AN1034

1RF Application InformationFreescale Semiconductor

Three Balun Designs for Push-PullAmplifiersSingle RF power transistors seldom satisfy today’s design

criteria; several devices in separate packages1, or in the samepackage (balanced, push-pull or dual transistors), must becoupled to obtain the required amplifier output power. Sincehigh power transistors have very low impedance, designersare challenged to match combined devices to a load. Theyoften choose the push-pull technique because it allows theinput and output impedances of transistors to be connected inseries for RF operation.Balun-transformers provide the key to push-pull design, but

they have not been as conspicuous in microwave circuits asat lower frequencies. Ferrite baluns2 have been applied up to30 MHz; others incorporating coaxial transmission linesoperate in the 30 to 400 MHz range3.The success of these two balun types should prompt the

microwave designer to ask if balun-transformers can beincluded in circuits for frequencies above 400 MHz. Theoryand experimental results lead to the emphatic answer: yes!Not only will baluns function at microwave frequencies, but aspecial balun can be designed in microstrip form that avoidsthe inherent connection problems of coax.On the next six pages, you will observe the development of

three balun-transformers — culminating with the microstripversion. None of the baluns was tuned nor were the parasiticelements compensated. In this way, the deviation of theexperimental baluns from their theoretical performance couldbe evaluated more easily. The frequency limitations imposedby the parasitic elements also were observed more clearly.1. A balun transforms a balanced system that is

symmetrical (with respect to ground) to an unbalancedsystem with one side grounded. Without balun-transformers,the minimum device impedance (real) that can be matched to

50 ohms with acceptable bandwidth and loss is approximately0.5 ohms. The key to increasing the transistors’ output poweris reducing this impedance ratio. Although 3 dB hybridcombiners can double themaximum power output, they lowerthematching ratio to only 50:1. Balun transformers can reducethe original 100:1 ratio to 6.25:1 or less. The design offersother advantages: the baluns and associated matchingcircuits have greater bandwidth, lower losses, and reducedeven-harmonic levels.

A 500-W Push-Pull Amplifier for DME Band

180

OUTPUTMATCHINGNETWORK

50

50180

OUTPUT BALUN(BALANCE-UNBALANCE)

TRAN-SISTORS

INPUTMATCHINGNETWORK

INPUT BALUN(UNBALANCE-BALANCE)

00

Figure 1.

AN1034Rev. 0, 7/1993

Freescale SemiconductorApplication Note

Freescale Semiconductor, Inc., 1993, 2009. All rights reserved.

2RF Application InformationFreescale Semiconductor

AN1034

2. Baluns are not free of disadvantages.Coupling a pairof push-pull amplifiers with 3-dB hybrids avoids (forfour-transistor circuits) one of these: the higher broadbandVSWRs of balun-transformers. A second disadvantage, thelack of isolation between the two transistors in each push-pullconfiguration, is outweighed by the advantages of the balundesign in reducing the critical impedance ratio.3. In this simple balun that uses a coaxial transmission

line, the grounded outer conductor makes an unbalancedtermination, and the floating end makes a balancedtermination. Charge conservation requires that the currentson the center and the outer conductors maintain equalmagnitudes and a 180-degree phase relationship at any pointalong the line. By properly choosing the length andcharacteristic impedance, this balun can be designed tomatch devices to their loads. In the case shown, if A = 90degrees, the matching condition is:

ZA2 = 2 x R x 50.

4. By adding a second coaxial line, the basic balun canbe made perfectly symmetrical. In this symmetrical coaxialbalun, the bandwidth (in terms of the input VSWR) is limitedby the transformation ratio, 50/2R, and the leakages, whichare represented by lines B and C. If ZA = 50 ohms and R =25 ohms, the bandwidth is constrained only by the leakages.

Experimental Version of a Simple BalunUsing Coaxial Lines

50

500

-- 90

QUAD--RATURECOMBINER

0

-- 90

INPUT(LOW VSWR)

OUTPUT(LOW VSWR)

QUAD--RATURECOMBINER

Figure 2.

