OFF CENTER FED DIPOLE CENTER BALUN/INSULATOR CONSTRUCTION Antenna & Balun Concepts Education

Transcription

1 OCF Cente Balun OFF CENTER FED DIPOLE CENTER BALUN/INSULATOR CONSTRUCTION Antenna & Balun Concepts Education Godon Gibby KX4Z Vesion 2.0 Apil Poject Desciption Building cente balun(s) / insulato simila to that of the multi-band B******** commecial off-cente fed dipole, fo a small faction of the cost of that commecial antenna. Use supplies thei own wie / coax 1:1 Cuent balun using FT (Type #43 feite) (good up to 300 W) Voltage Balun: eithe 4:1 o 6:1 with coe choice fo eithe type based on powe level, as follows Powe Level Voltage Balun Coe <100W SSB / 50-75W CW/Dig FT (Type 43 feite) <200 W SSB / 100W CW/Dig FT (Type 61 feite) Goal of Poject: 1. Povide use with a deployable o fixed multi-band HF antenna suitable (depending on wie length selected) fo 80/40/30/20/etc o 40/30/20/etc. 2. Education on impotant manual skills of soldeing / assembly / wie connections, antenna constuction. 3. Education on tansfome concepts, inductance concepts, adio fequency intefeence; coaxial cable effects; SWR (standing wave atio); antenna impedance; off-cente fed vs. cente fed dipoles. Applicable to the U.S. Geneal and Exta Class license examination pepaation Estimated Cost: Less than $20 depending on hadwae selected Additional items to be supplied by the use: 135 (90, 45) feet of suitable wie if the antenna is to be used as low as 3.5 MHz. 65 feet of suitable wie if the antenna is to be used as low as 7 MHz Suitable coaxial cable Any necessay tune to moe pefectly match to 50 ohm 1

2 OCF Cente Balun tansmitte output (This system may wok acceptably with no tune o with a limited ange tune, but of couse will benefit fom a highly capable antenna tune) Additional 1:1 cuent mode balun fo the adio end of the coax if RFI emains a poblem (may o may not; the suggested build includes a 1:1 cuent balun). Wie size depends on the application and may ange fom as lage as #12 to as small as #24 (not ecommended above 100 watts) UNDERSTANDING CORE DESIGNATIONS EXAMPLE: FT FT Feite Tooid (as opposed to ion powe) 140 Oute Diamete = 1.40 inches 43 Feite mateial #43 (with a mu of appox 885 and a Cuie Tempeatue of appox 150 C) 2

3 OCF Cente Balun CENTER BALUN MAJOR PARTS Typical components: QTY Name Comment 1 2 PVC Couple this could be cut fom PVC if you wished to educe cost even moe 2 2 PVC Male Cap makes top and bottom 3 1/4 zinc plated eye povide stain elief and bolt (may use stainless vetical mounting points. steel if desied) NOT necessay fo the electical connections 1 RTV caulk o any othe To seal antenna wies kind of caulk 2 Shot length of maine tinned #16 wie To connect to antenna wies 2 Male teminal spade connectos To connect to antenna wies 1 SO-239 female connecto To connect coax 4 #6 x 3/8 sheet metal scews To secue the SO-239 socket in the PVC 1 PVC cement standad type is fine. Clean dy pats don't need pime PERFORMANCE 1. Patten. Installed as an inveted Vee, the antenna will have components of hoizontal and vetical polaization. On the band whee it is a half-wave in length, it will have the typical two-lobed half wave dipole patten with most adiation boadside and a null off the tips. On highe fquency bands it will develop a multi-lobed patten. See antenna books fo moe infomation. 2. Gain: This antenna will function similaly to a dipole. The Balun will intoduce loss (typically 1 db). Coaxial cable will intoduce additonal loss. This antenna may be expected to be compaable to typical dipole, tap-dipole o fan-dipole antennas. It will have lowe loss than esistively-loaded boadband tilted-folded-wideband designs. It will have somewhat highe loss than a well constucted non-esonant dipole fed with high quality balanced window-line 3

