Design of a Compact Planar Transmission Line for Miniaturized Rat-Race Coupler With Harmonics Suppression

This paper presents an elegant yet straightforward design procedure for a compact rat-race coupler (RRC) with an extended harmonic suppression. The coupler’s conventional <inline-formula> <tex-math notation="LaTeX">$\lambda $ </tex-math></inline-formula>/4 transmission lines (TLs) are replaced by a specialized TL that offers significant size reduction and harmonic elimination capabilities in the proposed approach. The design procedure is verified through the theoretical, circuit, and electromagnetic (EM) analyses, showing excellent agreement among different analyses and the measured results. The circuit and EM results show that the proposed TL replicates the same frequency behaviour of the conventional one at the design frequency of 1.8 GHz while enables harmonic suppression up to the <inline-formula> <tex-math notation="LaTeX">$7^{\mathrm {th}}$ </tex-math></inline-formula> harmonic and a size reduction of 74%. According to the measured results, the RRC has a fractional bandwidth of 20%, with input insertion losses of around 0.2 dB and isolation level better than 35 dB. Furthermore, the total footprint of the proposed RRC is only 31.7 mm <inline-formula> <tex-math notation="LaTeX">$\times15.9$ </tex-math></inline-formula> mm, corresponding to <inline-formula> <tex-math notation="LaTeX">$0.28\,\,\lambda \times 0.14\,\,\lambda $ </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">$\lambda $ </tex-math></inline-formula> is the guided wavelength at 1.8 GHz.


I. INTRODUCTION
Microstrip rat-race couplers (RRC), also known as hybrid ring couplers, are widely used microwave circuits for dividing/combining microwave input power in their four ports [1]. Conventional RRCs are composed of six 90 • transmission lines (TLs), making them undesirably large components and susceptible to unwanted harmonics. An extensive number of attempts have been made to minimize the circuit size and attenuate the unwanted harmonics of the conventional RRC [2]. Artificial TLs were used to achieve 64% footprint reduction based on planar circuit lines without external lumped components [2].
The associate editor coordinating the review of this manuscript and approving it for publication was Qi Luo .
In an attempt for size reduction as well as harmonic suppression, slow-wave transmission lines are used to develop an RRC with the 5th harmonic suppression capability [3]. The compact branch-line coupler (BLC) application with low pass filter and open stubs was demonstrated, resulting in a significant size reduction and harmonic suppression [4]. Despite promising results in [3] and [4], the former results in a complex design and the latter has a high pass-band insertion loss.
In a different approach, external lumped reactive components are introduced in the RCC configuration in [5]- [8], where a considerable harmonic rejection and miniaturization up to 60% compared with the conventional RRC are reported. But, the usage of external lumped reactive components is not desirable in fabrication processes [8]. VOLUME 9, 2021 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ In [9], a planar discontinuous microstrip lines are used for size reduction of the BLC, which more than 60% size reduction is achieved compared to the normal coupler. But, this circuit does not have harmonics elimination.
In [10], shorted trans-directional (TRD) coupled lines along with T-type transmission have been used to develop an RRC, achieving a size reduction of 73% and harmonic suppression up to the fifth harmonic. However, several capacitors and holes are associated with the TRD that may not be desirable for some applications due to the fabrication complexity.
In [11], compensated spiral compact microstrip resonant cells were proposed in the RRC structure for 45% miniaturization and suppressing the third harmonic. However, applied resonator cells in this structure lead to high passband insertion loss.
In several studies [12], electromagnetic bandgap and defected ground structure techniques have been used for harmonics suppression and size reduction. In [12], photonic bandgap (PBG) cells have been utilized to design a small RRC with 23% size reduction. Apart from RRC, the PBG has a wide application in other passive microwave devices, such as various types of power dividers, filters, and frequency selective surfaces [13]- [17]. In [18], an RRC was designed based on defected ground structure technique, eliminating the third harmonic. T-shaped PBG cells were proposed to reduce the strip section length for the size reduction of RRCs [19]. While an acceptable size reduction has been demonstrated based on PBG, its complex manufacturing is not suitable for many applications [20]. In [21], a compact LC branch line was developed based on miniaturizing inductor and two transmission lines for harmonics removal and miniaturization.
Besides, neural networks, which are useful tools in solving the engineering problems [22]- [26] have been recently used to model the power dividers and couplers [27]. In [27] a power divider is designed and modeled using artificial intelligence, however designing of a coupler or divider by neural networks is not straightforward and the method is mostly suitable for modeling of the device.
In this work, a highly miniaturized RRC capable of rejecting unwanted harmonics up to the 7 th harmonic is presented, fabricated, and successfully tested. In this design, the proposed TL comprises three sections; two high impedance lines, loaded by a low-impedance line at the middle, where the conventional λ/4 long lines are made redundant.