V

(a) COAXIAL BALUN DESIGN 1

--V

R

R

(b) EQUIVALENT CIRCUIT

R

R

LINE A

LINE A

LINE B

50

50

ZP

LINE A: ZA, ALINE B: ZB, BZP = jZB TAN B AND ZP & R

Figure 3.

SYMMETRICAL COAXIAL BALUN (DESIGN 1)

R

R

LINE A

LINE B

50

LINE A: ZA, ALINE B, LINE C: ZB = ZC; B = C

LINE C

Figure 4.

AN1034

3RF Application InformationFreescale Semiconductor

5. The equivalent circuit for the symmetrical balunshows the effect of the leakages (lines B and C) on itsperformance. A broadband balun can be obtained by using arelatively high characteristic impedance for these leakagelines. In theory, the construction of the baluns insures perfectbalance.

SYMMETRICAL BALUN EQUIVALENT CIRCUIT

RRLINE A

50 LINE C

LINE B

Figure 5.

6. The symmetric balun’s input equivalent circuitfurther simplifies its configuration and allows the input VSWRto be calculated.4 In this design, line A has a characteristicimpedance of ZA = 50 ohms, a length of LA = 1799 mils, anda dielectric constant (relative) of r = 2.10. For lines B and C,Z0 = 30 ohms, L = 1799 mils, and eff = 2.23.

SYMMETRIC BALUN INPUT EQUIVALENT CIRCUIT

RLLINE AA

50

LINE BB

LINE AA: ZAA = ZA; AA = ALINE BB: ZBB = 2ZB; BB = BRL = 2R

Figure 6.

7. The theoretical input VSWR has been calculated for50-ohm values of ZA and 2R, and for two other sets of valuesfor these parameters. The performance of an experimentalbalun will be compared with these theoretical results.

THEORETICAL INPUT RESPONSE OFTHE SYMMETRIC BALUN (DESIGN 1)

3:1

ZA = 102R = 2ZA = 25

2R = 12.5

ZA = 502R = 50

2.5:1

2:1

1.5:1

1:10.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

INPUTVSWR

FREQUENCY -- GHz

Figure 7.

4RF Application InformationFreescale Semiconductor

AN1034

8. Two /16 line-section Chebyshev impedancetransformers match the experimental balun to a 50-ohm

measurement system. The balun was tested from 0.6 to1.5 GHz.

EXPERIMENTALCOAXIAL BALUN (DESIGN 1)

WITH OUTPUT TRANSFORMERS

25

/16 LINE-SECTIONCHEBYSHEV IMPEDANCE

TRANSFORMERMICROSTRIP

LOAD25 LINESMICROSTRIP

BALUNCOAXIAL/

MICROSTRIP

R

R

LINE A

LINE B

50

LINE C

LINE E LINE F

LINE D LINE E LINE F

25

LINE D

FOR LINE A: Zo = 50 L = 1799 MILS; r = 2.10LINES B AND C: Zo = 30 L = 1799 MILS; eff = 2.23LINES D AND D: Zo = 25 L = 750 MILS; eff = 2.23LINES E AND E: Zo = 61.5; L = 464 MILS; eff = 2.10LINES F AND F: Zo = 20.3; L = 441 MILS; eff = 2.31

Figure 8.

9. The measured phase difference and insertion lossdifference, which indicate the maximum unbalance for theDesign 1 experimental balun, are 3 degrees and 0.2 dB,respectively.

BALUN MEASURED PERFORMANCE FOR DESIGN 1

185

180

175

0.5

0

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

PHASEDIFFERENCE

--0.5

FREQUENCY -- GHz

--DEGREES

0.6

INSERTIONLOSS

DIFFERENCE--dB

Figure 9.

10. The maximum VSWRmeasured for the first designis 1.5:1. Note the comparison between the calculated andmeasured response. The performance shown can beconsidered valid for amplifier applications up to an octaverange.

BALUN PERFORMANCE FOR DESIGN 1

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

INPUTVSWR

FREQUENCY -- GHz0.6

2:1

1.5:1

1:1

CALCULATED MEASURED

Figure 10.

