Designing Wide-band Transformers For HF And VHF Power Amplifiers

work is not practical for transformersthat go from balanced to unbalancedsources and loads (baluns) as theequivalent series inductances from theunbalanced port to the balanced portsare not identical.10To begin the process of designing thewide-band transformer into a matchingnetwork, we must first decide what sortof passband performance is desired, andthen select the appropriate filterprototype values from Table 1. Now,with reference to the componentreference designators of Fig 5, thedesign process proceeds as follows:101. Calculate the maximum usablefrequency ωmax using:ω max Lnorm RSLEQ1(Eq 16)where RS is the source resistance2. Calculate the value for the inputmatching capacitor C1 using:C1norm C11(Eq 17)ω max RS3. Calculate the value for the output matching capacitor C2 using:C1 n 2 C 2norm C 22(Eq 18)ω max RS4. If required, calculate the valuefor the capacitor C3 using:Magnetic MaterialsThe first concern in the design of awide-band transformer is the choiceof the magnetic material. Both ferriteand powdered iron materials can beused, but ferrite is preferred overpowdered iron as the losses are lower.Powdered iron is lossier because of thedistributed air-gap nature of thematerial,13 and the excessive losses notonly result in decreased gain performance, but in power amplifierapplications they also result inexcessive heating that can damageinsulating and PC board materials.There are three essential types offerrite materials that can be used forHF and VHF frequencies. These arelisted in Table 2. The first of these ismanganese-zinc (MnZn), which isgenerally suited for lower frequenciesand low power. Fair-Rite type 77material is an exception. It is availablein the form of E-I cores which can beused for high-power transformer coresat lower HF frequencies.The second, which will be discussedlater, and undoubtedly most populartype of ferrite is nickel-zinc (NiZn). Ofthe three NiZn materials listed inTable 2, the Fair-Rite types 43 and 61are by far the most widely because oftheir low loss, high saturation flux,and the wide variety of shapes andsizes that are available. They can bereadily used for both HF and VHFapplications, with the 61 materialbeing preferred for VHF. These twoferrites will be the focus of theapplications to be discussed later.The third type of ferrite suitable forHF and VHF applications is cobaltnickel-zinc (CoNiZn), available fromFerronics as types K and P. Theseferrites are available in a limitednumber of shapes and sizes. Toroidsmade from these materials can be usedto make transformer cores by stringing them along a brass tube in a frame,as will be discussed later. The onedrawback to this material is that it canbe permanently damaged if it issubjected to excessively high fluxdensities.10Transformer CoresThe ferrite materials mentioned inthe previous section are available in afairly wide variety of shapes such asrods, toroids, beads (or sleeves), E-IC2 C3 n C3normω max RS C12(Eq 19)Fig 7—High-power rftransformer core.Fig 6—Binocular core.Table 2—Commercial Ferrites Suitable for Power Amplifier ApplicationsManganese-Zinc (MnZn) 72000SaturationFlux (Gauss)4900LossFactor15UsableFrequency1 MHzResonanceFrequency2MHzNickle-Zinc (NiZn) 50325023503600855 MHz10MHz3225 MHz15 MHz50MHz25MHz50 MHz80 MHz60 MHz100 MHz850850125125Cobalt-Nickle-Zinc (CoNiZn) FerritesFerronicsK125FerronicsP406 Mar/Apr 200532002150

