Resonant Quadrifilar Helix Antenna

Transcription

1 . TECHNOTE R.W. Hollande Mandaijnstaat S DEN HAAG WORKING GROUP SATELLITES Resonant Quadifila Helix Antenna Theoetically the ideal antenna fo the eception of pola obiting satellite signals; in pactice a nightmae. R.W. HOLLANDER

2 Resonant Quadifila Helical Antenna by Robet Hollande Acknowledgements to Ruud Jansen Tanslated by Chis van Lint Contents Foewod and back-gound Intoduction 3 30 yeas RQHA; a shot eview of developments 4 Poblems encounteed and solutions 7 Design of the RQHA- Measuement esults 5 Bibliogaphy 7 Appendix A Detemining of the impedance of a single loop 8 Appendix B Impedance model of a RQHA 0 Appendix C Connecting a self-phasing RQHA 4 Appendix D Infinite balun 6 Appendix E Dimensional calculations fo the RQHA 7 Appendix F Coaxial - lines 9 Appendix G Detemining the electical length of coaxial cables 3 Appendix H Measuing set-up 3 Appendix I Input impedance and noise of the aeial amplifie 33 Appendix J Analysis of measued data, fomulae in RQHA.xls 38 R.W. Hollande RQHA

3 Foewod and back-gound The RQHA is an ideal type of aeial, at least in theoy. In pactice it may appea that some RQHA aeials give medioce pefomance. Sometimes even aeials that have been constucted with the utmost of cae appea to give poo pefomance. Ruud Jansen, who intoduced the RQHA to ou Woking goup, has always been vey enthusiastic about the achievements of his aeials, which wee constucted with coax cables. I myself on the othe hand had to epot time and time again that the esults of my labou did not wok, which to put it mildly is some indication of the fustations I encounteed. My aeials always exhibited consideable vaiations in all-ound sensitivity and wee so insensitive that satellite eception was only possible, when passing vitually ovehead and fo that, one does not need a RQHA! In the meantime I had collected and analysed just about all aticles elating to RQHA s, all full of paise fo this type of antenna, as was to be expected. What was I doing wong? I did notice that hadly anyone povided measuement data and that thee was a high level of copy-cat content (efe next paagaph). In ode to find out what the natue of the poblem was, I had to cay out some measuements. Ruud offeed fo us to meet in Haalem, so that we could make some measuements togethe, using the equipment available at the Highe Technical College. The fist day meely esulted in the obsevation that we leaned a little moe about the measuing set-up. On the second day, we managed to measue something on one of Ruud s aeials and one of mine. Howeve intepeting the measued values was hopeless, as we simply did not know what it was we had measued! In addition, measuing just one aeial took about one and a half hou. The analysis of the measued values togethe with the pepaation of a Smith chat took some moe hous. The analysis can be speeded up consideably by enteing the measued values into an Excel speadsheet. This has the additional advantage that automatic coections can be made to cable length and cable losses. Additionally gaphic chats can be poduced, including a pola plot of the eflection coefficient (vesion of a Smith diagam). On the thid day we managed to poduce some eal esults. The esonant fequency was too high. Whilst thee is a eduction facto applicable to open dipoles, as a esult of the capacitive end-effects (which causes an open dipole to appea lage), the RQHA equies an elongation facto to be applied because of capacitive effects at the bends, (which makes the loop appea smalle). Additionally the impedance is vey dependent on the diamete of the tube o cable used to constuct the RQHA. The impedance in tun influences the quality o bandwidth of the aeial, which in tun means that the deviation fom the esonant fequencies of the lage and small loop, needed to poduce the equied 90 o phase shift, depends on the tube diamete. The intepetation of the measued data of the RQHA as a whole can only be done popely by compaison with a model. Slowly I am beginning to ealise, what we ae tying to do. I have stated to wite down exactly how an aeial is to be measued, what exactly it is you ae measuing, how to coect fo cable length (also within the aeial), the cable losses (not to be neglected!), as well as how to poduce Smith-chats and how to intepet them. This esults in a wok with lots of fomulae, not eally suitable fo publication in ou magazine De Kunstmaan. By tansfeing all the fomulae to appopiate appendices, the whole stoy becomes moe eadable. By leaving out all of the appendices, it becomes suitable fo publication. Howeve R.W. Hollande RQHA

4 anyone who wants a detailed desciption of exactly how eveything functions and wishes to have access to the complete stoy, complete with appendices, the full wok is available as Technote 999-, the Resonant Quadifila Antenna, R.W. Hollande, which is a new Initiative of the woking goup. In the meantime Ruud has managed to scape togethe almost all the components used in the measuement set-up fom disposal stoes and has offeed me a loan of this equipment. I am now at home in my living oom measuing a RQHA attached to the wooden ceiling, o weathe pemitting I am outside in the gaden. I have abandoned my fist plan, (to build a RQHA using 4mm tubing) and I have changed to a RQHA constucted of mm tubing. The impedance of a 4mm RQHA is so low (the bandwidth so small), that it is necessay to fiddle aound with millimete dimensions in ode to achieve the coect 45 degee phase shift pe loop. Maybe one of these days, when I have lots of time I might look at this once again. The mm design causes less nevousness, although millimete, athe than centimete accuacy is still equied. Definitive dimensions may be found in the paagaph Design of a RQHA- Intoduction The Resonant Quadifila Helix Antenna (RQHA) is an ideal antenna fo the eception of APT on 37 MHz. Not only in theoy, but also in pactical use, it pefoms pefectly povided it has been constucted coectly. As long as this poviso is satisfied, the antenna pefoms as would be expected fom theoetical consideations, i.e. ight-hand ciculaly polaised (RHCP) sensitivity fom hoizon to hoizon. Unfotunately it is not easily detemined whethe a self-phasing RQHA has been constucted coectly, just on the basis of good eception. In ode to obtain optimum pefomance, impedance measuements have to be made, which will detemine whethe o not the equied phase shift elationship in both loops has been achieved. An RQHA in which the phase shift elationship is not coect, will often still poduce a easonable image, because in the absence of RHCP-selectivity, poblems will occu only wheneve stong eflections ae encounteed. In a pooly constucted RQHA, difficulties may be encounteed in the adiation patten (uneven all-ound sensitivity), as well as in the symmety (symmety point at the base not dead and/o hand effect on the cable). A pope RQHA does not suffe fom these poblems and assues eception of weathe images fom hoizon to hoizon, without noise bands. R.W. Hollande RQHA 3

