A Simple Equivalent Circuit Model for Plasma Dipole Antenna

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IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 43, NO. 12, DECEMBER 2015

A Simple Equivalent Circuit Model for Plasma Dipole Antenna Mona M. Badawy, Hend Abd El-Azem Malhat, Saber Helmy Zainud-Deen, and Kamal Hassan Awadalla

Abstract— Plasma antenna is an emerging technology that utilizes ionized gas as a conducting medium instead of metal. It is often convenient to represent the input impedance of the antenna by a lumped-element-equivalent circuit. Input impedance of the plasma dipole antenna is deduced using finite integration technique. A five-lumped-element equivalent circuit for the plasma dipole antenna variation with plasma frequency is investigated and optimized using the genetic algorithm (GA). The effect of plasma frequency and collision frequency of the ionized gas on input impedance variations of the plasma dipole antenna is studied with the help of the equivalent circuit model. Another equivalent circuit is synthesized using a rational function and GA. The Cauer realization method is used to deduce a new lumped-element equivalent circuit. Index Terms— Genetic algorithm (GA), lumped-element equivalent circuit, model-based parameter estimation (MBPE), plasma dipole antenna.

I. I NTRODUCTION N ANTENNA, input impedance can be represented by an equivalent lumped-element impedance. The equivalent impedance is replacing the original antenna across the two terminals that are used to connect the antenna to a transmitter or a receiver. The input impedance at the feeding terminals depends on many factors, including the operating frequency, the method of excitation, its geometry, and its proximity to the surrounding objects [1]. Most dipole antennas are designed to operate at or near their first resonance frequency (minimum S1 1, dipole length close to λ/2). The solid conductor antenna can be replaced by a plasma antenna as the plasma parameters can be controlled and the plasma can be switched OFF. The plasma antenna is an emerging technology that utilizes ionizing gas as the conducting medium instead of metal. A plasma antenna consists of a glass tube, or any similar dielectric, filled with a low-pressure noble gas like argon, neon, or xenon. The radiation characteristics of a plasma antenna are electrically controlled by the applied ionizing voltage as well as the dimensions of the plasma column. The radiation characteristics of a plasma antenna are similar to a copper antenna when the signal is transmitted or received [2]. When a plasma antenna is turned OFF (the gas is not ionized), it becomes transparent and allowing other adjacent antennas to transmit or receive without

I

Manuscript received June 25, 2015; revised September 7, 2015; accepted October 19, 2015. Date of current version December 9, 2015. The authors are with the Faculty of Electronic Engineering, Menoufia University, Menouf 32952, Egypt (e-mail: [email protected]; [email protected]; [email protected]; kamal_awadalla@hotmail. com). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPS.2015.2494626

interference [3]. Plasma antennas are highly reconfigurable (i.e., rapid reconfiguration of the resonant length). Plasma can be generated by dc discharge, RF discharge, or laser excitation. The input impedance of a plasma dipole antenna in free space can be accurately represented by lumped-element equivalent circuit. The literature has many articles dealing with antenna equivalent circuits [4], [5]. The input impedance of a plasma dipole determines the efficiency of the antenna and facilitates the design of a matching network to the feed line. The simple equivalent circuit is just a series resonant circuit (to deal with the first resonance of the antenna) connected in series with a parallel resonant circuit (to deal with the first antiresonance of the antenna). The elements of the compound circuit can be adjusted to produce the same behavior of the antenna input impedance in the considered range of frequency. A resistance R p is added to cope with the radiation [6]. Equivalent circuit can be used in many ways to: 1) replace an antenna with its equivalent dummy load for measurement purposes; 2) determine the antenna matching circuit; and 3) understand the antenna operation. The disadvantage of the lumped-element model is that the representation of each additional overtone response requires another circuit branch. Antennas, normally, have overtone responses, but lumpedelement circuits do not [7], [8]. In this paper, an equivalent lumped-element circuit model is proposed for representing the plasma dipole antenna. It demonstrates the effect of changing the component values of the equivalent circuit model in comparison with the plasma frequency and collision frequency of the simulated plasma dipole. Different optimization techniques can be used for estimating the values of the lumped-element equivalent circuit of the antenna over its frequency band [9]. A genetic algorithm (GA) technique is used to optimize the equivalent circuit of the plasma dipole antenna. GA is very easy to understand and can be employed for a wide variety of optimization problems. It performs very well for large scale problems that may be very difficult or impossible to solve by other traditional methods. The antenna is simulated using the finite integration technique (FIT) as a full wave numerical modeling tool and the results are compared with the results obtained from the equivalent lumped-element circuits. The use of a GA [10] is demonstrated to optimize a conventional lumped-components antenna equivalent circuit model for the best impedance fidelity over the considered frequency band. Another circuit model is presented using a rational function of reasonable order. The GA is utilized to determine the optimum values of the elements of the equivalent circuit with the help of model-based parameter estimation (MBPE) technique.

