching were required. This may we be a that is required in some circumstances, and as detaied earier, it coud be switched with the existing networks, but woud resut in poor phasing due to the ack of antenna symmetry. THE EFFECT OF PHASING ERRORS It is interesting to ook at the difference in pattern for this compromised arrangement if 8

6 May 2017 RadCom Pus Technica Feature DRIVING POINT IMPEDANCES ELE 1: WEST j15.2 FREQUENCY = MHz ELE 2: CENTRE j20 ELE 3: EAST j21.15 WEST 1A +135 CENTRE 2A 0 EAST 1A -135 Antenna 1 Antenna 2 Antenna V V V G3WZT Vaues for Z, I and V beaming West: Antenna 1 DRIVING POINT IMPEDANCES ELE 1: WEST j22.96 FREQUENCY = ELE 2: CENTRE j19.01 ELE 3: EAST j21.21 WEST 1A -135 CENTRE 2A 0 EAST 1A +135 ¼ λ ¼ λ ¼ λ ¼ λ Zo=25Ω Antenna 1 Antenna 2 Antenna V V V ¼ λ ¼ λ ¼ λ ¼ λ Zo=25Ω 0.594A A A V V 90 50V j j j Ω// Ω 200.3Ω//118.2Ω 0.612A A A V V 90 50V j j j C6 L Ω//108.88Ω Ω//104.16Ω L ±j ±j0 C9 L1 C ±j0 C4 L3 C6=275.3pF C7=654pF L6=1.83uH L9=1.83uH L6 C7 50V 90 50V 90 50V ±j j ±j0 COMBINED IMPEDANCE J6.58Ω C10 L7 L8=5.35uH L7=6.41uH C9=545.7pF C10=545.7pF LOW PASS C2 L2 50V 90 50V ±j j ±j0 L1=4.93uH C4=384pF L2=3.96uH C3=472.5pF ALTERNATIVE C1=883pF COMBINED IMPEDANCE L3=2.54uH PHASE SHIFT C2=883pF 13 +J6.41Ω L4=2.54uH NETWORK FOR L3,L4,C3 8.67uH: 138pF C3 L4 FIGURE 7: The computed data with phase shift network vaues for the compete 3-eement array when it is beaming towards antenna 3. FIGURE 8: The fina design beaming towards antenna 1 (West) shows the compete set of vaues for Z, V and I, aong with phasing component vaues derived from the measured vaues in Tabes 1 and 2. the array is switched in the opposite direction using the same phasing networks designed for firing towards antenna 3. The centre (reference) eement current wi aways be correct, 2A 0 as it is fed directy, with no phasing components. Simuation shows that when firing towards antenna 1 with the existing phasing networks, the current is 0.7A -124 in Antenna 1, and 0.97A 149 in Antenna 3. The required vaues, by design, are 1A -135 for antenna 1 and 1A 135 for antenna 3. Simuating these vaues using EZNEC gives the 9

7 May 2017 RadCom Pus John Matthews, G3WZT Technica Feature need for symmetry of individua antennas within the array when using common phasing components. Phasing errors wi occur as the frequency is changed, even in a perfecty designed system. The /4 verticas aone are unikey to cover the compete 80m band without additiona matching components. This combined with the bandwidth imiting effect of phasing networks and coaxia phasing ines wi give a gradua change in front to back performance. I woud suggest somewhere around 5% bandwidth is to be expected. Forward gain wi change very itte over a much wider bandwidth but the VSWR wi then start to bite. As this is a DX antenna there wi be itte FIGURE 9: EZNEC gives this pattern when the simiation is run. requirement to design for the midde of the 80m band and pattern shown in Figure 9. It can be seen, the so wi be designed degradation in front to back performance is now for 3.5 or 3.8MHz depending on the operators unacceptabe. It highights exacty why every preference. It certainy wi not cover both the artice written on phased arrays emphasises the 80m CW and SSB DX sectors and is in common 10 with most antennas. SWITCHING DIRECTION In order to switch direction and maintain a good poar pattern, the design process just carried out beaming towards antenna 3 must be repeated for the opposite direction. This is the price that must be paid for a non symmetrica and compromised array. It is ony two additiona networks for the outer antennas and some additiona switching and number crunching. Athough it is quite straightforward to use the same fie used earier to obtain the drive point impedances and votages, I have arranged one specificay for beaming towards antenna 1 (West in the exampe). This is West_DrivePoint_135deg. mcdx or the read ony fie West_DrivePoint_135deg.pdf. Cacuations for phase shift networks are made using the same fie as before. The fina design beaming towards antenna 1 (West) shows the compete set of vaues for Z, V and I, aong with phasing component vaues derived from the measured vaues in Tabes 1 and 2 are shown in Figure 8. PHOTO 1: PHOTO 2: COMPLETED SYSTEM For competeness, a circuit diagram is given in Figure 10. It shows the required switching and the phase shift networks that have been cacuated in the design procedures described previousy. These vaues wi of course change with each individua