5 30 yeas of the RQHA, a shot eview of developments The quality of a wieless connection is the poduct of the quality of the tansmitte antenna, the eception antenna and the medium in-between the two antennas. The ecipocity theoem states that in theoy, the quality of the connection is not affected by an exchange between tansmission and eception antenna. This howeve does not mean that both antennas should be identical. Thee ae cicumstances, which will cause non-symmetical pefomance, e.g. eflections fom the eath s suface by the eception antenna, the possibility of pointing the antenna in a specific diection, antenna mass, etc. Satellite designes do thei utmost to poduce good antennas. It is theefoe logical that eceiving antennas too should be affoded simila consideation. Fo tansmission of APT signals oiginating fom pola obiting weathe satellites, antennas have been designed [7-], which exhibit:. A cone shaped adiation patten in the lowe hemisphee, as shown in Fig.. A ight-hand ciculaly polaised (RHCP) field, which is independent of the adiation diection. 3. Robust constuction 4. Low mass. Requiement () esults fom the fact that tansmitting antennas ae diected downwad. The patten has been chosen in such a way that the signal stength is almost independent of the distance between the eceiving antenna and the satellite. Requiement () esults fom the desie to take advantage of the phenomena that EM waves, when eflected ae subject to a evesal in helicity, i.e. RHCP (negative helicity by definition) becomes LHCP (positive helicity). Requiement (3) must be satisfied, as the antenna is subject to consideable foces duing launching. Requiement (4) is of geat impotance when dealing with satellites since evey gam counts. In contast, the eceiving antenna can be pointed (to the satellite) and can follow the satellite duing a pass. It is howeve moe convenient to mount the antenna in a fixed position. This would thus esult in equiement (5): a adiation patten, which is equally sensitive eveywhee in the uppe hemisphee. (the distance effect is aleady coected fo at the tansmitte side!). e.g. When a NOAA satellite appeas ove the hoizon, the elevation of the obseve as seen fom the satellite is equal to accos (R/Rh)), whee R epesents the adius of the eath and h is the distance of the satellite to the suface of the eath. With R6367km and h850km the esulting elevation is 8 degees! R.W. Hollande RQHA 4

6 By using eception antennas, which ae sensitive only to RHCP fields, the connection will be insensitive to eflections! In paticula at the hoizon, the antenna must be RHCP (equiement 6). Fo the eception of pola obiting satellites theefoe, it is desiable to have an antenna which: 5. Exhibits a adiation patten in the uppe hemisphee, which matches the patten shown in Figue. (the antenna is diected upwads and has omni-diectional coveage). 6. Is sensitive in all diections only to ight-hand polaised EM waves. Requiements such as study constuction and low weight ae of less impotance in teestial antennas. If something goes wong, caying out epais is a mino poblem. It may be impotant to limit the eception angle upwads, fom e.g. 80 to 40 (intefeence fom distant teestial souces), depending on eception location and/o in ode to impove shielding fom the gound plane (self geneated intefeence, such as fom the compute). The RHCP equiement is paticulaly impotant when thee ae a lage numbe of eflecting objects in the vicinity. Though the yeas antennas have been developed, which ae moe o less satisfactoy (Lindenblad-antenna, tunstile antenna, cloveleaf antenna, cossed yagi [-3]). In ode to satisfy the RHCP equiement, these antennas have to be diected towads the satellite. When used in a fixed position (diected towads the sky), these antennas ae linealy polaised at the hoizon, which due to intefeence o eflections at low elevation angles will almost always esult in noise bands. Fig. diagam of tansmission antenna Fig. patten of eceiving antenna R.W. Hollande RQHA 5

7 In 947 G.H. Bown and O.M Woodwad conceived an antenna consisting of a vetical dipole placed on the axis of a hoizontal loop [4]. When both antennas ae fed in the coect phase elationship, a RHCP EM field can be obtained in fee space. This antenna was the basis fo the Resonant Quadifila Helical Antenna (RQHA). C.C. Kilgus ealised that a combination of two twisted wie fames (Fig. 3), fed in quadatue would poduce the same adiation patten as that of the dipole-loop combination, howeve in only one hemisphee. The RQHA, fist published in 968 by C.C. Kilgus [7], satisfies the equiements established ealie fo both the tansmitting and eceiving antenna. Now 30 yeas late the RQHA is paticulaly popula. A lage numbe of GPS eceives make use of the RQHA. Howeve the RQHA is not only popula fo eceiving puposes. As it may be poduced using lightweight constuction techniques and does not equie a efeence (gound) plane, these chaacteistics make it paticulaly suitable fo use as a tansmitting antenna in satellites. R.W. Bicke and H.H. Ricket constucted an S band RQHA fo mounting on the TIROS-N satellite [] back in 975. This antenna seved as a model fo all late designs, including the 37 MHz vesions, despite the diffeences in fequency. Fig. 3. Example of an RQHA of the ½ tun, ½ lambda type. Two twisted wie fames ae placed upon each othe at ight angles and ae connected to the antenna cable at the top. The diection of the twist detemines polaisation (RHCP). The cuents, which ae poduced in both wie fames, exhibit a phase diffeence of 90. By using a ¼ lambda phaseloop, both wie fames can be coupled. Depending on which of the wie fames is attached to the loop and the method of connecting the balun (exchange of shield and cente conducto of one of the baluns), the antenna will exhibit eithe upwad o downwad sensitivity (!). The type shown, has a adiation patten simila to that shown in Fig., and is suitable as a eceiving antenna, when the diamete/length atio of the imaginay RQHA-cylinde equals appoximately 0.44 [4]. Tansmitting antenna ae of the ½ tun, ¼ lambda type and display the adiation patten shown in Fig. [5]. The development of the RQHA may be divided into two peiods:. The development of pofessional tansmitting antennas fom 968 to 99 [7-4].. The development of eceiving antennas by amateus fom 993 up to the pesent [6-4]. R.W. Hollande RQHA 6

