In this paper, we discuss how the classical fundamental-limit theory can be .... the antenna, it turned out that the notch was caused by an equivalent slot stub ...
The Design of Ultra-wideband Antennas with Performance Close to the Fundamental Limit Taeyoung Yang, William A. Davis, and Warren L. Stutzman Virginia Tech Antenna Group, Blacksburg, VA 24061-111, USA {mindlink, wadavis, stutzman} @vt.edu
Abstract In this paper, we discuss how the classical fundamental-limit theory can be interpreted for ultra-wideband antennas and how one can design an antenna with size and performance close to fundamental limits. The frequency response of Chu’s equivalent circuit model for spherical modes suggests the concept of an ideal antenna. The transfer function of the ideal antenna, showing ultra-wideband antenna characteristics, simply has an entire function and two complex poles. An antenna design strategy is explained, based on observations of ideal antenna characteristics. The evolution process of antenna design to make the antenna close to theoretical performance limit is demonstrated. The final design suggested a general approach using a high-pass filter structure and a tapered feed to make an antenna close to the limit. Performance of the final design is evaluated in both frequency and time domains.
1. Introduction There has been tremendous demand for antennas occupying a small volume in wireless communication applications to reduce cost and increase mobility. Furthermore, because a single antenna is preferred to handle multiple bands and radios, wider operating bandwidth of the antenna also becomes important. A small size antenna is required with a wide operational bandwidth, but without sacrificing radiation efficiency or gain. In fact, size, bandwidth, and efficiency are trade-offs; the fundamental-limit theory on antenna performance addresses the trade-offs. Thus, it is necessary to understand the theoretical limits in order to obtain an optimum design. In addition, if there is a gap between the theoretical and practical limits, it is also important to understand how to modify the antenna to reduce the gap. The essence of the fundamental-limit theory for antennas is that size, efficiency, and bandwidth are trade-offs in the design process, and only two of these factors can be optimized simultaneously close to the theoretical limit. In addition, the limit theory of antennas provides a theoretical limit to assist in the evaluation of antenna performance in terms of antenna size and radiation-Q, as well as avoiding the search for an antenna with unrealistic performance parameters. Since Wheeler [1] first introduced the concept of fundamental-limit theory on antennas, there have been many investigations into the theoretical limitation of antenna performance versus size [2 - 6]. Over half century, these research efforts emphasized development of an accurate minimum radiation-Q formula with various approaches. In addition, previous research efforts on the limit theory also focused on electrically small, resonant antennas even though the classic limit theories are not necessarily restricted to the electrically small, resonant antennas. In this paper, we discuss how the classical fundamental-limit theory can be interpreted for ultra-wideband antennas and how one can design an antenna with size and performance close to fundamental limits.
2. Re-examination of Classic Fundamental-Limit Theory for Ultra-wideband Antennas One frequently-asked question about Chu’s equivalent circuit [2] is where the antenna is located? Actually, one implicit assumption of Chu’s circuit is that the arbitrarily-shaped antenna in the antenna sphere has an all-pass-filter characteristic. Thus, the antenna is not shown in Chu’s equivalent circuit. The phase delay of the energy propagation to the far-field region is not also included because this delay is irrelevant to the evaluation of the radiation-Q. In addition, Chu’s model basically represents an one-port problem. However, if we consider how much power is delivered to space (radiation), Chu’s ladder circuit becomes to a two-port problem. Port 1 can be the antenna terminal with a system reference impedance Z0. Port 2 is the far-field region where radiated power is delivered (the intrinsic impedance in Fig. 1). Therefore, |s21|2 of the extended model represents the transfer of power from the antenna terminal to the radiated far field. For example, s21 the spherical TM01 mode of two-port equivalent of Chu's model can be written as
s21 =
⎛ ⎞⎟ 1 1 ⎟⎟ = 1 − 0.5 ⎜⎜ + ⎟ ⎜ ⎝ − − + − − − ⎠ ( 0.5 0.5) ( 0.5 0.5) s j s j 2s + 2s + 1 2s 2
(1)
2
where s = jka. The reference impedance of Port 1 is assumed to be same with that of Port 2, i.e. Z0 = 1. This form shows that s21 for the fundamental spherical mode (TM01) consists of an entire function and two complex poles. This represents what we refer to as an ideal antenna, to meet the theoretical performance and size limit. The entire frequencydomain and time-domain responses of the ideal antenna can be completely described with only two poles and entire function. Thus, the characteristics of the ideal antenna can be easily included in simulations to evaluate communication system performance without introducing a significant computational load. In fact, Chu’s circuit model has a characteristics of high pass filter, as modeled by the ladder network form. Thus, the ideal antenna has ultra-wideband chatacteristics. 2n − 3 jka
n jka
Z TM
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jka 2 n −1
jka 2n − 5
1
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Figure 1. The mode circuit model: (a) Definition of antenna sphere, (b) Chu’s circuit model [2].