8 May 2017 RadCom Pus Technica Feature FIGURE 10: The circuit diagram shows the required switching and the phase shift networks that have been cacuated in the design procedures. design. Coaxia phasing ines are not shown as they form part of the feed network and are common, whatever the direction. I have used 50 ohm coax but 75 ohm coud be used if convenient providing the centre feed has haf the characteristic impedance of the outer ones. Photos 1 and 2 show a practica impementation of the circuit from Figure 10 using hand wound inductors and a mixture of ATC ceramic and Semco mica RF capacitors. UNEQUAL ANTENNA SPACING So what can be done, if for some reason, spacing between the verticas cannot be made equa? This is another situation where a compromise may have to be made. The array is sti the 3-eement in-ine phased array and needs to be switched. Let s assume that the design is sti for the CW end of the 80m band and the supports, natura or otherwise, are spaced at 0, 12 and 29 metres (0.14 and 0.2). Design procedure is the same as before using current forcing method proposed by W7EL and a current distribution. The most effective way I have found is to simuate using EZNEC and try feeding the array with different current phases. In the case above, assuming the centre is the reference eement at 2A 0, 1A 125 and 1A -105 for the outer eements provides an acceptabe pattern with good rejection. The resut for this feed arrangement is shown in Figure 11. Forward gain reduction is virtuay unchanged from the origina design and performance off the rear at ow eevation anges is very good. At high anges (around 60 ) rejection is poorer but high ange rejection can be improved by changing the outer eement feeds to 1A 125 and 1A -115, see Figure 12. The trade of is sighty ess ow ange rejection, which may not be too much of a probem. For most of us it s a about compromise, and making the very best of what is avaiabe. Switching to the opposite direction is simpy a case of reversing the current phase of the outer eements as before, and crunching the numbers using the fies provided. COMPONENT RATING Component RF ratings need some carefu consideration if high power is used. For exampe, assuming a 50 ohm feed impedance, the capacitor in the matching network (C5) must be capabe of 5 amps RMS with 400 watts into the array (V/XC). Items within the phasing networks are under ess current stress as the power is distributed 3 ways. The votages cacuated for each of the phasing ines shown in Figures 7 and 8 provide the votages present, with the design vaue of 1 Amp into antennas 1 and 3. The vaue of 50V ( 90 ) shown in Figure 8 wi be 72V RMS at 400W RF input given the combined input impedance of 13 ohms. In this case, C2 (Figure 8) must be rated at 72V RMS (pus a safety margin) and have a current rating of 1.4 amps RMS. (XC2=51 ohms, VC2 = 72V) A based on an operating frequency of 3.52MHz. GROUND RADIAL SYSTEM The subject of grounds, radias and earth osses coud easiy fi a compete edition of RadCom and I have no intention of doing that! There are many we documented artices written by those with a far deeper knowedge than I have on the subject, most of which is derived from hours of practica work and carefu measurement. Poor ground systems in the near fied reduce the efficiency of the system and the higher the osses due to ground resistance, the ower is the efficiency. Vauabe RF power ends up heating the ground. It is important to make every effort to get as symmetrica a ground system down as space wi aow. The omission of radias in one direction wi degrade and distort the azimuth poar pattern. Put down as much as you can and read the exceent 7-part artice written by Rudy Severns, N6LF pubished in 2009 QEX6 and ook at his website [7]. 11

