Compact Band-Selective Power Divider Using One-Dimensional Metamaterial Structure

A band-selective power divider is demonstrated for the first time. By replacing lumped element right-handed (RH) and left-handed (LH) transmission lines (TL) in a conventional Wilkinson power divider, it is possible to achieve both power division and filtering simultaneously. By utilizing the positive phase propagation property of an RHTL, which works as a low-pass filter, and the negative phase propagation property of an LHTL, which works as a high-pass filter, the band-selective quarter-wave sections required to construct a Wilkinson power divider are implemented. The fabricated circuit shows an insertion loss in the range 1.7 dB–2.5 dB in the passband, with the circuit dimensions of merely 12 mm by 10 mm.


Introduction
Many radio-frequency and microwave systems require power dividing and combining processes. As a Wilkinson power divider [1] can match all the ports with the same characteristic impedance and isolate ports effectively, various types of such dividers have been introduced [2][3][4][5][6] to minimize the size [3,4] and increase the bandwidth [5,6]. Recently, several dual-band Wilkinson dividers have been reported [7,8] but they still require long microstrip transmission lines, making the size of the power divider large. Moreover, it is difficult to select the desired band in such structures. To overcome such limitations, a compact and broadband tunable Wilkinson power divider has been introduced in [9].
Furthermore, band-pass filtering is an essential process to filter out unwanted signals in many wireless systems. Particularly, in a modern multimode and multiband communication system, effective signal filtering is a very important issue. When it is required to split power and filter signals, a power dividing element and a band-pass filter must be cascaded.
is may degrade the overall system performance in terms of loss, size, and efficiency. To improve these degradations, various research studies have been carried out to achieve both power dividing and filtering characteristics in a single circuit [10][11][12]. e author of reference [11] used a series connected band-pass filter and a low-pass filter to replace the quarter-wave section of the Wilkinson power divider, and the author of reference [12] suggested a power divider using a coupled microstrip line structure.
Recently, various applications of left-handed transmission lines (LHTLs) have been demonstrated for novel microwave circuits [13][14][15]. A synthetic transmission line composed of series capacitors and shunt inductors shows negative phase propagation [13][14][15]. It is evident that the structure itself is a high-pass filter. is structure is the dual of a right-handed transmission line (RHTL), where series inductors and shunt capacitors are periodically loaded. is conventional RHTL works as a low-pass filter.
Our main idea is to combine a synthetic RHTL and a synthetic LHTL to realize quarter-wave sections in a conventional Wilkinson power divider. With this method, it is possible to achieve effective power division and band-pass filtering simultaneously. Moreover, as this circuit is made with lumped elements only, it is compact in size especially when the circuit is designed for low-frequency band. Due to this advantage, proposed circuit is a good candidate for many compact and portable microwave systems.

RHTL and LHTL Theory
As there are many articles regarding the structures and analysis of RHTL and LHTL, we briefly review the theories to explain the operation of a band-selective power divider. Figure 1(a) shows a section of an RHTL. e section is constructed with two series inductors and a shunt varactor. As this is a low-pass filter structure, the periodic cut-off frequency (Bragg cut-off frequency) is given by equation (1) when several identical sections are cascaded [11]: Here, L R is a series inductor and C R is a shunt capacitor. In this synthetic transmission line, the characteristic impedance (Z 0R ) also can be approximated as follows: e phase propagation constant (β R ) is given by the following equation [11]: (3) Figure 1(b) shows a section of an LHTL. e Bragg cut-off frequency, characteristic impedance (Z 0L ), and phase propagation constant (β L ) [11] are, respectively, given as follows: e structure is high-pass filter with negative phase propagation, as shown in equation (6).

Band-Selective Power Divider
where m and n represent the number of identical sections of the RHTL and LHTL, respectively. Note that β L is negative in (7). us, we can implement a compact, band-selective power divider. When designing the proposed circuit, one should carefully select the values of inductors and capacitors for the desired phase propagation constant, characteristic impedance, and cut-off frequency.

Realization and Measurement
e band-selective power divider shown in Figure 3 is realized on an FR4 board. e whole circuit is merely 12 mm by 10 mm in size. For the RHTL, we used C R � 7 pF and L R � 36 nH so that Z 0R � 71.7Ω and f R Bragg � 634 MHz. For the LHTL, we used C L � 3 pF and L L � 15 nH; therefore, Z 0L � 70.7 Ω and f L Bragg � 375 MHz. We cascaded four sections of RHTL and three sections of LHTL. Using (3), (6), and (7), we calculated that the 90°phase propagation occurs at 475 MHz. We verified that the simulation result is consistent with our calculation. Figure 4 shows the measured phase balance between output ports (a) and the magnitude response between ports

Conclusion
In this paper, we presented a band-selective divider based on the RH, LHTL structure and demonstrated our idea through experimental results. Owing to the RH, LHTL combination structure, we could achieve an effective power dividing with the passband as 410 MHz-540 MHz. A size reduction due to the replacement of λ/4 sections of conventional Wilkinson power divider to lumped elements would be more significant when the operational frequency band is lower. is circuit can be effectively applied to various compact microwave systems since it can perform both power dividing and filtering although it occupies an area for only a single circuit.

Data Availability
e data used to support the findings of this study are available from the corresponding authors upon request.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.  International Journal of Antennas and Propagation