In applications involving mixers andpush-pull rf power amplifiers, balunsare used for the transition from thesymmetrical to the asymmetrical sec-tion. Whilst for short-wave applica-tions a transformer can be used, manydifferent techniques are used for UHFapplications.

1.Introduction

In rf technology, baluns (balanced tounbalanced) play an important role. Inantennas, we need to guarantee a transi-tion from the coaxial line to the sym-metrical two-wire system with as littlereflection as possible. The same isneeded in the rf electronics itself, i.e. inthe designing of mixers and, in particu-lar, in push-pull power amplifiers. Agood overall view of various types ofbalun (even if it is not complete) can befound, among other things, in [1-3].A balun has to have the following char-acteristics:

• As precise a 180° phase shift aspossible must be maintained betweenthe two terminals of the symmetricalport.

• In power amplifiers, the impedance

presented to the symmetrical portmust be equal. If this is not the case,then there will be a decrease in theefficiency.

• The symmetrical port must be wellisolated from earth. This is especiallyimportant for power amplifiers, sinceparasitic oscillations can occur.

• The insertion loss should be kept aslow as possible.

When power amplifiers are used in classC, not only is an optimal loaded imped-ance needed at the operating frequency,but a very low-impedance load is neededat the second harmonic, with an opencircuit at the third harmonic, in order toobtain optimal amplifier efficiency [1].The basic idea behind the construction ofa balun can easily be outlined. Twosignals 180° out of phase (symmetricalport) are “synchronised” in their phasesand their outputs are added. Many de-signs involving λ/4 phasing lines (90°)and λ/2 phasing lines (180°) have crys-tallised out of this basic idea.Over time, a large number of designshave been collected. This article, though,will concentrate on designs that can berealised using no more than double-sidedprinted circuit boards, and that are usedfor applications in push-pull power am-plifiers. Naturally this implies the use ofmicrostrips and discrete components

Winfried Bakalski DL5MGY and co-authors

Baluns For MicrowaveApplications Part 1

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such as coils and capacitors. A line basedsolution will be discussed first followedby the LC balun and its further develop-ments.

2.The line balun with matchingnetwork

Fig. 1 shows the optimal design for apower amplifier balun in the range fromapproximately 400MHz to 1.5GHz.The actual balun is in this case a λ/4 longline section with a series connectedmatching circuit. The line balun de-scribed in [1, 3] (called a bazooka balunin [3]), we are normally dealing with asemi-rigid line with Zw = 50Ω. Thelength is precisely λ/4. As a rule we canstill not achieve optimal matching withthe line balun alone, an additional match-ing network is connected to it in series.This consists of a microstrip, with animpedance, Zw, of 50Ω and trimming

capacitors.Since power amplifiers are usuallymatched with a low load impedance, thisresults in a Zw which must be lower than50Ω (cf. λ/4 transformer equation). Theprecise impedance can thus be selected tohave another value, depending on thedesired input impedance of the balun.With CM and CE, the real and imaginarycomponents of Z0 can be set. The capaci-tors, CK, act as DC block capacitors. TheDC feed comes through two λ/4 trans-formers. This gives a short-circuit, at thesecond harmonic, at the two collectors ofthe rf transistors, because the λ/4 trans-former transforms a short-circuit into ashort-circuit again at double the funda-mental frequency, 2f0.An open circuit is achieved on the collec-tors of the rf transistors by means of aresonant circuit with CA at third har-monic, 3f0. This circuitry is required toachieve a high efficiency in non-linearoperation. Fig. 2 shows a 900MHz poweramplifier with an integrated circuit. ThisIC contains a push-pull power amplifierthat is set to a 50Ω output using the

Fig. 1: Line balun with matching network.

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circuit described above.This design has two disadvantages:-

• The electrical length of the λ/4 linesection must be guaranteed withinnarrow tolerances.

• The design requires manualcalibration.

