Design of a UWB Phase Shifter Using Shunt λ/4 Stubs

Xinyi Tang, Koen Mouthaan

Department of Electrical and Computer Engineering, National University of Singapore

Abstract — In this paper a novel phase shifter covering the

whole UWB frequency range with small phase error is presented. The proposed topology employs a single layer substrate and is easy to fabricate. The phase shifter uses shunt quarter wavelength stubs in the resonator branches and transmission lines (TLs) in the reference branches to achieve phase shifts ranging from 20º to 70º while keeping the return loss above 10 dB. The shunt stubs are used to control the phase response. An additional half wavelength TL is inserted in the large phase shifts to improve the return loss. As examples 22.5º and 45º phase bits are designed and fabricated. Theoretical phase errors of ±2º and ±3º are obtained for the 22.5º and 45º phase bits respectively. The measured phase shifts of the two phase bits are 23.6º±2.7ºand 45.8º±4.5º with return losses better than 11 dB and 13.4 dB from 3.1 GHz to 10.6 GHz respectively. The measured amplitude imbalances are less than 0.3 dB.

Index Terms — phase shifters, ultra-wide band.

I. INTRODUCTION

Phase shifters are used in electronic beam-scanning phased array systems, modulators and other control modules. Ideally, the phase shifter should provide a constant phase shift over an infinite bandwidth with zero loss. In practice, broadband phase shifters are difficult to realize, especially when both phase error and return loss are considered simultaneously. Phase shifters using lumped inductors and capacitors, such as high-pass/low-pass networks and all-pass networks, are popular since they are compact in size and have a relatively large bandwidth up to an octave [1]-[3].

However, for UWB applications from 3.1 GHz to 10.6 GHz, a larger bandwidth (109%) is required. Furthermore, in PCB realizations, the use of discrete inductors may influence the performance substantially when the frequency is higher [4]. Therefore, designs that avoid discrete inductors on PCB are preferred. In [5], coupled lines together with open and shunt stubs were employed to design a 180º phase bit with a ±5º phase error over an octave bandwidth. In [6], the bandwidth of the 45º phase bit was extended up to 100% with a small phase error of ±3º by employing an optimized bell-shaped structure. In [7], a multi-layer topology was presented to provide phase shifts from 25º to 48º for the UWB frequency range. The coupling between the top and the bottom layers through an elliptical slot in the middle layer was utilized to control the coupling factor. As examples, a 30º bit and a 45º bit were presented.

In this work, a novel phase shifter topology, providing a larger phase shift range for UWB applications on a single layer substrate, is presented. In Section II, the theoretical

analysis is given and the theoretical phase shift ranges of the proposed topology are shown. In Section III, two phase bits are designed according to the theory. The selected phase bits (22º and 45º) fit the binary phase shifter design requirement. In Section IV, measured results for the fabricated phase shifters are provided and conclusions are presented in Section V.

II. ANALYSIS

Fig. 1 (a) shows the proposed topology for the 22.5º phase shifter, which contains the single stub resonator branch and the reference branch. Fig. 1 (b) shows the proposed topology for the 45º phase shifter, which contains the double stubs resonator branch and the reference branch. The wavelength λ refers to the wavelength at the center frequency.

The shunt quarter wavelength stubs in both Fig. 1 (a) and (b) are used to control the slope of the insertion phase of the resonator branch. In Fig. 2, the influence of the characteristic impedance of the single shunt stub on the insertion phase and return loss is shown. It is found that the larger the Z1, the smaller the phase slope and the higher the return loss. If the phase slope is the same as the phase slope of the reference branch, a constant phase shift is obtained. Since the resonator branch has an insertion phase of zero degree at the resonant frequency, the phase shift value between the two branches is determined by the phase of the reference branch. Therefore, to obtain a large bandwidth for small phase shifts, the phase slope of the resonator branch is also required to be small. For

(a) (b) Fig. 1. Proposed UWB phase shifter topology (a) single stub phaseshifter for small phase shift and (b) double stubs phase shifter forlarge phase shift.

