The Art of Power Dividing: A Review for State-of-the-Art Planar Power Dividers

Yongle Wu, Lingxiao Jiao, Zheng Zhuang, Yuanan Liu

School of Electronic Engineering, Beijing Key Laboratory of Work Safety Intelligent Monitoring, Beijing University of Posts and Telecommunications, Beijing 100876, China

* The corresponding author, email: ywu@bupt.edu.cn

I. INTRODUCTION

The power divider (also known as power splitter) is one of the fundamental components in constructing a wireless communication system, which is used to equally or unequally divide the input power into a number of smaller amounts of power. If the roles of input and output ports are exchanged, a power divider becomes a power combiner, for combining multi-way signals into one. The nature of a three-port network determines that it can not be simultaneously lossless, reciprocal, and matched at all ports.

Generally speaking, most passive, linear microwave components will turn out to be reciprocal, and matched ports are required in most applications. Wilkinson power dividers[1] were proposed with a resistive device mounted between the output ports. When all ports are matched, the Wilkinson power divider appears the property of lossless power dividing. However, the reflected power caused by output mismatch is absorbed by the resistive devices, and ideal output isolation is realized at the mean time. The Gysel power divider [2] was then proposed in 1975, which modified the isolation structure by introducing two grounded resistors that improve the heat dissipation performance under a high power level. The two prototypes merely satisfy the basic requirements for a power divider, which is dividing powers at a certain frequency band with all ports matched and outputs isolated.

Nowadays, power dividers have already gone far beyond the original prototypes [1],[2], for keeping pace with the rapid development of modern communication technologies.This paper aims to review the state-of-theart planar power dividers in various aspects and conclude their implementation methods.For both the engineers and researchers, what they care about are the performance, functions and technology of a power divider. Because the performance is the first consideration for a passive component, thus firstly, different aspects of power dividers’ performance are discussed, including different frequency, power-division and phase configurations. Power dividers with different performances are broadly used in various circuits, and they are selected according to the required performances. Subsequently, since power dividers with various function integration are welcomed,several function-integrated power dividers are exhibited. In this section, the functions of impedance transformation, balanced-signal handling, filtering and harmonic suppression are integrated in power dividers. Moreover, some unconventional transmission lines may perform some interesting characteristics. Therefore the power dividers with unconventional transmission lines are summarized, including the ones using coupled lines, composite right-/left-hand transmission lines (CRLH TL), low temperature cofired ceramic (LTCC) and substrate integrated waveguide (SIW). Finally,the trends of the power-divider innovations are summarized and the future of power dividers is predicted. This article could inspire researchers for the development of power dividers, and provide a useful selection guide for system designers.

This review paper overviews some stateof-the-art power dividers, which have either excellent performance or abundant functions. The future trends of power-divider development are predicted.

II. STATE-OF-THE-ART POWER DIVIDERS WITH DIFFERENT PERFORMANCES

2.1 Power dividers with different frequency configurations

In the modern communication systems, supporting multiple communication standards becomes a fundamental requirement. Therefore,systems and their comprising components should work concurrently at multiple frequency bands. To cover required frequency ranges,there are two schemes for “multiband” operation. One is to design components operating at several discrete bands that include the required frequencies. The other method is to design wideband components, operating under a wide and continuous band that covers the supporting frequency standards. Correspondingly,there are quantities of power dividers working under dual- [3]-[18], multiple- [19],[20], and wide-frequency [21]-[29] bands.

Among dual-band ones, there are two major methods to achieve the concurrent dual-band operation. One idea is utilizing dual-mode resonators for constructing power dividers[12], [13]. This kind of dual-band power dividers usually possesses bandpass-filtering performance, due to the natural frequency selection of resonators. One example of this type is shown in Fig. 1(a), and alongside are its simulated and measured performances. Another way for dual-band feature is finding the port-matching and output-isolation condition directly, then establishing design equations[3]-[11], [14]-[18]. This method could obtain closed-form design equations for circuit-parameter values. By inspecting all these circuits, there is no exception that their design equations includeterms, whereis the electrical length at the lower frequency pointTherefore, assuming thatis the electrical length at the higher frequencywill be unchanged ifEventually,specifying the frequency ratiothe dual-band performance can be obtained by designating electrical lengthsatA typical representative proposed in [7]is shown in Fig. 1(b). The ciruits constructed by this method are easy to obtain through the extraction of the rigorous design equations,which are usually with respect to the frequency ratio, the impedances and the electrical lengths. But the major shortfall of this kind of dual-band realization is that the bandwidth of each band cannot be explicitly controlled.

There is one more method to realize dual-band operation by introducing composite right/left-handed transmission lines, which will be discussed in Section 4.2.

Literature [20] realizes tri-band operation by cascading three coupled lines and mounting resistors at the inter-connected position. The three-section coupled line and resistors provide six characteristic impedances (even- and odd-mode impedances of each coupled line),three electrical lengths and three resistors’ resistances, the quantity of parameters sufficient to satisfy all the equations at three arbitrary frequencies simultaneously. As a matter of fact, a power divider comprising stepped-impedance transmission lines can support multiband operation as a generalized realization.

Fig. 1 Dual-band power dividers with (a) dual-mode resonators [12] (b) coupled lines [7]

Fig. 2 Multi-band power dividers with embedded transversal filtering sections [19]

Nevertheless, literature [19] reports another thought by embedding transversal signal-interference sections which is usually used for designing filters, as shown in Fig. 2. This method is able to generate inter-band transmission zeros to separate the discrete operating bands and is valid for any number of operating frequencies theoretically.

