Baluns: What They Do And HowThey Do lt By Roy lV. Lewallen,* IVTEL eurrentsin the two conductorsto be imbalaneed, that is, other than equal and opposite. If this *5470 SW 152ndAve., Beaverton,OR 97007 happens,the balanced feed line will radiate like a coaxial cable that has current on the outside of the I've always been a bit botheredby balunst shield. This occurs becausethe eomponentsof the since I was never sure what they are supposedto dot currents on the two conductors that are equal and let alone hotv they might go about doing it. The opposite create fields whieh cancel. But the field majority of articles deal with various ways of from any remaining eomponent on either eonductor building and testing baluns, or the advantagesof (cailed a eommon-mode,seeondary-mode, or antenna one type over another,but almost never a word about current) will cause radiation.\4.5.6In this ar- when or why a balun is neeessaryrif at all. Like ticle, the eurfent on the outside of the coaxial most amateurs,there have been few occasionswhen I shield, or the antenna eurrent on the twin lead, have been able to tell if a balun has any effect on will be ealled the imbalanee current: They are an antennasystem, and when it has, the effect caused by the same things and produce the same hasn't alwaysbeen good! The turning point came when effeets. I was trying to measurethe resonantfrequency of a Imbalanee eurrent, on either kind of line, is folded dipole through a one-vravelengthcoaxial line. the cause of a number of undesirable effects: The bridge null varied a great deal as I moved my o pattern distortion (caused by the feed-line hand around the coaxial cable, or if the line or radiation adding to the antenna-radiatedfield, bridge was moved. A hastily eonstructed balun in- or by unequal currents in the antenna halves) stalled at the center of the dipole eliminated the o TVI (radiation from a feed line coupling into problem.But why? nearby television sets, house wiring, and so I found a brief, but clear explanation of one on) rrhottt phenomenoninvolved in a paper by lllaxwell' W2DU.U o RF in the shack (eaused by a radiator - - However,many questionsremained. This led me to an the feed line residing in the shack) investigation of just how baluns are supposedto If you have read other articles on baluns, youtll work, and what problemsthey are supposedto cure. recognizethese as the problemsbaluns are supposed One surprisingconclusion I found from my research to solve. What isntt usually too clear is that they is that one popular type of balun' when properly are all caused by eurrent imbelanss, on either designedand used in an antenna system, may not eoaxial or twirrlead feed line. Of eourse, if the solve the probiems that baluns &re expected to imbalance current is suffieiently small to begin solve. Other results indicated that the type of feed with, a balun is not necessaryat all. Or it ean be Iine (balancedor unbalanced)has little to do with said that a properly designedbalun will not solve how well a system is balanced.ln order to verifyt the problem being experienced. or refute, the theoretical results, several What Causes S5ntem Imba-lance? experiments were earefully set up and run, and the data analyzed. The result is a much elearer view of The first eause of i mbalanee currents was the operationof balunsin antennasystems, and some explained by I\4axwell.It will be repeated here for definite t'dosttand t'donttst'regarding their use. completeness.When a balancedantenna is fed with eoaxial eable (Fig.1), the outside of the shield appearsas an extra, separateeonductor conneeted to What Prpblems ale Baluns fupposed to Solve? the right side of the antennaat the feed point. The Baluns usually solve problems caused by an cunrent in the cablers center conductor flows into imbalance. An imbalance of what? To answer this the left half of the dipole. The equal and opposite question,we need to look at current flow in eurrent on the inside of the shield flows partly transmissionlines. into the right half of the dipole, and partly along In a coaxial cable, the curents on the inner the outside of the shield. The proportion of current conductorand the inside of the shield are equal and which flows eaeh way is determinedby the relative opposite. This is because the fields from the two impedancesof the two paths. The current on the eurrents are confined to the same spaee.\2 With the outside is the greatest when the total effective presence of skin effeet, a different current flows length of the path along the outside of the eoaxial on the outside of the shield than on the inside.\] eable from the antenna to ground is an integral The current on the outside,if significant,causes number of half wavelengths,since this makes the the feed Iine to act like an antenna, radiating a impedancepresented by the undesirable path field that is proportionalto this current. relatively low. If the rig is effectively an odd A twin-iead feed line has similar properties, number of quarter wavelengthsfrom actual ground,it despiteits different physical nature. Since it is is at a voltage maximumand can be hot. On the other physieally symmetrical, if the currents flowing hand, there are other combinationsof lengths for through the conductorsare equal and oppositerthe which the imbalance current will be negligible - radiation from the line is minimal (assumingthat cases where a balun does not make any notieeable the conductor spacing is very small relative to a difference. wavelength).However, several factors may cause the The obvious solution to this problem is to feed