8 The contibution of W. Maxwell [5] liteally constitutes an intemediate phase; Maxwell was involved in pofessional development and caied the idea futhe into the amateu community. In the initial development phase, the RQHA was based on theoetical concepts and vaious ideas wee veified by expeimental means. In the second phase, we saw vaious attempts to tansfom these concepts, in paticula the magic ecipe of Bicke, into well pefoming antennas fo APT eception. In many cases this was without awaeness of the conditions unde which the ecipe was valid. This led to both fustation with pooly pefoming designs and paise, when an (accidentally) well woking pototype was poduced. The next section will show that attention to pactical constuction details plays an allimpotant pat in obtaining good pefomance. Even once a pope design has been established, i.e. (mechanically obust, use of commonly available components), good pefomance unfotunately can only be guaanteed when an exact clone is poduced. Poblems encounteed and solutions To poduce a popely functioning RQHA, a numbe of poblems have to be solved, which ae not unique to the RQHA. These include symmety, impedance matching and coect phasing. - The RQHA loop is a signal souce with symmetical connections, wheeas fo the tansmission of the signal an asymmetical coaxial cable is used. - The impedance of a RQHA loop should ideally confom to one of the common coax cable impedance s (50 and 75 Ω). - The signals of both RQHA loops should be combined, howeve the phase shift of the (voltage) signals between two equal loops is 90 o, when RHCP is used. The attaction is that thee ae a vaiety of possible solutions. The poblem is to find which is most suitable, based upon the needs of the end-use. A lightweight antenna suitable fo use when tavelling, would be diffeent to an antenna which has to be used in advese weathe conditions. An antenna fo city use, whee thee ae consideable obstuctions at the hoizon, would equie a diffeent adiation patten, when compaed to one fo a quiet county setting. One designe will demand that the antenna is simple to epoduce (with acceptable eception esults), whilst anothe might be peoccupied with poducing an outlandish design which gives optimum esults, but at the expense of it being easy to epoduce. When designing the RQHA the following stategy should be followed: R.W. Hollande RQHA 7

9 - Detemine the desied adiation patten. When using ½ λ, ½ tun types, it will in most cases be possible to obtain a suitable patten by adjusting the elationship R, between the diamete, to the axial length of the imaginay cylinde aound which the RQHA is wound. I chose an ½ λ, ½ tun type, with R0.44 (appoximately the ecommendation in [4], which esults in a 3dB beam width of 40 and a 6dB beam width of 80 ). I live in the city and I pefe to use the boost in the adiation patten of the tansmitting antenna of the NOAA s at the hoizon, athe than build additional sensitivity at the hoizon into the eception antenna. At the hoizon, polaisation is pactically RHCP; the coss polaisation (sensitivity to LHCP in db minus the sensitivity to RHCP in db), is appox. -8dB. - Choose the diamete of the conductos to be used in the RQHA. Note that the shape of the loops is citical, hence thei constuction must be ugged. The initial choice was to use coppe pipe with a 4mm outside and a 3mm inside diamete. The oute diamete is simila to that of the shield of RG58 cable, which infes that the esults of my antenna should also be valid fo a RQHA constucted with RG58 cable. The inne diamete is just big enough, to allow a Teflon cable to be pulled though (see late efeence). I finally settled on mm pipe, because the impedance of a 4mm antenna is too low, which esults in a too naow bandwidth. - Detemine the adius of the bends. Coppe pipe with a 4()mm diamete can still be bent easily, without nicking, at a adius of mm (to the cente line), povided the pipe has been annealed. Anneal only those sections, which ae to be bent. When using mm pipe, it is moe convenient to use loose bends, which can be soldeed in place. Thee is a numbe of vaieties available commecially; I use lage coppe (not bass) bends (not knees), with a adius (to cente line) of 5mm, though which a cable can be easily pulled though. Note: the adius of the bend is impotant with espect to the elongation facto! - Detemine the esonant length of one half loop. This should be a little moe than ½ λ. Exactly how much moe, will have to be detemined expeimentally (depends on the tube diamete and the adius of the bend). The elongation facto is.045 when using a 4mmdiamete tube and a bending adius of mm. When using a mm-diamete tube and a bending adius of 5mm, the elongation facto is Detemine the impedance of the RQHA esonant loop. A 4mm -loop has been found to have an impedance of Ω with the impedance of a mm -loop being 30Ω. - Decide on whethe you will be using two equal loops, each with symmetical impedance and phase matching, pio to signal summing, o whethe a self-phasing RQHA is to be constucted, with two unequal loops and an infinite -balun. In the latte case, symmety, phase matching and summing is achieved in one opeation. Impedance matching can be accomplished by using an electical length fo the infinite -balun, equal to an uneven numbe of ¼ λ lengths, which causes e.g. the 30Ω of the self-phasing RQHA-, to be tansfomed to 83Ω, though the use of 50Ω impedance balun cable. This aangement would be suitable fo use with the HA-37 antenna amplifie, using a capacitive divide at the input, consisting of pf and 39pF capacitos. This appoach howeve is quite difficult! R.W. Hollande RQHA 8

