Table of Contents Author Guidelines Submit a Manuscript
International Journal of Antennas and Propagation
Volume 2019, Article ID 1564346, 9 pages
https://doi.org/10.1155/2019/1564346
Research Article

Novel Gysel Power Dividers with Negative Group Delay Characteristics

School of Information Science and Technology, Dalian Maritime University, Dalian, Liaoning 116026, China

Correspondence should be addressed to Zhongbao Wang; moc.liamxof@umldbzw

Received 14 May 2019; Accepted 29 July 2019; Published 14 August 2019

Academic Editor: Giorgio Montisci

Copyright © 2019 Zihui Zhu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A novel Gysel power divider with negative group delay (NGD), good matching, and low insertion loss is proposed. Resistors connected with short-circuited coupled lines (RCSCL) are shunted at output ports of the Gysel power divider to obtain NGD characteristics, and another resistor is shunted at the input port to realize perfect input and output matching. To verify the proposed structure, an NGD Gysel power divider is designed and fabricated. At the center frequency of 1.0 GHz, the measured NGD times for different output ports are −1.94 ns and −1.97 ns, the input/output port return loss is greater than 38 dB, the insertion loss is less than 8.3 dB, and the isolation between output ports is higher than 41 dB. To enhance the NGD bandwidth, two RCSCL networks having slightly different center frequencies are connected in parallel, which provides wider bandwidth with good input matching characteristics.

1. Introduction

Power dividing is widely adopted for various microwave applications such as antenna feeding networks and amplifiers [14]. Because the branch-line hybrid coupler operating in simple power dividing needs an extra port, power dividers are used more commonly. Besides, the Gysel power divider has the advantages of high power-handling capability because of the external isolation resistors and monitoring capability for imbalances at the output ports [5]. Structure with negative group delay (NGD) characteristics has been used to enhance the efficiency of feed-forward amplifiers [6]. Usually, the time mismatch between the envelope and the RF paths in supply-modulated power amplifiers will decrease linearity [7] and cause instability [8]. NGD power dividers can be used to compensate the group delay through different transmission paths in the supply-modulated power amplifier. Recently, some NGD power dividers have been presented in [912]. However, only one output port of these power dividers has the NGD characteristics and suffers from very high insertion loss (IL), which is more than 15 dB. Therefore, a Wilkinson divider based on the shunt resistor that connected with short-circuited coupled lines is used to decrease the IL and obtain the NGD characteristics for two output ports [13]. A T-type divider based on a coupling matrix approach is presented in [14]. However, its isolation between output ports is less than 16 dB.

In this paper, a novel Gysel power divider with high power-handling capacity, good matching, low IL, and NGD characteristics is proposed. Design formulas are derived and both the theoretical and experimental results are given and discussed.

2. Design Theory

The schematic of the proposed NGD Gysel power divider is shown in Figure 1. It is based on the conventional Gysel power divider, which is composed of two-section transmission lines (TLs) with the characteristic impedance of Z01 and the electrical length of θ, two-section TLs with different characteristic impedance of Z02 and same electrical length of θ, and a TL with the characteristic impedance of Z03 and the electrical length of 2θ. And its output ports are, respectively, shunted by a resistor R1 connected with short-circuited coupled lines (RCSCL) to realize the NGD characteristics. What’s more, all the resistors are grounded directly or grounded by the coupled lines, which makes adequate heat sinking of the resistors possible; thus, the main power-limiting factor caused by the resistors will be decreased significantly, and it is better than the Wilkinson power divider with the power-handling capacity of 100-watt continuous wave [5]. The short-circuited coupled lines have an equivalent characteristic impedance of Zc and electrical length of θc. Z0e and Z0o are the even- and odd-mode impedances of the coupled lines, respectively, which can be expressed aswhere k is the coupling factor of the coupled lines. In addition, a resistor R2 in parallel with the input port is added to realize perfect matching with port impedance Z0. The even- and odd-mode equivalent circuits are shown in Figure 2.