cores, and multi-aperture cores. Amongthe various multi-aperture coresavailable, there is one form, shown inFig 6, that is commonly referred to as a“binocular core” as the shape suggeststhat of a pair of field glasses. This shapeis available from numerous small sizessuitable for small-signal transformersto larger sizes suitable for poweramplifiers up to 5 W. Similar coresavailable from Fair-Rite having arectangular rather than an oval crosssection are available in larger sizessuitable for amplifiers of 25 W or more.Higher-power amplifiers requirecores with larger cross-sections that canaccommodate the higher flux densitiesin the magnetic material. For theseapplications, it is more suitable toconstruct a transformer core usingferrite beads (or sleeves) supported bya frame made from brass tubing andPC board material, such as those thatare available from CommunicationsConcepts and made popular by thenumerous applications notes and otherpublications by Norman Dye and HelgeGranberg.14,15,16,17 An illustration of aCommunications Concepts RF600 coreassembly is shown in Fig 7. Notice thatthe left-hand endplate has two separateconductors while the right-hand endplate has a single conductor. This ishelpful in forming a center-tap groundconnection in some applications. In anapplication to be described later in thedesign of balun transformers, it will beseen that there are times when it isadvantageous to dispense with thiscommon connection.The transformer core of Fig 7 canbe made for higher power levels byusing multiple ferrite beads along thesupporting tubes, such as the RF-2043assembly offered by CommunicationsConcepts. Such an assembly techniquecan also allow for the use of toroids toprovide a transformer core having alarger cross section or to provide ameans of using ferrite materials in theform of toroids when beads are notavailable as was mentioned earlier.side of the transformer is provided byway of a piece of insulated wire thatis passed through the tubes.There are at least two problems withtransformers constructed in thismanner, the first of which is the wirefor the unbalanced side of the circuitthat is exposed in the left-hand end ofthe assembly. The field created by thisexposed wire is not coupled to either thebrass tubes of the balanced side of thecircuit nor the ferrite material, and thisresults in excess leakage inductance.The second problem is that the couplingbetween the two sides of the circuit isnot uniform as the physical placementof the wire cannot be tightly controlled.This can lead to some small amount ofimbalance. Despite these problems, thisform of transformer remains verypopular in the design of amateur,commercial, and military HF and VHFpower amplifiers.For demonstration purposes, a 1:1balun transformer was constructed,using a Communications Concepts RF600 transformer core assembly, whichuses a pair of Fair-Rite 2643023402beads, made with type 43 material andhaving an inside diameter of 0.193 inch,an outside diameter of 0.275 inch, anda length of 0.750 inch.The performance for this balun,shown in Fig 9, is marginal at best. Theaverage insertion loss for HFfrequencies is in the neighborhood of 2dB, and the cutoff frequency is around4 MHz. At higher frequencies, theinsertion loss improves to 1.2 dB, buteven this is of questionable value. Theslowly degrading return loss is more aresult of the increased losses caused bythe ferrite material, as was evidencedby the fact that adding matching capacitors (see Fig 5) did little to improve theperformance. The increased transmission loss above 85 MHz is duemostly to the leakage inductancecaused by the exposed conductor on theleft-hand end of the assembly.Transmission-Line TransformersThe leakage inductance of the baluntransformer of Fig 8, however small, isthe limiting factor for higher frequencyperformance. To fulfill the need forwide-band transformers at higherfrequencies and power, coaxial cable isoften employed as the conductors. Sincethe coupling takes place between theinner conductor and the outer shield,there is very little opportunity for anystray inductance. This means that wecan anticipate good performance atFig 8—Conventional1:1 baluntransformer.Conventional Wide-bandTransformersThe most common method used inthe design of power amplifiers for HFand VHF frequencies is shown inFig 8. Here, a 1:1 balun is made usingthe transformer core previously shownin Fig 7. The balanced side of thetrans-former is provided by the brasstubes that support the ferrite sleeveswith the center tap being provided bythe common connection foil of theright-hand endplate and the and– terminals provided by the foil of theleft-hand endplate. The unbalancedFig 9—Conventional 1:1 balun transformer performance.Mar/Apr 2005 7

much higher frequencies, and it alsomeans that we can usually dispensewith the matching capacitors thatare often used with wide-band transformers.In the design of transmission linetransformers, the cable should have acharacteristic impedance that is thegeometric mean of the source and loadimpedances:Z0 ZS Z L(Eq 20)In most cases, the use of coaxial cablehaving the exact impedance is simplynot possible as coaxial cable is generallyoffered in a limited number of impedances, such as 50 and 75 Ω. Otherimpedances such as 12.5, 16.7, 25, and100 Ω are available, but usually on alimited basis for use in military andcommercial applications. Low impedances such as 6.12 Ω are difficult toachieve, although it is possible toparallel two 12.5 Ω cables, which isstandard practice.16 The insertion losswill increase as the impedance of thecoaxial cable deviates from theoptimum impedance of Eq. 20. For mostapplications, the effects of using cablehaving a non-ideal characteristicimpedance is not great as long as theequivalent electrical length of the cableis less than λ/8. In general, the lineimpedance is not critical provided thatsome degree of performance degradation is acceptable.16The equivalent electrical length ofthe cable is actually longer than thephysical length due to the electricalproperties of the insulating materialbetween the inner and outer conductors, and the relationship is:LE LP ε rFig 10—Transmission-line1:1 baluntransformer.Fig 11—Conventional vs. Transmission-line 1:1 balun transformer performance.(Eq 22)where µi is the relative permeabilityof the magnetic material. In general,a close approximation to the equivalent electrical length of the cable willbe a combination of Eq. 21 and Eq. 22,with the former applied to the lengthof cable that is outside the transformercore and the latter used for thatportion of the cable that is inside thetransformer core.The 1:1 balun transformer of Fig 8is now modified by replacing theinsulated wire conductor with an8 Mar/Apr 2005this design places the terminals for boththe balanced and unbalanced sides ofthe transformer on the same end ofthe core.Semi-rigid coax is also availablewith the same 0.141 inch OD, but it isdifficult to use when small radii arerequired. The solid outer conductoroften splits or collapses if the bendingradius is too small. Semi-flex will bendto smaller radii, but will still splitwhen an excessively small radius isattempted. A mandrel, such as youwould use when bending copper(Eq 21)where LE is the equivalent electricallength, L P is the actual physicallength, and εr is the relative dielectricconstant of the insulating material,typically 2.43 for PTFE. When thecable is inserted in a magneticmaterial, the equivalent electricallength is further lengthened by themagnetic properties of the material:LE LP ε r µiappropriate length of 0.141 inch OD50 Ω semi-flex coax cable, with a solderfilled braid outer conductor, as shownin Fig 10. Here, the cable is bent into aU shape and passed through the holesof the transformer core. The center tapfor the balanced side of the transformeris provided by soldering a wire to theouter conductor at the very center of thecurve. Because of the displacement ofthe center tap from the endplate, thecommon connection provided by thecopper foil on the right-hand endplate(see Fig 7) must be broken. Notice thatFig 12—Coaxialtransmission-line 1:1balun.