157 Current to ri -o..qhf ha'l f -- y' of dipole

Tnnan fanndrrnl-nn Current = CUrrenI to left half of dipole Current on outer surface of shield

Rte Current on

inner surface ts^r1a | )nd ^f ^Li ^t i UI JTTIgf,U AnnAcl to currents

Fig. 1 -- Inbalance causd by arrother path to ground frorn only one side of the dipoJ-e. - providing the balanced antenna with a balanced feed line 5).\g This type is commonly used for twin lead. This solves the problem neatly, until you single-endedto differential conversion for driving It encounter the problem which most of us have todayt balanced mixers, push-pull amplifiers, and so on. illustrated in Fig. 2. Suppose that we went ahead seems to be suitable for our purpose. An analysis of and connected the line as shown schematically in its operation (see Appendix 1) shows that it does Fig.3. If the rig could be totaUy isolated front indeed perform an unbalanced-to-balancedcon- ground, the feed-line conductor currents would be version. The voltages at the balanced port are -qual and opposite, just as they would be if coaxial caused to be equal, and opposite, in phase relative cable were used; the imbalance current would be to the cold side of the unbalanced port. Thus, the zero, and the feed line would not radiate.\1. use of this sort of balun will eliminate the problem However,when we connectthe rig to ground,as shown of current flow on the outside of a line only if tbe by the broken line, wetve again provided a third antenna is perfectly ba-laaced. There is nothing conductor in parallel with the right side of the gained by forcing the voltages of the two antenna feed line, and the same problem occurs as with the halves, whether balanced or not, to be egual and coaxial cable (see Fig. 4). So either type of line opposite relative to the cold side of the balun is unbalanced if a direct path to ground is provided input (usuaUy connected to the shield of a coaxial from one side, and both can be a balanced, non- feed line), since the antenna field is proportional radiating line if the imbalance current is eli m- to the cunents in the elements, not the voltages at inated. the feed point. I will call this type of balun a Imbalance current can be eaused also by voltage balun to emphasize that it balances the situations where the two sides of the antenna are output voltages regardlessof load impedances. not precisely symmetricall Coupling to nearby ob- jects, tne tilt relative to ground, or slight dil- ieren"es in lengths of the two antenna halves.\8 Another cause of imbalance currents is induction. lf the feed line is not exactly placed at a right angle to the antenna, a net current is induced into it by the antenna fieid. This current appears as an im- balance current. At UHFr where the diameter of c oaxial cable is a substantial fraction of the length of the antenna elements, coaxial line is more difficult to place symmetrically relative to the antenna than twin lead is (ttris is sometimes given as the only reBson for using a balun!). The problem is negligible at VHF (except perhaps with very Iarge diameter coaxial cable) or below. What Baluns Do Letts recall what we want a balun to do: cause the currents in the feed-Iine conductors to be equal FLg. 2 - Ore solution to the inba-Lance probJ-en in magnitude and opposite in phase, resulting in a is to feed the balanced antenna with a balanced zero imbalance current. IIow well do the popular feed line - twirr 1ead. balun types do this? One type of balun is known as a transformer- type balun- or balun with a tertiary winding (Fig.