Figure 1: Configuration of the proposed NGD Gysel power divider.
Figure 2: Equivalent circuits of the proposed NGD Gysel power divider. (a) Even-mode. (b) Odd-mode.

The ABCD matrix of the even-mode circuit are derived aswith

The normalized ABCD matrix elements are obtained as

The normalized S-parameters of even-mode can be expressed as

Referring to Figure 2(b), the S-parameters of odd-mode can be expressed aswith

Then, the S-parameters of the proposed NGD Gysel power divider can be calculated by using the even- and odd-mode scattering parameters as

Applying the frequency-dependent electrical length of θ = θc = πf/(2f0), the group delay (GD) τ of the proposed NGD Gysel power divider can be obtained as

For perfect matching of all the input/output ports and infinite isolation between two output ports at f0, the following relations are found as

Moreover, the magnitude of transmission coefficient and group delay of the proposed NGD Gysel power divider at f0 are, respectively, found as (11) and (12) assuming R1 = R2 = R.

It can be found from (8), (9), and (11), the magnitude of transmission coefficient (i.e. IL) is only controlled by R. And (9) and (12) imply that R, k, Zc, Z02, and Z03 have effects on GD.

Figure 3 gives the effects of R on IL and τ × f0 of the proposed NGD Gysel power divider with Z02 = 100 Ω, Z03 = 100 Ω, k = 0.17, and Zc = 550 Ω. It can be observed that the maximum absolute value of NGD time at f0 increases as R decreases from 100 to 80 Ω, but IL also increases. Therefore, there is a tradeoff between the IL and NGD time.

Figure 3: Effect of R on the IL and τ × f0 of the proposed NGD power divider.

Figure 4 shows the calculated τ × f0 of the proposed NGD Gysel power divider with Z02 = 100 Ω, Z03 = 100 Ω, and R = 91 Ω. As shown in Figure 4(a) for fixed Zc = 550 Ω, the absolute value of NGD time at f0 increases as k decreases from 0.19 to 0.15. However, the NGD bandwidth (i.e., the bandwidth for GD less than 0 ns) will be decreased. Similarly, increased Zc leads to a larger absolute value of NGD time but narrower NGD bandwidth, which can be seen from Figure 4(b). Therefore, there is a tradeoff between the maximum absolute value of NGD time and the NGD bandwidth.

Figure 4: Effect of coupled lines on τ × f0 of the proposed NGD power divider: (a) k. (b) Zc.

As shown in Figure 5(a), the absolute value of NGD time and NGD bandwidth will be improved when Z02 is increased. But there is a slight enhancement of the NGD time and bandwidth when Z02 is more than 100 Ω. Figure 5(b) shows that Z03 influences NGD characteristics slightly.

Figure 5: Effect of Z02 and Z03 on τ × f0 of the proposed NGD Gysel power divider: (a) Z02. (b) Z03.

3. Circuit Layout and Implementation

3.1. Power Divider with Single-Stage RCSCL Networks

To verify the design concept of the proposed structure, an NGD Gysel power divider with single-stage RCSCL is designed with the center frequency of f0 = 1 GHz, predefined NGD time of −2 ns, and IL less than 9 dB. The circuit is implemented on PTFE/woven-glass substrate with a relative permittivity of 2.65 and thickness of 1.5 mm.