tubing, should be used at all timeswhen bending these cables to thesmall radii required. A great deal ofcare must be exercised, which is bestdone by first bending the cable to alarger radius and then slowlydecreasing the radius until it issufficiently reduced so as to passthrough the two holes of the core withlittle effort. This method reduces therisk of splitting the outer conductor byway of distributing the mechanicalstresses over a longer length of thecable. For transformer cores havinglarger hole diameters, larger coaxialcables such as RG-58 and RG-59 canbe used, provided the outer vinyljacket is removed.Fig 11 shows that the use of coaxialcable has done little to improve the lowfrequency characteristics of the 1:1balun transformer, however the highfrequency characteristics showsignificant improvement, especiallywith regard to the return loss. Withthe better coupling between the twocircuits, the losses induced by theferrite material have been reducedand a better match has been attained.Also, the lack of any appreciableincrease in the transmission lossabove 85 MHz indicates that theleakage inductance has been reduced,as was expected by using the coaxcable instead of wire for the conductor.Fig 13—Coaxial transmission-line 1:1 balun performance (-0102 cores).Transmission-Line BalunsReplacing the wire with coaxialcable in the 1:1 balun transformer ofFig 7 and Fig 10 helps the highfrequency transmission loss andreturn loss performance to somedegree. It does not, however, improvethe low frequency performance nor thetransmission loss. This is due to thefact that the coupling coefficient of thetransmission line transformer ishighly dependent upon the length ofcable used.Let’s take a broader look at the useof transmission line in the design of awide-band transformer. In this case,we’ll use a pair of 1:1 baluns as shownin Fig 12. We will use a length of 50-Ωsemi-flex cable as was used in theprevious example, but this timerequiring a tighter radius. The core forthe first of these transformers is a FairRite 2843000102 binocular core, and forthe second a Fair-Rite 2861000102binocular core is used to demonstratethe differences in the performance ofthe two ferrite materials. Theperformance of these baluns is shownin Fig 13. It is immediately obvious thatthere is room for improvement. First,the transmission loss is 1.8 dB for thetransformer using the type 43 materialFig 14—Coaxial transmission-line 1:1 balun performance (-6802 cores).Fig 15—Extended coaxial transmission-line 1:1 balun using e-cores.Mar/Apr 2005 9

