3 IGN NER 1 0 S S2 DE WIN IM NT N alun E IO B D U TIT band T S PE ide M W O C

A Wideband Balun for HF, VHF, and UHF Applications Bryant Baker

T

here is an industry need for wideband baluns to operate across several decades of bandwidth covering the HF, VHF, and UHF spectrum. For readers unfamiliar with the term “balun,” it is a compound word that combines the terms balanced and unbalanced. This is in reference to the conversion between a balanced source and an unbalanced load, often requiring an impedance transformation of some type. It’s common in literature to see the terms “balanced” and “unbalanced” used interchangeably with the terms “differential” and “single-ended,” and this article will also share this naming convention. These devices are particularly useful in network matching applications and can be constructed at low cost and a relatively small bill of materials. Wideband baluns first found widespread use converting the balanced load of a dipole antenna to the unbalanced output of a single-ended amplifier [1], [2]. These devices can also be found in solid-state differential circuits such as amplifiers and mixers where network matching is required to achieve the maximum power transfer

to the load. In the design of RF power amplifiers, wideband baluns play a critical role in an amplifier’s performance, including its input and output impedances, gain flatness, linearity, power efficiency, and many other performance characteristics [3], [4]. This article describes the theory of operation, design procedure, and measured results of the winning wideband balun presented at the 2013 IEEE Microwave Theory and Techniques Society (MTT-S) International Microwave Symposium (IMS2013), sponsored by the MTT-17 Technical Coordinating Committee on HF-VHF-UHF technology. The wideband balun was designed to deliver a 4:1 impedance transformation, converting a balanced 100 Ω source to an unbalanced 25 Ω load. It was constructed using a multiaperture ferrite core and a pair of bifilar wires with four parallel turns. The measured results at IMS2013 spanned over three decades, from a starting frequency of 410 kHz to a maximum frequency of 562  MHz while meeting all the performance requirements set forth by MTT-17 coordinators [5]. Careful consideration was given to the magnetic materials, conductor, and construction

Bryant Baker ([email protected]) is with Portland State University, Oregon, United States.

Digital Object Identifier 10.1109/MMM.2013.2288715 Date of publication: 21 January 2014

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1527-3342/14/$31.00©2014IEEE

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method, which contributed to the overall performance of the wideband balun.

Competition Rules A discussion of the competition rules, design specifications, and measurement details are first presented so that the reader fully understands the scope of this competition and expectations of MTT-17 coordinators. There has been some level of confusion by students surrounding this competition in past years in regard to the design specifications, and it’s the hope of this author to clear up any confusion in an effort to encourage the participation of more students in the future. The competition requires students to design, construct, and test a wideband balun that meets the design specifications outlined below with a minimum starting frequency of 1 MHz: •• female subminiature version A (SMA) connectors to terminate all three ports •• minimum impedance transformation ratio of two •• maximum voltage standing wave radio (VSWR) of 2:1 at all ports •• insertion loss of less than 1 dB •• common-mode rejection ratio (CMRR) greater than 25 dB •• imbalance less than 1 dB and 2.5° •• balun must be completely passive. The design specifications further stipulates that the balun must be packaged in such a way that the judges can visually inspect the physical details, and the use of commercial baluns is strictly prohibited. Students are required to inform the judges of the impedance transformation ratio prior to performing the measurement. The winning balun is selected by achieving the highest possible bandwidth while meeting all the design specifications [5]. The success of this wideband balun presented at IMS2013 can be contributed in part to a thorough understanding of these design rules and the capabilities of the measurement equipment used to interpret the results.