The length of this λ/4 line also representsthe limit for the application at low fre-quencies, since this becomes longer asthe frequency decreases.If the frequency exceeds 1.5GHz, it isapparent that trimming capacitors arepractical up to a maximum of 1.5GHz,since better microwave trimming capaci-tors have their resonant frequency at 1 to2GHz. Thus this design is unusable forfrequencies exceeding approximately1.5GHz. On the other hand, it offers anoptimal load impedance, among otherthings, for the amplifier in that, even forthe non-linear application case (class C)even the harmonic load can also bematched. Thus this design can be used toachieve very high efficiencies, which is

not possible with fundamental frequencymatching alone.

3.The LC Balun

The LC balun [2, 5] is actually a bridgecircuit (Fig. 3) and is also referred to inEnglish speaking countries as a “lattice-type” balun. It made its first appearancein a patent document from 1934(C.Lorenz AG Berlin, Tempelhof )[5]. Itconsists of two capacitors and two in-ductances, which create a phase displace-ment of ±90° for each connection of thesymmetrical input.One very good characteristic of the balunis the ability to match any symmetricalinput impedance and any asymmetricalreal output impedance. Moreover, it isoutstandingly suitable for integration,and is therefore also used for smallerpower amplifiers (Fig. 4). We shouldalso look at the power supply of rf

Fig. 2: A 900-MHz GSM power amplifier module with line balun.

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transistors. If the whole assembly ismounted on a double-sided printed cir-cuit board, then the rf shunt can bereplaced by a radial stub [6-8] and thechoke by a λ/4 transformer with animpedance as high as possible.For calculation:1. First all impedances and the operatingfrequency are determined. Using the for-mula to calculate the circuit frequency:

Subsequently, the characteristic imped-ance of the bridge circuit can be deter-mined using the expression:

where R1 is the symmetrical input resist-ance from Fig. 4 and RL.2. Now the component part values aredetermined. For the typical case in whichreal impedances are used:

and:

For the inductances, L, we obtain theexpression

and for the capacitances

The important thing about this calcula-tion is that we are assuming that thecomponents are ideal and, more impor-tantly, that the connection lines are infi-nitely short. If we now construct such abridge for high frequencies (from500MHz), we should also take the con-nection lines into account. With a simula-tion tool such as Ansoft Serenade [S1] orEagleware Genesys [S3], this is done byinserting the appropriate microstripes(for tracks) and/or inserting computedinductances (1mm wire 1nH).We should also take care that the loadimpedance actually corresponds to reality(is the connection line, for example,actually 50Ω? what happens if a DCblock is used?) otherwise the aboveequations will not apply.When selecting component parts, weshould take care that we are operatingbelow their resonance frequencies whichbecomes more and more difficult as thefrequency increases. So it is recom-mended to use the S-parameter files fromthe component part manufacturer. Wesoon understand here that the lumpedcomponent parts used put an upper fre-quency limit on the design.Using microstrips as a replacement for

Fig. 3: The LC balun bridge in classical representation.

fπω 2=

Lc RRZ ⋅= 1

21 LLL ==

21 CCC ==

ωCZL =

CZC

ω1=

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the lumped component parts can be asolution:-An inductance can be realised by select-ing an appropriate ratio between the lineimpedance and the length. Likewise, acapacitance can be realised by using anopen circuit microstrip. A good rf short-circuit (rf shunt) can be created using aradial stub [6-8].

4.The Microstrip Based LCBalun [9]

With the knowledge that we can replacelumped component parts by microstrips,we can design a balun that makes use ofthese features. Fig. 5 shows such abalun:-In comparison with an LC-balun usingdiscrete component parts, this type ofdesign has a number of advantages:

Saving on expensive microwave compo-nent partsGreater freedom to design with a simula-tor (every miscrostrip is defined in termsof length and width). We can also obtaina low load impedance for the secondharmonic and an open circuit for thethird harmonic.A direct power supply feed for the powertransistors of a push-pull amplifier ismade possible through the line structure.The radial stub fulfils two tasks here:-

• Rf shunt for the power supply

• Defined shunt for the inductance L1A method for the calculations of thisbalun is available when using the exam-ple of Ansoft Serenade. The above balunhas been calculated and simulated for anoperating frequency of 2.45GHz andsymmetrical input impedance of 28Ω.The substrate used was Rogers RO4003,with a substrate thickness of 510µm andεr = 3.38.

Fig. 4: The LC-balun for a push-pull power amplifier.

