A novel unit cell for a high pass filter was designed based on a composite right/lefthanded structure that uses a folded coplanar waveguide. The equivalent circuit model for the unit cell was extracted from the geometry of the unit cell, and the effect of each main parameter of the unit cell was analyzed. The equations to calculate the immittance values of the equivalent circuit elements were formulated, and moreover, the dispersion characteristics and energy the distributions of the electromagnetic fields were simulated to determine the characteristics of the composite right/lefthanded structure. Finally, the high pass filters were implemented as a series of the proposed unit cells. We show that the experimental results were in good agreement with those obtained from the simulation. Thus, the high pass filter was found to achieve a baseband insertion loss of 3 dB and a stopband attenuation of 70 dB.
1. INTRODUCTION
In communication systems, filters have been widely used for selecting the desired frequency from multiple input signals. For the development of the systems or the instruments, filters are required to have compact sizes and low loss, as well as the ability of lowpower operation. In order to achieve these requirements, special structures or materials should be taken in filter design. Over the last decade, lefthanded material (LHM) has received much attention since it has simultaneously negative values of permittivity ε and permeability μ
[1]
and demonstrated successfully in 2000
[2]
. After that, a transmission line approach of LHM was introduced in 2002
[3]

[4]
. The LH transmission line is widely used because of its advantages, such as high frequency selectivity, low loss and wide bandwidth. It can be practiced in planar configurations and compatible with modern microwave integrated circuits (MICs)
[5]
. However, the LH transmission line always has a spurious righthanded (RH) range because the transmission line gets typically an inherent series inductance and shunt capacitance. So a purely lefthanded (PLH) transmission line does not exist in fact and the transmission line, which has both a LH range and a RH range, is called a composite right and lefthanded (CRLH) transmission line (TL)
[6]

[8]
. An effectively homogeneous CRLH TL can be constructed by cascading LCbased unit cells. The LCbased unit cell for a CRLH transmission line consists of the impedance constituted by a RH inductance with a LH capacitance in series components and the admittance constituted by a RH capacitance with a LH inductance in parallel components.
In the respect of designing filters by MICs or monolithic microwave integrated circuits (MMICs), coplanar waveguide (CPW) is more suitable than conventional microstrip lines since the fabrication of CPW is simple and crosstalk effects between the adjacent lines are weak
[9]

[10]
.
In this paper, to design a high pass filter with a compact size and a steep skirt performance, the unit cell with high pass property is proposed on the folded CPW transmission line with a CRLH structure. To analyze the performance of the unit cell, the equivalent circuit of the unit cell is introduced and the immittance elements of the equivalent circuit are formulated. And then the dispersion characteristics and electromagnetic energy distributions over the CRLH structure are simulated. Finally, a high pass filter is fabricated by cascading the proposed unit cells in series arrangements and Sparameter characteristics of the filter are measured by a vector network analyzer (Agilent N5230A). And the measurement results are compared with the simulation results.
2. UNIT CELL CONSTRUCTED ON FCPW TL
The unit cell based on CRLH using folded coplanar waveguide transmission line (FCPW TL) is shown in
Fig. 1
[11]
. A FCPW TL is a kind of CPW, which consists of a dielectric substrate and two conductors placed on both sides of the substrate. And each conductor is structured as a conventional CPW on both bottom and top layer, with a signal line between two ground planes separated by a narrow gap. In order to build a CRLH structure on the FCPW TL, the signal lines on both top and bottom layer are reformed as shown in
Fig. 1
. The center section of the signal line on the top layer has been cut off. On the other hand, the end sections of the signal line on the bottom layer are removed and the rest of the line is connected at the one of ground planes on the same layer. Therefore, the input signal is entered in the signal line on the top layer only, and transmitted into the signal line on the bottom layer due to the electrical reactance components between two signal lines.
Physical geometry of the unit cell
As the physical geometry of unit cell adds an additional parallel capacitance and serial reactance component (C
_{L}
, L
_{L}
) to the distributed element components (R
_{S}
, L
_{R}
, G
_{S}
, C
_{R}
) of the transmission line, it can be modeled as the circuits combined a series RLC resonant circuit (R
_{S}
, L
_{R}
,, C
_{L}
) and a shunt GLC parallel resonant circuit (G
_{S}
, L
_{L}
, C
_{R}
). Therefore, the equivalent circuit for the proposed unit cell can be represented as shown in
Fig. 2
. The distributed element components (R
_{S}
, L
_{R}
, G
_{S}
, C
_{R}
) are distributed in a folded CPW transmission line. In a LH components, the series capacitance C
_{L}
is distributed in the overlapped area between the signal line on the top layer and the signal line on the bottom layer, which is in proportion to the relative area. Moreover, the parallel inductance L
_{L}
depends on the narrow strip line in which connects the signal line with the shorted ground plane on the bottom layer.