Compared to the multi-band solution, a power divider with wideband configuration is more preferred, for it is not only applicable to multi-band system but is a key component in systems with high-speed data transfer. One simple realization is to design a multi-band power divider whose bands are close to each other and extend bandwidths of each one. By doing so, the multiple frequency bands will merge into a single but wide band, thus the wideband operation is obtained. For example,in the aforementioned literature [7], when the frequency ratio(Fig. 4(c) in the literature), the dual-band power divider becomes a UWB (Ultra Wideband) one. Generally speaking, a component with multi-section or stepped-impedance lines is capable of wideband operation. Literature [27] (Fig. 3(a))theoretically analyzes this power-divider type and provides a universal design methodology.This method usually offers closed-form design equations, but the multi-section structure occupies too much layout area.

Another solution is employing coupled lines. Drawing on the concept of filters comprising coupled lines, the components based on coupled lines generally perform wide-band characteristic [30]. Structures using parallel-coupled lines [21], [22], [26], [28], [29]and microstrip-to-slotline transitions [22],[24], [25] are sufficiently explored, the schematics and results of which are illustrated in Fig. 3(b) and 3(c). It can be observed that the analysis of [21] is based on the single frequency point of the power divider, and the port is matched approximately in a relatively-wide band due to the coupling of the lines. Hence,the bandwidth is not controllable, and the tuning process would consume much time.

Differently, power dividers in [22], [26],[28], [29] are designed on the basis of coupled-line resonator, which is widely used in designing a wideband filter. This kind of power dividers shows multiple poles in their transmission performance, as a filter performs.If from the aspect of functions, this kind of power dividers can also be classified as the filtering ones, as discussed in Section 3.3.Moreover, the microstrip-slotline transitions[23]-[25] can be modeled as transformers, and at the meantime, coupled lines are equivalent to transmission line transformers. Hence, the power dividers with this kind of transitions can be classified as the ones with coupled lines, as [22], [26], [28], [29]. If the filter synthesis process is introduced, the bandwidth can be predicted according to the filter performance. Therefore, the tuning process could be omitted in this solution, which would save considerable time.

Although the multi- and wide-band realizations mentioned above are simple and convenient, the trend of the multi- and wide-band power divider is constructing them on special material or artificial transmission lines. The nature of the meterials and lines could contribute to the size miniaturization and bandwidth enhancement while providing the multi- or wide-band characteristic.

2.2 Power dividers with diff erent power-division configurations

Practical applications, including antenna feeding networks, antenna arrays, and power amplifiers, need customized power division ratios. Therefore, it is an urgent need for a power divider to support equal- and unequalpower division ratios simultaneously. In general, there are three methods to realize unequal power division: the uneven-impedance method [4], [6], [8], [11], [15], [27], [31]–[39], the phase-modification method [40], and the hybrid method [32].

Fig. 3. Wideband power dividers: (a) using multi-stage transmission lines [27],(b) with parallel-coupled lines [22], and (c) with microstrip-to-slotline transitions[25]

Fig. 4 Power dividers with arbitrary power divisions: (a) the impedance method[34], (b) the phase method [40], and (c) the hybrid method [32]

The first method, which is conventional and widely used, is to alter the characteristic impedance of the two bisection for power division. The uneven-impedance method leads that more power is transmitted through the path with smaller impedance. Power dividers like [4], [6], [8], [11], [15], [27], [31]–[39]realize modified power division by employing this method. Changing the line impedance,although widely used, is not capable of large power-division ratios, for line impedances are limited by the implementable physical line widths during the planar fabrication process.To avoid using extremely-narrow or -wide lines, constant voltage-standing wave ratio(VSWR)-type transmission-line impedance transformers (CVTs) and constant conductance-type transmission-line impedance transformers (CCTs) are introduced for a high-power division [34], which provides up to 9:1 power-division ratios, as depicted in Fig. 4(a). Additionally, due to the asymmetric configuration, circuits of this type can not be decomposed by using even- and odd-mode method, leading to a complicated analysis process.

Literature [40] (shown in Fig. 4(b)) provides another thought, by altering the power division with proper electrical lengths,i.e.the phase of the transmission lines. Since tuning the line phases is more convenient than tuning the line impedances, this configuration is capable of high-power division ratio and easy to construct a power divider with tunable power division.

The last method is named as “hybrid method”, for its unequal power division is realized by modifying the impedance and phase of the lines simultaneously. As shown in Fig. 4(c),literature [32] proposes a power divider, whose power division ratio can be tunned by changing the capacitances of the varactors. In this structure, there are two varactors mounted between the two conductors of a coupled line, at the two ends of the power divider. In essence,mounting capacitors between coupled lines will affect the odd-mode capacitance of the coupled transmission lines, and further alter the odd-mode impedance and phase velocity.Moreover, since this structure is deduced from a symmetrical four-port coupled line coupler,the analysis can be facilitated by using evenand odd-mode decomposition. This method is the best choice for a power-division-tunable power divider, because the tunability is easy to obtain by replacing the mounted capacitor with varactors. However, the tunable range is not very wide compared with the phase-modification method.

2.3 Power dividers with phase considerations

In fact, what we called “the power divider”is the in-phase power divider, whose outputs share identical phases. But out-of-phase (or anti-phase) power dividers are widely required in designing feeding networks of differential antennas. And the out-of-phase one functions like a balun, which is designed for converting the balanced ports to a single-ended port and vice versa. The simplest and most straightforward way is cascading a phase inverter at one of the output port, but the one with embedded out-of-phase performance is more preferred for miniaturization and low-loss consideration.One solution is to utilize the inherent 180ophase shifting characteristic of the short-ended coupled-line section, like methods in [29],[37] (the power divider in [37] is exhibited in Fig. 5(a)). The second method is manipulating the electromagnetic fields by employing microstrip-to-slotline transitions to get inversed fields at two outputs, as literatures [22], [24]( [22] is shown in Fig. 5(b)). The last mean is based on the DSPSL-to-microstrip transitions[10], [18]. The two symmetric microstrip branches of the outputs are connected to the“+” and “-” conductors of the DSPSL respectively, thus they output “+” and “-” signals with equal magnitude. Fig. 5(c) depicts the structure in [10]. It is observed that the last two methods exhibit a super wide 180ophase difference, but the multi-layer structures are relatively complicated compared with the first single-layer method.

