He-xiu XU, Guang-ming WANG, Chen-xin ZHANG, and Yong HU
Quadrature Q-phase power splitters, with their 90-deg. difference between output ports, are useful components in communications systems applications. They can be used, for example, to realize amplifiers, phase shifters, and balanced mixers for receivers and transmitters.1,2 Because of the wavelength dependence of microstrip and stripline circuits, however, maintaining the small size of a printed quadrature power splitter can be challenging. The current project details the use of a new type of composite right/left-handed transmission line (CRLH TL) constructed in microstrip by Minkowski loop-shaped complementary split ring resonators (M-CSRRs) to form an extremely compact quadrature power splitter with low insertion loss and high isolation. To demonstrate the technique, an experimental design was developed for frequencies from 2.7 to 6.6 GHz with better than 15 dB isolation between ports and tightly matched phase and amplitude characteristics between the two output ports.
Challenges in fabricating compact quadrature power splitters include maintaining the tight 90-deg. difference between output ports as well as consistent electrical performance over broad frequency ranges. Efforts have been made with quadrature power splitters based on CRLH TLs using lumped-element approaches,3,4 CRLH TLs on coplanar waveguide (CPW) technology,5 and using metamaterial TLs.6 Although these approaches brought different levels of success, they were inadequate to providing good broadband performance with miniature size.
Fractal geometries have often been considered in efforts to create multiband but compact circuits.7,8 Recently, a square Sierpinski fractal curve was used in the design of complementary split ring resonators (CSRRs),9 resulting in significant miniaturization. For the novel broadband quadrature power splitter detailed here, Minkowski loop-shaped CSRRs (MCSRRs) with electrically small dimensions are proposed and examined for their merits. A CRLH TL was then fabricated and experimentally validated via its use in a broadband quadrature power splitter.
The classical Koch curve, named after mathematician Helge von Koch, has been applied to the miniaturization of a number of different conventional microwave components. The algorithm for generating the curve can be found in ref. 10. In the current report, a nonuniform Koch curve, the Minkowski loop, was applied to the design of CRLH TLs for use in a compact quadrature power splitter. The curve was determined by its iteration factor 1/4 and iteration order.
Figure 1 shows the topology of the proposed CRLH TL element. It was implemented by etching M-CSRR structures in the ground plane of a microstrip substrate, along with an interdigital capacitor formed in the microstrip conductor strip. The LH negative permeability is realized by the interdigital capacitor while its negative permittivity is realized by the M-CSRRs. Since Fractal perturbation doesn't result in additional lumped elements in the equivalent-circuit model, a conventional equivalent T-circuit model Fig. 1(b)> can be used for simulations.
The physical interpretation of this structure can be found in a number of previous reports and will not be detailed here. Minkowski loop perturbation in the CSRRs is considered from the point of miniaturization and broadband application. It has been experimentally proved that the fractal geometry used in CSRRs effectively extends the transmission line length, with the transmission zero of the CRLH TL cell shifted downward in frequency accordingly. Thus, the use of a fractal geometry in a CSRR-based circuit provides a size advantage even at lower frequencies. For broadband applications, however, the approach must be experimentally validated.
Figure 2 shows a prototype of the proposed M-CSRR-based CRLH TL cell. The CRLH TL cell is electrically small, with an overall dimension of only 0.16λ, where λ is the waveguide wavelength of the desired operating center frequency. The prototype was fabricated on RT/duroid 5880 laminate material from Rogers Corporation, glass-microfiber-reinforced polytetrafluoroethylene (PTFE) composite. The circuit board material was used with thickness (h) of 0.508 mm. It exhibits a typical relative dielectric constant (er) of 2.2 in the z-axis.
The physical dimensions of the CRLH TL cell were carefully optimized (Fig. 1). The electromagnetic (EM) behavior of the proposed CRLH TL cell was assessed by means of EM simulation by using Ansoft Designer 3.5 from Ansoft as well as electrical simulation by means of Ansoft Serenade. For comparison, measurements were performed on the prototype circuit by means of a model ME7808A vector network analyzer (VNA) from Anritsu Company. During the electrical parameter extraction process, the T-circuit model was run in Serenade to determine electrical parameters by matching the S-parameters of the circuit model to the EM simulated ones characterized by Designer 3.5. Extracted lumped-element parameters for the novel CRLH TL cell are summarized and given in the table.
Figure 3 plots the S-parameters of the proposed CRLH TL element. The curves show good agreement between the EM simulations, the equivalent-circuit models, and the measured data, from 0.5 to 8.0 GHz. The plots also show that the transmission 3-dB fractional bandwidth (about 2 to 8 GHz) of M-CSRRs-based CRLH-TL is significantly broadband, and the operating frequency has shifted down compared with a conventional circuit loaded with CSRRs (covering a bandwidth of about 2.6 to 4.3 GHz). The nonlinear phase response of the novel CRLH TL cell can be observed from the phase response curve.
Considering the excellent performance of proposed CRLH TL cell, it was decided to explore its practical application in the design of a compact, broadband quadrature power splitter. The novel quadrature power splitter is comprised of three parts: a 90-deg. differential phase-shift line that consists of the proposed CRLH TL cell, a conventional microstrip line, and a two-stage Wilkinson power divider that can be optimized to operate over a broad bandwidth. The new quadrature power splitter can provide balanced output magnitude with a 90-deg. phase difference between output ports and good isolation between any two ports just by adjusting the physical parameters of three parts for operation in the same frequency band.
Figure 4 shows the simulated and measured S-parameters for the proposed quadrature power splitter. The measurement results in Fig. 4(a) indicate that input port1 is perfectly matched, exhibiting minimum return loss of better than 40 dB at 4 GHz and return loss of better than 10 dB from 2.1 to 7.6 GHz. Figure 4(b) shows consistent transmission coefficients |S21| and |S31|; magnitude differences between the simulation and measurement results are apparent, except at the high frequency band, mainly due to the losses of the M-CSRRs etched in the ground plane and dissipative losses from the low-dielectric-constant substrate. Radiation losses are also apparent, with loss rising with increasing frequency. The measured magnitude difference is better than 0.8 dB from 2.15 to 6.6 GHz.
In Fig. 4(c), a comparison of the measured and simulated isolation can be seen. From 2.1 to 7.8 GHz, isolation is less than 15 dB. Discrepancies between the simulated and measured results can be mainly attributed to differences in the chip resistors used in the simulation compared to the prototype. In the simulation, the dimensions of these resistors are 60 30 mil, while in the prototype, 120 x 60 mil components were used. Discrepancies may also be due to the non-ideal nature of the isolation resistors in the prototype compared to in the simulation. Figure 4(d) shows that phase differences occur between the simulations and measurements over the entire frequency band of interest. The measurement results show that the phase differences between two outputs are less than 90 7 deg. from 2.7 to 7.1 GHz.
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In summary, the performance of the prototype quadrature power splitter validates the effectiveness of using the novel CRLH TL approach for passive component design. The technique offers an alternative design approach and a simple method for improving the performances of conventional CRLH TL designs.
This work is supported by the National Natural Science Foundation of China under Grant No. 60971118; special thanks are also due to the China North Electronic Engineering Research Institute for fabricating the experimental quadrature power splitter.
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