In the design, R is first selected as 91 Ω for IL less than 9 dB. Using (9) with R1 = R2 = R, Z01 is calculated as 84.63 Ω to realize perfect input/output port matching at f0. Referring to Figure 5, Z02 is selected as 100 Ω for obtaining a larger absolute value of NGD time, and Z03 is also selected as 100 Ω for simplicity. Then, Riso is calculated as 90.1 Ω using (10). Based on Figure 4(b), after making a tradeoff between the NGD time and the NGD bandwidth, Zc is selected as 530 Ω. Then, the coupling factor of the coupled lines is tuned with (12) to obtain the NGD time of −2 ns and determined as k = 0.17. Using (1), even- and odd-mode impedances of the coupled line are Z0e = 108.5 Ω and Z0o = 77 Ω, respectively. Furthermore, the electrical length of TLs at f0 is θc = θ = π/2. Using the TL synthesis tool ADS Linecalc, the physical dimensions of TLs are calculated. However, optimal physical dimensions of TLs must take account of distributed capacitance effect of the strip open-ends and distributed inductance effect of via holes. Therefore, the final dimensions are obtained by using the HFSS EM simulation. At last, the final dimensions of the NGD circuit are given in Table 1, and the photograph of the fabricated NGD Gysel power divider with R1 = R2 = Riso = 91 Ω is given as Figure 6. The overall circuit dimension is 82 mm × 79 mm.

Table 1: Dimensions of power divider with single-stage RCSCL networks (unit: mm; refer to Figure 6).
Figure 6: Photograph of the fabricated NGD Gysel power divider.

The simulated and measured performances of the proposed NGD Gysel power divider are shown in Figure 7. The measured GD times at f0 = 1 GHz for ports 2 and 3 are −1.94 ns and −1.97 ns, respectively. The measured NGD bandwidth of the proposed circuit is 31.3 MHz. The IL and IL bandwidth are shown in Figure 7(b), where IL bandwidth is defined as the 3 dB variation from the center frequency IL. The IL is 8.29 dB at f0, and the measured IL bandwidth is 155 MHz. The return loss (RL) of input port 1 at f0 is 44.4 dB and the RLs of output ports 2 and 3 are 38.3 dB and 40.1 dB, respectively. The measured isolation is 41.2 dB at f0. Furthermore, the measured amplitude imbalance and phase differences between output ports 2 and 3 are ±0.05 dB and 0.55°, respectively.

Figure 7: Performances of the proposed power divider. (a) Simulated and measured group delay. (b) Simulated and measured ILs and RLs. (c) Simulated and measured isolation. (d) Measured amplitude and phase imbalance characteristics.

The comparison of the proposed NGD Gysel power divider with other works is summarized in Table 2. The NGD power dividers [912] have larger NGD and IL bandwidths, but only one output port of the power divider has NGD characteristics and the IL is destructive (larger than 15 dB). Compared with [913], the proposed NGD Gysel power divider has a much lower IL. For the NGD power divider in [14], its isolation is poor (less than 16 dB), and it has a narrow IL bandwidth. The NGD power divider in [15] has the greatest IL bandwidth, but its output ports are not isolated (the isolation only is 1.2 dB). Except [12], the proposed NGD power divider has a better figure of merit (FOM). The FOM is defined as

Table 2: Performance comparison.

This FOM definition takes |τ(f0)| × BWNGD to evaluate the performance of the NGD circuit. |S21| and BWIL are added in the FOM for a better description of the transmission performance of the NGD circuit. At last, the relative bandwidth is introduced for a better comparison among different operation frequencies. Furthermore, the proposed power divider has the best RL performance with the smallest circuit size.

3.2. Power Divider with Parallel Connected Two-Stage RCSCL Networks

The NGD bandwidth of the power divider can be enhanced by using parallel connected NGD networks with slightly different center frequencies. However, the parallel connected RCSCL networks will change the port impedance of the ports 2 and 3. In order to match the 50-Ω port impedance, a simple method is to insert two λ/4 impedance transformers with the characteristic impedance of ZTF, as shown in Figure 8.

Figure 8: Configuration of the proposed power divider with parallel connected RCSCL networks.