Measurement Details The competition measurements at IMS2013 were recorded on a modern-day Agilent ENA Series E5071C vector network analyzer (VNA), which is a multiport network analyzer with the capability of displaying mixed-mode scattering parameters [6]. This instrument was also the same used by the author during the prototype and evaluation phase leading up to the IMS2013 student design competition. Post-processing of the data in advanced design systems (ADS) was used to efficiently evaluate the capabilities of each prototype to determine the optimal impedances presented to the single-ended and balanced ports. Since this instrument is only capable of exporting singleended S-parameters, we were required to convert the single-ended S-parameters to extract the differential

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and common-mode performance results. Brockelman demonstrated how the adaptation of single-ended S-parameters could be used to describe differential networks. This adaptation is commonly referred to as mixed-mode S-parameters and addresses the conversion of single-ended S-parameters to differential and common-mode operation [7], [8]. The following paragraphs in this section will describe the conversion of single-ended S-parameters to mixed-mode S-parameters. The single-ended VNA measurement of the balun can be represented by the three-terminal device shown in Figure 1, where terminal A represents the single-ended/unbalanced port and terminals B and C represent the differential/balanced port. When the device is measured on the VNA, it is measured in a 50‑Ω environment, recorded to a S3P touchstone file, and is imported into ADS where the single-ended data is converted to mixed-mode S-parameters. The nomenclature used to represent the three different modes is represented by d for differential, c for common, and s for single-ended. We can use mixed-mode S-parameters to determine the input VSWR, output VSWR, differential-mode insertion loss, CMRR, magnitude imbalance, and phase imbalance. The input reflection coefficient on the single-ended/unbalanced port is represented as S ss 11 and is equal to single-ended S 11 results returned by the VNA. The balanced output reflection coefficient can be represented as S dd 22, and can be calculated using the single-ended S-parameter data using

S dd 22 = 1 $ 6S ss 22 - S ss 23 - S ss 32 + S ss 33@ . (1) 2

The input and output VSWR can be determined from the reflection coefficients in the normal fashion and is covered in more detail in [9]. The differential insertion loss of the device is represented as S DS 21 and can be found from the single-ended S-parameters using S ds 21 = 1 $ ^S ss 21 - S ss 31 h . (2) 2



Similarly, the common-mode response can be derived from the single-ended S-parameters using Term B Term A Balun Single Ended (Port 1)

Differential (Port 2) Term C

Figure 1. The single-ended VNA measurement representation requires conversion to differential-mode response.



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S cs 21 = 1 $ ^S ss 21 + S ss 31 h . (3) 2 The differential- and common-mode responses are typically expressed in decibels and can be found by taking 20 log of the value. The CMRR is a key figure of merit of any balun because its primary role is to reject undesired common-mode currents with minimal impact on the desired differential-mode currents [10]. It is defined as the ratio of powers of the differential gain to the common-mode gain found in (2) and (3)

CMRR = 20 $ log c

S ds 21 m . (4) S cs 21

The imbalance is also an important figure of merit when describing the performance of a balun. As the name suggests, the imbalance is the measurable difference between the two single-ended balanced ports and is typically reported in both magnitude and phase. At lower frequencies, the inequality of the wire lengths are negligible, however as the frequency is increased, any offset in lead inductance will degrade the imbalance. The imbalance can be calculated from the singleended S-parameters using

imbalance =-

S ss 21 . (5) S ss 31

Now that we’ve discussed the conversion of singleended to mixed-mode S-parameters we can now move on to discuss the design of the wideband balun.

Theory of Operation The wideband balun presented at IMS2013 is a transmission line transformer (TLT) that transmits energy by way of transverse electromagnetic (TEM) mode and differs from conventional transformers that transmit energy through flux linkages. This TLT uses two conductors that possess line currents that are equal in magnitude and opposite in phase and is more clearly illustrated in Figure 2. If we recall Maxwell’s boundary conditions, the transverse electric (TE) and transverse magnetic (TM) refer to conditions in which the electric field or magnetic field of a propagating wave is parallel to a boundary plane. In the case of TEM, the boundary condition of both the electric field and magnetic

V i

i V

Figure 2. The transmission line in TEM.