and 1.5 dB for the type 61 material. Thecutoff frequency is 2.5 MHz for the type43 material and 11 MHz for the type61 material.Another pair of transformers wereconstructed, this time using Fair-Rite2843006802 and 2861006802 binocularcores, approximately twice as long asthe previous -0102 cores. As shown inFig 14, this increase in the length oftransmission line improves thetransmission loss to about 1.1 dB forboth materials. As expected by virtueof the longer line length, the cutofffrequencies are significantly lower, lessthan 1 MHz for the type 43 materialand 4 MHz for the type 61 material.Clearly, the longer length of coaxialcable has distinct advantages in termsof insertion loss and cutoff frequency.It would therefore appear obvious thatincreasing the length of the cable andferrite balun core further would resultin additional performance improvement. However, in the design of poweramplifiers we often encounter alimitation in terms of the amount ofphysical board space that is availablefor the various components.A solution to increasing the lengthof the cable without sacrificing valuableboard space is to form the cable into aseries of two or more loops and embedit into an E-core, a two-turn version ofwhich is shown in Fig 15.16,17 Here, sixpieces of ferrite E-core have beencemented together to form a single pieceof ferrite. The method of constructionis to first cement two sets of three piecesof core material together to form theupper and lower halves of the to becompleted core. Next, the cable isformed to the shape necessary to fitwithin the channels of the core. Finally,the cable is placed inside the channelsof one core half and the second half iscemented in place.The construction itself is fairlystraightforward, but implementing itonto a circuit board reveals a couple ofproblems, specifically the length of theleads for the two balanced ports areunequal and the coax loop on the righthand side interferes with the unbalanced and balanced positive terminals.At lower frequencies the inequality ofthe lead lengths will not presentsufficient imbalance in lead inductanceto create any problems, but withincreasing frequency the transformerwill become unbalanced and compensation will be required to offset theexcessive lead inductance, which will bedifficult to bring into balance. Anadditional constraint in the use of thisapproach is that the required E-coresare only available in the Fair-Rite type77 material, which is not well suited10 Mar/Apr 2005Fig 16—Extended coaxial transmission-line 1:1 baluns using binocular cores.Fig 17—Extended-length coaxial transmission-line 1:1 balun performance.Fig 18—Coaxial transmission-line 4:1 balanced transformers.

above lower HF frequencies. Even withthese shortcomings, the wide-bandtransformer approach of Fig 15 is wellworth consideration for applications atHF frequencies.An alternative approach is shown inFig 16. A pair of ferrite binocular coreshave been used in place of the E-coresof Fig 15. Here, both ends of the cablehave equal lead lengths, and there isno mechanical interference to be dealtwith. The construction presents no moredifficulty than before. The cable is firstformed into a U shape, then passedthrough the holes of the first, or upperbinocular core. The free ends of thecable are then bent back over the firstcore, and subsequently passed throughthe holes of the second or lower core.The two cores may then be cementedtogether to make the assembly whole.A pair of endplates similar to thoseshown for the left-hand end of thetransformer-core assembly of Fig 7 maybe used to hold the two cores togetherand to ease mounting the transformeron the amplifier PC board.A single example of the 1:1 baluntransformer of Fig 16 was constructed,using a pair of the longer Fair-Rite2843006802 binocular cores. The testresults shown in Fig 17 indicate thatfurther lengthening of the coaxial cablecontinues to improve the performance.A comparison of the three balunexamples using Fair-Rite type 43 ferritematerial is listed in Table 3, where thetransmission loss is as an average overwhat would be considered the usablefrequency range.Even with the lower transmissionloss of the balun transformer of Fig 16,this performance of the transmissionline balun transformer remainssignificant. When used as an outputtransformer in a power amplifier, thisexcess loss degrades the powerefficiency, which should be taken intoconsideration in the overall design.Fig 19—Coaxialtransmission line 9:1balancedtransformer.Fig 20—Twisted-wire capacitances.Fig 21—Two-conductor twisted-wire transformer configurations.Other Transmission-LineTransformersThere are many possible impedanceratios that can be realized usingtransmission-line transformers.Fig 18 shows two methods for makingbalanced transformers having animpedance ratio of 4:1.15,16,17,18 The firstof these makes use of a singlebinocular core, and it should beTable 3ConfigurationCutoffFrequencyDouble 2843006802 Core 1.1MHzSingle 2843006802 Core 3.9MHzSingle 2843000102 Core 11MHzInsertionLoss0.8dB1.1dB1.8dBFig 22—Three-conductor twisted-wire transformer configurations.Mar/Apr 2005 11

obvious from the examples shown formaking balun transformers that thecore should be as long as possible. Thesecond method makes use of the samebent cable design used for making theearlier baluns of Fig 12,18 and theextended length design of Fig 16 canalso be used here to conserve boardspace, decrease the cutoff frequency,and decrease the transmission loss.Fig 19 shows a method by which ab

wideband transformers are gener-ally understood to be distributed, but it is inconvenient to model transformers by way of distributed capacitances per se, so lumped ca-pacitances are used. In Fig 1, capaci-tor C 11 represents the distributed primary capacitance resulting from the shunt capacitance of the primary winding. Likewise, C 22 represents