Institute of Physics Publishingdoi:10.1088/1742-6596/43/1/333

Journal of Physics: Conference Series 43 (2006) 1362–1365
7th European Conference on Applied Superconductivity

Developments of a Novel Impedance Matching Circuitfor Electrically Small Antennas
K. Yoshida, S. Sakaguchi, S. Oda and H. Kanaya
Department of Electronics, Graduate School of Information Science and ElectricalEngineering, Kyushu University, Fukuoka 812-8581, Japane-mail: yoshida@ed.kyushu-u.ac.jp
Abstract. In order to reduce the size of a wireless system, we have proposed the design
formulas for an electrically small antenna (ESA), i.e. an antenna whose dimension is muchsmaller than a wavelength, with a miniaturized matching circuit which connects to a 50ohm
external circuit. We designed a slot dipole antenna with the aid of the simulations using theelectrical circuits as well as the electromagnetic field (EM field) simulator. The size of thedesigned antenna including the matching circuit is 4.1mm × 1.9mm on MgO substrate withrelative permittivity of 9.6 at the center frequency of 5GHz, and the designed fractional
bandwidth is 13%@RL=3dB. We also made experiments on the slot dipole type ESA with amatching circuit using YBCO thin films on MgO substrates.

1. Introduction
In recent years, the miniaturization of antennas is essential in radio communication devices such as
wireless LAN, RF-ID and MIMO, and extensive studies are made of an electrically small antenna(ESA), i.e., the antenna whose dimension is much smaller than a wavelength, towards further
reduction of the antenna size[1]-[3]. It is widely known, however, that in order to realize
superconducting ESA we must simultaneously realize an impedance matching circuit which
compensates the narrow bandwidth peculiar to the superconducting small antenna with low radiation
resistance [4]-[6].
In this paper we propose a design theory for the impedance matching circuit which connects anESA to a 50Ω load. It is shown that the proposed matching circuit has performances similar to that of
the n-pole bandpass filter (BPF) [7]. By using the quarter wavelength transmission line and J-inverter,
we can reduce the total antenna size more than the previous works. Theoretical performances of theslot dipole antenna with the impedance matching circuit designed by the present theory are studied by
the electrical circuits using transmission lines (Transmission Line Model) as well as the EM field
simulator. In order to demonstrate the theory, we also carried out experiments on the slot dipole
antenna with the matching circuit of pole number n = 1 using high temperature superconductors
YBCO on MgO substrates in the 5 GHz band.
2. Design Formulas of Impedance Matching Circuit for ESA
Figure1(b) shows the equivalent circuit for the electrically small slot dipole antenna, whose schematic
figure is shown in Fig. 1(a). When the length of the slot is sufficiently smaller than half wavelength,
the input impedance of the antenna Za is given by Z a = R a + jωLa , where Ra is the radiation resistance© 2006 IOP Publishing Ltd1362

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and La is the inductance, and ω is the angular frequency. In Fig.2 (a) we show the prototype singlepole bandpass filter with J inverters, where the design formulas are given by [7],Y0 b1
J 0,1 = w,
(1)g 0 g1J 1, 2 = w

b1Y0,
g1 g 2(2)⎛ ω ω0 ⎞⎟⎟ ,B1 = b1 ⎜⎜−(3)⎝ ω0 ω ⎠where w is the fractional bandwidth, Y0 (=1/50 Ω−1) is the system admittance, ω0 is the centerfrequency, gi (i=0, 1, 2) is the normalized element value, B1 is the susceptance for parallel-resonanceand b1 is its slope parameter. In Fig. 2(b) we show the equivalent circuit for the matching circuit
which is the analogue of Fig. 2(a). The input admittances seen from the left of J1,2, Y and Y′, as shownin Figs. 2(a) and 2(b), are given bybY = 1 + jB1 ,(4)Qe1
Z 01 + jZ a tan θ(5)= G ′ + jB ′ ,Y′ =Z 01 (Z a + jZ 01 tan θ )where Qe1 = g 0 g1 / w , Z01 is the characteristic impedance of the transmission line with length l,G ′(ω , θ ) = Re(Y ′), B ′(ω , θ ) = Im(Y ′) , θ = ω LC l is the electrical length, whose value is slightly
smaller than π/2, i.e., l is nearly equal to quarter wavelength.

(a)

(a)
Y0

jB1

J0,1J1,2Y

Za

(b)

(b)
Za

RaZa

Z01 , θLa

Fig.1 (a) Schematic of electrically small
dipole antenna, (b) its equivalent circuit

lJ1,2Y0Y′

Fig.2 (a) Prototype single pole bandpass
filter with J inverters, (b) proposed
matching circuit for ESA.