9 Technica Feature May 2017 RadCom Pus FIGURE 11: FIGURE 12 CONCLUSIONS I have consciousy written this artice without fiing the pages with masses of formuae and cacuations. An instant turn-off for many readers, but essentia when designing such an antenna and the required phasing components. A of this information is avaiabe in the fies provided with this artice, simpy as a read ony pdf fie, or to cacuate shoud you wish using PTC Mathcad Prime. There is aso a mass of information referenced in the Bibiography. The primary purpose was to construct a 3-eement vertica, in ine phased array and achieve acceptabe azimuth performance in both switched directions with a compromised ayout. In order to accompish this it must be treated as two individua arrays. One beaming East and the other to the West, or whatever direction is required. With the arrangement described here it is ony the outer pair that require ine stretcherphasing networks as the centre eement is the reference eement and fed directy with the 25 ohm current forcing feeder. It might seem ike a ot of extra work, but reaisticay, when the first direction is competed sufficient knowedge wi have been gained to make the second iteration much more straightforward. I appreciate that the software I have used may not suit everyone but it is what I used at the start and have continued to do so. A dedicated piece of SW on a patform avaiabe to a woud perhaps be more convenient but is not something I want to take on! My particuar interest was in 80m and, owing to accessibiity and size, was why compromises had to be sought. No three tower vertica array here with unimited space avaiabe for ground radias, just insuated wires cataputed over suitabe oak trees and designed to suit. For 40m operators, the space requirements are haved, aong with the height, and woud be easier to achieve with imited space. However I appreciate that in the UK many woud find that too arge, but the design process is the same for any frequency. This arrangement has worked we for me, and the performance seems to offset the effort required to put it together. The origina idea to chase US counties on 80m CW and the abiity to do it, has been improved greaty with this compromised vertica array. 922 US counties worked on 80 CW ony with just 2150 to go! It aso works very we to ZL and the Pacific on ong path. 12

10 May 2017 RadCom Pus Technica Feature The secret is to put down as many radias as possibe, accept compromise if there is no aternative, make meaningfu measurements and then do the design. BIBLIOGRAPHY There are very many fine artices written on the subject of vertica phased arrays. Listed here is a seection of what I consider as some of the best. 1: Vertica Phased Arrays: Forrest Gehrke K2BT: Ham Radio, May-Juy, October, December 1983, May : ARRL Antenna Book 21st Edition, Chapter 8.10, Phased Array Techniques written by Roy Lewaen, W7EL. 3: ARRL Low-Band DXing 4th Edition, ON4UN. Chapter 11, Phased Arrays. With information from other respected experts on the subject. W0UN, W1MK, K9DX. 4: Feeding Phased Arrays, an aternative method. A Christman, KB8I (K3LC). Ham Radio May : Phased Driven Arrays for the Low Bands. A Christman, KB8I (K3LC). Ham Radio May : ARRL QEX March/Apri 2009: Experimenta Determination of Ground System Performance for HF Verticas: Rudy Severns, N6LF. 7: Seaside antenna workshop. Rudy Severns, N6LF. 8: EZNEC Antenna anaysis software by Roy Lewaen, W7EL. A fies in the RadCom Pus section of the RSGB website fies were converted to the ater version of PTC Mathcad Prime 3.1. For those famiiar with Mathcad it might appear that some of the cacuations coud be done more simpy. This is accepted as I have not competey re-worked a of the fies. However the end resuts are the same. As stated earier, owners of the ARRL book, Low Band DXing by ON4UN wi find software Low Band Dxing software incuded that aso does these cacuations. In my 2nd edition copy this software was in DOS and this is sti the case in the 4th edition and may not run in Windows ater than XP. I wanted to fuy understand the processes invoved, and for this reason chose to take the route that I did. PTC Mathcad is a powerfu maths too to hep with compex repetitive cacuations, it can be downoaded for free after registration from www. ptc.com/engineering-math-software/mathcad/ free-downoad with the foowing imitations as stated on the PTC website. When you downoad PTC Mathcad Express and choose the 30-day fu functionaity option, you get access to the fu version of PTC Mathcad Prime 3.1 for 30 days. At the end of 30 days, you then automaticay have ifetime access to PTC Mathcad Express, a ighter version of PTC Mathcad 3.1. Mathcad I have used Mathcad fies for a of the compex cacuations needed to propery design vertica phased arrays based upon rea practica measurements. The project was started some years ago and much of the work was done on eary versions of the program. These oder 13