II. DESIGN PROCEDURE
The design procedure of the proposed RRC is shown in Fig. 1 through 6 steps. In step 1, an LC equivalent circuit of the compact TL with the desired response is presented. The proposed LC model shows a wide suppression. In step 2, the realization of the proposed compact TL is presented in the schematic environment of the ADS software as a circuit simulation. In step 3, the proposed compact TL is designed in the momentum environment of ADS software, showing good agreement with the circuit simulation. Subsequently, the proposed compact TL is utilized in the conventional RRC to make a compact and harmonic-free RRC as shown in step 4. Next, the circuit simulation and EM simulation of the proposed RRC is performed in steps 4 and 5, respectively. Finally, the proposed RRC was fabricated on a RT/Duroid substrate and measured as shown in step 6.  of two high impedance lines loaded by a low-impedance line placed at the center. According to the fabrication limits, the minimum width used is equal to 0.1 mm, corresponding to a 167.5 high impedance line. This high impedance line is loaded by a low impedance line with 7.7 mm thickness at middle, which equals to 14.3 line.

III. PROPOSED COMPACT TRANSMISSION LINE DESIGN
Both the conventional λ/4 line and the proposed line have input and output ports with 50 .ohms impedance. According to the substrate specifications, 50 ohms is achieved for 1.56 mm width of the transmission line.
The LC equivalent circuit of the proposed compact TL is extracted and shown in Fig. 3  To show the theoretical relation of frequency response for the presented resonator, the transfer function of this LC model is extracted as written in equation (1), as shown at the bottom of the next page.
The bode plot for the obtained transfer function is plotted by MATLAB software and depicted in Fig. 4. There is good agreement between the simulation results of the LC model frequency response and the Bode plot of the extracted transfer function, validating the theoretical analysis. In this equivalent circuit, C S and l S model the open ended stub of the TL, generating a transmission zero at f 0S calculated by (2) as depicted in Fig. 5. This transmission zero would then contribute to largening the suppression band of the power divider. Furthermore, the high impedance lines in Fig. 3(a) are modeled by two l 1 inductors in the LC model, acting as a three-pole lowpass filter (LPF) in conjunction with C S . The bandwidth of the TL equals the LPF cut-off frequency (f C ) estimated by (3). In detail, l S has a negligible contribution in locating cut-off frequency of the filter; firstly, because the capacitive effect is dominant in the open stub, and secondly because l S is considerably smaller than l 1 . The components of the proposed compact TL resonator are graphically explained in Fig. 5. For the designed compact TL resonator, the values of the lumped inductors and the capacitor are selected as l 1 = 8 nH, l S = 0.2 nH and C S = 0.9 pF. So, according to equations (2) and (3) the calculated bandwidth (BW) and transmission zero (f 0S ) are 2.7 GHz and 11.9 GHz, respectively, which are very close to the simulation results of BW = 2.8 GHz and f 0S = 11.9 GHz, verifying the accuracy of the circuit modeling.
The scattering parameters of the conventional λ/4 line and the proposed compact TL are illustrated in Fig. 6.  To summary, it is confirmed that the proposed TL line replicates the same frequency behavior of the conventional lines at the operating frequency of 1.8 GHz. Additionally, it has an additive advantage of harmonic elimination over the frequency window of 5.6 GHz up to 14.6 GHz with high attenuation level (more than 20 dB), as depicted in Fig. 6.

IV. CONVENTIONAL RAT RACE COUPLER DESIGN
The structure of the conventional RRC, designed at 1.8 GHz is illustrated in Fig. 7 (1)  The insertion losses (S12 and S13) are less than 0.3 dB, and the S11 and S14 are better less than −20 dB, over the operating frequency band of 20%.
In this conventional design, we use the same RT/Duroid substrate with a thickness of 20 mil, where the λ/4 line has a physical length of 30.3 mm at 1.8 GHz with a 70.7 characteristic impedance, corresponding to 0.89 mm width. The overall size of the conventional RRC is 61.8 mm × 31.3 mm (0.50 λ × 0.25λ).
The scattering parameters of the conventional RRC is illustrated in Fig. 8. As can be seen from this figure, the coupler operates at 1.8 GHz, where the input return loss and the ports isolation are better than 48 dB and 65 dB, respectively. The insertion losses of other ports are in a very good range dB (S 12 = S 13 = −3.1 dB).
As highlighted in Fig. 7, the insertion losses (S 12 and S 13 ) of the conventional RRC are less than 0.3 dB throughout FIGURE 11. The scattering parameters of the proposed RRC. (a) S11 (b) S12 (c) S13 (d) S14.
the fractional bandwidth of 22%, extending from 1.6 GHz to 2 GHz with S 11 and S 14 better than 20 dB.