In plenty of promising applications, like phased arrays, some multi-fed antennas, and reflectometers, the feature of arbitrary phase differences at outputs is indispensable. The power divider with arbitrary phase differences is capable of those applications, and can be an alternative to some couplers in designing antennas’ feeding networks [41], Doherty power amplifiers [42] and multi-port correlators [43].The power divider aforementioned in [34] is a typical example, which has already been illustrated in Fig. 4(a) above.

Fig. 5. Power dividers with different phase configurations: (a) out-of-phase coupled-line power divider [37], (b) out-of-phase microstrip-to-slotline power divider[23], and (c) out-of-phase DSPSL-to-microstrip power divider [10]

Fig. 6. Power dividers with different phase configurations (continued): power divider with negative group delay [45]

Fig. 7. Band-tunable power dividers based on (a) coupled lines [47], and (b) resonators [48].

Negative group delay is an interesting characteristic in electronic circuits, for it exhibits“reversed” time and the future seems to be predicted. It is also very meaningful in designing a power amplifier, for it minimizes the time mismatch between the envelope and the RF paths in supplying modulated power amplifiers to improve the linearity [45]. Fig. 6 is a power divider reported in [45]. By mounting some coupled-line stubs at the conventional Wilkinson power dividers, this structure shows negative group delay in specific frequency bands. Meanwhile, a power divider with small phase delays is proposed in [46].

2.4 Tunable power dividers

Introducing tunable performance to a power divider is of great value in constructing a multi-standard or self-adapted system. The tunability of power dividers mainly focuses on the power division and operating frequencies.The one with tunable power divisions [32] has already been discussed above, as shown in Fig. 4(c).

The other tunable type is tuning the frequency bands. Literature [47] presents a frequency-tunable power divider comprising coupled transmission lines. Similar to [32], its tunability is resulted from altering the impedance and phase velocity of the coupled and non-coupled lines, which is accomplished by tuning the capacitances of varactors. Literature [48] is inspired by the synthesis of coupled-resonator filters and integrates filtering function in the power divider. The basic elements of the power divider are varactor-loaded transmissionline resonators, the resonance of which are controlled by the capacitances of varactors. Then tuning the varactors alters the resonant frequencies of resonators, without affecting the coupling coefficient and quality factors. Hence, this power divider is tuned to operate under different frequency bands, but with constant absolute bandwidths. The two power dividers introduced in this subsection are illustrated in Fig. 7.

It is expected for a power divider whose band positions, bandwidths and power divisions are all tunable, and independently controlled. Unfortunately, as far as the authors know, such a tunable power divider has not been proposed yet. Additionally, the tunable output-phase difference, although more required in designing a coupler, is also a promising feature for a power divider in its future development.

III. FUNCTION-INTEGRATED POWER DIVIDERS

3.1 Power dividers with different terminated impedances

Many RF components, including antennas,amplifier transistors, etc., are not initially matched to the 50-Ohm impedance, thus impedance matching circuits should be introduced. Nevertheless, if the impedance-transformation function is integrated in power dividers, the system integration will be further improved and the insertion loss could be minimized. Therefore, massive power dividers with impedance-transformation functions [10],[18], [21], [31], [49]–[51] have been proposed in recent years. For the broadest applicability,an analytical design procedure is preferable,and applicable to arbitrary and designated port impedances. Accordingly, all of the instances [10], [18], [21], [31], [49]–[51] process closed-form design equations and analytical design methodology. However, the obvious shortcoming of these power dividers is that they cannot transform arbitrary impedances.Their transformable impedances lie in limited scopes, and they are not capable of transforming impedances with extremely-high or -low values

3.2 Power dividers operating in balanced systems

The developing trend of communication systems is becoming more complex and integrated in a tight space, but this causes a high level of electromagnetic interaction between circuit nodes and interference/crosstalk from substrate coupling and free space [52]. The balanced components have the ability to reject common-mode signals, and more immune to environment noise compared with the single-ended ones. Generally speaking, there are two kinds of balanced power divider, the single-ended-to-balanced one [53] and the balancedtobalanced one [28], [29], [54]. The key point in designing a balanced power divider is to suppress the common-mode signals (reflected or absorbed) while the differential-mode signals maintains a low-loss and efficient power dividing. To analyzing a balanced power divider, the mixed-mode Sparameters should be utilized [55]. The design methodology of a single-ended-to-balanced power divider is to equalize the circuit and the expected S-parameters for establishing design equations, then proper circuit parameters are extracted, which satisfy the expected performance expressed by mixed-mode S-parameters. Its analysis is similar to the four-port and five-port networks.

When designing a balanced-to-balanced power divider, the balanced power divider can be decomposed to two simplified circuit under differential- and common-mode excitations.One thought to suppress the common-mode signal is intentionally making mismatch at the common-mode circuits [56]. The second is constructing a band-stop or all-stop structure under the common-mode excitation [29], [54](shown in Fig. 8(a)). The last method is etching both slot and aperture on the common ground of the back-to-back microstrip, terminating the path of common-mode transmission [28](shown in Fig. 8(b)). Then accordingly, the common-mode signal is reflected and further suppressed covering the entire frequency band.

The existing balanced power dividers are all constructed by two symmetrical circuits,thus they consume double layout area in planar or vertical dimensions. Therefore, the major challenge of the balanced ones is to reduce the circuit size while maintaining the balanced-signal handling.

3.3 Power dividers integrating filter functions

Both power dividers and filters are the indispensable components in constructing wireless communication systems. If filters are integrated in power dividers, the improvement of component integration will contribute to the size miniaturization of systems. Additionally,the power-divider-and-filter co-design will greatly facilitate the design procedure and eliminate the mismatching loss caused by the cascaded filter sections.

