Time-Domain Pulse-Matched Synthesis of Ultra-Wide Band Antennas

Razvan D. Tamas*(1), George Caruntu(1), and Teodor Petrescu(2)

(1) Maritime University of Constanta, C.P. 202, O.P. 2, 900780 Constanta, Romania Email: tamas@ieee.org, tamas@imc.ro

(2) Politehnica University of Bucharest, Bd. Iuliu Maniu 1-3, Sect. 6, 061071, Bucharest, Romania

ABSTRACT: Antenna synthesis can yield optimal radiating structures in terms of pattern diagram, gain, bandwidth or other figures of merit. Although the synthesis might be more difficult for continuous sources than for antenna arrays the resulting radiating structures are cheaper and easy to manufacture. In this paper, we propose a time-domain synthesis approach for ultra-wide band antennas. The method is based on a finite expansion of the antenna time-domain response. The synthesis is performed with regard to the resemblance between the time-domain radiated waveform and the waveform at the antenna input. The approach is validated by synthesizing a planar, ultra-wide band antenna designed for a particular waveform of excitation. INTRODUCTION Due to the increasing interest in Ultra-Wide Band (UWB) communications, novel approaches have been developed in the last years in order to analyze and evaluate the behavior of antennas to pulsed excitations. Thus, new fundamental tools and descriptors have been defined [1], [2], [3] prior to analyze and further synthesize UWB antennas. There are mainly two ways to conceive a UWB antenna: either by modeling and optimizing a specific, known radiating structure [4], or by synthesis. The synthesis may be oriented either towards continuous sources or towards arrays [5] and may be performed either in the frequency domain or in the time domain. Array beam synthesis based on adaptive projections is thoroughly treated in the literature [6]. Synthesis of continuous sources is obviously more complicated but technologically preferred. Some approaches are based on an initial design which is iteratively optimized by using specific algorithms in terms of classical descriptors such as gain, directivity or bandwidth [7], or with respect to the new descriptors, such as the similarity of the time-domain waveforms of the electric field radiated in different directions [8]. In this paper, we propose a pulse-matched synthesis approach based on a finite expansion of the time-domain antenna response. The basis functions in that expansion are time-domain responses of short wire segments and the corresponding weights are computed by using the method of moments (MoM). The resulting set of weights is finally assimilated to current projections on a particular axis in order to synthesize the physical radiating structure. PROPOSED SYNTHESIS APPROACH For the sake of simplicity we will focus on the synthesis of a planar current distribution that should yield a non-distorted field towards a specific direction, e.g. the perpendicular one (Fig. 1). This is a common problem to be solved in practice and planar antennas are often technologically convenient. Let us consider the case of a planar symmetrical dipole; the shape of the dipole arms is still to be synthesized. We define an equivalent current I(z’) flowing along the OZ axis. Then the far electric field radiated by a current filament in a perpendicular direction can be written as Eθ(r, t)| θ=�/2= – Ez(r, t)= – dAz(r, t)/dt (1) with '.d

4)/,'(),( 00

z zr

crtzItrAπ

μ −= (2)

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978-1-4244-9134-6/11/$26.00 ©2011 IEEE

That is, Ez(r, t) ~ dI(z’, t – r / c0) / dt (3)

Fig. 1 Radiation from a planar current distribution.

Now we assimilate the dipole to a degenerated, open-ended transmission line. Let l be the length of each dipole arm and Vg(t) the excitation at the antenna input. Consequently,

���

����

� −−−���

����

�−��

�

����

�+

000

'2dd'

dd~

czltV

tcztV

tcrtE ggz

(4)

A normalized electric field can be defined by compensating the effects of the propagation, i.e., attenuation and time delay. Relation (4) shows that the normalized electric field can be approximated to a finite expansion in terms of delayed versions of the first derivative of the excitation pulse:

�=

��

�−−

−−⋅

��

�−−

−−≅==N

ngn N

tclntV

tNtcl

ntpete1

supp0supp0

1/2

)1(dd

1/2

)1() ,2/,2/( πϕπθ (5)

in which p(t)=1 if t � tsupp and p(t)=0 otherwise; tsupp is the time support assigned to the expansion functions. For a given waveform of ) ,2/,2/( te πϕπθ == , usually the same as Vg(t) the coefficients en can be found by using the method of moments (MoM). According to (4) the expansion in (5) should contain pairs of weights of equal magnitude and opposite sign since part of the radiation is due to the current reflected at the open end of the antenna. That can be easily accomplished for ) ,2/,2/( te πϕπθ == odd or even since the basis functions would be of opposite parity. The corresponding current distribution in the XOZ plane can then be synthesized as a continuous, piecewise-straight wire profile. The far-field contribution of each wire segment can be weighted according to the coefficients en by choosing proper segment skew with respect to the OZ axis. EXAMPLE OF SYNTHESIS. RESULTS Let us consider as an excitation a waveform proportional to the first derivative of a Gauss function. The spectrum of the excitation is centered on 5 GHz, with a –3dB bandwidth of 5.8 GHz. We aim to synthesize a planar, dipole type antenna that yields a normalized electric field with the same time-domain waveform in a direction perpendicular to the plane containing the current distribution. In that case a length of l = c0 tsupp for each of the dipole arms would be convenient and the time-domain radiation should be investigated within a time slice of 2tsupp. That ensures that the reflected pulse generated at the open end of the antenna has completely passed beyond the source end.