10 A self-phasing RQHA, although vey elegant, is also difficult to design, due to the need to satisfy all the elevant paametes of the individual equiements at the same time. Using two equal loops in the RQHA is simple, because a sepaate phase-netwok can be used to povide phase coection. Futhemoe, the povision fo symmety and impedance matching use classical methods. My final choice was fo the self-phasing RQHA, because of the challenge it pesented me with. I accepted having made a compomise, in the sense that this design will be moe difficult to duplicate successfully. To me, the elegance of this type of design was of geate impotance. - The Q facto of the loop can be found fom a measuement of the impedance as a function of fequency. At esonance the eactance X 0 and the de-tuning v 0. At a de-tuning of v /-/Q the eactance X /-R. At the coesponding fequencies the phase shift between cuent and voltage is -/ 45. The esonant length of the lage loop has to be chosen in such a way, that the fequency fo which v /Q is equal to 37.5 MHz, in which case the voltage acoss in the lage loop leads the cuent by 45. The esonant fequency of the smalle loop is chosen to ensue that the fequency fo which v -/Q is equal to 37.5 MHz as well, which causes the voltage acoss the small loop to lag 45 behind the cuent. By coupling both loops in such a way that the cuent (the E-vecto of the EM field) in the lage loop lags the cuent in the small loop by 90, the voltage acoss both loops will be in phase! - In ode to each this stage, a numbe of loops should have aleady been constucted, to enable detemination of the elongation and quality facto Q, of one loop at 37.5 MHz. If at the fist attempt the esonant fequency is not too fa emoved fom 37.5 MHz, the Q facto of that loop may be used. The pefomance of the final constuction (two loops inteconnected), will now need to be veified by measuing the impedance, as a function of fequency. By compaing the cuves detemined fo R and X with a simulation model, it is possible to veify that points v /Q of the lage loop and v -/Q of the small loop do indeed coespond to 37.5 MHz (efe also to the paagaph dealing with measuement esults). If necessay, calculate the coection factos fo the loop lengths and stat all ove again, which will equie the constuction of anothe RQHA. In the meantime the elative elongation and Q facto of a 4mm and a mm RQHA have been successfully detemined. It has been shown, that the impedance is athe low (Ω and 30Ω espectively), with a coespondingly high Q facto. This means that the deviation of the esonant fequency fom 37.5 MHz of both loops is only ±.8 MHz (RQHA-4), espectively ±3. MHz (RQHA-). Fom this, it is obvious that the end esult is vey dependent on the mechanical constuction; a few millimetes divegence fom the equied dimensions is sufficient to uin pefomance. Since we now know what the factional elongation l and the factional deviation of the esonant fequency f fo a 4mm and mm RQHA is, we can compae these values with the R.W. Hollande RQHA 9

11 esults obtained with antennas made fom diffeent diamete tubing, e.g. by plotting the l and f values against the logaithm of the ecipocal diamete d (Fig. 4). Fom this gaph it is clea that the factional deviation depends stongly on the diamete, which eflects the dependency of the impedance (and thus the quality facto Q and thus the bandwidth) on the diamete. The elongation facto depends not diectly on the diamete, but moe on the atio of pipe diamete ove the bending adius of the bends used. This atio will be the same fo many pipe diametes; only fo vey small diametes, like 4mm tubes, the elongation is consideably less than 7%. 7% l f 3 0 9mm [] 5mm [4] mm 8mm [] 4mm 0 log (00/d) d (mm) Fig 4. deviation of the esonant fequency and elongation as a function of pipe diamete. R.W. Hollande RQHA 0

12 Design of the RQHA- The RQHA- is moe suited fo epoduction as compaed to the RQHA-4. Fo this eason the values indicated in the table below elate to the RQHA-. In the calculations we stat with the design fequency, the numbe of tuns of the twisted loop and the appoximate length of a half loop (in wavelength). Fom expeiments we know the elongation facto (Fig. 4). This sets the mean loop length. We now select the diamete/height atio fo the desied adiation patten [4]. This gives the mean diamete and mean height of an imaginay cylinde on which suface the antenna is situated (if the tube diamete would have been zeo). Since in pactice bends ae used with a adius of 5mm, measued on the axis of the tube, the tube length along this axis-line is somewhat shote than measued on the suface of the imaginay cylinde. We theefoe have to enlage the cylinde, to coect fo this bend-shotening. Next we have to adjust the factional fequency deviation, defining at which fequencies the lage and smalle loop will esonate. This facto has to be detemined expeimentally (Fig. 4). These deviations fom the mean values will now define two cylindes on which the axis of the mm tube of the lage and the smalle loop ae found. The length of the adial components equals the cylinde adius minus the 5mm taken by the bend. Use had, staight coppe pipes. Depending on the constuction of the connections at the antenna axis, which will take some length, the adial components will have to be shotened. The helical components have been calculated assuming the axis of the pipes to be on the cylinde. Hee too, the calculated length has to be coected fo the length of the two bends. Use soft coppe pipe fo the helical pats. Fist staighten fou lengths of about 0 cm (oll them ove a flat table), and mak the cente of the lengths. Measue the equied lengths of the helical components, coected fo the bends, fom the cente, as pe the table. It will be vey had to measue the length and mak the cente afte bending of the helical pats. Use a mandel fo this job. Note that the diamete of the mandel has to be the diamete of the cylinde minus two times the pipe adius, in ode to get the pipe axis on the cylinde suface. Since thee ae a lage and a small loop, two mandels will be needed (which can be combined of couse). The values indicated in ed have to be chosen / supplied. R.W. Hollande RQHA

13 design-fequency (MHz) 37.5 phasing aangement small and lage loop numbe of tuns (n) 0.5 half-loop length of antenna (lambda) 0.5 wavelength in fee ai (mm) 80 pecentage elongation 7.0% mean loop-length 337 aspect atio Height/diamete.5 Diamete/height 0.44 mean diamete 3 mean height 70 mean deviation.50% cuvatue (cente-line to cente-line) 5 effective length of bend 4 small loop 78.9 loop length, coected fo bend shotening adial components (X4) 53.9 adial component, coected fo bend 38.9 helical components (X) helical component, coected fo bends 84.5 axial length lage loop 397. loop length coected fo bend shotening 43.0 adial components (X4) 6.8 adial component, coected fo bend 46.8 helical components (X) helical component, coected fo bends axial length 70.3 I decided upon a constuction, using components which I have tuned myself, using a lathe. This allows poduction of a neatly constucted device. Howeve a neat appeaance is not a peequisite fo pope opeation. On the othe hand, it is impotant to ensue that the capacitance of the gap at the feed point (on top) is kept low. Finish the ends of the adial tubes off with conical plugs. A sot of clamp will be useful to keep the helices in position whilst soldeing. I use a wooden coss at half of the cylinde height (hee the cente mak on the helical pats is vey useful). R.W. Hollande RQHA