AN1034

5RF Application InformationFreescale Semiconductor

11. The second balun design adds two identical coaxlines to the simple balun just described. The inputs of theidentical lines are connected in series to the output of the firstbalun. By putting their outputs in parallel, the final outputbecomes symmetrical. The output impedance is halved.

LINE B AND LINE C: IDENTICAL

SECOND SECTIONFIRST SECTION

R

RLINE A

LINE B

50

LINE CLINE F

LINE D

LINE E

LINE G

LINE D AND LINE F: IDENTICAL

LINE E AND LINE G: IDENTICAL

COAXIAL BALUN DESIGN 2

Figure 11.

12. The equivalent circuit for the Design 2 balunindicates that its bandwidth, in terms of input VSWR, is limitedby the transformation ratios of the first and second sectionsand the leakages represented by lines B, C, E, and G. If thebalun is designed with ZA = 50 ohms, and ZD = ZF = 25 ohms,and if the load, 2R, is set at 2 x 6.25 ohms, all of thetransmission lines will be connected to their characteristicimpedances. In this case, the bandwidth will be limited by theleakage alone, and a broadband balun can be obtained bychoosing lines B, C, E, and G with relatively high impedanceand /4 length for the center frequency. The balun achieves atransformation from 50 ohms to twice 6.26 ohms withoutcausing a standing wave in the coaxial cables.

DESIGN 2 BALUN EQUIVALENT CIRCUIT

R

LINE F

50

LINE ELINE C

LINE D

R

LINE A

0

H

180 180

LINE GLINE B

I

0

Figure 12.

13. The performance of the Design 2 balun can becalculated using its equivalent circuit. The calculatedVSWR shows a response very close to the simple coaxialbalun (Figure 10) because the new second section has fourtimes the bandwidth of the first section. This design and its twocompanions are intended to have octave bandwidthscentered at 1.1 GHz, the central frequency used in distancemeasuring equipment (DME, 1.025 to 1.150GHz) and tacticalair navigation (TACAN, 0.960 to 1.215 GHz). For line A: ZA =50ohms, LA=1799mils, r = 2.10; for linesB,C, E, andG: Z0 =30 ohms, L = 1799 mils, eff = 2.23; lines D and F: Z0 =25 ohms, L = 1799 mils, r = 2.10.

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

INPUTVSWR

FREQUENCY -- GHz

2:1

1.5:1

1:1

2.5:1

THEORETICAL INPUT RESPONSE OF THE COAXIAL BALUN (DESIGN 2)

Figure 13.

6RF Application InformationFreescale Semiconductor

AN1034

14. Two /4 transformers match the experimentaltwo--sectlon coaxial balun’s 6.26-ohm impedance to the50-ohm load. Although these transformers drastically reducethe bandwidth (in terms of the VSWR), they don’t affect thebalance.

Two-section balun often used in the 100- to400-MHz range

SECONDSECTION

FIRST SECTION

LINE A

LINE B50

LINE CLINE F

LINE D

LINE E

LINE G

EXPERIMENTAL BALUN (DESIGN 2) WITH TRANSFORMERS

FOR LINE A: ZA = 50; L = 1799 MILS; r = 2.1LINES B AND C: ZB = ZC = 30; L = LC = 1799 MILS; eff = 2.23LINES D AND F: ZD = ZF = 25; LD = LF = 1799 MILS; r = 2.1LINES E AND G: ZE = ZG = 30; LE = LG = 1799 MILS; eff = 2.23LINES H AND H: ZH = ZH = 25; LH = LH MILS; eff = 2.23LINES I AND I: ZI = ZI = 17.7; LI = LI = 1772 MILS; eff = 2.30

LINE H

LINE H

LINE I

LINE Z

50

50

6.25

6.25

CONNECTION25 LINESMICROSTRIP

/4TRANSFORMERMICROSTRIP

LOAD

Figure 14.

15. The measured phase difference and measuredinsertion loss difference are plotted for the two-sectioncoaxial balun (Design 2). The maximum unbalances forthese two measurements over the octave bandwidth are1 degree and 0.2 dB.