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fields are parallel to the boundary plane, and no longitudinal components of either field exists [11]. TLTs are especially useful in wideband balun applications because they possess wider bandwidths and greater transmission efficiencies by arranging the windings of the TLT to have uniform transmission line properties that produce nearly equal delay. By introducing a magnetic core, we can greatly reduce any common-mode currents from the input to the output. One of the primary challenges of the competition was to meet all of the design specifications at the 1  MHz low-frequency limit while maintaining the widest possible bandwidth. This low-frequency requirement eliminates the use of Marchand and other planar balun types. However, the desired response can be easily attained using magnetic materials. The introduction of the ferrite core increases the magnetically induced inductance of the conductors to achieve the low-frequency bandwidth limit required to meet the minimum VSWR and insertion-loss requirements on the single-ended and balanced ports. The magnetic coupling between the primary and secondary dominates at low frequencies, while at higher frequencies the leakage inductance increases and the permeability of the magnetic material decreases, limiting the highfrequency bandwidth unless tight capacitive coupling is provided [12]. The low-frequency response is dominated by the magnetizing inductance of the windings, where the magnetic material increases the length of the transmission line by approximately l’ = l n, where l’ is the apparent length of the transmission line, l is the actual physical length, and n is the permeability of the ferrite core. This approximation is especially appropriate for TLTs made with twisted or parallel wires because they are directly influenced by magnetic material due to stray coupling [13].

Design Procedure Several ferrite cores of varying shapes, sizes, permeability, and number of turns were evaluated before down-selecting to multiaperture ferrite core. Often this type of core is referred to as a “binocular core” because its physical shape resembles a pair of field glasses. The ferrite material is made up of nickel-zinc (NiZn) and is commonly used in HF and VHF applications because of its low loss and high saturation flux [14]. This core type ensures that the windings possess nearly identical electrical lengths and provide equal propagation delay on both sides, leading to improved bandwidth of the imbalance phase response [3]. Although it is possible to use a pair of toroidal cores to produce a balun of comparable performance, it is discouraged in wideband applications because the permeability from one batch to another varies, producing undesired effects such as common mode currents and phase imbalance. The wideband balun was realized using a Fair-Rite 2843002402 multiaperture ferrite core and MWS Wire

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Industries (MWS) #28 insulated quadrafilar magnet wire. The quadrafilar wire was divided into a pair of bifilar conductors and wound around the ferrite core as shown in Figure 3. The insulated magnet wire offers exceptional dielectric properties and low losses, but the polyurethane nylon insulation can be easily damaged when passing it through the multiaperture ferrite core. This was encountered during the prototyping phase when attempting to pass twisted bifilar pairs through the core in an attempt to improve the distributed mutual inductance. Due to the physical constraints of the core’s inside diameter, the act of passing four turns of twisted wires through the core would damage the insulation, resulting in short circuits. Ultimately, a design compromise using four parallel turns was carried out to achieve the desired low frequency response, thereby decreasing the distributed mutual inductance. The design arrangement in Figure 3 shows the balanced port on the left where conductors A and D terminate to individual female SMA connectors and conductors B/C are twisted together terminating to ground. The balanced port of the balun represents the 100-Ω impedance measured across the two-single ended terminals where each terminal represents a 50-Ω single-ended impedance. The unbalanced port on the right represents a 25-Ω single-ended impedance showing the twisted pair of conductors A/B terminating to ground and the twisted pair C/D terminating to a female SMA connector. Figure 4 shows the final wideband balun design mounted on a 62.5‑mil FR4 substrate. The FR4 substrate provides a rigid surface to mount the female SMA connectors and also provides a convenient method of sharing a common ground between the three single-ended terminals. The equivalent circuit model for the wideband balun design can be seen in Figure 5. By examination, we can see L3 is shorted to ground between nodes B and C on the single-ended port. Intuitively, it would seem that shorting L3 would impede the function of L4, resulting in a degraded high frequency performance. This unique design arrangement has led to improvements in differential insertion loss, CMRR, and phase imbalance due to the symmetrical uniformity of the design layout and increased magnetic core flux. This design arrangement effectively leads to a reduction in common-mode currents and group delay extending its wideband capabilities into the UHF spectrum. Several attempts to improve the high-frequency performance by reducing the design arrangement to a trifilar twist presented in [3] were unsuccessfully carried out. The wideband performance was suitable for HF and VHF applications, but it fell short of reaching the UHF region with any impedance transformation ratio greater than 2:1. The performance of the 4:1 twisted trifilar balun, at least

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2R+ Ground 2R-

A

A/C C/D

B/C

A/B D

R+ Ground

B/D

Figure 3. The design arrangement of the wideband balun featuring a multiaperture ferrite core.