The conditions that Y=Y′ near the resonant frequency ω0 are given byB ′(ω 0 , θ 0 ) = 0 ,bG ′(ω 0 , θ 0 ) = 1Qe1b1 =Y0

ω0 dB′(ω ,θ )
ω ∂B′
θ ∂B′
π−1
= 0+ 0= Z 01 ,22 ∂ω ω =ω 0 2 ∂θ θ =θ 0 4dω ω =ω 0where θ 0 = ω 0 LC l is the electrical length at the center frequency.
From Eqs. (6)-(8), we obtain the design formulas for θ0, and Z01 as(6)
(7)
(8)

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⎞
⎛
Qa
1
⎟⎟ ,
θ 0 = Sinc -1 ⎜⎜(9)2⎝ 2Qe1 − Qa ⎠(10)
Z 01 = X a tan θ 0 ,where Qa = X a / Ra , X a = ω 0 La ,where Sinc( x) = sin x / x is the sampling function, Qa is the quality
factor of ESA. J1,2 is given by Eq. (2). In the calculation we assumed the condition Z a << Z 0 , i.e.,
the antenna impedance is sufficiently low.
3. Experimental Result
In Fig.3 we show the layout of the electrically small slot dipole antenna designed by using theformulas (9), (10). In this layout we also show the photograph of the J-inverter and meander line. We
made experiments on slot dipole antenna using high temperature superconductor YBCO thin films onMgO substrate with relative permittivity of 9.6. This antenna was placed in a vacuum cryostat, andwas measured by using coplanar waveguide probes.

size : 4.1mm × 1.9mm

LaDesigned valuelZ01

WaJ inverterLMeander Line

GLJ-inverter

GWThe center frequency : 5 GHz
Return Loss : -3 dB
Normalized bandwidth : 13 %J-inverter : J=0.00466
GW = 284 μm
GL = 270 μm
Slot dipole antenna
Wa = 1500 μm
La = 2000 μm
λ/4 line : Z01 = 49.40 Ωl = 1054 μm
L =1816 μm

Fig.3 The layout of the slot dipole antenna with matching circuit.

In Figs. 4(a) and 5(a) we show the experimental results for the return loss and the input impedanceof the slot dipole antenna with the matching circuit. The frequency response of the slot dipole antenna
was measured with vector network analyzer (HP-8722C) at 20K. The values obtained in thismeasurement include the residual loss due to the contact between the YBCO film and the metal probe.
The center frequency is slightly sifted to the lower frequency (4.84GHz) compared to the designed
frequency of 5GHz since we neglected the effects of the kinetic inductance of the YBCO.
Considering experimental errors due to the over-etching and the residual loss form the contact of theprobe, the observed data are in reasonable agreement with simulation results shown in Figs. 4(b) and5(b).

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1000

0(a)

(a)

800
Input Impedance [Ω]Return Loss [dB]-2-4-6-8-10Re(Z)
Im(Z)

600
400
200
0-200

4.84 GHz

4.84 GHz-400

-12

4.2

4.4

4.6

4.8

4.2

5

4.4

4.6

4.8

5

Frequency [GHz]Frequency of experiment [GHz]
01000

(b)

(b)

Re(Z) of Transmission Line Model

800
Input Impedance [Ω]Return Loss [dB]-10-20-30-40-50

Electromagnetic Field Simulation
Transmission Line Model

600
400

Re(Z) of Simulation

20005 GHz-200

Im(Z) of Simulation-400Im(Z) of Transmission Line Model
44.555.5

6Frequency [GHz]Fig.4 Return Loss (a) Experimental
Result, (b) Simulated Result.

-600

44.555.5

6Frequency [GHz]Fig.5 Input Impedance (a) Experimental
Result, (b) Simulated Result.

4. Conclusion
We have designed a slot dipole antenna whose dimension is much smaller than a wavelength withminiaturized impedance matching circuits. The impedance matching circuits connect ESA to a 50 Ωexternal circuit. The size of the designed antenna with matching circuits is 4.1mm × 1.9mm at thecenter frequency of 5 GHz and the designed fractional bandwidth of 13%@RL=3dB on MgO substratewith relative permittivity of 9.6. We also made experiments on the slot dipole antenna with thematching circuit using HTS YBCO thin films on MgO substrates.
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[2] M.S.A. Salameh, Y.M.M. Antar, and G. Seguin 2002 IEEE Trans. Antennas Propagat. 50 14151419.
[3] S. Ohshima 2000 Supercond. Sci. Technol. 13 103-108.
[4] K. Yoshida, T. Takahashi, H. Kanaya, T. Uchiyama, and Z. Wang 2001 IEEE Trans. Appl.
Supercond. 11 103-106.
[5] Y. Tsutsumi, H. Kanaya, and K. Yoshida 2005 IEEE Trans. Appl. Supercond. 15 1020-1023.
[6] K. Yoshida, Y. Tsutsumi, H. Kanaya 2005 IEICE Trans. Electron. E88-C 1368-1374.
[7] G. L. Matthaei, L. Young, and E. M. T. Jones 1980 Microwave Filters, Impedance-Matching
Networks, and Coupling Structures. (Norwood, MA: Artech House) Chapter 8.