V. DESIGN OF THE PROPOSED RAT RACE COUPLER
In order to reduce the size of the conventional RRC designed in the last section and to eliminate the unwanted higher-order harmonics, the conventional long λ/4 lines are replaced by In the calculation of the FBW, the insertion losses (S12 and S13) are less than 0.3 dB, while S11 and S14 are considered less than −20 dB, which the operating bandwidths are highlighted with colored boxes in the figure.  the proposed compact TLs. The schematic diagram of the proposed RRC is illustrated in Fig. 9.
The proposed coupler only occupies 31.7 mm × 15.9 mm (0.28 λ × 0.14 λ, where λ is the guided wavelength at 1.8 GHz). Thus, compared to the conventional one, the proposed device has a 74% size reduction. The scattering parameters of the proposed RRC are illustrated in Fig. 10.
As shown in Fig. 9, the scattering parameters of the new RRC with the proposed TL are very similar to the conventional coupler over its operating frequency band, with insertion losses and isolation better than 0.3 dB and 20 dB, respectively. The new coupler has a 20% fractional bandwidth, extending from 1.62 GHz −1.98 GHz.   The circuit electromagnetic (EM) simulated results of the proposed RRC are illustrated in Fig. 11.
It can be seen from Fig. 12 that the proposed RRC demonstrates excellent performance at the design frequency  isolation (S 14 ) of around 55 dB at 1.8 GHz. It should be noted that some interblock coupling effects are neglected in the circuit simulation, resulting in some minor out-of-band discrepancies between the EM and circuit simulations.
The proposed coupler has a significant harmonic suppression capability, as demonstrated in Fig. 12. In detail, the 2 nd harmonic to the 7ths harmonics are suppressed by 16 dB, 19 dB, 24 dB, 29 dB, 32 dB, and the 38 dB, respectively, where the lowest attenuation levels of S 31 and S 21 are used. Table 1 shows the performance summary of the proposed RRC at its operating frequency. The dimensions of the proposed compact TL not only determine the stop-band bandwidth, but also has a direct effects on the operating bandwidth. To demonstrate this, the relationship between the FBW and Cs, ls values (extracted lumped component) are depicted in the Figure 12. Table. 2, shows the size reduction and harmonics suppression of the proposed RRC compared to the normal coupler.
The proposed RRC has a significantly smaller size than the conventional RRC. The layout of the proposed RRC and normal RRC at 1.8 GHz with the same substrate are shown in Fig. 13. The proposed RRC only occupies 26% of the size of the conventional RRC, which offers 74% size reduction, while it has the additive advantage of harmonic suppression.
The output phase difference of the conventional and proposed RRC are depicted in Fig. 14. The results show that the phase differences between output ports of the conventional and proposed coupler at the design frequency of 1.8 GHz are 1.6 • and 0.8 • , respectively, showing an improvement of this parameter by the proposed coupler.

VI. FABRICATION AND MEASUREMENT
One prototype of the RRC on RT/Duroid substrate (ε r = 2.2 and H = 20 mil) was fabricated and shown in Fig. 15.
The S-parameters of the prototype are measured by a twoports HP 8720D network analyzer, shown in Fig.16.
The measured scattering parameters of the proposed RRC are demonstrated in Fig. 17. A comparison among circuit simulation, EM simulation, and the measurements are shown in Fig. 18. It can be seen from this figure that there is excellent agreement between measured and simulated results over the frequency band; however, some insignificant discrepancies appeared in the higher out-of-band. The results demonstrate that the proposed RRC operates at 1.8 GHz and suppresses harmonics from 2 nd up to 7 th with good suppression levels.
As measured results show, the prototype RRC has output insertion losses below 0.2 dB (S 12 = S 13 = −3.2 dB) and input return loss and ports isolation better than 35 dB at the design frequency of 1.8 GHz.
The proposed RRC exhibits superior performance as compared with other related works. In Table 3, some microstrip branch-line couplers (BLCs), rat-race couplers (RRCs), Wilkinson power dividers (WPDs), and Gysel power dividers (GPDs) with harmonics suppression and size reduction are listed. As results show, the proposed RRC offers the smallest size and provides wide stop-band bandwidth, eliminating seven unwanted harmonics.

VII. CONCLUSION
In this paper, a compact RRC capable of harmonic suppression is presented. In this design, the conventional TLs of RRC are replaced by compact and efficient TL to operate at 1.8 GHz. The proposed RRC was fabricated and tested, showing a good performances compared to the other related works. The insertion losses for two output ports are better than 0.2 dB, while an excellent input return loss and port isolation are obtained for the proposed RRC (better than 35 dB). In the proposed RRC six compact proposed TLs are used, which shows more than 74% size reduction and suppresses 2 nd -7 th harmonics. MOHAMMAD AMI received the B.Sc. and M.Sc. degrees in electrical engineering from Islamic Azad University, Kermanshah Branch, Kermanshah, Iran, in 2017 and 2020, respectively. His research interests include the low-power and low-size integrated circuit design, microwave circuits, power dividers, couplers, filters, and diplexers.
SOBHAN ROSHANI received the B.Sc. degree in electrical engineering from Razi University, Kermanshah, Iran, in 2010, the M.Sc. degree in electrical engineering from Iran University of Science and Technology (IUST), Tehran, Iran, in 2012, and the Ph.D. degree in electrical engineering from Razi University, in 2016. He is currently an Assistant Professor with the Department of Electrical Engineering, Kermanshah Branch, Islamic Azad University, Kermanshah. He has published more than 70 papers on international journals and conferences. His research interests include switching power amplifiers, optimization and neural networks, artificial intelligence, modeling, microwave circuits, power dividers, couplers, filters, and diplexers.