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MAGDY et al.: SIMPLE EQUIVALENT CIRCUIT MODEL FOR PLASMA DIPOLE ANTENNA

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II. P LASMA C HARACTERISTICS Plasma is the fourth state of matter. It is a gas in which atoms have been broken up into free negative electrons and positive ions by applying dc discharge, RF discharge, or laser excitation [11]. The plasma is a dispersion material. The behavior of plasma is given by the Drude dispersion model. The Drude dispersion model describes simple characteristics of an electrically conducting collection of free positive and negative charge carriers with very large spacing between ions, relative to their dimensions, at room temperature or higher. The dielectric constant of the Drude model is given by ω2p (1) εr = εo 1 − ω(ω − j ν p ) where ω is the angular resonance frequency of the antenna. ν p is the angular collision frequency of the plasma, and ω p is the angular frequency of plasma, which is given by [12] n e e2 (2) ωp = εo m e where n e is the electron density of the plasma, m e is the electron mass, and e is the charge of the electron. The collision frequency is given by [13] ν p = n e k(Te )

Fig. 1. Detailed structure of the plasma dipole antenna. (a) Side view. (b) Top view. (c) Lumped-element equivalent circuit.

(3)

where k is Boltzmann’s constant and Te is the free electrons temperature within the plasma (the measure of kinetic energy of free electrons), and the conductivity of plasma medium is given by [14] ε0 ωω2p ε0 ν p ω2p −j . (4) σ = σ + jσ = ν 2p + ω2 ν 2p + ω2 As the operating frequency increases, the conductivity decreases due to the 1/ω term in the expression. Also, the conductivity depends on the electron collision frequency, as given in (4). In fact, either the conductivity (4) or the dielectric constant (1) is enough to be used in the analysis as both are related. Since the plasma at ω ω p acts as a good conductor, it can be used as an antenna with flexible parameters and adjustable characteristics. Plasma is highly reconfigurable (i.e., plasma antennas have rapid reconfiguration of the resonant length). The effective length of plasma dipole antenna is given by [14] √ (5) h = B( p) p0 where B( p) is a constant for a given pressure and p0 is the input power. Equation (5) shows that the effective length of antenna should increase as the square root of the applied power is increased. III. G ENETIC O PTIMIZATION GA technique is quite suitable to optimize the equivalent circuit models of plasma dipole antenna. GAs are powerful and widely applicable search and optimization methods. GAs are applying the principle of the survival of the fittest [10]. It is started with a set of solutions represented by species known as chromosomes. This number of chromosomes in a

certain step is usually called a population. Solutions from one population are taken and used to form a new population for a better one. Solutions that are selected to form a new population are selected according to their fitness. Comparison with a suitable objective function G identifies the best performance chromosomes of each generation; the objective function is given by [15] G=