Figure 4. The 4:1 wideband balun mounted to a 62.5-mil FR4 substrate.

2R+ L1 D R+ L2 C L3 B

R-

L4 A 2R-

Figure 5. The equivalent circuit model of a 4:1 wideband balun.



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4

m1 Frequency = 572.5 MHz Input_VSWR = 2.000

Output VSWR

Input VSWR

4

3 m1 2

0

m2 Frequency = 581.0 MHz Output_VSWR = 2.000

3 m2 2

0 0

100

200 300 400 500 Frequency (MHz) (a)

-0.0

600

700

0

80

m4 Frequency = 563.2 MHz dB (SD S21) = -1.000 m4

-1.0

200 300 400 500 Frequency (MHz) (b)

600

700

m3 Frequency = 813.1 MHz dB (CMMR) = 25.003

70 60 CMRR (dB)

Insertion Loss (dB)

-0.5

100

50 40 m3

30 20

-1.5

10 0

-0.2

5 4 3 2 1 0 -1 -2 -3 -4 -5

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200 300 400 500 Frequency (MHz) (c)

600

700

0

10

m5 Frequency = 835.3 MHz dB (Imbalance) = 1.000

5 m5

0 Imbalance (°)

Imbalance (dB)

0

100 200 300 400 500 600 700 800 900 Frequency (MHz) (d)

m6 Frequency = 565.7 MHz Phase (Imbalance1) = 2.500

m6

-5 -10 -15 -20 -25

0

100 200 300 400 500 600 700 800 900 Frequency (MHz) (e)

0

100

200 300 400 Frequency (MHz) (f)

500

600

Figure 6. The wideband balun measured results for (a) input VSWR, (b) output VSWR, (c) differential-mode insertion loss, (d) CMRR, (e) magnitude imbalance, and (f) phase imbalance. those constructed by this author, were impeded by elevated common-mode currents which degraded the CMRR and phase imbalance seen in Figure 6 (red).

Measured Results The measured results at IMS2013 were recorded on an Agilent ENA Series E5071C using the balun fixture simulator that conveniently converts single-ended S-parameters to mixed mode S-parameters [6]. The MTT-17 coordinators stepped through each of the performance requirements, documenting the highest frequency achieved for each test parameter. The student’s

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final score was determined by the lowest frequency bandwidth reported by either its input VSWR, output VSWR, differential-mode insertion loss, CMRR, magnitude imbalance, or phase imbalance. The wideband balun at IMS2013 achieved a maximum bandwidth of 562 MHz and was highfrequency limited by its differential-mode insertion loss and phase imbalance. The measured results shown in Figure 6 (blue) were recorded after the student design competition using the same VNA model and is representative of the results reported during the competition. The minimum input and output VSWR

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specification of 2:1 shows a maximum bandwidth of approximately 572 and 581 MHz, respectively. The CMRR met the minimum 25.0-dB design specification out to a maximum frequency of 813 MHz, while the maximum magnitude imbalance requirement of 1 dB stretches to a maximum frequency of 835 MHz. We can observe at approximately 800 MHz the CMRR begins to decrease rapidly while the magnitude imbalance increases exponentially. The degraded response is due largely to the physical length of the magnetic wire approaching its quarter-wavelength.

Conclusion The success of this wideband balun design at IMS2013 can be attributed in part to the selection of magnetic materials, construction method, and thorough understanding mixed-mode S-parameters. The design features a multiaperture ferrite core and a pair of bifilar wires with four parallel turns configured to perform an impedance transformation ratio of 4:1. The official measurement at IMS2013 spanned over three decades from 410 kHz to 562 MHz and was high-frequency limited by its insertion loss and phase imbalance. To the best of this author’s knowledge the wideband balun described in this article was the only balun at IMS2013 to use a multiaperture ferrite core and resulted in a 300-MHz separation between first and second place. The multiaperture, binocular core ensures that the windings possess nearly identical electrical lengths and provides equal propagation delay on both sides. These attributes led to improved bandwidth of the imbalance phase response and the reduction of common mode currents. The performance of this wideband balun can be improved to extend the bandwidth of this device while still meeting the MTT-17 design criteria. For example the high-end frequency response can be improved by reducing the electrical length of the bifilar wire on the single-ended and differential ports. Further experimentation following IMS2013 showed the bandwidth could be extended to approximately 625 MHz using the same bill of materials and design arrangement described in this article by reducing the physical length of the magnet wire. Further experimentation using multiaperture cores of varying size, permeability, and number of turns is needed to fully explore the wideband capabilities of this design. Additionally, a method to quickly evaluate the VNA’s measured results was created using EDA software. This method finds the optimal impedance on the single-ended and differential ports to deliver the maximum allowable bandwidth while meeting the required design specifications. This method was created to greatly reduce the time required to evaluate prototypes in future design efforts.