14 70 mm 40 mm Fig. 5 coss-section (top) and top view (below) of the feed section at the uppe side of the RQHA. The DELRIN- box consists of thee pats: one ing and two lids. Scale (the small squaes) is.5mm. The only impotant measuement is the distance between the cente lines of the lage and small loop. This must be 8mm (half the diffeence between the axial length of both loops). The lage loop is on top. The conical plugs have been dilled though, to allow the coax to be fed though (small loop) and to allow inte-connection of the loops. Standad educed 45 degee bends wee used. R.W. Hollande RQHA 3

15 40 mm 40 mm Fig 6. Coss-section of the lowe pat of the RQHA. The coppe box consists of two lids. Scale is.5mm. The only impotant measuement is the distance between the cente lines of the lage and small loop. This must be 8mm. The small loop is on top. A hole has been dilled though the lid on the bottom side to allow a BNC-connecto to be mounted. The adial measuements povided elate to the vetical axis of the antenna. Depending on constuction, the adial tube pieces may have to be adapted. In my constuction e.g. the adial pieces on the bottom of the antenna wee shotened by 0mm, compaed to the stated measuements in the table (these 0mm ae aleady contained in the coppe block). R.W. Hollande RQHA 4

16 Measuement esults Ou impedance measuements of the RQHA have always been made as a function of fequency. To facilitate measuements, a Geneal Radio 60 Admittance Bidge was used. The esults can be illustated in the fom of a gamma plot (Smith-Diagam), as R jx, whee R and X ae functions of the fequency, o the VSWR. Below is an illustation of the latest, and until now the best, vesion the RQHA-. Futhe details elating to measuement methods and the analysis of the data obtained, ae contained in the appendices. eflection coefficient MHz MHz ,5 MHz Fig 7. Cental section of the RQHA- gamma-plot, with an elongation of 6.65% and a diffeence of.5%. The distance between the points measued equals 0.5 MHz. The esonant fequencies ae 35. and 4.3 MHz. The fequency shift equied to achieve a phase shift of 45 degees is 3. MHz fo both loops. The impedance of the loops is 30Ω, The impedance of both loops connected in paallel is 9Ω. R.W. Hollande RQHA 5

17 aeial-impedance R data X data R X R X R sim X sim Fig. 8 Impedance of the RQHA- with an elongation of 6.65% and a diffeence of ±.5%. VSWR Fig. 9 VSWR of the RQHA- with an elongation of 6.65% and a diffeence of ±.5%. It is clea, that the elongation is still not sufficient (middle fequency is 38., instead of 37.5 MHz) and has to be inceased to 7.% R.W. Hollande RQHA 6

18 Bibliogaphy [] G.H.Bown, The tunstile antenna, Electonics 9, Ap. 936, p.4-7 [] N.E.Lindenblad, Television tansmitting antenna fo Empie State Building, RCA Rev. 3, Ap. 939, p [3] P.H.Smith, Cloveleaf antenna fo F.M. boadcasting, IRE Poc. 35, Dec. 947, p [4] G.H.Bown, O.M.Woodwad, Ciculaly-polaized omni-diectional antenna, RCA Rev. Vol 8, 947, p [5] H.Jasik, Antenna Measuements in Antenna Engineeing Handbook, McGaw-Hill 96, p.34- [6] H.Meinke, F.W.Gundlach, Leitungsbauelemente und schaltungen, Symmetieungs-schleifen in Taschenbuch de Hochfequenztechnik, Spinge Velag, 968, p [7] C.C.Kilgus, Multi-element, Factional Tun Helices, IEEE Tans. AP-6, Jul. 968, p [8] C.C.Kilgus, Resonant Quadifila Helix, IEEE Tans. AP-7, May 969, p [9] C.C.Kilgus, Resonant Quadifila Helix Design, The Micowave Jounal, Dec. 970, p [0] A.T.Adams, R,K,Geenough, R.F.Wallenbeg, A.Mendelovicz, C.Lumjiak, The Quadifila Helical Antenna, IEEE Tans. AP-, Ma. 974, p [] R.W.Bicke, H.H.Ricket, An S-band Resonant Quadifila Antenna fo Satellite Communication, RCA Enginee Vol. 0 No.5, Feb.-Ma. 975, p [] C.C.Kilgus, Shaped Conical Radiation Patten Pefomance of Backfie Quadifila Helix Antenna, IEEE Tans. AP-3, May 975, p [3] J.M.Tanquilla, S.R.Best, A Study of the Quadifila Helix Antenna fo Global Positioning System (GPS) Applications, IEEE Tans. AP-38, Oct. 990, p [4] H.S.C.Wang, Theoetical Design and Pedictions of Volute Antenna Pefomance, IEEE Tans. AP-39, August 99, p [5] M.W.Maxwell, Chapte The Quadifila Helix Antenna in ARRL-book Reflections, 99, ISBN [6] Matjaz Vidma, Eine Quadifila-Backfie-Helixantenne fu GPS- und GLOSNASS-Empfang, UKW-Beichte No. 4, 993, p. 4-6 [7] Mak Peppe, A Compact, Cheap, Volute Antenna, RIG 37, Jun. 994, p [8] Ruud Jansen, De Quadifila 37 Antenne, De Kunstmaan, Dec. 995, p [9] Chis van Lint, A Potable/collapsable Quadifila Helix Antenna fo the 37 MHz APT Band, RIG 44, Ma. 996, p [0] Eugene F.Rupeto, The W3KH Quadifila Helix Antenna, QST, Aug. 996, p [] Hay van Deusen, De Nationale Antennetest, De Kunstmaan, Okt. 996, p [] Bill Sykes, Taming the QFH, RIG 48, Ma. 997, p. 7-. [3] Rene Reudink, De Quadifilai Helix Antenne, De Kunstmaan, Okt. 997, p. 6-4 en Dec. 997, p [4] Bob Thop, The Coppe Pipe QFH, RIG 53, Jun. 998, p R.W. Hollande RQHA 7