158 cable, it ean be visualized as an RF choke aeting only on the outside of the coaxial-eable shield, reducing the current to a very small value. This is the exact function a balun needsto aecomplishwhen used in an Bntennasystem. A current balun can be constructed by winding coaxial feed line into a coil, winding either type of feed line onto a core, or by stringing ferrite cores along either type of line.\I[ Even if the balun is mediocre, there wilL be no effect on the desiredproperties of the line itself (impedance, eleetrical length, SIVR, and so on). A less- than-perfect voltage balun ean have a profound effect on the impedanceseen at its input beeauseof the tertiary winding. Impedance-transforming(4:1) I balunsare discussedin Appendix3. I I H-7 Fig. 3 -- If the rig were isolated fronr gror.rnd, the feed-line conductor currents would be equal and opposite, the jnbalance current would be zero and the feed ]i-ne would not radiate.

Fig. 5 - Voltage balun (see text). The bottom winding is sometires referred to as a tertiary winding. AlJ- windings are cl-osely coupled. w OUT IN Lr.lJ"A/ . Fig. 6 -- Current bafun (see text). Both windings are closely coupled.

Erperiments A series of experiments was designedto test the validity of the results of the theoretical investigation. A 10-meter dipole was set about 12 feet above the ground,and about five feet abovethe edge of an elevated woodendeck (Fig. ?). One-half wavelengthfrom the eenter of the dipole, a 4-foot Fig. 4 -- Wlrenthe rig is connected to ground, _ rod was driven into the ground,whieh was eompletely a ihirO conductor in para1le1 with the right side saturated with water at the time the experiments of the feed ]lne is introduced. This causes an were run (during November, in Oregon).To further imbalance in both coaxial cable and twin lead lower ground-systemimpedance, six radials were feed thes. placed on the ground around the ground rod. Two feed lines were eut to a half wavelength:one of RG-S9/U Another type of balun that appears in the coaxial eable, and one of 72-ohm transmitting twin literature has been called a choke-type balun (Fig. lead. The velocity factors of the eables were not 6).U-0 It resemblesthe voltage balun, exeept that taken into aceount,since the intent was to have the the tertiary winding is missing. The analysis of outside of the coaxial cable, or the two parallel both types of balun in Appendix 1 shows that the conduetorsof the twin lead, be an electrieal half- effect of a tertiary winding is not a minor one. The wavelengthlong. A low-power 10-meter transmitter two types of baluns produce fundamentally different loeated at, and conneetedto, the ground system was results. The voltage balun causes equal and opposite used as a signal souree. voltages to appear at the balanced port regardless Current probes and baluns were built as de- of load impedanees,but the second type of balun seribed in Appendix 2. Two of the eurrent probes eausesequal and opposite currents on the conductors were permanentlywired into each side of the dipole at both ports for any load impedanees.For this near the feed point, and a third was used for all reason, I will call this type of balun a curent feed-line measurements.A single detector was used balun. Intuitively, the cument balun produces the for all measurements,and it was calibrated over the sort of effeet we would expect. When wound with range of encounteredoutput Ievels by using a signal twisted pair or twin lead, it is nothing but & source and precision attenuator. The results of the bifilar RF choke that impedesany net eurrent which experiment have been corrected to aeeount for the tries to flow through it. When wound with coaxial measurednonlinearity of the deteetor.