For this purpose, the RCSCL networks are designed at f1 = 0.984 GHz and f2 = 1.016 GHz. For simplicity, most circuit element values of the Gysel power divider are same as previous, except for the values of resistances and the characteristic parameters of the coupled lines. Ra, Rb, Zc, and k are selected as 41 Ω, 41 Ω, 350 Ω, and 0.28, respectively. To meet the requirement of zero reflection from three ports and infinite isolation between ports 2 and 3, Rc and Rd are determined as 59 Ω, and the characteristic impedance of the transformer is given aswith

The characteristic impedance of the impedance transformer is calculated as 36 Ω.

Taking the effect of parallel connection into consideration, the physical dimensions of the circuit are optimized using HFSS EM software. Finally, the dimensions of the NGD circuit with Ra = 30 Ω, Rb = 47 Ω, Rc = 56 Ω, and Rd = 47 Ω are given in Table 3. The photograph of the fabricated power divider with parallel connected RCSCL networks is shown in Figure 9.

Table 3: Dimensions of power divider with two-stage RCSCL networks (unit: mm; refer to Figure 9).
Figure 9: Photograph of the fabricated NGD Gysel power divider with parallel connected RCSCL networks.

The simulated and measured performances of the NGD Gysel power divider with parallel connected RCSCL networks are shown in Figure 10. At f0, the measured NGD and IL are obtained as −0.5 ns and 15.5 dB. In the mean time, the measured isolation is 33.3 dB, the RL of input port 1 is 40.3 dB, and the RLs of output ports 2 and 3 are 34.6 dB and 34.3 dB, respectively. The achievable GD time is obtained as −1.15 ± 0.65 ns with an NGD bandwidth of 62 MHz, which is wider than the power divider with single-stage RCSCL networks. Moreover, the 20-dB RL bandwidth of input port 1 is also wider. The maximum absolute value of NGD time is slightly less than the power divider with single-stage RCSCL networks, which is due to the positive GD of the impedance transformers. Furthermore, the measured amplitude imbalance between output ports 2 and 3 ranges from −0.2 to 0.1 dB and phase difference from −0.5 to 1.1 deg (Figure 10(d)).

Figure 10: Performances of the Gysel power divider with parallel connected RCSCL networks. (a) Simulated and measured group delay. (b) Simulated and measured ILs and RLs. (c) Simulated and measured isolation. (d) Measured amplitude and phase imbalance characteristics.

4. Conclusions

In this paper, a novel Gysel power divider with NGD characteristics was proposed, which can be easily synthesized with the prescribed NGD time and IL. The analysis results show that a resistor shunted at the input port can be used to realize perfect matching, and the IL is controlled by the resistance value. What’s more, a larger coupling factor k of the coupled lines results in a wider NGD bandwidth, and a larger equivalent characteristic impedance Zc leads to a larger absolute value of NGD time. To enhance the NGD bandwidth, a Gysel power divider with parallel connected RCSCL networks was also presented in this paper. The proposed NGD power dividers have good RL, high isolation, and wide bandwidth, which can be applied to compensate group delay in microwave systems.

Data Availability

The data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under grant nos. 61871417, 61571075, and 51809030, in part by the Natural Science Foundation of Liaoning Province, in part by the Youth Science and Technology Star Project Support Program of Dalian City under grant 2016RQ038, and in part by the Fundamental Research Funds for the Central Universities under grant nos. 3132019219 and 3132019211.

