Ultra-Wideband Balun using a Multiaperture Ferromagnetic Core Bryant Baker, Richard Campbell Qorvo, Hillsboro, OR 97124, USA, Portland State University, Portland, OR 97102, USA Abstract — This paper will describe the design of an ultrawideband balun using a multiaperture ferromagnetic core. The balun is designed to operate over several decades of bandwidth to provide a broadband solution to an increasingly complex spectrum. This design is intended for receiver frontend applications where wideband performance is a critical device requirement. The characteristics of the ferromagnetic material and unique design arrangement provides state-ofthe-art insertion loss performance when compared to commercially available baluns. Index Terms - Ferrite, mutual inductance, magnetic core flux, transmission line transformer, ultra-wideband balun.
I. INTRODUCTION There is an industry need for wideband baluns to operate across several decades of bandwidth to provide a broadband solution to an increasingly complex spectrum. Wideband baluns can be used in a number of applications, where the conversion of a balanced source to an unbalanced load is required. In early radio communications it found widespread use in converting the balanced load of a dipole antenna to the unbalanced output of a single-ended amplifier [1], [2]. The balun later found its way into the design of solid-state differential circuits such as mixers and amplifiers, where network matching is required to deliver the maximum power transfer to the load. In the design of RF power amplifiers, the balun plays a critical role in amplifier performance, including its input and output impedances, gain flatness, linearity, and power efficiency. [3], [4]. These devices can be constructed at low cost and with a relatively small bill of materials, making its deployment in communication systems both practical and commercially viable. This paper describes the design of an ultra-wideband balun that is capable of performing over 3.7 decades of bandwidth, encompassing the MF, HF, VHF, and UHF spectrum. It was constructed using a multiaperture ferrite core, and a pair of bifilar wires with three parallel windings. The design arrangement, first presented in [5], is evaluated using new ferrite material and magnet wire to provide stateof-the-art wideband insertion loss performance. The physical size of the multiaperture ferrite core is reduced by a factor of five, and uses a higher gauge quadrafilar magnet wire to accommodate the smaller inside diameter of the
Fig 1. The transmission line TEM is equal in magnitude and opposite in phase.
core. The balun was measured on an Agilent ENAE5071C vector network analyzer in a 50 Ohm system and converted to mixed-mode S-parameters using EDA software. The balun is evaluated with a 2:1, 3:1, and 4:1 impedance ratio, where the unbalanced port is held constant at a 50 Ohm impedance. Measured results are reported for input VSWR, output VSWR, differential-mode insertion loss, common-mode rejection ratio (CMRR), magnitude imbalance, and phase imbalance. II. THEORY OF OPERATION The ultra-wideband balun is a transmission line transformer (TLT) that transmits energy by way of transverse electromagnetic mode (TEM), and differs from conventional transformers that transmit energy through flux linkages. The TLT uses two conductors that possess line currents that are equal in magnitude and opposite in phase, and is more clearly illustrated by Fig 1. 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 transverse electromagnetic (TEM) the boundary condition of both the electric field and magnetic fields are parallel to the boundary plane, and no longitudinal components of either field exist [6]. TLTs are especially useful in wideband applications because they possess greater transmission efficiencies by arranging the windings to have uniform transmission line properties that produce nearly equal delay.
The desired low frequency response of this particular design eliminates the use of Marchand and other planar balun types; however the desired performance can be easily attained using magnetic materials. The introduction of a ferromagnetic core increases the magnetically induced inductance of the conductors to achieve the low frequency response required to minimize the VSWR and differentialmode insertion loss. 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. This characteristic limits the high frequency bandwidth, unless adequate capacitive coupling between the coils is maintained [7]. 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(µ), where l' is the apparent length of the transmission line, l is the actual physical length, and µ is the permeability of the ferrite core. This approximation is especially appropriate for transmission line transformers made with twisted or parallel wires because they are directly influenced by magnetic material due to stray coupling [8]. III. DESIGN PROCEDURE The ultra-wideband balun was realized using a Fair-Rite 2843002302 multiaperture ferrite core and MWS Wire Industries #32 insulated quadrafilar magnet wire [9]. The multiaperture ferrite core, presented in this work is approximately five times smaller than the ferrite core used in [5], leading to enhanced wideband performance extending into the microwave spectrum. A higher gauge quadrafilar magnet wire is selected for this design in an effort to scale to the physical dimensions of the ferrite core while maintaining low leakage inductance at higher frequencies. The quadrafilar magnet wire is split into a pair of bifilar conductors and wound around the ferrite core as shown in Fig 2. The polyurethane nylon insulated magnet wire offers exceptional dielectric properties and low losses. Due to the physical constraints of the cores inside diameter, 3 turns of twisted wires through the core would damage the insulation resulting in short circuits. Alternatively, a design
Fig 2. The design arrangement of the ultra-wideband balun.