Equivalent circuit model for the unit cell
According to analysis on the unit cell structure, the values of the equivalent capacitances (C
_{L}
and C
_{R}
) and the equivalent inductance (L
_{L}
) can be expressed as
where S, L, D, FE and K are the design parameters of the unit cell. ε
_{0}
, μ
_{0}
and c are the permittivity, permeability and light velocity of free space, respectively. And σ
_{c}
and σ
_{d}
are the conductivities of signal line and dielectric substrate in a FCPW TL. H is the thickness of dielectric substrate in a FCPW TL.
The capacitances C
_{oe}
and C
_{oe}
’ are the capacitive components on the top and the bottom transmission line, respectively. C
_{oe}
^{a}
is the capacitance when replacing the dielectric materials by air. The characteristic impedance Z
_{01}
, Z
_{02}
and the effective dielectric constant ε
_{eff}
are calculated by the equations in
[12]
.
Consequently, the equivalent impedance Z, admittance Y, the series resonant frequency
ω_{se}
and the shunt resonant frequency
ω_{sh}
can be formulated as follows:
And the propagation constant, attenuation constant and phase constant of the equivalent circuit model can be calculated from the transmission parameter of
S
_{21}
.
The dispersion characteristics of
β
generally appears a continuous function of frequency as a curve varying within 
β
 ≤
π
. And l and
ϕ
(
S
_{21}
) represent the physical length (2L+D) of the unit cell in a specific implementation and the phase of
S
_{21}
, respectively.
3. SIMULATION RESULTS
The unit cell is implemented on the FCPW TL with the relative dielectric constant ε
_{r}
of 2.5 and tangent loss of 0.001. The thickness H of the dielectric substrate is 0.787 mm and the thickness T
_{c}
of the conductor sheet is 35 m. The values of the signal feeder line width W and the gap width G between the feeder line and the ground plane can be calculated by the commercial simulation tool (ADS Linecalc), corresponding to 50 Ω characteristic impedance of a CPW structure. Moreover, the input and output ports of the unit cell are set to 50 Ω characteristic impedance in FCPW configuration, which results in the feed line width W = 8.74 mm and the gap width G = 0.3 mm.
To analyze the behaviors among the design parameters, three dominant sets of the parameters L, D and S are evaluated. In the process of the simulation, while the one of the parameters is calculated, the other parameters are fixed on the constant values.
From the simulation results, the resonant frequencies decrease because of the increments of the immittance components (C
_{R}
, L
_{R}
, C
_{L}
, L
_{L}
) according as L and D increase. Those are different values, so that there are two resonant frequencies which are represented by a LH resonant frequency and a RH resonant frequency. Particularly, when the length of L is close to the guided wavelength of
λ
/16 (6.4 mm), two resonant frequencies get closer and the stopband frequency range is very well specified on the graphs in
Fig. 3
(a) and (b).
S_{21} (dB) characteristics as a function of geometrical parameters
In addition, when the length of S is shorter than
λ
/64 (1.3 mm), the resonant frequencies decrease as shown in the
Fig. 3
(c). It is reason that the resonant frequencies increase since the augmented effects of the inherent capacitances C
_{oe}
and C
_{oe}
’ increase the component C
_{R}
and C
_{L}
. Therefore, the capacitances primarily depend on the widths and lengths of the signal lines. The optimal widths and lengths of the design parameters are shown in
Table 1
. Also, in case of a low loss FCPW TL, the equivalent immittance components calculated by the equations (1) to (6) are R
_{S}
= 1.08 Ω, G
_{S}
= 0.001 S, C
_{R}
= 0.54 pF, C
_{L}
= 0.85 pF, L
_{R}
= 3.48 nH, L
_{L}
= 2.24 nH, respectively.
Physical dimensions of the proposed unit cell (Unit: mm)
Physical dimensions of the proposed unit cell (Unit: mm)
The Sparameter characteristics are shown in
Fig. 4
as comparing the simulation results of the proposed unit cell done by ADS and HFSS, which has high pass property. The magnitude curves of S
_{11}
in the passband and the magnitude curves of S
_{21}
in the stopband are excellent agreements with good performances. In the passband, the S
_{11}
ripples are below  15 dB, and at the same time the magnitude curves of S
_{21}
get maximal flatness. Also, the cutoff frequency is 1.75 GHz, and the length of L, space of S and distance of D are
λ
/16,
λ
/128 and
λ
/8, respectively. Compared with conventional filters, which stubs are
λ
/8
[13]
or
λ
/4
[14]
in general, this is more advantageous to achieve small size in filter design.