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To determine the track widths it is best touse the “Transmission Lines” tool fromSerenade, or something similar such as,for example, Appcad [S2]. We obtain awidth of approximately 1.15mm. for a50Ω line.(To be continued)

A1.Literature References ForPart 1

[1] Mongia, R., Bahl, I. and Bhartia, P,RF and Microwave Coupled-Line Cir-cuits, pp. 321-322, Artech House, Nor-wood, MA 02062, First edition, 1999[2] Alois Krischke, K.Rothammel, Roth-ammels antenna book, Franck-KosmosVerlag, Stuttgart, 11th edition, 1995[3] Johnson, Richard C. and Jasik,Henry, Antenna Engineering Handbook,

McGraw-Hill, New York, Second edi-tion, 1984[4] S.A.El-Hamamsy, Design of High-Efficiency RF Class-D Power Amplifier,IEEE Transactors on Power Electronics,Vol. 9, Pp. 297-308, May, 1994[5] C.Lorenz AG Berlin-Tempelhof, Cir-cuit layout for transition from a sym-metrical to an asymmetrical electricallayout, in particular for high-frequencyapplications German patent, April 1932,no. 603816[6] Gunthard Kraus, Earthing in HF andmicrowave circuits, VHF Communica-tions 3/2000 pp 167 - 178[7] J.R.Vinding, Radial line stubs aselements in strip line circuits, NeremRecord, Pp. 108-109, 1967[8] Agilent Technologies (previouslyHewlett-Packard), Broadband microstripmixer design the butterfly mixer, AgilentTechnologies Application Note, (http://www.agilent.com), Vol. 976, Pp. 4 6,1988

Fig. 5: Microstrip LC balun for the 2.45GHz ISM band with a differentialinput impedance of 28ΩΩΩΩ . (Substrate: Rogers RO4003 with εεεεr = 3.38 and athickness of 0.510mm.).

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[9] W.Bakalski, W.Simbürger, H.Knapp,A.L.Scholz, Lumped and DistributedLattice-type LC-baluns, Proceedings ofthe International Microwave Symposium(IMS2002) Seattle, June 2002

A2.Software on the internet

[S1] Ansoft Serenade 8.5: http://ww-w.ansoft.com, A restricted student ver-sion is available[S2] Appcad 2.0: http://www.agilent-.com/, This is a freely available tool forall possible calculations involving elec-trical engineering and metrology

[S3] Eagleware Genesys: http://ww-w.eagleware.com, Not to be confusedwith the Eagle CAD program from Cad-soft. You can also, from time to time,find a demo version of the EaglewareGenesys Suite on this page

A3.Co-authors:

Winfried Bakalski DL5MGY, HerbertKnapp OE1RNC, Werner SimbürgerOE6RUD, Arpad L.Scholtz OE4SZW

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VHF CommunicationsBlue Binders

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Continuation

To determine the track widths of amicrostrip-based LC balun [9], it is bestto use the “Transmission Lines” toolfrom Serenade, or something similarsuch as, for example, Appcad [S2]. Herewe obtain a width of approximately1.15mm. for a 50Ω line.

4.1. Dimensioning of an ideal LCbalun in accordance with Section 2:For the load RL = 50Ω and a differentialinput impedance of R1 = 28Ω, we obtaina characteristic impedance of

Thus with f = 2.45GHz, we can use theformulae (1) to get the values for C =1.73pF and L = 2.43nH. Fig. 6 shows theSerenade circuit diagram for the firstsimulation run and Fig. 7 shows theresult, which reproduces a differentialfeeding of the balun with two idealtransformers (S33). To ensure that thisdifferential impedance does not arise dueto complete asymmetry of the two con-nections, the two connections for thedifferential input must be individuallyinspected for two-port balance. With asymmetrical resistance of 28Ω, this givesthe termination through 2 x 14Ω (port 1(S11) and port 2 (S22)). We can alreadyrecognise the phase displacement by 90°

of connections 1 and 2 on the Smith chart(Fig. 7) whilst perfect matching is ob-tained differentially (port 3).