z’ Ez az

r O

Z Planar current distribution

Js(z’)

X Y

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Figure 2 shows the basis functions used for the MoM expansion and Fig. 3 gives the resulting weights, en.

Fig. 2 Basis functions. Fig. 3 Field expansion weights. It should be noted that there is no unique current profile complying with a given set of weights. Moreover, using multiple wire profiles or a continuous conducting patch can result in a better input impedance matching. The resulting wire model of the synthesized antenna is given in Fig. 4. The impulse response of the wire model can be found by using GNEC and an inverse Fourier transform. Figure 5 shows time-domain waveform of the normalized far, electric field. It should be noted that a good fidelity was achieved although the expansion contains few terms and no thorough matching optimization was performed. The input matching of an antenna with pulsed excitation can be quantified by an energy-based descriptor similar to the frequency-domain VSWR, i.e., the pulse matching ratio, s [3]. The above antenna exhibits values of s=5.84 on a normalizing impedance of 50�, and a minimum of s=2.19 is achieved on 250�. The fidelity factor or normalized correlation coefficient is K=0.973 and the energy gain is G= 2.16dB for the above excitation.

Fig. 4 Wire model of the synthesized antenna. Fig. 5 Time-domain response of the synthesized antenna for an excitation pulse proportional to the

first derivative of the Gauss function.

1 2 3 4 5 6 7 8 9 10 11 -0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1 Expansion weights, en

Sample number

0 0.2 0.4 0.6 0.8 1 1.2-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

t[ns]

r Eθ (t, θ=π/2, ϕ=π/2) [V]

0 0.1 0.2 0.3 0.4 0.5 0.6 -1

-0.5

0

0.5

t[ns]

Basis functions, �n(t)

Z

X O

Excitation

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CONCLUSION As shown before the proposed synthesis approach leads to accurate results in terms of fidelity. The resulting antenna structure has a good energy gain figure and good input matching. It should be emphasized that the synthesis is linked to a specific waveform of excitation and therefore might not yield acceptable response for other types of excitation. By using a solid substrate antenna dimensions can be dramatically reduced, as well as the equivalent characteristic impedance of the antenna so it could be driven by a standard 50 � feeding circuit. Further research will be conducted in order to extend the area of application on synthesis of radiating objects that could produce low-distortion radiation in several directions. ACKNOWLEDGMENT This study was supported by the Romanian Ministry of education, research, and innovation – National center for program management (CNMP) under the project SIRADMAR. REFERENCES [1] E. Heyman, “Analytical Methods for Antenna Analysis and Synthesis in the Time Domain” 28th European

Microwave Conference, pp. 607-612, 1998. [2] A. Shlivinski, E. Heyman, R. Kastner, “Antenna characterization in the time domain”, IEEE Trans. Antennas

Propagat., vol. 45, no. 7, pp. 1140–1149, Jul. 1997. [3] R.D. Tamas, L. Babour, E. Fond et al., “Energy-based Input Reflection Coefficient for the Characterization of

Ultra-Wide Band Antennas” IEEE International Workshop on Antenna Technology (IWAT 2008), pp. 330-333, March 2008.

[4] L. Babour, E. Fond, R.D. Tamas, P. Saguet et al., “An UWB folded dipole antenna: time and frequency domain characterization” The 2nd European Conference on Antenna and Propagation (EuCAP 2007), pp. 1-7, November 2007.

[5] M. Ciattaglia, G. Marrocco, “Time Domain Synthesis of Pulsed Arrays”, IEEE Trans. Antennas Propagat., vol. 56, no. 7, pp. 1928–1938, Jul. 2008.

[6] J. L. Quijano, G. Vecchi, “Alternating Adaptive Projections in Antenna Synthesis”, IEEE Trans. Antennas Propagat., vol. 58, no. 3, pp. 727–737, March 2010.

[7] Z. Raida, J. Lacik, Z. Lukes, “Multi-Objective Synthesis of Multiband Planar Antennas in Time Domain” International Conference on Electromagnetics in Advanced Applications (ICEAA 2007), pp.539-542, Sept. 2007.

[8] L. Lizzi, L. Manica, A. Massa, “Time Domain Analysis for UWB Antenna Synthesis” European Microwave Conference, (EuMC 2009), pp. 93-96, Sept. 29 2009-Oct. 1, 2009.

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