19 Appendix A detemining the impedance of a single loop When developing a RQHA, it is necessay to detemine the impedance of a single loop, with the othe loop pesent, but not connected in paallel to loop. Jasik [5, p.34-] descibes how the impedance of an aeial can be influenced by the pesence of a second antenna. When the phase elationship between the cuents I and I is constant in both aeials, (e.g. at a specific fequency), the measued impedance of aeial ( ) can be expessed as the impedance of aeial without aeial (,self ) being pesent, togethe with the situation esulting fom the pesence of aeial (,mutual ). A compaable definition is valid fo the impedance of aeial ( ):, self, self I I I I, mutual, mutual (A-) We can look at the RQHA as being a pai of identical aeials., self, mutual (A-), self, mutual self mutual It follows that aeial impedance is dependant on I /I. When measuing a RQHA, we need to know the impedance of one loop, (without the second loop being connected in paallel) unde dynamic conditions, i.e. we do need to take the pesence of the second loop into account. This equies two measuements: - Measuing loop, with loop shoted, - Measuing loop, with loop open. In the fist instance 0, hence: shot self I I I 0 self I mutual mutual (A-3) We can now expess mutual as shot and self : mutual ( ) (A-4) self self shot In the second case is infinite and I 0, hence: (A-5) open self R.W. Hollande RQHA 8

20 We can assume that unde dynamic conditions the cuent in both loops is identical. Supplying values fo (A-4) and (A-5) in (A-) povides the answe: self mutual open self ( self shot ) open ( shot open ) (A-6) In a caefully constucted RQHA, the coupling between the two loops, placed at ight angles upon one anothe will be small and ( shot - open ) will be small in elation to shot o open. The oot may be appoximated with ½ : open shot open (A-7) whee the impedance of loop unde dynamic conditions. cannot be measued, howeve it can be detemined fom the measued impedance s of loop, with loop open espectively closed (without being connected to loop )! Example: Measuement of the small loop has shown that: - open 30 Ω - shot 30 Ω It has been found that in an RQHA-4, the values of open and shot show a maximum diffeence of Ω; sometimes open is lage, compaed to shot while at othe times open is smalle than shot. Whilst these diffeences ae small, they ae howeve maginally geate than the measuing toleance. The assumption that is small in elation to open theefoe appeas to be justified. Thus we find fo the impedance of the small loop in a RQHA- unde dynamic conditions (oughly equivalent to that of the lage loop): 30 Ω. In a popely designed RQHA this will also be the impedance of the whole RQHA at the specific fequency in use (efe Appendix B). Bicke [] quotes 40 Ω fo his RQHA (at 800 and 00 MHz)! NB. When the lage loop is not pesent the measued impedance will be 3 Ω. NB. Fitting the lage loop will have a small effect on the esonant fequency of the small loop, (600 khz)! NB. Within the limits of measuement eos, the esonant fequency of the small loop is independent of whethe the loop is open o shoted (± 00 khz). R.W. Hollande RQHA 9

21 Appendix B impedance model of a RQHA When developing a RQHA, the esonant fequency f and the impedance RjX of one loop have to be detemined. If a self phasing RQHA, i.e. a RQHA in which the phase shift is obtained by means of paallel connection of a loop which is too small (capacitive below wanted fequency) and a loop which is too lage (inductive above the esonant fequency), it is of cucial impotance to detemine at which fequency R X (fo the lage loop) and the fequency at which R -X (fo the small loop). Both of these fequencies have to be 37.5 MHz. In a self-phasing RQHA only one of the loops can be measued; the one with the coaxcable connected. It is elatively simple to intepolate the esonant fequency (X 0) and the fequencies at which R /-X fom the measuement esults of one loop. These fequencies can be detemined moe accuately by compaing the measued data with a model, which expesses the impedance as a function of fequency. If ultimately the impedance of the whole RQHA is to be measued, a model becomes indispensable, since it is no longe possible to detemine diectly at which fequencies R /-X. A esonant aeial may be descibed as a dampened seies esonant cicuit. Damping is bought about by the adiation esistance R (fig. B-). The impedance is: R jω L (B-) jω C may also be expessed as a function of the esonant fequency ω (by definition the angle fequency wheeby is eal), quality Q of the cicuit and detuning v fom the following substitutions: ω LC v ω ω ω ω f f ωl Q R ω RC f f (B-) The impedance is expessed as: R ( jqv) (B-3) In ode to adjust the model to the measued data, it is desiable to have as few adjustment vaiables as possible. It boils down to using as much pevious expeience as possible. Take e.g. the esonant fequency f and the esonant-impedance R as adjustable vaiables. The value of Q will be fixed at a multiplication facto πl afte (B-). Self induction L is popotional to the suface of the loop, hence popotional to the length squaed. The length of the loop is invesely popotional to the esonant fequency, fom which we deive fo Q: f L const Q π R f R (B-4) R.W. Hollande RQHA 0

22 The constant value must be obtained fom measuements. It is theefoe to some extent also an adjustable facto, but nevetheless one, which is the same in all measuements. The esonant impedance and the esonant fequency now emain to allow analysis of the measued values, of which howeve the esonant fequency is aleady known, due to the choice of loop length, which takes the elongation facto into account (Appendix E), which is the same fo all measuements. We now have two loops, each with its own R, Q and v (because thee ae two esonant fequencies), which ae connected in paallel (fig. B-). R R R L L L C C C Fig.B- Model fo single loop and fo two loops connected in paallel. The sum of the admittance of both cicuits may be calculated as follows: Y Y Y (B-5) Geneally the total impedance can be expessed as RjX. Afte some calculations it follows that: R R ( QvQ v )( R R ) R R ( Qv Q v )( RQv RQv R ( R R ( R Q v R Q ) ) v ) R R ( Qv Qv )( R R ) R R ( QvQ v X ( R R ( R Q v R Q v ) )( R Q v R Q v ) ) (B-6) Due to de-tuning v and v, R and X ae a function of the fequency. If R R and Q v -Q v (at the opeating fequency of a well designed RQHA) then R R (R ) and X 0. R.W. Hollande RQHA