DESIGN 2 BALUN MEASURED PERFORMANCE

185

180

175

0.5

0

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

PHASEDIFFERENCE

--0.5

FREQUENCY -- GHz

--DEGREES

INSERTIONLOSS

DIFFERENCE--dB

Figure 15.

AN1034

7RF Application InformationFreescale Semiconductor

16. The calculated and measured values for the inputVSWR for the Design 2 balun show close agreementbetween the experimental and predicted performances. Thisindicates that the parasitic inductors at the connections arenegligible to at least 1.4 GHz. Moreover, the balun hasexcellent balance to 1.4 GHz and achieves the 4:1transformation without causing a standing wave in the coaxialline. Despite the many excellent qualities of the Design 1 andDesign 2 baluns, the necessary coaxial line connection limitsthem to approximately 2 GHz.

DESIGN 2 BALUN PERFORMANCE

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

INPUTVSWR

FREQUENCY -- GHz

2:1

1.5:1

1:1

:CALCULATED :MEASURED

3:1

2.5:1

Figure 16.

17. The problems associatedwith the previous coaxialbaluns can be reduced or eliminated by using a balun thatallows a microstrip coplanar arrangement of the input andoutput lines, which greatly simplifies the connections to theamplifier. This balun5 consists of an input line, A, connectedin series to three elements in the center of the half-wavelengthcavity: a reactive open-circuit stub, B, and the /4 output lines,C and D. LINE A LINE B

LINE C

LINE F

LINE D

LINE E

INPUT

DESIGN 3 COAXIAL BALUN

/4/4

OUTPUT

E (0) E (180)

OUTPUT

BALUN JUNCTIONCAVITY

ZC = ZD AND ZE = ZF

Figure 17.

18. The equivalent circuit of the Design 3 coaxialversion balun shows lines C and D connected to place theirinput signals in antiphase, thereby producing two antiphasesignals at their outputs. Transmission line impedances andlengths are optimized to achieve the correct input/outputtransformation ratio and a good match across the desiredbandwidth. If only one frequency or a narrow bandwidth isdesired, and all lengths are /4, thematching condition ZA2/50= 2ZC2/R, will occur. In this case, ZE (ZE = ZF) and ZB have nosignificance except for loss.

BALUN EQUIVALENT CIRCUIT (DESIGN 3)

R50

LINE C

R

LINE F

LINE B

LINE AE (180)

E (0)

LINE D

LINE E

Figure 18.

8RF Application InformationFreescale Semiconductor

AN1034

19. The coplanar arrangement of input and outputlines can be accomplished with mlcrostrip technology.The uppermost conductor plane contains input line A, outputlines C and D, and the open stub B. Coupling between theselines is avoided by separating them by at least one line width.The middle conductor carries the ground plane for the lines.To avoid radiation loss, the center conductor must extend atleast one linewidth to either side of the upper plane circuit line.The balun resonant cavity is formed by the region between themiddle and the lower conductor planes. A hole for the cavity

is cut in the circuit fixture, filled with dielectric, and coveredwith the middle conductor plane. The end-to-end length of thecavity is nominally a half-wavelength at midband. To avoiddisturbance of the field distribution, the cavity width must beat least three times the width of the middle conductor plane.The arms of the balun cavity are folded to produce two paralleland proximate output transmission lines. This configuration ismore suited to coupling two transistors than the original layoutin which the two outputs were on opposite sides (Figure 17).

MICROSTRIP BALUN (DESIGN 3)

LINE A

LINE CINPUT

/4

OUTPUT

E (0)

E (180)

OUTPUT

BALUNJUNCTION

MIDDLE CONDUCTORPLANE

MIDDLE CONDUCTORPLANE

CIRCUITFIXTURE

CAVITYDIELECTRIC

CIRCUITDIELECTRICCAVITYLINE DLINE B

LINE F

LINE E

/4

Figure 19.