Fig. 8. Power Dividers in balanced systems: (a) Balanced-to-Balanced one using Marchand Balun [29], and (b) Balanced-to-Balanced one using common ground[28].

As is well known, resonators are the basic elements that constitute filters, thus the configurations of filtering power dividers can be based on resonators, and the analysis is imitated from filter designs. Recently, filtering power dividers using spiral resonators [57],cascaded band- and low-pass filter sections[58], coupled resonators [22], [36], [59]–[61],and dual-mode resonators [12], [13], [62] have been extensively discussed. [61] proposes a generalized methodology for designing a filtering power divider by studying the coupling schematic, and detailed design procedure is given. Then for verification, an instance using frequency-dependent-coupled resonators is investigated, as shown in Fig. 9, where a three-pole and skirt transmission characteristic is observed. Meanwhile, the power divider previously analyzed [12] employs dual-mode resonators for realizing filtering function, as shown in Fig. 1(a), where two dual-pole transmission bands are observed

3.4 Power dividers with harmonic suppression

Unwanted harmonic signals are usually harmful when designing many active devices, like power amplifiers, low-noise amplifiers, and mixers. To solve this problem, power dividers with additional shut stubs [50], EBG cells[63], and cascades lumped inductors [64] are proposed. In essence, the one with shut stubs[50] suppresses the harmonics by creating short-circuit at the the harmonic frequencies,and [63] suppresses the harmonics by embedding EBG cells, which can be taken as lowpass filters.

IV. STATE-OF-THE-ART POWER DIVIDERS WITH UNCONVENTIONAL TRANSMISSION LINES

Because the strip and slot type transmission lines, including microstrip, stripline, coplanar waveguide, and slotline, are easy to fabricate and simple to determine the dimensions, most power dividers are fabricated by using these technologies. But for more advanced performance, functionality or configuration, power dividers with coupled transmission lines [7],[20], [22]– [24], [49]–[51], [68], composite right/left-handed transmission lines (CRLH-TL) [8], [65], [69]–[71], substrate integrated waveguides (SIW) [67], [72], [73], and low temperature cofired ceramic (LTCC) [66] attract researchers’ interests.

4.1 Coupled-line power dividers

The coupled transmission line, owing to its tight configuration, is especially applicable for size miniaturization of a power divider. When applying even- and odd-mode excitations,the coupled line will exhibit different characteristic impedances,i.e.even- and odd-mode impedances. Hence, the impedances of a pair of coupled lines could provide two-degree of freedom, which is especially useful in constructing multi-band [7], [20] and wide-band[22]–[24] power dividers. The major limitation in designing a coupled-line power divider is the coupling level of the coupled lines. For instance, for the standard microstrip fabrication, the coupling coefficient of the coupled strips is usually smaller than -8 dB. Therefore,the even- and odd-mode impedance values are not arbitrary and have to satisfy the fabrication technology.

Another problem is the different phase velocity under even- and odd-mode excitations,which exists in the quasi-TEM transmission lines, like microstrip, coplanar waveguide and slot-lines. For the quasi-TEM lines, not only the impedance, but the electrical lengths,are different under even- and odd-mode excitations. Usually, the even- and odd-mode electrical lengths are considered to be equal, and no analysis is given in existing literatures. But the phase-coupling effect would become significant especially as the operation approaches to higher frequencies. If taking the phase coupling into consideration, there will be four-degree of freedom for a pair of coupled lines.Unfortunately, there is no any available formulas indicating the even- and odd-mode electrical lengths, and controlling the phase-coupling effect is extremely complicated.

4.2 Power dividers using CRLH-TL and LTCC

Fig. 9 The filtering power divider reported in [61]

The composite right-/left-handed (CRLH)transmission line (TL) has attracted more and more interest in the researches of microwave devices owing to its non-linear phase response, wide bandwidth and low loss. The so-called CRLH TL comprises a conventional right-handed (RH) TL loaded with series capacitors and shunt inductors. Due to its unique dispersion characteristic, CRLH TL is capable of being basic elements for designing wideband [71] and dual-band [8], [65], [70] power dividers. The last but most important feature of the CRLH power dividers is that the circuit size is dramatically reduced, compared with a conventional right-handed one. Fig. 10(a)depicts the CRLH-TL-based power divider presented in [65].

The low-temperature co-fired ceramic(LTCC) technology is a multi-layer fabrication technology which can significantly reduce the circuit size. And its multi-layer configuration facilitates the implementation of broadside coupling for tight coupling, thus wideband power dividers are easy to implement like[66], which is exhibited in Fig. 10(b). However, due to the unavoidable high substrate loss and limited machining accuracy, the power divider based on lumped components [74]may exhibit better performance than the one constructed by distributed circuits.

Fig. 10 Power Dividers with unconventional transmission lines: (a) CRLHTL power divider in [65], (b) LTCC power divider in [66]

4.3 Power dividers with substrate integrated waveguide

Metallic waveguides possess the merits of low insertion loss, high quality factor (Q-factor),high power capability, etc, which is particularly suitable for millimeter-wave application. However, they also suffer their bulky size, stringent manufacturing precision, and non-planar geometry. Substrate Integrated Waveguides (SIW) preserve the most significant advantage of waveguide technology and provide a possible solution for complete integration of all the components on the same substrate. To make use of these merits, power dividers fabricated with SIW technology are proposed in [67], [73], [75], of which [67] is demonstrated in Fig. 11.

Since SIW is actually a kind of waveguide,the transmission-line theory is no longer applicable to analysis. Therefore, the main process of designing such a power divider is tuning, due to the lack of analytical design equations. Additionally, when feeding the SIW cavity or integrating it with other components,cavity-to-strip transitions or couplings are required, which would introduce unnecessary insertion loss.