tradeoff using 3 parallel turns is used to obtain the desired low frequency response, resulting in a slight reduction to the capacitive coupling of the device. The design arrangement shown in Fig. 2, depicts 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. For a balun with a 2:1 impedance ratio, the balanced port represents the 100 Ohm differential impedance measured across terminals A and D, where each terminal represents a 50 Ohm impedance. The unbalanced port on the right represents a 50 Ohm single-ended impedance where the twisted pair of conductors A/B terminate to ground and the twisted pair C/D terminate to a female SMA connector. The ultra-wideband balun is mounted on 62.5 mil FR4 substrate. The FR4 substrate provides a rigid surface to mount the female SMA connectors and also provides a common ground between SMA ports. The equivalent circuit model for the ultra-wideband balun design can be seen in Fig 3. By examination we can see L3 is shorted to ground between nodes B and C and the single-ended port where A/B terminates to ground. Intuitively it would seem that shunting L3 to ground would impede the function of L4, resulting in degraded high frequency performance. However, this design arrangement has led to improved wideband performance, because its symmetrical design layout and increased magnetic core flux reduces common-mode currents and group delay, thereby extending its wideband performance.
Fig 3. Equivalent circuit model of the ultra-wideband balun.
IV. MEASURED RESULTS The balun was measured using an Agilent ENA-E5071C vector network analyzer, where its 3-port scattering parameters were recorded in a 50 Ohm system. The singleended S-parameters were converted to mixed-mode Sparameters using EDA software, using the method described in [10]. The measured results in Fig. 4 provides the results for the input VSWR, output VSWR, differential insertion loss, CMRR, magnitude imbalance, and phase imbalance. The performance of the balun was evaluated
Fig. 4. Ultra-wideband balun measured results with an impedance ration of 2:1 (blue), 3:1 (red), and 4:1 (green).
with an impedance ratio of 2:1, 3:1, and 4:1, where the single-ended unbalanced port is held constant at 50 Ohms. The device is evaluated with varying impedances at the balanced port to expose the performance tradeoffs of this design in various system impedances. The performance of the balun evaluated with a 2:1 impedance ratio reports an input and output VSWR less than 2.2, a differential insertion loss less than 3dB, and CMRR greater than 15 dB from 300 kHz to 1.5 GHz. The magnitude imbalance less than 2 dB is reported up to 1 GHz, with a phase imbalance less than 10 degrees from 300 kHz to 1.5 GHz. The imbalance of the device can be calculated from the single-ended S-parameters using the following equation.
imbalance
Sss 21 Sss 31
(1)
The magnitude and phase imbalance can be improved by adjusting the spacing between the turns on the multiaperture ferrite core, which affects the capacitive coupling between coils. Alternatively, trimming the physical length of the magnet wire A or D, in an effort to make the physical length of the two conductors equal, has shown to improve the magnitude and phase imbalance. This trimming method can also lead to improved CMRR due to the reduction in common-mode currents and group delay [5]. The reduction in the common-mode response can be observed by inspection from the sum of magnitudes given in the following equation derived from the singleended S-parameters.
SCS
1 SSS 21 SSS 31 2
(2)
The performance of the balun evaluated with a 3:1 and 4:1 impedance ratio produces an improved input and output VSWR, from its low frequency response and extends well into the UHF spectrum. The impedance on the unbalanced port is held constant at 50 Ohms, and by observation we can see that increasing the impedance on the balanced port improves the match for both the input and the output of the device. This suggests that the device characteristics of the ferrite core and inductance of the magnet wire possesses a higher device impedance. The impedance of the device at lower frequencies is a result of the magnetic coupling between the primary and secondary. As the frequency increases the permeability of the ferromagnetic material decreases, while leakage inductance increases, limiting the higher frequency performance. The differential insertion loss also benefits from the improved match, reporting insertion loss less than 2 dB for frequencies ranging from 300 kHz to 800 MHz. 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. The CMRR results are comparable to the 2:1 results for frequencies under 800 MHz, but degrades from 900 MHz to 1800 MHz. The phase imbalance also improves for these impedance ratio conditions, but it comes at the cost of increased magnitude imbalance. Due to the bandwidth limitation of the vector network analyzer, it is thought that the low frequency performance extends below 300 kHz. Further work investigating the frequency response of the ultra-wideband balun for frequencies below 300 kHz is required to confirm this theory.