159 No attempt was made to keep the power level or impedance match constant from one test to another. When running an experiment with no balunr a current balun, and a voltage balun, the only -variation in the system was to change the balun. Initially' the inteni was to use the antenna current probe readings as a measure of cument balance in the antenna halves. However, a case was encounteredin which tbe antenna halves showed equal currents, but a large imbalance current was measured in the feed line at the antenna feed point - a seemingly intpossible combination! (Tne equal antenna currents were even more suspiciousbecause no balun was being used, and 7,-7- the antenna had intentionally been made nonsym- metrical for that test.) A bit of thought provided the answer. The imbalance current is measured by placing the feed Iine through the current-probe ioroid-. In conjunction with the detector, it measuresthe magnitude of the vector sum of all currents flowing through the toroid. Each antenna current probe, with the deteetor, measurestbe Fig. 7 - Experirental setuP. magnitude of the current in each half of the an- point. What must be happeningis tenna, at the feed e"l. 5 in the dipole halves are equal in that the currents ino barun !.1 magnitude,but not 180 degreesout of phase.A check of the current-probe outputs with a good-quality dual-channel oscilloscope confirmed the hypothesis: {1 The currents were 230 degrees, rather than 180 degrees,apart, althoughequal in magnitude.What an interesting pettern that dipole would have! But this illustrates how misleading the magnitudesof element Hltl currents can be when judging balance. Measuringthe l*j imbalancecurrent in the feed line at the feed point tti ' .q does, however, provide a good indication of the ._i currents in the antenna halves. If balance of the -- il the imbalancecurrent is very small, the currents in Fig. 8 Setup arrd results of experirnents 1 k{ the sides of the antenna must be nearly equal in and 5. Nwbers are r€asured bal"ance in de. tu4 magnitude and opposite ih phase. A significant im- balance current, on the other hand, indicates that Discussion one or both conditions have not been met. If dipole balance (sYmmetry) were indeed Measurementof the imbalance current on the the perfect for experiment L, we would expect the feed line also indicates how much the feed line will curents in the sides of the dipole to be unbal- radiate. The imbalancecufrent at the rig providesa resulting in imbalance current on the feed measure of RF in the shack. In the following testst anced, line. This is because the outside of the eoaxial the magnitudeof the euruent w&s measuredin each H shield appe&rs as a conductor in parallel with half conducior, then the magnitudeof the imbalance of the dipole. Also, either a current or voltage current was neasured by placing the complete feed balun should reduce the imbalance - rnt to zero. line through the current-probe toroid. A single Since the feed Iine is placed symmetrically relative w1hd figure of merit, balance, was calculated as: jr rll no additional current should be l',.'! to the antenna, ii: ':1 induced into the feed line, so the imbalance should quite small at the end of the line when Gverage of nagnit also be of currents in each either type of balun is used. With the nonsymmetrica-dipole (experiment 5)' = ffi balance (dB) 2o rog we would expect the voltage balun to do worse than in experiment f. iVe would also expect the current balun to do about the same, and the no-balun case to ffi be considerablyworse. ffi Experiments 1 through 4 were- done using a nominally symmetrical dipole, although results Results fi1F'i indicate that some asymmetry was present' For ex- voltage balun did not 5 through i, the dipole was intentionally In experiment 1r the Hrj feriments perform as well as the current balun, indicating $,i t"O" nontymmetricalby lengtheningone side by five *i some asymmetry in the dipole. At the frequency inches, anb shortening the other side by the same chosen, the small differences in connections and a amount. slight tilt of the antenna could easily account for Bperiments I and 5: what happened. When no balun is usedr a curious much better balance at the rig end See Fig. 8. The dipole was symmetrical for result is the than at the antenna end of the feed line. This may experiment 1, nonsymmetricalfor experiment 5' be because the feed lines werenrt exactly an ef- fective half wavelength longr because there was a ffi 160 t;. I wire of about six inehes in length conneeting the erp. 3 .xp. 7 4.8 0.3 rig to the ground system' or because the feed line 3.J was doubled baek on itself for a short distance near l9.l 14.5 the rig to provide strain relief. Perhaps the doubling baek generated enoughinduetance to cause a eurrent balun, or RF choking effect. The better 13,4 t 0.4 12.5 balance at the rig end can be seen in the results of all experiments. l.3.4 10.4 The no-balun result was worse with the non- L2,O 33.7 symmetrical dipole than the symmetrieal oner 8s expected, and the current balun did about the same in both cases. The voltage balun, although slightly - worse with the nonsymmetricalantenna, was better Fig. 10 Setup and results of experinents 3 than expected, but still definitely inferior to the and 7. Nmrbers are neasured balance in dB. cument balun. these experimentsshould be similar to those of the Bperiments 2 and 6: previous pair. See Fig. 9. The dipole was symmetrical fon Results: experiment 2, nonsymmetriealfor experiment 6. With no balun, the results were those of ex- Discnssion periments 1 and 5 (the test with no balun was not The results of these experiments should dupli- rerun). With the current balun, the results were cate those of the previous pair, sinee the feed line similar to those of experiments2 and 6, indieating is placed symmetricaily relative to the antenna to that coaxial cable can be used as a balanced feed avoid indueed current. The only difference is that line (in the sense diseussed earlier) with a bal- the balun is placed farther down in a symmetrical or anced or somewhat-unbalancedload. This data also nonsymmet.riealsystem. points to the possibility that a eurrent balun could be added to an existing antenna system at the rig end of the line, with results similar to those Results obtained by plaeing it at the antenn&, in some cases The trend is clearly the same as in experiments at least. This would certainly be worth a try in 1 and 5; the current balun provides the best bal- systemswhere the symptomsindicate tfe need for a ance, the voltage balun is seeond best, and a feed balun, but the antenna itself is diffieult to get line with no balun is the worst case. The balance to. With the symmetriealantenna, the voltage balun with no balun was better in this experimentt made balanee worse at both ends of the feed line however, (except at the rig end with the non- than no balun at all. The balanced port of the symmetrical antenna,whieh was about the same),and voltage balun sees two unequal impedancesto ground: the balanee at the rig end was substantially better the eoaxial center conduetor, ending in one dipole whenusing the current balun.Time did not permit me half, and the eoaxial shield terminating in the to run additional experiments to explain these dif- other. The shield is eapabie of radiating but the ferences, but the ability of the current balun to inner conduetor isnrt, and the two are of different achieve superior balance was again illustrated. diameters, aceountingfor the different impedanees. The voltage balun predictably generates unequal currents in the different impedances,eausing exD. 2 -ex^ t additional current imbalanee. A voltage balun was io balun 9,1 2,7 voltate balun not evaluated in this applieation with a non- current bal,un 21.3 I9. 5 symmetrical dipole, having shown distinctly inferior results even with a svmmetrical one.