V. THE TREND AND FUTURE OF POWER DIVIDERS

5.1 Beyond “power dividers”

The modern communication development requires the components to become increasingly integrated. Therefore, it is expected that the power divider could possess as many functions as possible, while maintaining the good power dividing performance. For example, if the aforementioned functions, including but not limited to multi-band/wideband operation,arbitrary power division, impedance transformation, filtering and harmonic control, are all integrated in a single power divider, the super power divider is beyond its original definition and many other components could be omitted in the system. Besides, it might be possible to propose a universal methodology for co-designing a multi-functional power divider,which will further simplify the design procedure when designing a microwave system.Moreover, power dividers with reconfigurable and tunable performance or functions become more and more welcomed in the future.

Additionally, power dividers on meta-materials begin to draw researchers attentions, like the one based on transformation optics constructed on nonisotropic and isotropic media[76], shown in Fig. 12.

5.2 Power dividers in terahertz or sub-terahertz domain

Terahertz (THz) technology has attracted more and more attentions and will be extensively investigated due to its promising applications in wireless communications, for it is a feasible solution for remitting the exiguous radio-spectral resource. Hence, power dividers should not be absent in the THz era.The existing solutions for constructing a THz power divider include THz waveguide [77],surface-plasmonic-polaritons (SPP) lines [78],and Goubau lines [79], all of which have the potential capability to operate in THz domain.But their functions and performance seem to be too simple compared with the microwave or millimeter-wave ones.

Since most of the planar power dividers are constructed on the basis of transmission lines,the key for enriching the functions of THz power dividers is to propose transmission lines with low loss, high fabrication tolerance and low dispersion in the terahertz domain. However, most THz-related researches focus on waveguide, for waveguide performs low-loss and high-power-capability characteristic. Recently, it is pleasing to see that THz transmission lines have attracted researchers’ interests.For example, literatures [80], [81] present two types of THz transmission lines, which might be the potential candidate for developing various THz power dividers.

Moreover, it should be recognized that different to the microwave components, the terahertz components have very small sizes which are sensitive to the fabrication tolerance and require very high fabrication accuracy.As a consequence, extremely-high accuracy fabrication process should be used in the fabrication for obtaining good fabrication quality,which is a quite challenging problem.

Fig. 11 Power Dividers with unconventional transmission lines (continued): SIW power divider in [67]

VI. CONCLUSION

This review overviews some state-of-the-art power dividers, which have either excellent performance or abundant functions. They are exhibited in the aspects of different performance configuration, various integrated functions, and irregular transmission-line technologies. Eventually, the future trends of power-divider development are predicted. This paper could be a reference for microwave/RF designers and inspiration of power-divider innovations.

ACKNOWLEDGEMENTS

This work was supported by National Basic Research Program of China (973 Program)(No. 2014CB339900), and National Natural Science Foundations of China (No. 61422103,No. 61671084, and No. 61327806).

[1] E. J. Wilkinson, “An N-way hybrid power divider,’Microwave Theory and Techniques, IRE Transactions on, vol. 8, no. 1, pp. 116-118, 1960.

[2] U. H. Gysel, “A new N-way power divider/combiner suitable for high-power applications,’ inMicrowave Symposium, 1975 IEEE-MTT-S International. IEEE, 1975, pp. 116-118.

[3] Y. Wu, Y. Liu, and X. Liu, “Dual-frequency power divider with isolation stubs,’Electronics Letters,vol. 44, no. 24, pp. 1407-1408, 2008.

[4] Y. Wu, Y. Liu, and S. Li, “An unequal dual-frequency Wilkinson power divider with optional isolation structure,’Progress In Electromagnetics Research, vol. 91, pp. 393-411, 2009.

[5] Y. Wu, Y. Liu, Y. Zhang, J. Gao, and H. Zhou, “A dual band unequal Wilkinson power divider without reactive components,’IEEE Transactions on Microwave Theory and Techniques, vol. 57,no. 1, pp. 216-222, Jan. 2009.

[6] Y. Wu, Y. Liu, Q. Xue, S. Li, and C. Yu, “Analytical design method of multiway dual-band planar power dividers with arbitrary power division,’IEEE Transactions on Microwave Theory and Techniques, vol. 58, no. 12, pp. 3832-3841, Dec.2010.

[7] Y. Wu, Y. Liu, and Q. Xue, “An analytical approach for a novel coupled-line dual-band Wilkinson power divider,’IEEE Transactions on Microwave Theory and Techniques, vol. 59, no. 2,pp. 286-294, Feb. 2011.

[8] M. Bemani and S. Nikmehr, “Nonradiating arbitrary dual-band equal and unequal 1:4 series power dividers based on CRLH-TL structures,’IEEE Transactions on Industrial Electronics, vol.61, no. 3, pp. 1223-1234, Mar. 2014.

[9] N. Gao, G. Wu, and Q. Tang, “Design of a novel compact dual-band Wilkinson power divider with wide frequency ratio,’IEEE Microwave and Wireless Components Letters, vol. 24, no. 2, pp.81-83, Feb. 2014.

[10] M. Liao, Y. Wu, Y. Liu, and J. Gao, “Impedance-transforming dual-band out-of-phase power divider,’IEEE Microwave and Wireless Components Letters, vol. 24, no. 8, pp. 524-526,Aug. 2014.

[11] Y. Wu, Y. Liu, and S. Li, “Unequal dual-frequency Wilkinson power divider including series resistor-inductor-capacitor isolation structure,”IET Microwaves, Antennas & Propagation, vol. 3, no.7, pp. 1079–1085, 2009.

[12] C. Cai, J. Wang, Y. Deng, and J.-L. Li, “Design of compact dual-mode dual-band filtering power divider with high selectivity,’Electronics Letters,vol. 51, no. 22, pp. 1795-1796, 2015.

[13] Q. Li, Y. Zhang, and Y. Fan, “Dual-band inphase filtering power dividers integrated with stub-loaded resonators,’ IET Microwaves, Antennas & Propagation, vol. 9, no. 7, pp. 695-699, May 2015.