23 antenna impedance Fig.B- Example of (B-6), in which fo 37.5 MHz the following is valid: R -X (Q v - ) and R X (Q v ). It is assumed that R R 30 Ω and Q Q.4 (thee is little diffeence between the two loops). The esonant fequencies ae 34.3 and 40.7 MHz (X 0 fo each sepaate cicuit) R total X total R X R X 46 When this simulated aeial with impedance is connected to an impedance of 0, the deviation of in elation to 0 may be expessed as the eflection coefficient Γ: Γ 0 0 (B-7) Gaphically this may be illustated as shown in fig. B-3. eflection coefficient MHz MHz 0.0 Im MHz -.00 Re Fig. B-3 The eflection coefficient unde the same conditions as fig. B-, howeve using fequency as the paamete R.W. Hollande RQHA

24 If the chosen esonant fequencies ae too close to (o too fa fom) 37.5 MHz, the phase diffeence of the voltages acoss both loops at 37.5 will not be 0 and the aeial will not function coectly (the cuents in both loops follow the RHCP-EM-field and will show a phase diffeence of 90 ). Figue B-4 illustates the esults obtained in a situation whee the esonant fequencies ae too close to 37.5, wheeas figue B-5 shows what happens when the esonant fequencies ae too fa away fom 37.5 MHz. antenna-impedance eflection coefficient MHz R total X total R X R X Im MHz Re Fig. B-4 Example of esonant fequency which is too close to 37.5 MHz (35, and 39,7) R 30 Ω and Q,4. antenna-impedance eflection coefficient MHz R total X total R X R X Im MHz Re Fig. B-5 Example of esonant fequencies which ae too fa emoved fom 37,5 MHz (33, and 4,7) whee R 30 Ω and Q,4. R.W. Hollande RQHA 3

25 Appendix C connecting a self-phasing RQHA Fo fequencies below the esonant fequency f, the impedance of one RQHA-loop is capacitive in natue, it is inductive above f. The small loop shows a f above 37.5 MHz and should theefoe be capacitive at 37.5 MHz. The big loop shows a f below 37.5 MHz and should theefoe be inductive at 37.5 MHz. Depending on the choice of R -X and R X fo the small, espectively the big loop at 37.5 MHz, the voltage acoss the lage loop will lead by 45 in elation to the cuent in this inductive loop, whee as the voltage acoss the small loop will lag 45 in elation to the cuent in this capacitive loop. The acoss the big inductive loop and the small capacitive loop ae theefoe in phase, povided that we ensue, that the cuent in the big inductive loop tails the cuent though the small capacitive loop by 90. This esults in the connection diagam shown in fig C-. Note: The phase elationship in a RQHA is not detemined by the hoizontal staight sections of the loops, but by the helices. The RQHA is a back-fie aeial, in which the diection of polaity is opposite to the diection of the twist (a standad helical aeial is an end-fie -aeial in which case the diection of polaity is identical to the diection of the twist). long Fig.C- Top-view of the inteconnection between the big and small loop. shot shot long It is necessay to connect a balun to the inte-connection points (Appendix D). An infinite balun was chosen because: - This type of balun is a eal cuent balun (advantages see [5]), - antenna-elements, balun and antenna-cable can be integated (weight savings), - This epesents a supisingly simple solution. It does not matte, which loop is used to constuct the balun. A cable though the small loop was chosen, because this has constuctional advantages on the bottom side of the aeial. Neithe does it matte, how the phase is selected (shield and inne conducto). Fig. C- illustates a possible solution. R.W. Hollande RQHA 4

26 long Fig.C- Top view. One of the possible methods fo connecting the infinite balun. In this example each of the fou ams can be used to allow the cable to un though them. shot shot long The shield of the cable has to be connected to both loops on the bottom side. This in fact is the dead symmetical, o eath point (Appendix D) and may be connected to the metal suppot mast. long Fig. C-3 Bottom view. On the bottom side, the loops have to be connected both to one anothe and to the shield. shot shot long R.W. Hollande RQHA 5

27 Appendix D infinite balun Meinke [6, p. 390, fig. 8.] shows nicely how the infinite balun woks. He descibes a symmetical cicuit, which opeates without impedance tansfomation, to which the souce and load ae connected. U mio- loop 0 inne conducto U/ shield - U/ Fig. D- left: ing shaped vaiant of the infinite balun; ight: equivalent cicuit of the symmetical cicuit ( economy tansfome ) without impedance tansfomation [6]. The outside of the shield in the section between load and the symmety point ( eath-symbol ) is fee fom cuent! In the RQHA, the EM-field is the souce, which acts on the outside of the shield and the mio-loop; i.e. the aeial itself. Poviding a good quality coaxial cable is used (dense webbing) cuent will flow only along the inside of the shield (when teminated with the chaacteistic impedance), as a esult of the skin-effect. The outside of the shield is fee fom cuent! The penetation depth d fo EM-fields is defined as the depth at which the field is educed by a facto of e (.7, base of the natual logaithm). ρ d 500 (D-) f Wheeas d is expessed in metes and ρ is the specific esistance (fo coppe, Ω.m at 0 C) and f epesents the fequency. In the case of coppe at 37,5 MHz this esults in a penetation depth of 5,6 µm, which is much smalle as compaed to the thickness of the shield, which is 0 µm (RG58). Theefoe the outside of the coaxial cable can be used fo othe puposes, e.g. as aeial. It follows that the RQHA makes good use of this skin effect, by applying the infinite balun pinciple. R.W. Hollande RQHA 6