balun 17.3 9,8 l-no Eperiment 4:

161 exp' 4

L!aBe balun 0, I balun 28.8 o1 balun 3.5 balun 26.4 n.l.h^6i D^-+

17.3 'rColdi'Side

41.6 The Yoltage Balun - Because of transformer sction, V1 - V3 = Y2 \,tb = - term comes about because Fig. U - SetuP and resufts of experi:rent 4. Yfi Vl. The third in AEr ntertiary'r winding shown at the bottom. llr-rrbers €rre lreasurd ba].ance of the - iearranging the last two- terms, v2 - v0 = {vl (the the cold the voltage balun, but with the moderate (unin- V0). So-relative to V! voltage at port), voltages at the tentional) irnbalance presented by the actual an- side of the unbalanced the tenna, the curent balance on the feed Une was balanced port are equal and opposite. winding seriously degraded. This configuration isnrt likely The current It flowing in the tertiary -([ + - (Ie - to be used in actual practice, but helps illustrate is, by inspection, lb I.2) and also - = (Ic - Because of the the operation of the baluns and feed lines. tt), s6 {Ii- + I0 12) I1). property of coaxial cable discussedin the body of - Conclusiors ihe- arficle, Ii = -Ier so Ic - I9 + 12 = Ic 11; Although some aspects of the experimental thus 16 = 11 + 12. So for the cument on the out- currents results remain to be explained (as they always will side of the shield, I!, to be zerot load be unless performed under extremely controlled I1 and 12 must be equal and opposite. Since Vl and eonditions)r they certainly support the theoretical V2 are forced to be equal and opposite relative to this analysis. The current balun gave superior balance at Yfit the only way f or I1 and 12 to f ulf ill side of every measuredpoint in each experiment. The voltage requirementis for the impedancesfrom each balun improved balance in most cases, explaining its the balanced port to the cold side of the unbalanced perfectly balanced acceptance in spite of the theoretieally and exper- port to be equal. Thus, onIV a the imentally demonstrated superiority of the current ioao will cause no current on the outside of balun to cure the problems we have discussed. coaxial cable. Ironieally, if this does occurt As always, finding the answers to questions current It = B, and the tertiary winding accom- generates yet more questions. Lack of time did not plishes no function. feed line placed non- permit experiments with the The Curent Balun symmetrically with respect to the antenna, to induce imbalance current into the feed line. The results of ln an ideal transformer of two windings having such an experiment should be interesting and en- an equal number of turns, the currents in the Iightening. windings are forced to be equal and opposite. So Ic -Ier - Is there an optimum point in the feed line to = -(Ii + Io). Again, Ii = so Ic = Ic Ior place a balun? Supposethe effective distance along resulting in Io = !. This result is independent of the feed line/ground wire from the antenna to ground the load impedances. And, since the load currents is an integral number of half wavelengths, and the are the winding currents, they are also equal in balun is placed a quarter wavelength below the an- magnitudeand oPPositein Phase. tenn&, as sometimesrecommended. Wouldnrt the im- If the balun is constructed by winding coaxial balance current be conducted as before? lVould in- cable on a core or into an air-core coil' or by duced cunent, if present, be reduced? Whatts the stringing ferrite beads on the outside' the oper- effect of poor coaxial shield coverage? ation can be understoodby observing that the inside t'canrt More work needs to be done in evaluating the of the coaxiel cable tellt whatrs going on - various styles of current baluns (such &s coaxial outside. The currents on the inside equal and cable wound into a choke, coadal cable wound on a opposite happen regardless of the outside en- ferrite or powdered iron core, insertion of the feed vironment, but the construction eauses a high tine through one or more ferrite coresr and so on) impedance to current flow on the outsider acting for their primary characteristie: causing currents like a choke to the imbalance current (hence the to be equal in magnitude and out of phase. The appropriate name choke balun). When constructed