3. Design Approach of Ultra-wideband Antenna Close to Fundamental Limits The concept of the ideal antenna having a high pass characteristic provides insight into antenna design strategies in terms of the trade-off relationship among antenna size, impedance bandwidth, and gain. For a given frequency, the product of wave number k and radius a of the antenna represents the antenna electrical size. If the product, ka, of an antenna is greater than unity, one may choose the system reference impedance equal to the real part of the antenna input impedance in order to maximize the impedance bandwidth of the antenna. For ka smaller than unity (giving an electrically-small antenna), the antenna should be tuned to reduce return loss and maximize realized gain. Based on the above antenna design strategy for an omni-directional antenna, it is a reasonable choice to set the size of the antenna to satisfy kLa = 1, where kL is the wave number at the lower bound of the operating frequency for an ultra-wideband antenna close to fundamental-limit performance and size. Thus, the size of the antenna is same as the size of the radiation sphere of the spherical TM01 mode at the lower bound of operating frequency. For example, if we choose 3 GHz as a lower bound, the radius of the antenna sphere, a, will be 15.9 mm. The next question is what shape of antenna will be close to the characteristics of the ideal antenna. One of the reasons that conventional antennas are not close to the limit curve is that these antennas do not efficiently utilize the volume of the given antenna sphere, reducing non-radiated stored energy and maximizing impedance bandwidth. This thought leads to a meshed spherical shape of antenna as a candidate, with a solid spherical shape causing difficulty in the feed of the structure. Recently, Yang et al [7] showed that an antenna without a slope discontinuity of current distribution on an antenna structure has wideband characteristics and reduces non-radiating near-field energy. This kind of antenna typically has a smooth variation in shape. The meshed spherical structure also satisfies this aspect. A similar structure to the meshed sphere, the folded spherical helix, was proposed by Best [8]. Best’s antenna has multiple arms connected in parallel (see Fig. 2a), where only half structure of the sphere is modeled over infinite PEC ground, i.e. a hemispherical helix. The antenna is excited at the bottom of one of the arms. Best demonstrated that the radiation resistance of the antenna increases as the number of arms increases. Thus, the folded hemispherical helix can easily be tuned at a desired frequency by adjusting the number and length of the arms. Unfortunately, the folded hemispherical helix has multiple resonances over a wide frequency range (Fig. 2c). Due to the unique feed location of the folded hemispherical helix, the antenna has resonances at every harmonic frequency. Thus, the current form of the folded spherical helix cannot be used for an ultra-wideband applications. In order to reduce the number of strong resonances, a center-fed version of the folded hemispherical helix antenna (Fig. 2b) is considered. As compared in Fig. 2c, the center-fed version has a deep resonance around 3 GHz and the number of the resonance frequencies was reduced significantly compared to Best’s original folded hemispherical antenna. The next step of this design evolution is to increase the impedance bandwidth of the center-fed folded spherical helix. Recall that we assumed the reference impedance for the extended equivalent model to be the normalized intrinsic wave impedance in order to maximize the impedance bandwidth in developing the concept of an ideal antenna. However, 50 Ohms is preferred as a system reference impedance in many applications. This suggests that an impedance transforming structure needs to be included in the center-fed folded hemispherical helix. Thus, a tapered feed structure
(cone) is added in the helix. The top of the cone structure is connected to the hemispherical helix through a wire as shown in Fig 3a. The impedance bandwidth of the center-fed folded hemispherical helix with a cone feed noticeably increased, compared to the version without the tapered feed (see Fig. 3c). However, a frequency notch is observed around 3.6 GHz. The notch splits the impedance bandwidth into two parts. After investigating the current distribution of the antenna, it turned out that the notch was caused by an equivalent slot stub existing between the top area of the cone and the helical arms on the cone. A solution to remove the notch is simply removing the wire connection between the helix arms and the top of the cone. Thus, the hemispherical helix is capacitively coupled to the cone (see Fig 3b). As shown in Fig. 3c, the notch was effectively removed. 0 -2 -4
-8
11
|S | (dB)
-6
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Arm feed Center feed
-18 -20
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Figure 2. Half structure of spherical helix [8], (b) Center-fed hemispherical helix, (c) Return loss comparison. Infinite PEC ground plane was assumed. A commercial moment method code [9] was used for simulations. 0 -2 Tapered Feed Capacitively Coupling
|S11| (dB)
-4 -6 -8 -10 -12 -14 1
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Figure 3. (a) Hemispherical helix with a cone feed (the top of feed is connected to the helix), (b) Capacitively-coupled hemispherical helix with a cone feed, (c) Return loss comparison. Infinite PEC ground plane was assumed. All-pass-filter characteristics of the Chu's model of the antenna in Fig. 1was implied in the classical fundamental-limit theory. However, it seems to be impossible to design such a antenna. Then, an alternative approach may be to design an antenna has a high-pass filter (HPF) characteristics like the characteristics of the spherical mode. If the cut-off frequency of the HPF antenna is lower than the cut-off frequency of the spherical mode, we may have an antenna design close to the fundamental limit. In fact, the capacitively-coupled hemispherical antenna of this design evolution is one such design. This antenna basically has a high-pass filter structure, i.e. the series capacitance due to the coupling between cone and helical arms and the shunt inductance due to the hemispherical arms connected to the ground.