Sparameter simulation results of the unit cell
To confirm a CRLH structure, the dispersion diagram is considered as shown in
Fig. 5
. The results are simulated with the physical dimensions in
Table 1
by ADS and HFSS. And the LH mode occurs in the frequency range lower than 2.66 GHz and the RH mode occurs in the frequency range higher than 2.66 GHz. It means that the propagating waves have backward and forward directions simultaneously. As a result, the proposed unit cell provides the CRLH characteristics.
Dispersion diagram of the unit cell
In addition, energy distributions of the electromagnetic fields are depicted as shown in
Fig. 6
. When input signal enters into the unit cell, the energy is accumulated inside the overlapping area between the signal lines on the top and the bottom layer, which is electric energy in
Fig. 6
(a). Because of the electromagnetic interaction, the electric energy turns to be the magnetic energy as time elapses. The magnetic energy distribution, corresponding to the accumulated energy distribution around the narrow line which connects the signal line to the ground plane on the bottom layer, is shown in
Fig. 6
(b). This process is done repeatedly while the signal energy is transmitted from the input to the output port.
Energy distributions of unit cell
4. MEASUREMENT RESULTS OF UNIT CELL AND HIGH PASS FILTER
The proposed unit cell is fabricated in the dimensions as shown in
Table 1
. The fabricated unit cell in
Fig. 7
is measured by vector network analyzer (N5230A). The comparison between the simulation and measurement results are shown in
Fig. 8
. The shapes of the Sparameter curves are similar, but there is a slightly mismatch between the cutoff frequencies. The measured cutoff frequency is shifted to high frequency band and it is considered that the implementation of ground plane is not enough to play a role of perfect ground plane. Therefore, the electrical energy, which is accumulated inside the overlapped area between the signal lines, is less than the desired simulation amount. Even so, the unit cell still can be used in designing the high pass filter since the S
_{11}
ripples in the passband get a regulation and it is favorable to get a wide passband. From these properties, the high pass filter is implemented by cascading three unit cells in series and the layout patterns are shown in
Fig. 9
. Also, the optimal dimensions of the high pass filter are listed in
Table 2
.
Fabricated geometry of the unit cell high pass filter
Sparameter simulation and measurement results of the unit cell
Fabricated physical geometry of the threecell high pass filter
Physical dimensions of the proposed high pass filter(Unit:mm)
Physical dimensions of the proposed high pass filter(Unit:mm)
The simulation and measurement results of the proposed high pass filter are shown in
Fig. 10
. The Sparameter curves have similar shapes, but the cutoff frequencies and passband ripples are partially a little mismatched because of the lack of the production techniques and insufficient ground effects. The measured cutoff frequency of the threecell high pass filter is 1.76 GHz, which is very close to the target cutoff frequency of 1.75 GHz. The attenuation of the filter is below 70 dB in the stopband, and the skirt effect is much better than that of the unit cell high pass filter. Also, the insertion loss is less than 3 dB in the passband. Even though the Sparameter characteristics of the fabricated filter do not completely same as those of the target filter, the measurement results are agreed well with the simulation.
Simulation and measurement results of proposed high pass filters (22.2mm × 90.5mm)
5. CONCLUSIONS
The unit cell with high pass property has been proposed on the folded coplanar waveguide with a CRLH structure. Also, the equivalent circuit components have been extracted from the geometry of the unit cell and the parameters have been investigated to design the high pass filter. Moreover, the Sparameter characteristics of the equivalent circuit model and the unit cell have been simulated and compared. Finally, we applied a good high pass property of the proposed unit cell to design the threecell high pass filter with a steep skirt effect and good suppression performance. The attenuation in the stopband and the insertion loss in the passband have been evaluated in 70 dB and 3 dB, respectively. Even if the measurement results of the fabricated filter do not perfectly same as those of the desired filter, this implementation scheme can be usefully used in designing the high pass filter.
Acknowledgements
This research was supported by the 2015 scientific promotion program funded by Jeju National University.
BIO
Lei Yang
She received the B.S., M.S in telecommunication engineering from Jeju National University, Korea in 2011, 2013, respectively. And then, she worked for one year at R&D Research Institute of Innertron in Korea. Since 2015, she has been with Key Laboratory of Network and Intelligent Information Processing, Hefei University, China. Her main research interests include RF devices and wireless communication system.
DooYeong Yang
He received the B.S. degree in telecommunication engineering from Jeju National University, Korea in 1984, and M.S., Ph.D. degrees in electrical and telecommunication engineering from Hanyang University, Korea in 1989, 1992 respectively. Since 1992, he has been a professor in telecommunication engineering of Jeju National University in Korea. His current research interests include RF devices, microwave circuits and wireless and satellite communication systems.
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