[14] X. Ren, K. Song, M. Fan, Y. Zhu, and B. Hu,“Compact dual-band Gysel power divider based on composite right- and left-handed transmission lines,’IEEE Microwave and Wireless Components Letters, vol. 25, no. 2, pp. 82-84, Feb.2015.

[15] C.-W. Tang and Z.-Q. Hsieh, “Design of a planar dual-band power divider with arbitrary power division and a wide isolated frequency band,’IEEE Transactions on Microwave Theory and Techniques, vol. 64, no. 2, pp. 486-492, 2016.

[16] X. Wang, I. Sakagami, Z. Ma, A. Mase, M. Yoshikawa, and M. Ichimura, “Miniaturized dual-band Wilkinson power divider with self-compensation structure,’IEEE Transactions on Components,Packaging and Manufacturing Technology, vol.5, no. 3, pp. 389-397, Mar. 2015.

[17] T. Zhang, W. Che, H. Chen, and W. Feng, “A compact four-way dual-band power divider using lumped elements,’IEEE Microwave and Wireless Components Letters, vol. 25, no. 2, pp.94-96, Feb. 2015.

[18] W. Zhang, Z. Ning, Y. Wu, C. Yu, S. Li, and Y. Liu,“Dual-band out-of-phase power divider with impedance transformation and wide frequency ratio,’IEEE Microwave and Wireless Components Letters, vol. 25, no. 12, pp. 787-789, Dec. 2015.

[19] R. Gomez-Garcia, R. Loeches-Sanchez, D. Psychogiou, and D. Peroulis, “Single/multi-band Wilkinson-type power dividers with embedded transversal filtering sections and application to channelized filters,’IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 62, no. 6, pp.1518-1527, Jun. 2015.

[20] Y. Wu, J. Shen, L. Liang, W. Wang, and Y. Liu, “A novel compact tri-band Wilkinson power divider based on coupled lines,’ Electromagnetics,vol. 33, no. 1, pp. 59-72, Jan. 2013.

[21] Y. Wu and Y. Liu, “A novel wideband coupled-line Gysel power divider with function of impedance matching,’ Journal of Electromagnetic Waves and Applications, vol. 26, no. 14-15, pp. 2012-2021, Oct. 2012.

[22] K. Song, Y. Mo, and Y. Fan, “Wideband four-way filtering-response power divider with improved output isolation based on coupled lines,’IEEE Microwave and Wireless Components Letters,vol. 24, no. 10, pp. 674-676, Oct. 2014.

[23] K. Song, Y. Mo, Q. Xue, and Y. Fan, “Wideband four-way out-of-phase slotline power dividers,’IEEE Transactions on Industrial Electronics, vol.61, no. 7, pp. 3598-3606, Jul. 2014.

[24] U. T. Ahmed and A. M. Abbosh, “Wideband outof-phase power divider using tightly coupled lines and microstrip to slotline transitions,’Electronics Letters, vol. 52, no. 2, pp. 126-128, 2016.

[25] K. Song, Y. Zhu, Q. Duan, M. Fan, and Y. Fan, “Extremely compact ultra-wideband power divider using hybrid slotline/microstrip-line transition,’Electronics Letters, vol. 51, no. 24, pp. 2014-2015, 2015.

[26] B. Zhang and Y. Liu, “Wideband filtering power divider with high selectivity,’Electronics Letters,vol. 51, no. 23, pp. 1950-1952, 2015.

[27] M. M. Honari, L. Mirzavand, R. Mirzavand, A.Abdipour, and P. Mousavi, “Theoretical design of broadband multisection Wilkinson power dividers with arbitrary power split ratio,’IEEE Transactions on Components, Packaging and Manufacturing Technology, vol. 6, no. 4, pp.605-612, 2016.

[28] J. Shi, J. Wang, K. Xu, J.-X. Chen, and W. Liu, “A balanced-to-balanced power divider with wide bandwidth,’IEEE Microwave and Wireless Components Letters, vol. 25, no. 9, pp. 573-575, Sep.2015.

[29] W. Feng, H. Zhu, W. Che, and Q. Xue, “Wideband in-phase and out-of-phase balanced power dividing and combining networks,’IEEE Transactions on Microwave Theory and Techniques, vol.62, no. 5, pp. 1192-1202, May 2014.

[30] L. Zhu, S. Sun, and R. Li,Microwave bandpass filters for wideband communications. Hoboken,NJ: John Wiley, 2012.

[31] Y. Wu, Y. Liu, and S. Li, “A modified Gysel power divider of arbitrary power ratio and real terminated impedances,’IEEE Microwave and Wireless Components Letters, vol. 21, no. 11, pp. 601-603, Nov. 2011.

[32] Y.-S. Liu and J.-S. Row, “Back-to-back microstrip antenna fed with tunable power divider,’IEEE Transactions on Antennas and Propagation, vol.63, no. 5, pp. 2348-2353, May 2015.

[33] Y. Wu and Y. Liu, “Closed-form design method for unequal lumped-elements Wilkinson power dividers,’Microwave and Optical Technology Letters, vol. 51, no. 5, pp. 1320-1324, 2009.

[34] H.-R. Ahn, “Compact CVT-/CCT-unequal power dividers for high-power division ratios and design methods for arbitrary phase differences,’IEEE Transactions on Microwave Theory and Techniques, vol. 62, no. 12, pp. 2954-2964, Dec.2014.

[35] Y. Wu, Y. Liu, S. Li, and C. Yu, “Extremely unequal Wilkinson power divider with dual transmission lines,’Electronics Letters, vol. 46, no. 1, pp. 90-91, 2010.

[36] K.-X. Wang, X. Y. Zhang, and B.-J. Hu, “Gysel power divider with arbitrary power ratios and filtering responses using coupling structure,’IEEE Transactions on Microwave Theory and Techniques, vol. 62, no. 3, pp. 431-440, Mar.2014.