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the single stub phase shifter, the phase shift response and the return loss of the resonator branch are plotted in Fig. 3.

From Fig. 3 it is observed that to ensure a return loss larger than 10 dB over the whole UWB frequency band, the phase shift range is from 10º to 30º. For phase shifts less than 20º, the fabrication tolerance needs to be considered since high impedance lines are required. For phase shifts above 30º, on the other hand, the return loss limits the bandwidth. Note that all phase shifts have a phase error less than ±2º.

To further improve the return loss for the larger phase shifts, a half wavelength TL is added between the two shunt stubs, as shown in Fig. 1(b). The extra 180º electrical length is compensated by adding the same length to the TL branch. Note that the design area is therefore larger by adding the extra length in both branches.

The inserted TL adds two transmission poles that help to increase the return loss bandwidth. The frequency of the

transmission poles can be found from the S-parameter analysis of the structure. By assuming S11=0, the following relation is obtained:

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3

2

2sin

5.0tan

cos25.0tan

sin

sinZZ

ZZ

Z ωπωπ

ωπωπ

ωπ

ωπ =+

+ (1)

Where 3,2Z are the normalized values of Z2,3 and ω is the normalized frequency. The values π and 0.5π represent the phase of the half wavelength and quarter wavelength TLs at the center frequency ( ω =1).

From equation (1), it is observed that for the resonator branch, the additional resonant frequencies are determined by the impedance of the transmission lines. Therefore, the return loss can be controlled by Z2 and Z3. To reduce the complexity, we fix 2Z to be 1. Then the extra resonant frequencies can be obtained from:

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115.0tanZ

+±=ωπ (2)

The two resonant frequencies are symmetrical with respect to the center frequency, and thus can be written as:

⎟⎟⎠

⎞⎜⎜⎝

⎛+−±=

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2,111arctan211Zπ

ω (3)

Fig. 4 shows the extended phase shift in the UWB frequency range. The extra transmission poles are clearly visible and they lead to a larger bandwidth of the resonator branch. From the figure, it is found that phase shifts up to 70º are feasible while the return loss is larger than 10 dB over the whole UWB frequency band. For the double stub phase shifters, the phase errors increase to ±3.5º, ±4.5º and ±5.5º for 50º, 60º and 70º phase shifts, respectively and remain ±2º for smaller phase shifts.

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Fig. 2. Characteristic impedance affect on phase and RL of the single stub.

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Fig. 4. Phase shift and RL response for double stub phase shifter. The phase difference at the center frequency is the electrical length of the TL branch minus 180º.

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Fig. 3. Phase shift and RL response for single stub phase shifter.The phase difference at the center frequency is the electrical lengthof the TL branch.

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Fig. 5 compares the phase response and return loss for a 45º phase shift by using the single stub and the double stubs topology. As predicted, the return loss for the double stubs topology is improved by the added transmission poles.

III. DESIGN

Two phase bits that fit the usual binary phase shifter requirement (360º/2n

, n=1, 2, 3…) are designed to cover the whole UWB frequency band. The selected phase shifts of 22.5º and 45º fall into the phase shift ranges shown in Fig. 3 and Fig. 4 respectively. Therefore, both single stub and double stubs topologies are used in the design.

Rogers 5870 (εr=2.33, h=31 mils) is chosen as the substrate. The impedance of the shunt stubs are selected to be 125 Ohm for both structures, which leads to a metal width of 0.4 mm (≈16 mils). A large grounding area is used to provide a good ground for high frequencies. The distance between the end of the stubs and the edge of the via-holes is 0.6 mm in our design. In the Momentum simulations the metal loss and the coupling between all lines and the ground are included.

Fig. 6 shows the fabricated phase shifters. The stubs for the

resonator branch are not precisely 0.4 mm due to fabrication tolerances. The effective area of the resonator branch for the 45º phase shifter is approximately 2 cm2.

Because the measurement is up to 10 GHz, the influence from the SMA connectors cannot be neglected. Therefore, a custom TRL calibration kit was fabricated for the measurement. Two lines are used in the TRL calibration of 1.50 cm and 0.83 cm longer compared to the thru to cover the frequency ranges of 3 to 7 GHz and 7 to 11 GHz.