Nf

2

2 ReFIT (Fn )− ReGA (Fn ) + ImFIT (Fn )− ImGA (Fn )

n=1

(6) where N f is the number of frequency points within the considered range of frequencies with those points are usually selected to be uniformly spaced. ReFIT (Fn ) and ImFIT (Fn ) are the real and imaginary parts of the impedance of the lumpedelement circuit resulting from applying the FIT, respectively. ReGA (Fn ) and ImGA (Fn ) are the real and imaginary components of the equivalent circuit model worked out by the GA. Details of the implementation of a GA and the various operations (i.e., selection, crossover, and mutation) are covered in [16]. IV. N UMERICAL R ESULTS A. Plasma Dipole Antenna Construction The construction of a plasma dipole antenna is shown in Fig. 1(a). The plasma dipole antenna consists of a hollow cylindrical dielectric tube with a dielectric constant εr = 3.4, an outer radius Ro = 2.5 mm, an inner radius Ri = 2 mm, and a length h = 110 mm filled with argon gas with plasma parameters f p = 28.7 GHz and υ p = 200 kHz. Five-lumpedelement circuits are used as an equivalent circuit for the plasma dipole antenna. The five-lumped-element equivalent circuit

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TABLE I E LEMENT VALUES OF E QUIVALENT C IRCUITS FOR P LASMA D IPOLE A NTENNA FOR D IFFERENT P LASMA F REQUENCIES

Fig. 2. (a) Variation of the input impedance versus frequency for the plasma dipole antenna with h = 110 mm, f p = 28.7 GHz, and υ p = 200 kHz. (b) Lumped-element equivalent circuit for plasma dipole antenna.

consists of a series circuit (L s , Cs ) connected to a parallel circuit (L p , C p , R p ) as shown in Fig. 1(c). The series section (L s , Cs ) represents the antenna first resonance at the input terminals. While the parallel circuit section (L p , C p , R p ) is a parallel resonant circuit representing the first antiresonance of the dipole length. For higher order antiresonance frequencies, one has to add another parallel resonant circuit for each one. In fact, usually dipoles are not used at higher order resonances because of the resulting radiation pattern. Thus, investigation is done only at the first resonance and the first antiresonance for the dipole. The plasma dipole antenna is designed and simulated using FIT, and then the input impedance data are fitted to the equivalent lumped-element circuit model using the GA to calculate the values of the five lumped elements L s , Cs , L p , C p , and R p . Good agreement between the two input impedance variation is depicted as shown in Fig. 2. B. Effect of Changing Plasma Frequency f p The plasma frequency f p can be considered to be the boundary between the lower frequency conduction region of

Fig. 3. (a) Variation of reflection coefficient versus frequency for different plasma frequencies. (b) Variation of conductivity versus plasma frequency.

the plasma and the higher frequency dielectric behavior of the plasma. The frequency range selected for operation is far lower than the plasma frequency (as a dipole working in the common communication bands), and of course, it is in the conduction band. However, the change in plasma frequency is still affecting the behavior. The effect of changing the plasma frequency on the reflection coefficient of the plasma dipole antenna is shown in Fig. 3(a) at υ p = 200 kHz. By increasing the plasma frequency f p , the resonant frequency shifts up to a higher frequency and the impedance matching is varied due to the change of the effective length of the plasma dipole antenna and the change of plasma conductivity as shown in Fig. 3(b). The operating frequency is kept constant at f = 499.3 MHz


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Fig. 4. Variation of the antenna input impedance versus frequency for different plasma frequencies. (a) Real part. (b) Imaginary part.