4 OCF Cente Balun with a high quality highe-powe manual antenna tune. 3. Standing Wave Ratio: Actual pefomance obtained is vaiable fom one build to anothe, and fom one installation to anothe. The infomation hee is fom a pototype constuction: Date: 2/12/2018 G. Gibby. Balun 6:1 voltage balun only FT mateial Wie: 90 feet #18 ; 45 feet #18 Installation: Inveted Vee, top appoximately at 30 feet in oak tee, sides daped downwads to about 5 feet above eath. Tansmission line: 100 feet of RG8X. Note this smalle coax has some significant loss which makes SWR figues look bette than they would, had it been measued at the antenna connection. SWR measuement: MJF-259B antenna analyze NOTE: this SWR gaph is BETTER than expected --- which pobably esults fom using the 100 feet of RG-8X (somewhat moe lossy) coax --- and may also indicate a less-than-pefectlylow-loss voltage balun. Remembe that highe losses make SWRs look bette! One autho went to fa as to suggest a manufactue of an end-loaded vetical antenna (fed by a high-tunsatio tansfome) chose high loss ion powde tooid in ode to make the SWR look bette! This homebew design attempts to ceate minimal losses --- but without a huge eseach budget we may not equal the highest quality commecial poduct. 4

5 OCF Cente Balun CONSTRUCTION INSTRUCTIONS: Building the 1:1 Cuent Balun. This is in effect a seies common mode inductance block fo unbalanced cuents. Nomal balanced desied RF cuents ceate NO magnetization of the coe! Only the undesied cuents magnetize the coe. We will use a high pemeability FT feite tooid fo this balun; you can even build with with steel bolt (but I don't ecommend it.) Ou constuction is simila to that of a commecially available MFJ device. 1. Ou goup poject kits will have an SO-239 aleady soldeed to appoximately 28 of two #18 teflon-coated, tinned wies. Pass the wies though the pe-dilled bottom 2 PVC cap (SO-239 on the outside) and secue the SO-239 with self-tapping #6 scews. Cove any shap points sticking out with small bits of ubbe tubing. 2. Using electical tape, tightly bind the two wies closely togethe. Make the tuns pitch of the tape lage so that you use minimum tape and don't add a lot of thickness. The goal hee is to have the ed and white wies expeience vitually the same field so that thei magnetic field cancel fo the desied opposite diection cuents in the two wies. 3. Stip the insulation fom appoximately 3/8 fom the ends. Teflon insulation is vey difficult to emove, use cae and shap stippes 4. Wap 12 tuns aound the FT coe. These will fit faily well and spacing isn't citical; you can bunch them up o spead them out. The fee ends will late connect to the VOLTAGE BALUN of you choice.. 1:1 cuent balun INPUT WIRES OUTPUT WIRES White to shield side of SO-239 White- to shield 50-ohm input of 4:1 o 6:1 balun (white wie) Red to cente conducto of SO-239 Red to cente conducto 50-ohm input of 4:1 o 6:1 balun (ed wie)11 See Appendix 1:1 Cuent Balun fo the explanation of how this balun woks. 5

6 OCF Cente Balun Build the Voltage Balun Choose eithe 4:1 o 6:1 step up atio Both ae basically auto-tansfomes. See schematics in this document. The 6:1 is the type utilized in the commecial B******** off cente fed dipole fed at the 33% mak; some people pefe the 4:1 (easie to build) balun, with feeding anywhee fom the 33% point to the 38% point. The 4:1 is much easie to build. The 6:1 may povide a bette match. NOTE ON FERRITE CORES Thee is a huge amount of both science and at to building these devices. Olde designs used ion-powde coes, but with thei much lowe pemeability losses could be highe on the lowe fequency bands. Ion powe coes toleate ove-poweing much bette than feites, howeve. Feites when diven past thei Cuie Tempeatue (point at which they lose all magnetic effects) can (upon cooling) not be the same exact popeties as they wee befoe the themal shock. While type 43 (vey high pemeabillity) coe may esult in lowe losses, it has a lowe Cuie Tempeatue of 130 deg C (still quite hot!!!) ; type 61 (high pemeability) has a much highe Cuie Tempeatue of 300 deg C. Theefoe I ecommend that Type 43 coes be used fo 100 W SSB max, and watts CW/digital --- to avoid ove heating them. If you want up to 200W SSB I suggest using the Type 61 feite coe. Building the 4:1 Voltage Balun This balun is a step up autotansfome with two windings same numbe of tuns in each (12) and wiing closely coupled fo best powe tansfe. Powe is applied to one of the windings (12 tuns) and the othe winding is then connected in seies with combining phase so that the antenna is fed fom 24 tuns --- twice the voltage, and ½ the cuent, hence 4 times the impedance. This balun will convet 200 ohms into 50 ohms, and you can actually test this with an antenna analyze and a 200 ohm esisto. If the wies become an appeciable potion of a wavelength, some undesiable phase changes can occu that can degade pefomance significantly. Theefoe, to obtain the widest possible usable bandwidth we use the cente connection of the two windings as the gound input, and one end as the cente-conducto input. See the APPENDIX: TRANSFORMERS & VOLTAGE BALUNS fo a futhe explanation of how these devices wok. 6