20. The input equivalent circuit for the microstripversion of the Design 3 balun allows its theoreticalperformance to be calculated. The design parameters shownprovide a microstrip circuit that can be compared with thecoaxial baluns of Design 1 and Design 2. Transmission line Aand lines C and D are loaded by their characteristicimpedances — in this case, 50 and 25 ohms. The cavity andthe stub impose the principal frequency limitation. Theimpedances of these elements are dictated by the propertiesof the available dielectric substrates (glass-Teflon 0.020 and0.0625 inches thick).

INPUT EQUIVALENT CIRCUIT (DESIGN 3 BALUN)

RL

LINE CC

LINE BB

LINE AA LINE DD

FOR LINE AA: ZA = 50; L 1888 MIL; ff = 2.10LINE BB: ZB = 25; L 1810 MIL; eff = 2.23LINE CC: 2ZE = 35.8; LE = 1772 MIL; ff = 2.33LINE DD: 2ZD = 50; LD 1546 MIL; eff = 2.23

RL 2 X R = 50

Figure 20.

AN1034

9RF Application InformationFreescale Semiconductor

21. The input VSWR can be calculated based on theequivalent circuit for the microstrip balun. For a one-octave bandwidth, the input VSWR is lower than 1.75:1. Thiscalculated performance is similar to that of the two previousbalun designs. The design of the microstrip has theoreticallyperfect balance.

THEORETICAL INPUT VSWR OF MICROSTRIP BALUN (DESIGN 3)

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

INPUTVSWR

FREQUENCY -- GHz

2:1

1.5:1

1:1

2.5:1

1.5

Figure 21.

22. The equivalent circuit of themicrostrip balun showsthe balun during performance measurements with /16matching lines. The experimental model uses 18-milglass-Teflon (r = 2.55) for the tap circuits and 62.5 milglass-Teflon for the cavity. Balance properties weremeasuredwith a 50-ohm system, which was transformed to 25 ohms bythe /16 line section, Chebyshev impedance transformerswhich have a bandwidth from 0.960 to 1.215 GHz.

The Experimental Microstrip Balun Showing the UppermostConductor Plane

R = 50

EQUIVALENT CIRCUITMICROSTRIP BALUN (DESIGN 3)

WITH TRANSFORMERS

50LINE C

R = 50

LINE F

LINE B

LINE A LINE D

BALUN

FOR LINE A: Zo = 50; L = 1888 MILS; ff 2.10LINE B: Zo = 25; L = 1810 MILS; ff 2.23LINES E AND F: Zo = 30; L = 1772 MILS; eff 2.33LINES C AND D: Zo = 25; L = 1546 MILS; eff 2.23LINES G AND H: Zo = 25; L = 140 MILS; ff 2.23LINES I AND J: Zo = 61.1; L = 466 MILS; eff 2.07LINES K AND L: Zo = 20.5; L = 443 MILS; eff 2.31

25TRANSMISSION

LINE

/16LINE-SECTIONTRANSFORMER

LINE H LINE J LINE L

LINE G LINE I LINE K

Figure 22.

10RF Application InformationFreescale Semiconductor

AN1034

23. The unbalance between output ports for aone-octave bandwidth is shown in themeasured 1.5 degreemaximum phase difference and 0.15-dB maximum insertionloss difference.

DESIGN 3 BALUN MEASURED PERFORMANCE185

180

175

0.5

0

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

PHASEDIFFERENCE

--0.5

FREQUENCY -- GHz

--DEGREES

INSERTIONLOSS

DIFFERENCE--dB

0.6 1.5

Figure 23.

24. The central frequency is 10 percent higher thanexpected, but response is close to the calculated values ifrelative frequency is considered. If the output transformersand their effect on input VSWR are disregarded, an octavebandwidth with a maximum input VSWR of around 2.0:1 canbe obtained. The 100 MHz shift between the two curves maybe caused by the improper determination of the folded cavity’selectrical length. Similar calculation inaccuracies may arisefrom effects at the balun junction and from the electrical lengthof the stub. As in the calculated response, the experimentalmicrostrip balun performs comparably to the two coaxialdesigns.

DESIGN 3 BALUN PERFORMANCE

INPUTVSWR

FREQUENCY -- GHz

2:1

1.5:1

1:1

CALCULATED MEASURED

2.5:1

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.40.6 1.5

Figure 24.