4. Performance Evaluation of Capacitively-Coupled Hemispherical Helix The capacitively-coupled hemispherical helix with a cone feed designed in the previous section was fabricated with brass on a finite, round ground (radius of the ground is 150 mm). VSWR performance of the fabricated antenna is shown in Fig. 4a. The simulation results (infinite ground was assumed) were obtained using two different commercial codes, Finite-Difference Time-Domain [9] and Method of Moments [10], match very well with the measurement result using an Agilent 8510 VNA. A small difference between simulation and measurement results at high frequencies are probably due to fabrication errors. The lower bound of the operational frequency range is about 2.14 GHz. The size of the fabricated antenna is 1/8 wavelength at the lower bound, which is 2 times smaller than conventional ultra-wideband antennas. The radiated pulse of the antenna for an Gaussian input pulse with the pulse width of 100 picosecond was evaluated at 1.5 m (to in far-field region) and the radiated pulse has a doublet waveform with minor ringing (see Fig. 4b).
1
10
Simulation [CST, 2007]
Measurement
9 8
Normalized Amplitude
FDTD [CST, 2007] MoM [FEKO, 2007]
VSWR
7 6 5 4 3
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Figure 4. (a)VSWR comparison between measurement and (b) Radiated pulse at 1.5 m from the antenna (simulation).
5. Conclusion In this paper, we focused on how the classical fundamental-limit theory on antenna performance can be interpreted from an ultra-wideband antenna perspective and be used to design an antenna with performance close to the limits. Investigation of the frequency response of Chu’s equivalent model for spherical TM modes suggests the concept of an ideal antenna, with the entire frequency response described by only two complex poles and an entire function. The ideal antenna has ultra-wideband characteristics. An antenna design strategy was discussed, based on observations of the ideal antenna characteristics. The evolution process of antenna design to make an antenna close to theoretical performance limit was demonstrated. The final design suggested a general approach using a high-pass filter structure and a tapered feed to make an antenna close to the limit. The designed, capacitively-coupled hemispherical helix with a cone feed had an approximate 10:1 impedance bandwidth and also showed a radiation pulse of doublet waveform for a Gaussian pulse input. The size of the designed ultra-wideband antenna was 1/8 wavelength at the lower bound of the band, two times smaller than conventional ultra-wideband antennas.
7. References 1. H. A. Wheeler, “Fundamental Limitations of Small Antennas,” Proceedings of the IRE, vol. 35, 1947, pp. 1479 – 1484. 2. L. J. Chu, “Physical limitations on omni-directional antennas, J. Appl. Phys., vol. 19, 1948, pp. 1163 – 1175. 3. R. E. Collin and S. Rothschild, “Evaluation of antenna Q, IEEE Transaction on Antennas and Propagation,” vol. 12, 1964, pp. 3 – 27. 4. J. S. McLean, “A reexamination of the fundamental limits on the radiation-Q of electrically small antennas,” IEEE Transaction on Antennas and Propagation, vol. 44, 1996, pp. 672 – 675. 5. D. M. Grimes, and C. A. Grimes, “Radiation-Q of dipole generated fields,” Radio Science, vol. 34, 1999, pp. 282 – 296. 6. W. A. Davis, , T. Yang, E.D. Caswell, and W. L. Stutzman, “Fundamental Limits on Antenna Size: A New Limit,” in preparation, 2008. 7. T. Yang, W. A. Davis, W. L. Stutzman, and M.-C. Huynh, “Cellular Phone and Hearing Aid Interaction – An Antenna Solution,” IEEE Antennas and Propagation Magazine, accepted and will be shown on June issue, 2008. 8. S. R. Best, “The radiation Properties of Electrically Small Folded Spherical Helix Antennas,” IEEE Transactions on Antennas and Propagation, vol. 52, 2004, pp. 953 – 960. 9. FEKO Suite version 5.3 (2007), EM Software and Systems, more information are available at http://www.feko.info. 10. CST Suite version 2006B (2007), Computer Simulation Technology (http://www.cst.com).