of method Irve used is briefly described in Appendix 2' twisted-pair line, the effect on imbalance current but how good is good enough? is the same and for the same reasons,but operation The basic investigation reported here does is more dif ficuit to visualize. answer some of the major questionsregarding baluns. The current balun I now know what symptoms I can expect a balun to cure, why it will (or wontt!) cure them, how to predict and measure the balunrs success in doing so, and what type of balun to use. I hope you dor too! Appendix 1: A Brief Analysis of Balun Operation Analysis of both balun types assumes I'idealx operation: All flux is linked to all windings (coefficient of coupling is one), and each winding has sufficient self-impedanceto make the mag- netizing current negligible.

L62 Appendix 2z Construetion and Test of Baluns, Appendix 3: Impedanee-Transforming (4:1) Baluns Curent Probes and Deteetor The common 4:1 balun, shown sehematically in Yoltage Belun Fig. A3-1, is a voltage balun. If used with a eur- The voltage balun was constructed using the rent balun as in Fig. A3-2, the combination acts methoddeseribed in Ref.8. A piece of no.26 wire like a 4:1 current balun. Or it can be converted to was laid along a length of RG-178/U cable (smal]- a 4:1 transforming eurrent balun by adding a third diameter Teflon-insulated eoaxial cable), and winding, as shown in Fig. A3-3. A 1:1 voltage balun heat-shrinkable tubing was applied over the assem- could be eonverted to a 4:1 current balun by re- bly. The modified cable was wound on an FT82-61 core eonnecting the existing windings. The difficulty using ten turns. This construetion method was with using this eonfiguration is that, Iike the 1:l decided on after trying to wind a balun with two voltage balun, all windings must be elosely coupled, pieces of coaxial cable in bifilar fashion, the and rather severe impedance changes ean occur be- shield of the seeondbeing connectedas the tertiary causeof transformer imperfections. winding. The latter construction method was much A better approaeh is shown in Fig. A3-4. Old- poorer in providing good voltage balanee. timers will recognize this as the eonfiguration used Voltage balance was evaluated by eonnecting the by the balun eoils commonly used some years ago. cold side of the unbalancedport to a ground plane This balun does foree equal and opposite cuments at and the balanced port to two resistors of unequal the input and output, so it is a true current balun, value, the other endsof whieh were connectedto the and it performs a 4:1 impedaneetransformation. Al- same point on the ground plane. Using resistors of though it does require two cores whieh must not be 27 and 54 ohms, the ratios of voltages appearing at coupledr* it has several advantages: Itrs much the two resistors were measured as about 3/4 and easier to tightly couple two eonductors than three, L-1/2 dB, dependingon which resistor was connected itrs mueh more forgiving than the other config- to which lead of the balaneedoutout. urations, and it lends itself to easy construetion. One method is simply to wind eoaxial eable on two Current Balun cores, with the center conductors being the con- The current balun consisted of 15 turns of duetors shown on the outsides in the figure. This RG-1?8/U coaxial eable on an FT82-61 core. Per- balun can also be used in all-eoaxial-cable systems. formanee was evaluated by connecting the output end Besides effecting a 4:1 impedanee transformation, it to 27- and 54-ohm resistors to ground, and measuring will greatly reduce any current flowing on the out- the voltages across them. A properly working current sides of the lines. balun should generate twice the voitage aeross the 54-ohm resistor than aeross the 2?-ohm resistor, * If ferrite rods or air-core coils are used, regardlessof whieh lead is eonneeted to eaeh donrt plaee them end to end. Place them side by side resistor. The results were within 0.2 dB of theo- and spaced a fair distance, or, better yet, at right retical, with either lead connected to either angles. Less eare needs to be taken with toroidal resistor. eoils. Cument Probe The current probes were constructed as shown in