for the results given in Fig. 3(b). From (4), as ω p goes higher, the conductivity σ goes higher. The variation of the input impedance of the plasma dipole antenna versus frequency for different plasma frequencies is shown in Fig. 4. As the plasma frequency is increased, the maximum resistance (which corresponds to the first antiresonance of the dipole) is decreased and shifts up to a higher frequency. The GA is used to fit the simulated input impedance data to the lumped-element equivalent circuit to end up with the values of the equivalent circuit elements given in Table I. A comparison between the input impedance determined using FIT and that determined from the equivalent circuit model for different plasma frequencies is shown in Figs. 5 and 6. All of these cases show good agreement with each other. The resistance R p is decreased by increasing the plasma frequency, while the inductors (L s , L p ) have an opposite behavior with capacitors (Cs , C p ), respectively, up to plasma frequency f p = 60 GHz and the response is approximately fixed for higher plasma frequency. The frequency range selected for operation is far lower than the plasma frequency, and by increasing the plasma frequency, the conductivity will increase to reach the case of a good electric conductor. The relations between the elements of the lumped circuit and the plasma frequency are shown in Fig. 7.

Fig. 5. Variation of the input impedance of the dipole versus frequency for different plasma frequencies at υ p = 200 kHz. (a) f p = 33.7 GHz. (b) f p = 38.7 GHz. (c) f p = 43.7 GHz.

C. Effect of Changing Collision Frequency ν p The variation of plasma dipole reflection coefficient versus frequency for f p = 28.7 GHz with different collision frequencies is shown in Fig. 8. By increasing the collision frequency, the resonant frequency, the reflection coefficient, and the impedance matching remain almost unaffected so that the antenna input impedance does not change. Thus, the plasma frequency is the dominant parameter affecting the plasma dipole antenna characteristics. This behavior is quite obvious from (4). As the collision frequency

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Fig. 7. (a) Variation of R p of lumped-element equivalent circuit versus plasma frequency. (b) Variation of L p and C p of lumped-element equivalent circuit versus plasma frequency. (c) Variation of L s and Cs of lumped-element equivalent circuit versus plasma frequency. Fig. 6. Variation of the input impedance of dipole versus frequency for different plasma frequencies at υ P = 200 kHz. (a) f p = 48.7 GHz. (b) f p = 58.7 GHz. (c) f p = 100 GHz.

rational function z(s) =

is very much smaller than the plasma frequency, which will not affect the values of the plasma conductivity. It always appear added to ω p , which is very much prevailing. D. Model-Based Parameter Estimation MBPE is a form of curve fitting. This technique has the advantage of providing a method for efficiently generating the model parameters. One form of a fitting model that is commonly employed in MBPE is represented by the

a0 + a1 s 1 + a2 s 2 + · · · + an s n b0 + b1 s 1 + b2 s 2 + · · · + b D s D

where ai and bi (i = 0, 1, . . . , 4) are unknown coefficients and s is the Laplace transform parameter in the case presented here. Function z(s) must be satisfied by the following. 1) The poles and zeros of z(s) are in the left half of the s-plane or on the imaginary axis. 2) The poles and zeros on the imaginary axis are real. 3) The degree of the numerator of z(s) cannot exceed the degree of the denominator by more than unity.


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TABLE II VALUES OF THE R ATIONAL F UNCTION C OEFFICIENT FOR N EW I MPROVED E QUIVALENT C IRCUIT OF P LASMA D IPOLE A NTENNA W ITH f p = 43.7 GHz AND υ p = 200 kHz

Fig. 8. Variation of reflection coefficient versus frequency for different collision frequencies.

of input impedance versus frequency for plasma dipole antenna for f p = 43.7 GHz and υ p = 200 kHz. This equivalent lumped-element circuit is more sophisticated than the previous one. This is why it produces smaller mean square error between the two impedance curves. The obtained final values for the coefficient ai and bi (i = 0, 1, . . . , 4) using GA for f p = 43.7 GHz are listed in Table II. V. C ONCLUSION

Fig. 9. MBPE equivalent circuit and variation of input impedance versus frequency for plasma dipole antenna for f p = 43.7 GHz and υ p = 200 kHz. (a) Input impedance. (b) MBPE-derived equivalent circuit.

