An Equivalent-Circuit Model of Miniaturized
Split-Ring Resonator
Sultan Can, Asım Egemen Yılmaz
Ankara University
Department of Electrical and Electronics Engineering
Ankara, Turkey
sultancan@ankara.edu.tr, aeyilmaz@eng.ankara.edu.tr
Kamil Yavuz Kapusuz
Ghent University/iMinds
Department of Information Technology
Ghent, Belgium
kapusuz.kyavuz@gmail.com
Abstract—In this paper, we present a new miniaturized split-
ring resonator (SRR) to be easily employed in the practical
realization of SRRs and derive its equivalent circuit model to
accurately predict the resonance frequency. The results of the
resonance frequency obtained by the developed equivalent circuit
model are in very good agreement with the simulated results.
Keywords—Conductor rod; equivalent circuit; miniaturization;
split-ring resonators.
I. INTRODUCTION
In the last few decades, high performance and small size
devices have attracted a high level of interests in modern
wireless communication systems. It is expected that these
devices in such systems will offer cost-effective and low profile
properties. Engineered materials, which are loaded in devices,
can improve the device qualities. In order to use such materials
efficiently, the array that gathered with high number of unit cell
structure is required and to minimize total array size that should
provide the same electrical properties for small size devices,
miniaturized unit cell may be used. In this frame, to reduce the
size of the unit cell, spiral resonator [1], multiple split-ring
resonator [1], labyrinth resonator [1], lumped elements
embedded resonator [2] or more complex geometries (like
fractals or asymmetric inclusions) [3] can be exploited. In this
study, a commonly known square SRR is miniaturized by
additional conductor rods. The proposed model is presented with
its equivalent circuit model having a good agreement when
compared to the commercial numerical software.
II. PROPOSED MODEL AND ITS EQUIVALENT CIRCUIT MODEL
Resonance frequency of SRR (Fig. 1.a) can be controlled by
tuning the capacitance and/or inductance values with the
relevant equation
= 1/(2√
) where
and
represent the equivalent capacitance and inductance values
(Fig.1.c), respectively. Those values can be calculated from the
studies in [4][5]. In such structures,
is a virtue of the gap of
the ring and coupling between adjacent cells, and
consist
of single turn metal ring. Inclusion of conductor rods, which will
achieve the miniaturization, will affect the equivalent
capacitance and inductance values in addition to CSRR and LSRR.
The geometry and corresponding equivalent circuit of the SRR
with the conductor rods are depicted in Fig 1.b and Fig 1.d.
h
s
g
a
x
l
h
s
g
g
via
a
x
l
(a) (b)
L
SRR
C
SRR
C
SRR
L
SRR
L
Rod
C
Rod
(c) (d)
Fig. 1. (a) The conventional square SRR. (b) Proposed miniaturized square
SRR. (c) Equivalent circuit of conventional square SRR. (d) Equivalent
circuit of miniaturized square SRR.
As seen from the equivalent circuit model, the self-
inductance value of the rod LRod are serially connected to the
inductance value of the LSRR. In addition to the inductance
values, capacitance values are also considered in the equivalent
circuit model, as well. When physically evaluated, it is expected
to obtain a self-impedance of two rods which can be calculated
by Equation (1);
≈
0
ℎ
−1
(
2
).ℎ
where
0
is the free space permeability value,
is the
substrate permeability value,
is the distance between center
of rods,
is the radius of the rod, and ℎ
is the thickness of the
substrate. In the equation above, LRod is the total self-inductance
value that is resulted from inserting the rods. The material used
in order to design the SRR has a permittivity value of 3.38.
Additional capacitance value, which is occurred due to the usage
of the conductor rods, can be calculated via Equation (2).
→
→
,
,
,
−
→
−
→
,
→
→
,
,
263 978-1-5386-3284-0/17/$31.00 ©2017 IEEE AP-S 2017
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