7 OCF Cente Balun 4:1 Schematic fo Entie B********-type commecial clone system with 4:1 Voltage balun and 1:1 Cuent Balun Take two 28 teflon coated wies, one ed and one white. Stip insulation fom appoximately 3/8 off the end of each wie. Tightly bind the two wies togethe with black electical tape. Leaving appoximately 2 fee, wind 12 tuns aound one of the FT tooids. Again the spacing isn't that citical. Have the beginning of the wies on the left side of you wokspace and the ending on the ight side of you wokspace. Connect the wies as follows: 4:1 Voltage Balun Left Side Right Side White wie goes to shield side White wie connects to Right hand output fom 1:1 cuent balun, and side of the antenna and also to cente also to the ed wie on the ight conducto output of the 1:1 balun.. hand side of the tooid. Red wie goes to the left hand side of the Antenna. Right sided Red wie to the left hand side white wie and the shield output fom the 1:1 balun. 7

8 OCF Cente Balun Building the 6:1 Voltage Balun This is actually a 6.25 step up auto-tansfome, but eveyone calls them 6:1. It has five windings, all closely coupled and of five tuns each. 6:1 B******** commecial Clone with 6:1 Voltage Balun and 1:1 cuent Balun All five windings will be wied in seies in this AUTOTRANSFORMER whee the pimay is pat of the seconday as well. The accompanying schematic is laid out to make it easie to see how to connect the wie --- but note that all the windings ae actually simply in seies, with inne taps being used to get the 50 ohm connection. The coaxial input will be wied to the 2nd and 3d windings, and the antenna will be connected fom the fathest end of the 1st and 5th windings. Theefoe the output voltage will be 5/2 of the input voltage, o 2.5 x input voltage. The output cuent then will be (1/ (2.5)) o 40% of the input cuent. With output voltage 250% of the input, and output cuent 40% of the input the output impedance (V/I) is (2.5/0.4) = 6.25 x the input impedance, and hence this is a 6:1 tansfome. 8

9 OCF Cente Balun In ou case we have five diffeent colos of wie but they ae not all the same thickness. At 100 watts, the cuent in a 300 ohm antenna is found this way: I * I * R = 100 watts I * I * (300) = 100 I*I = I = 0.57 ampees The smallest wie we have is #22 and is able to cay up to 5 ampees, so it will be completely sufficient fo powes into the many hundeds of watts ange. (Futhemoe, you can take two pieces of the #22 wie and twist them closely togethe with about 1 twist pe inch, connect the ends, and conside it as one thicke wie if you wish.) Eithe enameled solid wie, o vaious colos of Teflon-insulated wie can be used. Enameled wie has the advantage that it hugs the tooid vey closely once applied, but the enamel can be scatched --- if you choose to use enamel wie, wap the tooid with teflon (plumbe's) tape sufficiently to soften any shap cones. Fo the Alachua County LunchNLab we'll uses standed teflon coated wie of five diffeent colos. This insulation is pactically impevious! You'll need shap stippes to emove the insulation. Howeve, it is hade to get it to hug the tooid --- do the best you can. Cut five wies of inches length each. Stip just about 1/4-3/8 of insulation off evey end. 14 will wok, 15 will give you some exta length. Bundle them up (you don't have to twist, and they don't hold a twist vey well anyway) and wap tightly with black plastic odinay electical tape, going as fa linealy with each tun as possible you'e just tying to wap it, not make it any thicke! Wind five tuns aound the FT coe. Pick eithe diection and wind. Remembe that evey pass though the CENTER counts as a tun so it may look like 4 complete otations to you when it is 5 tuns. It tuns out you do NOT need to use the entie cicumfeence of the tooid, and you may actually get bette bandwidth/pefomance if you somewhat scunch the tuns up in 1/2-3/4 of the cicumfeence of the tooid. So do what whateve comes easiest and make the windings as easonably snug and tight as you can. Aange the beginning wie ends on the left and the ending wie ends on the ight of you wok space when you ae done. Then make the equied connections, as shown in the 9