TABLE I Comparison with State-of-the-Art
V. STATE-OF-THE-ART COMPARISON The insertion loss performance of the balun presented in this work is compared to those commercially available from MiniCircuits in Table 1. The ultra-wideband balun has a 3dB bandwidth of 3.7 decades, and a 2 dB bandwidth of approximately 3.3 decades with a 2:1 impedance ratio. However, please note that the insertion loss performance is relatively flat from 600 MHz to 1300 MHz, hovering just below the 2 dB insertion loss specification. This effectively produces a 2dB insertion loss bandwidth of 3.6 decades. Regardless, the 2 dB bandwidth performance represents state-of-the-art with a 2:1 impedance ratio. The bandwidth in decades can be found using the following equation where f1 is the lower frequency bound, and f2 is the upper frequency bound.
W
log f 2 / f1 log 10
(3)
The balun presented in this work possesses state-of-theart bandwidth performance in terms of its 2 dB and 3 dB insertion loss performance, when evaluated with an impedance ratio of 4:1. The 4:1 balun also returned the most favorable VSWR results because the design arrangement, characteristics of the ferromagnetic core, and magnet wire possesses a higher device impedance. The improved matching of the device is exhibited by its low frequency response and extending up to approximately 700 MHz. Due to the bandwidth limitation of the vector network analyzer, it is thought that the low frequency performance extends below 300 kHz. Therefore, the lower frequency bandwidth may be expanded, pending improved measurement capabilities. VI. CONCLUSION The ultra-wideband balun presented in this work possesses insertion loss performance extending over several decades of bandwidth. It was designed using a multiaperture ferrite core with 3 parallel windings of quadrafilar magnetic wire. The unique design arrangement
and characteristics of the ferromagnetic material led to its extended bandwidth capabilities. The increased magnetic coupling between the primary and secondary dominates at low frequencies, while at higher frequencies the leakage inductance increases and the permeability of the ferrite core decreases, limiting the high frequency bandwidth. The measured results of the balun were reported for a 2:1, 3:1, and 4:1 impedance ratios with the unbalanced port held constant at 50 Ohms. This balun design was compared with commercially available baluns and represents state-of-theart in terms of its wideband 2 dB insertion loss performance with a 2:1 impedance ratio as well as its 2dB and 3 dB insertion loss performance measured with a 4:1 impedance ratio. ACKNOWLEDGEMENT The authors' would like to thank Portland State University and Qorvo who supported this research. A special thanks to Fair-Rite Products Corporation and MWS Wire Industries for providing product samples, and making this work possible. REFERENCES [1] G. Guanella, "New Method of Impedance Matching in RadioFrequency Circuits," The Brown Boveri Review, September 1944, pp. 327-329. [2] J. Sevick, "Transmission Line Transformers" 1st Ed. American Radio Relay League. Newington, CT. 1987. [3] C. Trask, "Designing Wideband Transformers for HF and VHF Power Amplifiers," QEX, Mar/Apr 2005, pp. 3-15 [4] Pitzalis, O. and T.P.M. Couse, "Broadband Transformer Design for RF Transistor Power Amplifiers," 1968 Electronic Components Conference, pp. 207-216. [5] B.Baker, "A Wideband Balun for HF, VHF, and UHF Applications." IEEE Microwave Magazine. Vol 14, No 1. Jan/Feb 2014. pp. 86-91 [6] C. Trask, "Transmission Line Transformers, Theory, Design, and Applications, Part 1" High Frequency Electronics, December 2005, pp. 46-53 [7] H.Granberg, "Broadband Transformers and Power Combining Techniques for RF" Motorola Semiconductor Application Note, AN749. (2013). [Online]. Available: http://www.datasheetarchive.com/dlmain/Datasheets21/DSA-405881.pdf [8] C. Trask, "Transmission Line Transformers, Theory, Design, and Applications, Part 2" High Frequency Electronics, January 2006, pp. 26-33 [9] "Fair-Rite Product's Catalog Part Data Sheet, "2843002302" (2013).[Online].Available: http://www.fairrite.com/cgibin/ catalog.pgm#select:onepart [10] D. E. Brockelman, W. R. Eisenstadt; "Combined Differential and Common-Mode Scattering Parameters: Theory and Simulation"; IEEE Transactions on Microwave Theory and Techniques, Vol. 43, No. 7, pp. 1530-1539, July 1995