[37] S. Chen, Y. Yu, and M. Tang, “Planar out-ofphase Gysel power divider with high power splitting ratio,’Electronics Letters, vol. 51, no. 24,pp. 2010-2012, 2015.

[38] Z.-X. Du, X. Y. Zhang, K.-X. Wang, H.-L. Kao, X.-L. Zhao, and X. H. Li, “Unequal Wilkinson power divider with reduced arm length for size miniaturization,’IEEE Transactions on Components,Packaging and Manufacturing Technology, vol.6, no. 2, pp. 282-289, Feb. 2016.

[39] H. Chen, T. Zhang, W. Che, W. Feng, and Q. Xue,“Unequal Wilkinson power divider with wide range of arbitrary power division based on recombinant technology,’IET Microwaves, Antennas & Propagation, vol. 9, no. 2, pp. 166-175,Jan. 2015.

[40] K.-K. Cheng and P.-W. Li, “A novel power-divider design with unequal power-dividing ratio and simple layout,’IEEE Transactions on Microwave Theory and Techniques, vol. 57, no. 6, pp. 1589-1594, Jun. 2009.

[41] Y. Wu, M. Qu, W. Wang, and Y. Liu, “A frequency-independent dual-band printed quadrifilar helix antenna using nonuniform,unequal-length, asymmetrical coupled lines,’Microwave and Optical Technology Letters, vol.58, no. 7, pp. 1728-1733, 2016.

[42] S. Y. Zheng, Z. W. Liu, Y. M. Pan, Y. Wu, W. S.Chan, and Y. Liu, “Bandpass filtering Doherty power amplifier with enhanced efficiency and wideband harmonic suppression,’IEEE Transactions on Circuits and Systems I: Regular Papers,vol. 63, no. 3, pp. 337-346, 2016.

[43] S. O. Tatu, A. Serban, M. Helaoui, and A. Koelpin,“Multiport technology: the new rise of an old concept,’IEEE Microwave Magazine, vol. 15, no.7, pp. S34-S44, Nov. 2014.

[44] H.-R. Ahn, B. Kim, and S. Nam, “Compact UHF 3 dB MCCT power dividers,’IEEE Microwave and Wireless Components Letters, vol. 24, no. 7, pp.445-447, Jul. 2014.

[45] G. Chaudhary and Y. Jeong, “A design of power divider with negative group delay characteristics,’IEEE Microwave and Wireless Components Letters, vol. 25, no. 6, pp. 394-396, Jun. 2015.

[46] C. Miao, J. Yang, G. Tian, X. Zheng, and W. Wu,“Novel sub-miniaturized Wilkinson power divider based on small phase delay,’IEEE Microwave and Wireless Components Letters, vol. 24, no. 10,pp. 662-664, Oct. 2014.

[47] T. Zhang and W. Che, “Compact tunable power divider with wide tuning frequency range and good reconfigurable responses,’IEEE Transactions on Circuits and Systems II: Express Briefs,pp. 1-1, 2016.

[48] L. Gao, X. Y. Zhang, and Q. Xue, “Compact tunable filtering power divider with constant absolute bandwidth,’IEEE Transactions on Microwave Theory and Techniques, vol. 63, no. 10,pp. 3505-3513, Oct. 2015.

[49] Y. Wu, L. Jiao, W. Wang, Y. Liu, and Y. Siu, “An impedance-transforming coupled-line Wilkinson power divider with port isolations and extensions,’ Electromagnetics, vol. 35, no. 7, pp.453-460, Oct. 2015.

[50] Y. Wu, W. Zhang, Y. Liu, and W. Chen, “A novel harmonics-suppression coupled-line Gysel power divider for complex terminated impedances,’ Electromagnetics, vol. 34, no. 8, pp. 633-658, Nov. 2014.

[51] Y. Wu, J. Li, and Y. Liu, “A simple coupled-line wilkinson power divider for arbitrary complex input and output terminated impedances.’Applied Computational Electromagnetics Society Journal, vol. 29, no. 7, pp. 565-570, 2014.

[52] W. Feng, W. Che, and Q. Xue, “The proper balance: overview of microstrip wideband balance circuits with wideband common mode suppression,’IEEE Microwave Magazine, vol. 16, no. 5,pp. 55-68, Jun. 2015.

[53] K. Xu, J. Shi, L. Lin, and J.-X. Chen, “A balanced-to-unbalanced microstrip power divider with filtering function,’IEEE Transactions on Microwave Theory and Techniques, vol. 63, no. 8,pp. 2561-2569, Aug. 2015.

[54] W. Feng, C. Zhao, W. Che, and Q. Xue, “Wideband balanced network with high isolation using double-sided parallel-strip line,’IEEE Transactions on Microwave Theory and Techniques,vol. 63, no. 12, pp. 4013-4018, Dec. 2015.

[55] W. R. Eisenstadt, R. Stengel, and B. M. Thompson,Microwave differential circuit design using mixed-mode S-parameters, ser. Artech House microwave library. Boston: Artech House, 2006.

[56] J. Shi and K. Xu, “Compact differential power divider with enhanced bandwidth and in-phase or out-of-phase output ports,’Electronics Letters, vol. 50, no. 17, pp. 1209-1211, 2014.

[57] K. Song, F. Chen, X. Ren, and Y. Fan, “Compact in-phase power divider integrated filtering response using spiral resonator,’ IET Microwaves,Antennas & Propagation, vol. 8, no. 4, pp. 228-324, Mar. 2014.

[58] W.-M. Chau, K.-W. Hsu, and W.-H. Tu, “Filter-based Wilkinson power Ddivider,’IEEE Microwave and Wireless Components Letters, vol.24, no. 4, pp. 239-241, Apr. 2014.