10 OCF Cente Balun PHOTO below SCHEMATIC above and TABLE below. You can make those connections by just twisting the bae wies togethe and then soldeing befoe they fall apat. Insulate appopiately with eithe electical tape o shink wap. 10

11 OCF Cente Balun Schematic dawn to show how the windings fom a seies auto-tansfome. 6:1 Balun Connections Left connection WIRE COLOR/SIZE To left side of antenna (Please so mak) to ight end of blue wie and shield 50ohm input fom the 1:1 cuent balun to ight end of white wie Blue WHITE RED Right end connection To left end of white wie and shield 50-ohm input fom 1:1 cuent balun to left end of ed wie to left end of black wie and to cente conducto of 50 ohm input to ight end of ed wie and cente conducto of 50 ohm input BLACK to left end of GREENwie to ight end of black wie GREEN to ight side of antenna (Please so mak) 11

12 OCF Cente Balun CONNECTING THE VOLTAGE AND CURRENT BALUNS Place the 1:1 cuent balun you peviously built on the 50 ohm side of you voltage balun (eithe 4:1 o 6:1 ) and connect the two baluns togethe, using the coect connections as descibed peviously. Be cetain to connect the wies as detailed in the tables and in the schematics. PVC PHYSICAL CONSTRUCTION Glue the top cap to the 2 couple. The top cap will inset appoximately half way into the couple. Dill 3/16 o 7/32 holes in the top and two sides (slightly smalle than the 1/4 hadwae, but easy to twist the eye bolts into PVC) making cetain that a) the side holes ae such that the side hadwae will NOT touch the potuding top suppot bolt, but b) the side eye-bolts WILL go though both the couple AND the pvc of the top cap. These two side hold/eye bolts make the suppot physically vey stong. Inset the eye bolts. Use a stainless steel washe on the INSIDE and tighten up thei nuts fimly. Veify that all thei ends ae AT LEAST 1/4 away fom each othe. Antenna voltages won't jump 1/4 If you goof and they ae too close, eposition the holes and fill the pevious holes with caulk to make the assembly wate tight. We aen't going to use any of these bolts to make electical connections so they don't need to be coosion-fee stainless steel. The top bolt is to suspend the weighty cente insulato, and the two side 12

13 OCF Cente Balun bolts ae to take the tension (if any) of the antenna --- the electical connections will be made sepaately with tinned maine wie coming fom the baluns. Antenna wiing: Add appoximately 8 of maine tinned insulated #16 wie to each of the left and ight antenna voltage-balun outputs Dill appopiately sized holes (pobably 1/8 ) below the side eye-bolts, and pass the wies though. Wate seal the holes with RTV. I suggest to add male spade teminal lugs on each of these wies and SOLDER those connections against coosion. If you haven't done this step aleady: Run the input wies fom the 1:1 cuent balun though the hole fo the SO-239 connecto and solde, then mount the SO-239 with 4 #6 sheet metal scews. Befoe you seal the entie thing up fo good, put a 200-ohm (fo the 4:1) o 300 ohm (fo the 6:1) non-inductive esisto acoss the output and veify with an antenna analyze that you get a petty good SWR (< 1.5 desiable) acoss the fequency anges of inteest). If not, eview you wiing of the two baluns. FINAL ASSEMBLY I ecommend that you always install this balun/cente insulato VERTICAL with the coax end downwads, and that you dill a 1/8 dain hole in the bottom just to make sue that any collected moistue can get OUT. Stuff the two tooid coes into the cavity, with some electical tape, pieces of old ubbe inne tube, o something else non-conductive, non-feous and elatively non-combustible to keep them fom being damaged by the shap edges of the eye-bolts. You can also cove the eye bolts with ubbe tubing. The tooid coes ae faily self-shielding so exact oientation isn't that impotant. You can pack them in loosely with some shipping peanuts if you wish. It is pobably desiable to have at least a small gap between the two tooids. Secue the bottom cap with the SO-239 eithe by Gluing with pvc cement Scewed with two self taping scews chosen so as not to pesent shap edges on the inside o pinned with a thu pin on a chod of the cicumfeence 13