References

  1. Q. Liu, Y. Liu, Y. Wu, M. Su, and J. Shen, “Compact wideband circularly polarized patch antenna for CNSS applications,” IEEE Antennas and Wireless Propagation Letters, vol. 12, pp. 1280–1283, 2013. View at Publisher · View at Google Scholar · View at Scopus
  2. Q. Liu, Z. N. Chen, Y. Liu, F. Li, Y. Chen, and Z. Mo, “Circular polarization and mode reconfigurable wideband orbital angular momentum patch array antenna,” IEEE Transactions on Antennas and Propagation, vol. 66, no. 4, pp. 1796–1804, 2018. View at Publisher · View at Google Scholar · View at Scopus
  3. Y. Wu, L. Jiao, Z. Zhuang, and Y. Liu, “The art of power dividing: a review for state-of-the-art planar power dividers,” China Communications, vol. 14, no. 5, pp. 1–16, 2017. View at Publisher · View at Google Scholar · View at Scopus
  4. Y. Wu, Z. Zhuang, M. Kong, L. Jiao, Y. Liu, and A. A. Kishk, “Wideband filtering unbalanced-to-balanced independent impedance-transforming power divider with arbitrary power ratio,” IEEE Transactions on Microwave Theory and Techniques, vol. 66, no. 10, pp. 4482–4496, 2018. View at Publisher · View at Google Scholar · View at Scopus
  5. U. H. Gysel, “A new N-way power divider/combiner suitable for high-power applications,” in Proceedings of the IEEE-MTT-S International Microwave Symposium, pp. 116–118, IEEE, Palo Alton, CA, USA, May 1975.
  6. H. Choi, Y. Jeong, C. D. Kim, and J. S. Kenney, “Efficiency enhancement of feedforward amplifiers by employing a negative group-delay circuit,” IEEE Transactions on Microwave Theory and Techniques, vol. 58, no. 5, pp. 1116–1125, 2010. View at Publisher · View at Google Scholar · View at Scopus
  7. K. Bumman, M. Junghwan, and K. Ildu, “Efficiently amplified,” IEEE Microwave Magazine, vol. 11, no. 5, pp. 87–100, 2010. View at Publisher · View at Google Scholar · View at Scopus
  8. Z. Popovic, “GaN power amplifiers with supply modulation,” in Proceedings of the IEEE MTT-S International Microwave Symposium, pp. 1–4, IEEE, Phoenix, AZ, USA, May 2015. View at Publisher · View at Google Scholar · View at Scopus
  9. C.-T. M. Wu and T. Itoh, “Maximally flat negative group-delay circuit: a microwave transversal filter approach,” IEEE Transactions on Microwave Theory and Techniques, vol. 62, no. 6, pp. 1330–1342, 2014. View at Publisher · View at Google Scholar · View at Scopus
  10. G. Chaudhary, J. Park, Q. Wang, and Y. Jeong, “A design of unequal power divider with positive and negative group delays,” in Proceedings of the European Microwave Conference, pp. 127–130, EUMC, Paris, France, September 2015. View at Publisher · View at Google Scholar · View at Scopus
  11. G. Chaudhary, P. Kim, J. Jeong, and Y. Jeong, “A power divider with positive and negative group delay characteristics,” in Proceedings of the URSI Asia-Pacific Radio Science Conference, pp. 1195–1197, URSI, Seoul, Korea, August 2016. View at Publisher · View at Google Scholar · View at Scopus
  12. Y. Wu, H. Wang, Z. Zhuang, Y. Liu, Q. Xue, and A. A. Kishk, “A novel arbitrary terminated unequal coupler with bandwidth-enhanced positive and negative group delay characteristics,” IEEE Transactions on Microwave Theory and Techniques, vol. 66, no. 5, pp. 2170–2184, 2018. View at Publisher · View at Google Scholar · View at Scopus
  13. 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, 2015. View at Publisher · View at Google Scholar · View at Scopus
  14. G. Chaudhary and Y. Jeong, “A finite unloaded quality-factor resonators based negative group delay circuit and its application to design power divider,” Microwave and Optical Technology Letters, vol. 58, no. 12, pp. 2918–2921, 2015. View at Publisher · View at Google Scholar · View at Scopus
  15. H. Wang, Y. Wu, Z. Wu, W. Wang, and Y. Liu, “Compact arbitrary terminated power divider with bandwidth-enhanced negative group delay characteristics,” International Journal of Circuit Theory and Applications, vol. 47, no. 6, pp. 909–916, 2019. View at Publisher · View at Google Scholar · View at Scopus