Fig.12. The output voltage equals ten times the ui-L ? LLL6LL-L current, in amperes, being measured.Insertion Low-Z Unbal-anced resistanceis one ohm. Unbalanced Deteetor The detector is shown in Fig. 13. It was # precision ealibrated using a signal source and - attenuators, at the operating frequency. Calibration Fig. A3-1 The 4:1-vo:.tage balun. using a dc source was found to be inaceurate.

FT82-43 ferrite core H{ -L t

Low-Z

curtent-carryinB conductor lo oe neasured

Fig. A3-2 - The 4:1 vottage baLun used with a

bifilar lurns on FT37-72 feraire core 1;1 current balun.

detec!or Fig. 12 - Current probe.

DNCnale !o curlent probe I -Cemaniw diode r.t-tT--f-- No other connectlons .ool ro Dvlt (10 Hetolh inpu! resistance) Y = ,PaF to this polnt.

Fig. A3-3 - A 4:1 current bal"un. Fig. 13 - Detector.

163 \1 A very clear developmentof the phenomenonof skin effect may be found in Chapter 7 of Elee tric Tlansmission Lines by Hugh H. Skilling (McGraw-Hill,1951). Hi oh-7 \4 Winningstad,C. Norman, "NanosecondPulse Transformers,rr IRE tlansactions on Nuclear Scierrce,March 1959. \1 Matick, Richard E., I'TransmissionLine Pulse Transformers - Theory and Applicationrr Pto- eeedingsof the IEBE' Vol. 56, No. 1' Jan. 1968. \s Hall, Gerald L.' KITD, ed., The ARRL Anteruu Fig. A3-4 - A superior 4:1 current ba-l_un. Book, 14th ed., Chapter 5, (ARRL' 1982). V In practice, there is always an RF path from the rig to ground, and its impedanceshould be made References as low as possible. The rig should alwal's be de t'Some grounded for safetY. U Maxwell, Walter, W2DU' Aspectsof the p. \8 See Ref. 6. Balun ProblemrttQST, March 1983, 38. "High-Performance If a perfect shield is assumed(a reasonable \a Nagle, John J., K4KJr \2 p. 28. approximation for this analysis),the result BroadbandBalun," IIam Radio, Feb. 1980, Law. For a more See Ref. 1. follows directly from Amperers u-0 "Simple detailed explanation, see Electromagnetic Energy \u Reisert, Joe, WlJR, and Efficient p. Tlansmission and Radiation, by Richard B. Adler, BroadbandBalun,r' Ham Radio, Sept. 1978' Lan Jen Chu, and Robert M. Fano(Wiley, 1960). 1t The article of Reference 1 above is available at http://www.w2du/r2ch21.pdf

Thisarticle was publishedin the ARRLAntenna Compendium, Vol. 1 , copyrightO 1985 bythe American Radio Relay League, Inc. Reproduced by permission.

164