IV. MEASUREMENT

The measured results after the TRL calibration are shown in Fig. 7 to Fig. 10.

Fig. 7 shows the comparison of the simulated phase shifts

Fig. 6. Photo of the fabricated phase shifters.

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single stub, Z1=66.5 Ω double stubs, Z3=130 Ω

Fig. 5. Comparison of the 45º phase shift using two directly cascaded single stub and the double stub structure.

Fig. 7. Simulated and measured phase shifts.

Fig. 8. Simulated and measured return loss of the two bits.

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and the measured results of the two phase bits. The measured results show 23.6º±2.7º and 45.8º±4.5º for the two phase bits from 3.1 GHz to 10.6 GHz.

Fig. 8 shows the comparison of the return loss of the resonator branches only. The measured return loss for the 22.5º phase bit is better than 11 dB while for the 45º phase bit it is better than 13.4 dB. It is found that the resonant frequencies for the 45º phase bit are further separated than simulation due to the inaccurate fabrication of the shunt stubs.

Fig. 9 and Fig. 10 show the comparison of the measured

branches and the momentum simulation of the resonator branches. The small peaks near 9 GHz for all branches are due to the calibration. The amplitude imbalances of the insertion loss of both bits are within 0.3 dB.

V. CONCLUSION

In this paper, a novel and simple UWB phase shifter design topology is presented that can cover the phase range from 20º to 70º. A shunt quarter wavelength TL is used to control the phase slope of the resonator branch so that a constant phase shift over a large bandwidth is achieved. The realization employs a single layer substrate and has no coupled lines, which is advantageous in PCB fabrication. The topology is used to design phase bits of 22.5º and 45º. The measured results show phase shifts of 23.6º±2.7º and 45.8º±4.5º for the two bits. The measured return losses are better than 11 dB for the single stub topology and 13 dB for the double stub topology. The amplitude imbalance of the insertion loss is within 0.3 dB.

ACKNOWLEDGEMENT

This work was supported by the Home2015 Programme of SERC, A*STAR (Agency for Science, Technology and Research), Singapore.

REFERENCES

[1] R. V. Garvar, “Broad-band diode phase shifters,” IEEE Trans. Microwave Theory & Tech.., vol. MTT-20, no. 5, pp. 314-323, May 1972.

[2] Inder. J. Bahl and D. Conway, “L- and S- band compact octave bandwidth 4-bit MMIC phase shifters,” IEEE Trans. Microwave Theory & Tech.., vol. 56, no. 2, pp. 293-299, Feb. 2008.

[3] D. Adler and R. Popovich, “Broadband switched-bit phase shifter using all-pass networks,” 1991 IEEE MTT-S Int. Microwave Symp. Dig., pp. 265-268, June 1991.

[4] M. A. Morton, J. P. Comeau, J. D. Cressler. M. Mitchell and J. Papapolymerou, “Sources of phase error and design considerations for silicon-based monolithic high-pass/low-pass microwave phase shifters,” IEEE Trans. Microwave Theory & Tech.., vol. 54, no. 12, pp. 4032-4040, Dec. 2006.

[5] S. Eom, “Broadband 180º bit phase shifter using a λ/2 coupled line and parallel λ/8 stubs,” IEEE Microw. Wireless Compon. Lett., vol. 14, no. 5, pp. 228-230, May 2004.

[6] S. Zheng and et al, “Improved broadband dumb-bell-shaped phase shifter using multi-section stubs,” Electronics Lett., vol. 44, no. 7, pp. 478-480, Mar. 2008.

[7] Amin M. Abbosh, “Ultra-wideband phase shifters,” IEEE Trans. Microwave Theory & Tech.., vol. 55, no. 9, pp. 1935-1941, Sept. 2007.

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Fig. 9. Simulated and measured insertion loss of the 22.5º phase bits.

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Fig. 10. Simulated and measured insertion loss of the 45º phase bits.

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