25. The similarity in the performance of the three balundesigns within the considered frequency bands indicatesthat the parasitic elements do not significantly affect thetheoretical properties. The frequency limit is higher than1.5 GHz for all three. In the 0.960-to-1.215-GHz bandwidth(TACAN and DME applications), each performed withsatisfactory balance. The table compares the maincharacteristics of the balun designs.The phase differences ( 1.5 degrees) for all three baluns

are similar to those experiencedwith theminiature 3-dBhybridcouplers that are normally used to combine transistors formicrowave balanced amplifiers. But the insertion lossdifferences of the baluns are better-0.2 dB for a one-octavebandwidth compared with 0.5 dB.

The physically simple microstrip balun eliminates theconnection problem inherent in coaxial designs: physicalvariances that breed standing waves and unbalance.Microstripping the transmission lines allows a designer tochoose any value of characteristic impedance of the lines.Consequently, the microstrip balun is both more manageableand more controllable.Since the balun load impedancewill varywith frequency, the

best results will be obtained by simultaneously optimizing thebalun parameters with those of the matching network. Thetransistor’s internal prematching networkmust be considered.

Type of BalunBalun Loads, R

(ohms)

Maximum Experimental UnbalanceFor One-Octave Bandwidth Theoretical Input VSWR For:

MAG (dB) 960 -- 1215 MHzOne-OctaveBandwidth

Coaxial I (Design 1) 25 3 0.2 1.15:1 1.6:1

Coaxial II (Design 2) 6.25 1 0.2 1.15:1 1.6:1

Microstrip (Design 3) 25 1.5 0.2 1.20:1 1.8:1

Figure 25. Performance of the Three Balun Designs

AN1034

11RF Application InformationFreescale Semiconductor

References1. “35/50 Watt Broadband (160 -- 240 MHz) Push-Pull TV

Amplifier Band III,” TRW Application Note, TRW RFSemiconductors Catalog No. 97, p. 84AN.

2. “150 W Linear Amplifier 2 to 28 MHz, 13.5 Volt DC,” TRWApplication Note, TRW RF Semiconductors Catalog No.97, p. 108AN.

3. TRW Application Notes on the TPM-4100 (100 W, 100 --400 MHz); the TPM-4040 (40 W, 100 -- 400 MHz); the

TPV-3100 (110 W, Band III); and the TPV-5050 (50 W,UHF) available from TRW RF Semiconductors.

4. The program used for the circuit calculation wasCOMPACT (Computerized Optimization of MicrowavePassive and Active Circuits).

5. Gordon J. Laughlin, “New Impedance-Matched WidebandBalun and Magic Tee,” IEEE Transactions: MicrowaveTheory and Technology, Vol. MTT-24, No. 3, (March 1976).

12RF Application InformationFreescale Semiconductor

AN1034

Information in this document is provided solely to enable system and softwareimplementers to use Freescale products. There are no express or implied copyrightlicenses granted hereunder to design or fabricate any integrated circuits based on theinformation in this document.

Freescale reserves the right to make changes without further notice to any productsherein. Freescale makes no warranty, representation, or guarantee regarding thesuitability of its products for any particular purpose, nor does Freescale assume anyliability arising out of the application or use of any product or circuit, and specificallydisclaims any and all liability, including without limitation consequential or incidentaldamages. “Typical” parameters that may be provided in Freescale data sheets and/orspecifications can and do vary in different applications, and actual performance mayvary over time. All operating parameters, including “typicals,” must be validated foreach customer application by customer’s technical experts. Freescale does not conveyany license under its patent rights nor the rights of others. Freescale sells productspursuant to standard terms and conditions of sale, which can be found at the followingaddress: freescale.com/SalesTermsandConditions.

Freescale and the Freescale logo are trademarks of Freescale Semiconductor, Inc.,Reg. U.S. Pat. & Tm. Off. All other product or service names are the property of theirrespective owners.E 1993, 2009 Freescale Semiconductor, Inc.

How to Reach Us:

Home Page:freescale.com

Web Support:freescale.com/support

AN1034Rev. 0, 7/1993