14 OCF Cente Balun ANTENNA WIRE WIRING FOR 80/40...bands Use 90 feet of wie on the left side tie it to the left eye bolt and then connect to the left 300 ohm output. I suggest using a female spade lug (and solde it). Use 45 feet of wie on the ight hand side --- tie it to the ight eye bolt and then connect to the ight 300 ohm output. Again, a female spade lug. Wiing Fo 40m/20m//// (no 80 mete pefomance) Use a total of appoximately 65 feet and inset the balun at the 33% point (22feet, 44 feet). END INSULATORS Can be made by cutting off 2-4 pieces of PVC pipe and dilling 1/4 holes, one side fo antenna wie (which may be tied, o soldeed) and the othe side fo suppoting ope. Ideally, aange in an inveted Vee fomation with the ends above head level to avoid possible ham to bystandes. (Relatively high RF voltages can be pesent at the ends of dipoles.) ADJUSTMENT Check SWR on desied band(s). This antenna is not likely to pesent a pefect 1:1 anywhee. It is moe likely to stay below 2:1 o 3:1 thoughout seveal bands. If you use low-loss coax, you'll see highe SWRs (because highe loss coax obscues the tue SWR). If the SWRs ae highe than you desie, use an antenna tune, o possibly adjust the lengths of the antenna INVOLVEMENT (Please check you choice) q q q Would like to come and watch/help (not build) Would like to build VOLTAGE BALUN (1-coe) only: Would like to build both BALUNs (2 coes) : $14 $18 NAME: REFERENCES: Extemely helpful discussion of voltage balun constuction with lots of expeimental data:

15 OCF Cente Balun Appendix: 1:1 Cuent Balun THEORY: The common mode inductance can be calculated --- common mode cuents have to tavesse 12 tuns of the winding aound a FT coe ( 140 = outside diamete = 1.4 inches; 43 = coe type, with a mu of about 885) You can use this online calculato: it calculates to 127 micohenies. Hee's the fomula: uh=(al*tuns2)/1000 AL = 885 Tuns = 12 uh = (885 * 12 * 12)/1000 = 127 mico henies Now 127 micohenies will have an inductive eactance (lowe at lowe fequencies, highe at highe fequencies). Ou WORST pefomance thus will be at 3.5 MHz. Hee's an inductive eactance calculato: Plugging in 3.5 MHz and 127 micohenies gives 2,793 ohms --- o 56 times the 50 ohms in the input cicuit --- so the common-mode RFI-inducing cuent will see almost 3,000 ohms, while the desied powe will see the nomal 50 ohms. That's how a 1:1 cuent balun woks --it puts a lage impedance in the path of the common mode (undesied) cuent. 15

16 OCF Cente Balun APPENDIX: TRANSFORMERS & VOLTAGE BALUNS TRANSFORMER: A tansfome tansfes electical powe fom a pimay winding to a seconday winding by way of inductive coupling. The pesence of a CORE with a highe MU than ai may allow fo bette coupling (highe powe tansfe) between the pimay and seconday windings. Howeve, the CORE may also induce additional LOSSES. Losses will be detectable by head poduced. Losses may also esult fom the ohmic esistance of the wies utilized. Typically one designs a tansfome so that the inductive eactance of the pimay winding by itself is significantly highe impedance than the appaent impedance ecognized when powe tansfe is occuing. In othe wods, when thee is no load on the seconday, one pefes to have the tansfome consume MINIMAL CURRENT in the pimay! (Othewise it is just wasting powe). The seconday windings may develop a highe o lowe voltage than that impessed upon the pimay. The atio of the seconday voltage to the pmay voltage will be the same as the atio of the seconday numbe of TURNS to the pimay numbe of TURNS of wie. Since powe is conseved, if the seconday dives a simple esisto, the cuents in the pimay and seconday will be INVERSE to that atio of tuns. Since impedance is voltage divided by cuent, the IMPEDANCE atio (voltage out/cuent out divided by voltage in/cuent in) will be elated to the SQUARE of the tuns atio. By this means one may aise o lowe a voltage, o aise o lowe an impedance. Fo example, a tansfome with twice the numbe of tuns of wie in the seconday as in the pimay will quaduple the impedance. If a 200ohm esistance is placed acoss the seconday, the pimay will appea to be a 50 ohm load. Depatues fom desied pefomance will be seen as vaiations fom this expected pefomance --- and can be epoted as SWR on the pimay side. AUTOTRANSFORMER In an autotansfoe, the pimay windings ae actually pat of the seconday windings a well --so thee is a DC path between the pimay and the seconday. The most common example of this has been the ignition coil in an olde spak-based gasoline engine. The ignition coil had a few tuns of wie to which an intemittently boken 12-volt cuent was applied, connected to a much lage numbe of tuns diving a spak plug. The magnetic field initiated and boken by the vaying cuent in the pimay winding induced a fa highe voltage in the seconday (but at a much educed cuent) and ceated the spak needed to ignite the fuel on each compession stoke. In this antenna, a 6:1 balun is utilized whee the seconday has 5 tuns fo evey 2 tuns of the pimay (voltage atio 2.5; impedance atio 6.25) but the pimay windings ae also pat of the seconday windings. This is called a VOLTAGE balun because the output VOLTAGE is consideed to be contolled by balun. Fo easons that ae beyond the scope of this discussion, the voltage balun diving a non-symmetical set of antenna wies, can esult in non-equal cuents at its two output teminals. (The output is not a simple esisto, but is instead two non-symmetical pieces of wie, each of which may be consideed to be its own sepaate and 16