[59] C.-F. Chen and C.-Y. Lin, “Compact microstrip filtering power dividers with good in-band isolation performance,’IEEE Microwave and Wireless Components Letters, vol. 24, no. 1, pp. 17-19, Jan. 2014.

[60] Y. Wu, Q. Liu, J. Shen, and Y. Liu, “Compact Wilkinson pass-band filtering power divider based on quarter-wavelength side-coupled ring,’ Journal of Circuits, Systems and Computers, vol. 23, no. 10, p. 1450135, Dec. 2014.

[61] F.-J. Chen, L.-S. Wu, L.-F. Qiu, and J.-F. Mao, “A four-way microstrip filtering power divider with frequency-dependent couplings,’IEEE Transactions on Microwave Theory and Techniques, vol.63, no. 10, pp. 3494-3504, Oct. 2015.

[62] K. Song, “Compact filtering power divider with high frequency selectivity and wide stopband using embedded dual-mode resonator,’Electronics Letters, vol. 51, no. 6, pp. 495-497, 2015.

[63] C.-M. Lin, H.-H. Su, J.-C. Chiu, and Y.-H. Wang,“Wilkinson power divider using microstrip EBG cells for the suppression of harmonics,’IEEE Microwave and Wireless Components Letters, vol.17, no. 10, pp. 700-702, Oct. 2007.

[64] R. Mirzavand, M. M. Honari, A. Abdipour, and G.Moradi, “Compact microstrip wilkinson power dividers with harmonic suppression and arbitrary power division ratios,’IEEE Transactions on Microwave Theory and Techniques, vol. 61, no. 1,pp. 61-68, Jan. 2013.

[65] H. L. Zhang, B. J. Hu, and X. Y. Zhang, “Compact equal and unequal dual-frequency power dividers based on composite right-/left-handed transmission lines,’IEEE Transactions on Industrial Electronics, vol. 59, no. 9, pp. 3464-3472,Sep. 2012.

[66] B. Zhou, “Broadband and compact LTCC power divider,’Electronics Letters, vol. 51, no. 23, pp.1939-1941, 2015.

[67] G. Li, K. Song, F. Zhang, and Y. Zhu, “Novel fourway multilayer SIW power divider with slot coupling structure,’IEEE Microwave and Wireless Components Letters, vol. 25, no. 12, pp. 799-801, Dec. 2015.

[68] Y. Wu and Y. Liu, “Compact 3-11 GHz UWB planar unequal power divider using two-section asymmetric coupled transmission lines and non-uniform microstrip,’Electronics Letters, vol.49, no. 16, pp. 1002-1003, 2013.

[69] X. Ren, K. Song, F. Zhang, and B. Hu, “Miniaturized Gysel power divider based on composite right/left-handed transmission lines,’IEEE Microwave and Wireless Components Letters, vol.25, no. 1, pp. 22-24, Jan. 2015.

[70] M. Bemani and S. Nikmehr, “Dual-band N-way series power divider using CRLH-TL metamaterials with application in feeding dual-band linear broadside array antenna with reduced beam squinting,’IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 60, no. 12,pp. 3239-3246, Dec. 2013.

[71] Y. Wu, Z. Zhuang, L. Jiao, and Y. Liu, “A compact planar wide-band balun with high isolation based on coupled-line and composite rightleft-handed transmission line,’Microwave and Optical Technology Letters, vol. 58, no. 2, pp.372-376, 2016.

[72] G. Li, K. Song, F. Zhang, and Y. Zhu, “Novel fourway multilayer SIW power divider with slot coupling structure,’IEEE Microwave and WirelessComponents Letters, vol. 25, no. 12, pp. 799-801, Dec. 2015.

[73] Q. Chen and J. Xu, “Out-of-phase power divider based on two-layer SIW,’Electronics Letters, vol.50, no. 14, pp. 1005-1007, 2014.

[74] M.-Q. Liu, X.-B. Wei, P. Wang, and W. Wei,“Compact LTCC multilayer broadband power divider,’ inComputational Problem-Solving (ICCP),2011 International Conference on. IEEE, 2011,pp. 370-372.

[75] T. Djerafi, D. Hammou, S. O. Tatu, and K. Wu,“Bi-layered substrate integrated waveguide wilkinson power divider/combiner,’ inMicrowave SymposiumDigest (IMS), 2013 IEEE MTT-S International. IEEE, 2013, pp. 1-3.

[76] Y.-L. Wu, Z. Zhuang, L. Deng, and Y.-A. Liu,“Three-dimensional multiway power dividers based on transformation optics,’Scientific Reports, vol. 6, p. 24495, Apr. 2016.

[77] N. Granpayeh and A. Dolatabady, “L-shaped filter, mode separator and power divider based on plasmonic waveguides with nanocavity resonators,’ IET Optoelectronics, vol. 9, no. 6, pp.289-293, Dec. 2015.

[78] X. Gao, L. Zhou, X. Y. Yu, W. P. Cao, H. O. Li, H. F.Ma, and T. J. Cui, “Ultra-wideband surface plasmonic Y-splitter,’ Optics Express, vol. 23, no. 18,p. 23270, Sep. 2015.

[79] A. Treizebre, S. Laurette, Y. Xu, R. G. Bosisio,and B. Bocquet, “THz power divider circuits on planar Goubau lines (PGLS),’Progress In Electromagnetics Research C, vol. 26, pp. 219-228,2012.

[80] X. Shen, T. Jiang, Y. Liu, X. Tang, and G.Chen, "Suspended microstrip line covered with dielectric in the ground plate for THz transmission,’ in2014 3rd Asia-Pacific Conference on Antennas and Propagation(APCAP), Jul. 2014, pp. 201-202.

[81] F. Fesharaki, T. Djerafi, M. Chaker, and K. Wu,"Low-Loss and Low-Dispersion Transmission Line Over DC-to-THz Spectrum,’IEEE Transactions on Terahertz Science and Technology, vol.6, no. 4, pp. 611-618, Jul. 2016.