Acknowledgments This author would like to thank everyone at TriQuint and Portland State University who supported my participa-

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The success of this wideband balun design at IMS2013 can be attributed in part to the selection of magnetic materials, construction method, and thorough understanding mixed-mode S-parameters. tion in the Wideband Balun Student Design Competition at IMS2013. The amateur radio community at TriQuint was a valuable resource, providing measurement support, reference material, and the donation of ferrite cores. As recognition for their support a special thanks goes to Dale Hunt (WB6BYU), Greg Daly (WB7RSG), Dennis Rosenauer (AC7FT), Gary Shipley (WA7MLK), Lowell Brunson (KC7DX), Richard Campbell (KK7B), and George Steen. This author would also like to acknowledge the past work of Jerry Sevick (W2FMI) and Chris Trask (N7ZWY), whose dedication to this subject has laid the groundwork for many to follow.

References [1] G. Guanella, “New method of impedance matching in radiofrequency circuits,” Brown Boveri Rev., vol. 31, pp. 327–329, Sept. 1944. [2] J. Sevick, Transmission Line Transformers, 1st ed. Newington, CT: American Radio Relay League, 1987. [3] C. Trask, “Designing wideband transformers for HF and VHF power amplifiers,” QEX, no. 229, pp. 3–15, Mar./Apr. 2005. [4] O. Pitzalis and T. P. M. Couse, “Broadband transformer design for RF transistor power amplifiers,” in Proc. Electronic Components Conf., 1968, pp. 207–216. [5] (2013). Announcement of the student competition. [Online]. Available: http://www.ims2013.org/images/files/student_competition/ sdc-wbb-rev2.pdf [6] (2013). Agilent introduction to the fixture simulator function of the ENA series RF network analyzers: Network de-embedding/embedding and balanced measurement. [Online]. Available: http:// cp.literature.agilent.com/litweb/pdf/5988-4923EN.pdf [7] D. E. Brockelman and W. R. Eisenstadt, “Combined differential and common-mode scattering parameters: Theory and simulation,” IEEE Trans. Microwave Theory Tech., vol. 43, no. 7, pp. 1530– 1539, July 1995. [8] D. E. Brockelman and W. R. Eisenstadt, “Combined differential and common-mode analysis of power splitters and combiners,” IEEE Trans. Microwave Theory Tech., vol. 43, no. 11, pp. 2627–2632, Nov. 1995. [9] D. Pozar, Microwave Engineering, 3rd ed. Hoboken, NJ: John Wiley and Sons, 2005, p. 59. [10] R. Skelton, “Measuring HF balun performance,” QEX, no. 263, pp. 39–41, Nov./Dec. 2010. [11] C. Trask, “Transmission line transformers, theory, design, and applications—Part 1,” High Freq. Electron., vol. 4, no. 9, pp. 46–53, Dec. 2005. [12] H. Granberg. (2013). Broadband transformers and power combining techniques for RF. Motorola Semiconductor Application Note, AN749. [Online]. Available: http://www.datasheetarchive.com/ dlmain/Datasheets-21/DSA-405881.pdf [13] C. Trask, “Transmission line transformers, theory, design, and applications—Part 2,” High Freq. Electron., vol. 5, no. 1, pp. 26–33, Jan. 2006. [14] (2013). Fair-Rite product’s catalog part data sheet, 2843002402. [Online]. Available: http://www.fair-rite.com/cgibin/catalog.pgm ?THEONEPART=2843002402#select:onepart 



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