4.2. Substitution of concentratedstructural elements:First the substrate wavelength is deter-mined for the simulation:

wherefop is the operating frequency andεr,eff the effective permittivity.An estimation with εr,eff ≅ εr as startparameter is completely adequate for thefollowing simulation, but the calculatedlengths will all depart somewhat from thephysical lengths.Substitution of L1 [1]:

Winfried Bakalski DL5MGY

Baluns for microwaveapplications - part 2

Ω=⋅= 4.371 LC RRZ

00

1µεε

λ⋅⋅⋅

=reffop

op f

θω tan01 ⋅= ZL

<

49090 opoo λ

θ

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If we select Z0 = 38Ω for this, we obtainfor

With the relationship tan (45°) = 1, weobtain the length of the microstrip, sincecorrespondingly.

The length is calculated using λop =67mm at

as the start parameter for the followingsimulation.Substitution of C1 [1]:The substitution of the series capacitanceis not possible unless a λ/4 phasing lineis used. Since a line of this kind of lengthwould lead to a severe limitation of the

Fig. 7: Impedances of LC balun: S11 and S22 represent the impedance of aconnection to earth in each case. Note the 90° phase displacements of S11 andS22.

138

43.245.22tan ≈Ω

⋅⋅= nHGHzπθ

oop 458

=λ

mmmmL 3.88

671 ≈=

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operating bandwidth of the balun, thiscapacitance is retained as a separatestructural element. In the course of thesimulation, it will become clear that thefeed inductances (tracks) lead to a reduc-tion in the capacitance initially calcu-lated. The reason for this lies in the phasedisplacement by the connection lines andinductances (e.g. caused by bond induct-ances in chip capacitors, but also by theinductive element of the capacitor itself).

Substitution of L2 [1]:

The inductance obtained from the LCbalun corresponds to that from L1. Sincefor this application the stripline length islimited by the layout, we must select a

Fig. 9: Simulation result following substitution.

θω sin02 ⋅= ZL

=<

49090 opoo λ

θ

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higher value for Z0 here, which is ex-pressed in terms of a thinner stripline. If,for example, an impedance is selected ofZ0 = 72Ω (corresponds here to a width of0.6mm.), then using the above expressionwe obtain:

and using arcsin (0.5) = 30°, this gives usa microstrip length of approximately5.6mm.

Substitution of C2 [1]:

The substitution of the capacitance, C2,can be very simply accomplished byusing an open microstrip. If, as in L1, we

02

tanZ

C θω =

<

49090 opoo λ

θ

Fig 10 : Balun simulation results.

5.072

43.245.22sin ≈Ω

⋅⋅= nHGHzπθ

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select an impedance, Z0 = 38Ω, then weobtain

and this gives a length of 8.3mm. as thestart parameter.

4.3. Optimising of substitutedelementsSince the calculated values due to the useof εr,eff = εr represent only start param-eters (εr,eff is actually dependent on boththe track width and the frequency), theLC balun must be further optimised.However, this step need not be carriedout so intensively, since some furtherdisplacement can be brought aboutthrough the use of the T-pieces. AnsoftSerenade can calculate a Smith chartwhich is identical to that of the LC balun(Figs. 8 and 9).

4.4. Insertion of T-pieces andmatching of layout to geometricalrequirementsWe should proceed by stages here, andincorporate and simulate one T-pieceafter another into the circuit diagram.The incorporation of such T-pieces has avery strong influence on the behaviour ofthe bridge (alteration of microstriplengths) and because of the large numberof variables it becomes even more diffi-cult to optimise the situation. Fig. 10

shows the resulting overall circuit dia-gram, with a DC feed for the high-levelstage transistors of the power amplifier.Fig. 11 shows the final results of thematching circuit.

4.5. The dual-band LC balun [9]It would often be an advantage if theBalun could be used for any two differ-ent frequency ranges simultaneously (e.g.for 2m and 70cm band applications).This is in fact possible if a parallelresonant circuit is used instead of theinductance, L, and a series resonantcircuit instead of the capacitance, C (Fig.12).The bridge now exhibits interesting fre-quency dependent behaviour, as can beseen from Fig. 13.For frequencies which are lower than thefrequency of resonance of the resonantcircuit, this balun behaves like a standardLC balun. If the frequency is increased,then the roles of the capacitance and theinductance are reversed. If the bridge isre-designed to become a push-pull poweramplifier for the application, then weobtain the circuit diagram shown in Fig.14. This already contains the powersupply feed. For frequencies exceeding2GHz, the use of radial stubs is recom-mended, in addition to capacitors withhigh nominal values.