4) The real part of z(s) is not negative for any value of s (s = j ω). There are many types of network realization methods such as foster realization method which dependent on partial fraction, and caur realization method wich dependent on continued fraction. The Cauer realization method is used because its relatively simple. A fourth order rational function is used to derive the equivalent circuit for the plasma antenna used in the previous sections. The initial values of the coefficients are taken from the five-element lumped circuit. The GA is used to estimate the coefficients of the rational function. The simulated results determined using FIT are fitted to the rational function circuit model results using GA. The Cauer realization method [15], [17] is used to synthesize a new lumped-element equivalent circuit. Fig. 9 shows the variation

Effect of plasma frequency and collision frequency on input impedance variations of the plasma dipole antenna is studied. A GA technique is used to optimize two equivalent circuits for the plasma dipole antenna. At first, a five-lumpedelement circuit model is used as an equivalent circuit of the plasma dipole antenna. The five-lumped-element equivalent circuit consists of a series LC circuit connected to a parallel LC circuit. The series elements represent the first resonance of the dipole, and the parallel circuit represents the first antiresonance effect of the dipole length. By increasing the plasma frequency f p , the antiresonance frequency shifts up to a higher frequency and the impedance matching is varied due to the change in the conductivity of the plasma, and by increasing the collision frequency, the resonant frequency and the antenna input impedance almost are not affected. The other more sophisticated equivalent circuit has been deduced using rational function with its coefficients worked out using GA. The Cauer realization method is used to synthesize the new lumped-element equivalent circuit. This circuit gives a higher accuracy in representing the antenna input impedance. ACKNOWLEDGMENT The authors declare that they have no conflict of interest. R EFERENCES [1] C. A. Balanis, Antenna Theory: Analysis and Design, 3rd ed. Hoboken, NJ, USA: Wiley, 2005. [2] K. A. O’Connor, R. D. Curry, and S. Kovaleski, “Analysis of plasma antenna options for explosively-driven microwave generators and outline of plasma antenna design,” in Proc. 27th Int. Power Modulator Symp., 2006, pp. 380–384. [3] R. F. Ti˘grek, “An investigation on plasma antennas,” M.S. thesis, Dept. Elect. Electron. Eng., Middle East Tech. Univ., Ankara, Turkey, Aug. 2005.