17 OCF Cente Balun non-equal---antenna input impedances as each wie consumes and adiates powe! So the situation is consideably moe complicated than the simple esisto on the output of a tansfome.) CONCEPT: These non-equal cuents can be consideed as the sum of two equal and opposite cuents, plus a thid common cuent. Fo example, one output teminal may poduce 2A and the othe 1A, which is the same as Teminal 1 having 0.5 Amps, Teminal 2 having 0.5 Amps opposite diection and both teminals having 1.5 amps in the fist diection These add to poduce: Teminal 1 = = 2Amps Teminal 2 = = 1 Amps This common mode cuent is undesiable as it (o a cuent elated to it) can popagate down the OUTSIDE of the feeding coax and cause undesiable voltages and cuents on equipment supposedly all at equal gound potential. CONCEPT: While two pieces of equipment connnected by a gound wie to thei two chassis may be at nealy the exact same DC potential, things ae much diffeent if thee is a 7 MHz RF cuent flowing between the two pieces of equipment. In this case, 24 inches of wie may have a vey significant inductive eactance and thee may be a quite significant voltage dop acoss that 24 inches of wie, leading the two pieces of equipment to be at VERY DIFFERENT voltages evey few hunded nanoseconds! Gound isn't easy to find at shotwave fequencies!! Thus any cuent flowing in a gound wie is undesiable. This antenna design educes that common mode cuent (allowed by the VOLTAGE type balun) by inseting a CURRENT type balun (common-mode inductive impedance) into the system. The names VOLTAGE BALUN and CURRENT BALUN ae histoical in natue and ae an attempt to explain complex electical concepts in simple English wods. The key concept to know is that a VOLTAGE balun may allow feedline adiation and unbalanced cuents that can weck havoc with sensitive tansistoized digital equipment; and a CURRENT balun can educe o eliminate these issues. 17

18 OCF Cente Balun APPENDIX: Checking Flux Density REFERENCE: Fom: The following flux density limits fo both feite and ion powde coes can be used as an initial guide when making calculations fo coe size. 0.1 Fequency (MHz): AC Flux Density (gauss): Note: gauss = 1 Tesla = 1000 mtesla FT :1 Voltage Balun Bmax = (E * 102) / (4.44 * f * N * Ae) + (N * Idc * AL) / 10 * Ae Assume ohms ==> 71 V RF. Assume DC cuent is 0 (tems afte the + disappea) Now finding the values fo each of the potions of the equation (assuming 0 dc cuent) E = 71 Volts 100 watts. f = 3 (MHz) to 30 (MHz) (in fomula above, f is in MHz) N = numbe of tuns = 10 fo two cente windings in seies Ae = coss sectional aea in cm fo FT tooid is 1.6 cm*cm Bmax = 71 * 100 / (4.44 * 3 * 10 * 1.6) Bmax = 33 gauss which is quite acceptable! at 3 MHz Repeating fo 30 MHz: Bmax = 71 * 100/ (4.44 * 30 * 10 * 1.6) = 3.3 also well within limits. FT :1 voltage-balun Bmax = (E * 102) / (4.44 * f * N * Ae) + (N * Idc * AL) / 10 * Ae Assume ohms ==> 100 V RF. Assume DC cuent is 0 (tems afte the + disappea) 18

19 OCF Cente Balun Now finding the values fo each of the potions of the equation (assuming 0 dc cuent) E = 100 Volts 100 watts. f = 3 (MHz) to 30 (MHz) (in fomula above, f is in MHz) N = numbe of tuns = 10 fo two cente windings in seies Ae = coss sectional aea in cm fo FT tooid is 1.6 cm*cm Bmax = 100 * 100 / (4.44 * 3 * 10 * 1.6) Bmax = 46 gauss which is still quite acceptable! at 3 MHz 19