13873.145.22tan ≈Ω⋅⋅⋅= pFGHzπθ

Fig 12 : LC balun bridge with common impedances.

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For the calculations of the dual-bandbalun, the following procedures can bespecified:1. First all impedances and the operatingfrequencies are established. The circuitfrequencies are calculated, using the for-mulae

The characteristic impedances of thebridge circuit can be calculated using

This makes it clear that even frequency-dependent load impedances can bebrought into play for the calculations.2. For Ls, Lp and Cs, Cp, the followingexpressions are

It is again very important to note thatthese expressions are valid only for idealstructural elements. i.e., for a real layoutboth the feed sections and the parasiticelements of the structural componentshave to be taken into account. In realstructures, this will mean the resonantcircuits have to be “stretched” in theirfrequencies of resonance.Thus the use of S-parameter files is just

Fig 13 : Behaviour of LC balun with frequency.

11 2 fπω = and 22 2 fπω = ( )12 ωω >

LC RRZ ⋅= 11and

LC RRZ ⋅= 22

21

22

2211

ωωωω

−⋅+⋅= CC

SZZL

2211

2

1

1

221

CC

CC

p ZZ

ZZL

⋅⋅⋅

−⋅⋅

=ωω

ωω

ωω

1221

2

1

1

2

CCS ZZC

⋅⋅⋅

−=

ωωωω

ωω

( )21

2221

1221

ωωωω

−⋅⋅⋅⋅⋅=

CC

CCp ZZ

ZZC

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as important in the simulation as theprecise entering of the layout into thecorresponding simulator. Stage by stageinsertion of line sections and T-pieces isrecommended, as is already done withLC-baluns based on microstrips.

5.Bibloiography

[1] Mongia, R., Bahl, I. and Bhartia, P.RF and Microwave Coupled-Line Cir-cuits, pp. 321-322 Artech House, Nor-wood, MA 02062 First edition, 1999[2] Alois Krischke, K.Rothammel Roth-

Fig 14 : Dual band LC balun.

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ammels antenna book Franck-KosmosVerlag, Stuttgart 11th edition, 1995[3] Johnson, Richard C. and Jasik, HenryAntenna Engineering Handbook Mc-Graw-Hill, New York Second edition,1984[4] S.A.El-Hamamsy “Design of High-Efficiency RF Class-D Power Amplifier”IEEE Transactions on Power Electronics,Vol. 9, Pp. 297-308, May, 1994[5] C.Lorenz AG, Berlin-Tempelhof Cir-cuit layout for transition from a sym-metrical to an asymmetrical electricallayout, in particular for high-frequencyapplications German patent, April 1932,no. 603816[6] Gunthard Kraus Earthing in HF andmicrowave circuits VHF Communica-toions, issue 3/2000 pp 2-8[7] J.R.Vinding Radial line stubs aselements in strip line circuits NeremRecord, Pp. 108-109, 1967[8] Agilent Technologies (previouslyHewlett-Packard) Broadband microstripmixer design the butterfly mixer AgilentTechnologies Application Note (http://www.agilent.com) Vol. 976, Pp. 4-6,1988[9] W.Bakalski, W.Simbürger,H.Knapp,A.L.Scholtz Lumped and DistributedLattice-type LC-baluns Proceedings ofthe International Microwave Symposium(MS2002) Seattle, June 2002

6.Software On The Internet:

[S1] Ansoft Serenade 8.5: A restrictedstudent version is available http://ww-w.ansoft.com[S2] Appcad 2.0: This is a freely avail-able tool for all possible calculaitonsinvolving electrical engineering and me-trology http://www.agilent.com/[S3] Eagleware Genesys: Not to be con-fused with the Eagle CAD program fromCadsoft. You can also, from time to time,find a demo version of the EaglewareGenesys Suite on this page http://ww-w.eagleware.com

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