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[4] M. Hamid and R. Hamid, “Equivalent circuit of dipole antenna of arbitrary length,” IEEE Trans. Antennas Propag., vol. 45, no. 11, pp. 1695–1696, Nov. 1997. [5] G. W. Streable and L. W. Pearson, “A numerical study on realizable broad-band and equivalent admittances for dipole and loop antennas,” IEEE Trans. Antennas Propag., vol. 29, no. 5, pp. 707–717, Sep. 1981. [6] T. Tuovinen and M. Berg, “Impedance dependency on planar broadband dipole dimensions: An examination with antenna equivalent circuits,” Prog. Electromagn. Res., vol. 144, no. 1, pp. 249–260, 2014. [7] B. Long, P. Werner, and D. Werner, “A simple broadband dipole equivalent circuit model,” in Proc. IEEE Antennas Propag. Soc. Int. Symp., vol. 2. Salt Lake City, UT, USA, Jul. 2000, pp. 1046–1049. [8] Y. Liao, T. H. Hubing, and D. Su, “Equivalent circuit for dipole antennas in a lossy medium,” IEEE Trans. Antennas Propag., vol. 60, no. 8, pp. 3950–3953, Aug. 2012. [9] S. H. Zainud-Deen, S. I. El-Doda, K. H. Awadalla, and H. A. Sharshar, “The relation between lumped-element circuit models for cylindrical dielectric resonator and antenna parameters using MBPE,” Prog. Electromagn. Res. M, vol. 1, no. 1, pp. 79–93, 2008. [10] B. R. Long, P. L. Werner, and D. H. Werner, “Genetic-algorithm optimization of dipole equivalent-circuit models,” Microw. Opt. Technol. Lett., vol. 27, no. 4, pp. 259–261, Nov. 2000. [11] S. H. Zainud-Deen, H. A. Malhat, M. M. Badawy, and K. H. Awadalla, “Circularly polarized plasma curl antenna for 2.45 GHz portable RFID reader,” Plasmonics, vol. 9, no. 5, pp. 1063–1069, Apr. 2014. [12] L. Wei, Q. Jinghui, and S. Ying, “Analysis and design of plasma monopole antenna,” in Proc. Int. Conf. Antenna Theory Techn., Lviv, Ukraine, Oct. 2009, pp. 200–202. [13] H. Ja’afar, M. T. B. Ali, A. N. B. Dagang, H. M. Zali, and N. A. Halili, “A reconfigurable monopole antenna with fluorescent tubes using plasma windowing concepts for 4.9-GHz application,” IEEE Trans. Plasma Sci., vol. 43, no. 3, pp. 815–820, Mar. 2015. [14] J. P. Rayner, A. P. Whichello, and A. D. Cheetham, “Physical characteristics of plasma antennas,” IEEE Trans. Plasma Sci., vol. 32, no. 1, pp. 269–281, Feb. 2004. [15] Sahar I. El-Doda, “Equivalent circuits model for antennas,” M.S. thesis, Dept. Elect. Electron. Eng., Faculty Electron. Eng., Menoufia Univ., Menouf, Egypt, 2007. [16] R. L. Haupt and S. E. Haupt, Practical Genetic Algorithms. Hoboken, NJ, USA: Wiley, 2004. [17] H. A. Malhat and S. H. Zainud-Deen, “Equivalent circuit with frequencyindependent lumped elements for plasmonic graphene patch antenna using particle swarm optimization technique,” in Proc. 32nd Nat. Radio Sci. Conf. (NRSC), vol. 9. 6th of October City, Egypt, 2015, pp. 65–73. Mona M. Badawy was born in Menouf, Egypt, in 1990. She received the B.Sc. degree from Menoufia University, Menouf, in 2012, where she is currently pursuing the M.Sc. degree in antenna engineering. She is also a Demonstrator with the Department of Electrical and Electronic Engineering, Faculty of Electronic Engineering, Menoufia University. Her current research interests include plasma antennareflectarray and transmitarray-plasmonic materialsradio frequency identification.

Hend Abd El-Azem Malhat was born in Menouf, Egypt, in 1982. She received the B.Sc. and M.Sc. degrees from Menoufia University, Menouf, in 2004 and 2007, respectively, and the Ph.D. degree in antenna engineering from Menoufia University, in 2011. She is currently an Associated Professor with the Department of Electrical and Electronic Engineering, Faculty of Electronic Engineering, Menoufia University. Her current research interests include graphene antennas, plasma antennas, wavelets technique, transmitarray, reflectarray, and radio frequency identification.

Saber Helmy Zainud-Deen was born in Menouf, Egypt, in 1955. He received the B.Sc. and M.Sc. degrees from Menoufia University, Menouf, in 1973 and 1982, respectively, and the Ph.D. degree in antenna engineering from Menoufia University, in 1988. He is currently a Professor with the Department of Electrical and Electronic Engineering, Faculty of Electronic Engineering, Menoufia University. His current research interests include microtrip and leaky wave antennas, dielectric resonator antenna, radio frequency identification, optimization techniques, finite deference time domain and finite deference frequency domain, scattering problems, and breast cancer detection.

Kamal Hassan Awadalla was born in El-Santa, Gharbiya, Egypt, in 1943. He received the B.Sc. and M.Sc. degrees from the Faculty of Engineering, Cairo University, Giza, Egypt, in 1964 and 1972, respectively, and the Ph.D. degree from the University of Birmingham, Birmingham, U.K., in 1978. He is currently a Emeritus Professor with the Department of Electrical and Electronic Engineering, Faculty of Electronic Engineering, Menoufia University, Menouf, Egypt. His current research interests include microtrip and leaky wave antennas, dielectric resonator antenna, radio frequency identification, and optimization techniques.