28 Appendix E dimensional calculations fo the RQHA The helical components of the RQHA constitute an imaginay cylinde. If we wee to oll this cylinde out and flatten it, the helical shaped components will be tansfomed to staight lines. If we now daw the adial components in the same plane, figue E- esults, in which: πn L length of the helical component of a half loop, L ax length of the cylinde axis, adius of the cylinde, L L ax n numbe of tuns in the helix. Fig. E- Rolled out RQHA (ed). Fo a RQHA with a half loop length of appoximately a multiple of the half wavelength (in which adial components ae pesent both on top as well as on the bottom) the following equation is valid: λ L f l (E-) Expession f l epesents the elongation facto used to opeate at esonant fequency. Additionally, the following is valid too (fig. E-): ( n ) The atio between the diamete and the axial length of the cylinde constitutes a design paamete, which detemines the shape of the adiation patten. If we use R fo this atio, the following applies: flλ Lax ( nπ R) R (E-3) RLax The length of the helical element L is detemined by (E-): L L ax π (E-) L λ f l RL ax (E-4) In this equation L ax, L en ae expessed as a function of λ, R, n and f l. R and n detemine the shape of the adiation patten. The designe himself detemines them. The elongation facto f l (the facto used to lengthen the loop in ode to ensue that esonance is obtained at the desied fequency coesponding with λ) has to be detemined expeimentally. R.W. Hollande RQHA 7

29 Appendix F coaxial-lines At times it may be necessay to poduce a coaxial line, with a non-standad chaacteistic impedance. The impedance of a ound piece of wie o tube d inside a ound tube with an intenal diamete D is: l c D πµ µ 0 ln d D πε ε 0 ln d µ ε 0 0 µ ε ln D d 39 µ ε 0 log D d (F-) In this equation l and c epesent the inductance espectively capacitance pe mete, µ and ε the elative pemeability, espectively pemittivity of the medium, µ 0 and ε 0 the pemeability (,6.0-6 H/m), espectively pemittivity (8, F/m) of the vacuum. The popagation speed v of EM-waves in a medium which exhibits a pemittivity ε and a pemeability µ is expessed as: v c (F-) εµ ε ε 0µ µ 0 ε µ ε 0µ 0 ε µ Wheeas c epesents the speed of light in vacuum. It follows that the popagation speed is popotional to ε -/. Since fo a specific wavelength λ in a specific medium the following equation is valid: λ v f f ε c µ ε µ c f λ ε 0 µ βλ µ 0 (F-3) the wavelength is also diectly popotional to ε -/ and is shote in a specific medium by a facto β as compaed to the wavelength in vacuum. In (F-3) f epesents the fequency, λ 0 the wavelength in vacuum and β ε -/ the eduction facto of the medium. mateial ε -/ β ε PE polyethylene,3 0,659 SPE foam polyethylene,5 0,8 PTFE Teflon, 0,695 Table F-. Relative pemittivity ε and eduction facto β of commonly used dielectics. R.W. Hollande RQHA 8

30 Wheeve an impedance is equied, the atio D/d must be equal to (assuming µ ): D d ε 39 β (F-4) D/d (ε ) D/d (ε,3) d (D6mm, ε ) d (D6mm, ε,3) 35,79,4 3,35 mm,49 mm 50,9 3,5,6 mm,7 mm 70 3,9 5,80,88 mm,03 mm 00 5,4,33,4 mm 0,49 mm Table F- Examples of dimensions fo coaxial tubes at a given value of. When using an ai filled coaxial system of 50 Ω with an intenal pipe diamete of 6mm, the commonly used eath wie with a diamete of.6mm would be most suitable fo use as the cente conducto. An ai filled coax equies that the inne conducto is suppoted. Assume that we use suppots consisting of length t, spaced individually at distance s, now the elative pemittivity is expessed as ε : t s ε eff ε, (F-5) t s If the suppots ae constucted fom polyethylene (ε,3) and we ae pepaed to accept a β of 0,98 (ε,eff,04) the filling-faction should be t/s,8 %. In ode to ensue that the impedance emains constant fo the est of the line in those aeas whee the suppots have been placed, the diamete of the inne conducto needs to be educed slightly at the point of contact with the suppots. The appopiate facto f d can be deduced diectly fom (F-4): f d 0 39 β (F-6) In the example shown, the diamete has to be educed fom.6 to.577 mm. In most cases this efinement may be ignoed. The length of the suppots t must be consideably smalle as compaed to the wavelength within the pipe. Losses within coaxial cables ae caused by two factos: - esistive losses of the inne conducto and shield - Dielectic losses R.W. Hollande RQHA 9

31 The esistive losses ae popotional to the squae oot of the fequency, because as a esult of the skin-effect the effective coss-section of the conducto is popotional to the squae oot of the fequency (efe Appendix D fomula (D-)). Dielectic losses ae popotional to the fequency and causes them to become geate at high fequencies as compaed to esistive losses. PTFE is subject to lowe dielectic losses as compaed to PE and is theefoe suitable fo use at fequencies above GHz. At 37,5 MHz on the othe hand these dielectic losses can be ignoed. cable loss in db/m Inne conducto - diamete mm Shield diamete mm H RG-58C RG Table F-3 losses in commonly used 50 Ω cable types at 37,5 MHz. Losses in coaxial cables may be measued with the aid of the Geneal Radio 60 Admittance bidge. Use a easonable length of cable fo this pupose, e.g. 60 mm RG- 58C (7,75 wavelengths at 37,5 MHz) and detemine YGjB thoughout the fequency ange fo which the loss facto has to be detemined. admittance G B MHz Fig. F- admittance of RG58C coaxial cable of.60 m (open ended). R.W. Hollande RQHA 30

32 Now detemine G fo those fequencies whee B0. The loss α in db/m now follows fom G G 0 G G exp α 0 l ln0 0 (F-7) Whee G 0 is the standad-conductance (0 mmhos) and l the length of the measued cable in metes. The loss at 37.5 MHz is detemined fom the loss at 33 and 4 MHz by intepolation. f (MHz) G (mmhos) α (db/m) , Table F-4 loss α of a RG58C coax cable, as a function of fequency f. R.W. Hollande RQHA 3