Ultra compact CPW dual band filter based on π-generalized metamaterial NRI transmission line

This paper presents an ultra compact dual-band coplanar waveguide metamaterial filter based on generalized metamaterial transmission line. The detailed theoretical design steps of the filter are explained. The dual-band filter design performance has been validated using equivalent circuit modeling, electromagnetic full wave simulations, and practical measurement. The results illustrate the filter has dual passbands centered at 0.82 and 1.48 GHz with approximately 1 dB insertion loss and minimum 12 dB return loss. Good agreements between the circuit modeling, electromagnetic full wave simulations, and practical measurements are achieved. Moreover, the filter size is only (18 × 28 mm²) which is only less than (0.2λ_g × 0.31λ_g) at the center frequency of the first passband and (0.36λ_g × 0.56λ_g) at the center frequency of the second passband.

Keywords: dual-band; generalized NRI; metamaterial; band pass filter

During the last decade, there was great interest by electromagnetic community concerning investigating metamaterial structures characterized by equivalent negative permittivity and permeability named as metamaterials. These structures have unusual electromagnetic wave propagation properties. Metamaterials have been realized in planar configuration by loading planar transmission line (TL) with series capacitors and shunt inductors, the TL approach. This structure has been called a negative refractive index (NRI) medium [[1]] or a composite right left handed TL.[[2]] This TL has a left-handed (LH) passband with anti-parallel phase and group velocities in addition to conventional right-handed (RH) passband. Using this realization, many novel microwave components and antennas, with interesting properties and compact sized, have been proposed.[[3]]

The generalized NRI TL (G-NRI TL) has been presented as an extension of the metamaterial TL approach.[[18]] Thanks to this new modification, the generalized NRI TL can introduce up to dual LH and dual RH passbands. Based on the generalized NRI TL and its π modified version, multibands microwave components such as coupler, power divider, and filter were introduced.[[19]] Most of these components were realized in microstrip configurations. However, realizing simple series and shunt connections in coplanar waveguides (CPW) structures makes them attractive in designing microwave components. This makes it good candidate for RF systems that requires multibands and compact size operation.

In this paper, we introduce an ultra compact CPW dual-band filter. The filter design is based on using only one unit cell of a π G-NRI TL in symmetric configuration. The first filter passband covers the frequencies from 0.78 to 0.85 GHz. The second passband covers the frequencies from 1.38 to 1.56 GHz. These two frequency bands have been selected as examples for low frequency wireless application such as GSM, GPS, GSM, and UMTS applications which are interesting in compact size components.

The filter has an ultra compact size which is only 18 × 28 mm2. Throughout our work in this paper, we explain first the theoretical design principles of filter. The filter design was next validated using circuit modeling, electromagnetic full wave simulations, and confirmed using experimental measurements.

In this section, we introduce the detailed filter design procedures and its structure analysis. The configuration of the compact dual passband CPW filter based on π G-NRI TL is shown in Figure 1. In a summary, the proposed filter is designed so that it operates in the low frequency applications; hence, the filter compactness become very obvious. The first band is centered at 820 MHz with bandwidth 780–850 MHz and second passband is centered at 1.48 GHz with bandwidth 1.38–1.56 GHz.

Graph: Figure 1. The circuit model of the proposed dual-band filter based on π-generalized NRI TL.

As mentioned above, the proposed filter is designed to demonstrate dual passbands based on the π G-NRI TL model. The filter design specifications are based on achieving dual-band filter with center frequencies (f01 = 0.82 GHz, f02 = 1.48 GHz). The filter should have 3 dB insertion loss at the two cutoff frequencies (fc1 = 0.78 GHz, fc2 = 0.85 GHz) for the first passband and (fc3 = 1.38 GHz, fc4 = 1.56 GHz) for the second passband. Also, the filter should demonstrate a minimum attenuation = 12 dB before the first band (fa1 = 0.75 GHz), the middle frequency separating the band (fa2 = 1.78 GHz), and after the third passband (fa3 = 1.1 GHz).

These filter design specifications can be illustrated using the general dispersion diagram for a dual passband filter employing one unit cell of π G-NRI TL indicating the passbands cutoff frequencies is shown in Figure 2. Also, the insertion loss design criteria of transmission coefficient for designed filter are illustrated in Figure 3 for the general design frequencies.

Graph: Figure 2. A general dual passband filter design dispersion diagram for indicating the passbands cutoff frequencies.

Graph: Figure 3. A general dual passband designed filter transmission coefficients at the three bands.

The design of the proposed dual-band pass filter was achieved in two different steps for initial design and further final design. The first step was employing the image method for filter design to determine the cutoff frequencies of the two passbands. The specific 3 dB cutoff frequencies and the 12 dB attenuation frequencies are recalculated using the insertion loss method in the second step of the filter design. The second step was considered as a fine tuning of the pre-calculated lumped component values obtained from by applying the image method.

The initial design analysis of the proposed filter has been done by investigating the dispersion diagram of the filter. This can be done by applying the periodic analysis of the equivalent circuit in Figure 1 [[26]]. Hence, a dispersion equation can be extracted as in (1)

(1)

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where β is the propagation phase constant along the proposed dual-band filter, the variables Z, ZS, and ZSS are introduced to simplify (1) and defined in terms of the lumped elements in Figure 1 as follows

(2)

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(3)

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(4)

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(5)

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The initial design for the loading/parasitic inductor and capacitor values is specified by adjusting the cutoff frequencies of the proposed triple passband filter to the limits of the dispersion equation of the π G-NRI TL (1). There are four cutoff frequencies for two passbands named as (fc1, fc2, fc3, fc4). Two of these cutoff frequencies are corresponding to βd = 0 and the others are corresponding to βd = π as illustrated in Equations (6) and (7), respectively.

(6)

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(7)

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Using a one unit cell in Figure 1 for designing such filter, we have to design eight different lumped components, whereas solution of (6) and (7) is only possible for four variables. Hence, in order to solve them, we had to assume four variables. In order to achieve compact filter size, we selected three of these variables as (CS, CSH, and LSH). The other selected element is (CHH) which are the parasitic CPW elements. Although the selection is arbitrary, but we have selected the first three elements (CS, CSH, and LSH) for filter compactness as we will be explained in next section. On the other hand, the three parasitic elements were selected based on the CPW TL subsection which they belong to. In more details, the shunt capacitance (CHH) is the parasitic capacitance of the CPW subsection whose length is specified by the series capacitor (CS). Finally, LS is the overall of these two CPW subsections parasitic series inductance. Equations (6) and (7) are solved numerically, and the solution values for the elements are set as initial values for the second step of the design.

The second step was the design of the filter transmission shape within the passband and stopband. This is done by adjusting the filter bandwidth frequencies which is characterized 3 dB frequencies and the minimum attenuation frequencies which is selected as 12 dB. The design criterion for the 3 dB bandwidth frequencies (fc1,fc2,fc3, and fc4) and the 12 dB attenuation frequencies (fa2 and fa3) are given in (8) and (9) based on the insertion loss method.

(8)

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(9)

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where A, B, C, and D are the elements of the filter ABCD matrix. It is worth to mention that the frequency fa1 should lie in the start up of the first LH passband which has a high slop in NRI TL. So, we omitted the design constraint at this frequency, at the second step of the design, and made use of this degree of freedom for the filter compactness. Therefore, we solved (8) and (9) for 6 elements values and accordingly, we have selected two elements and not to design them. These elements were selected as CS and LSH. Also, the reason behind these two elements selection is due to the fabrication miniaturization since CS is chosen to be realized as interdigital capacitor, whereas LSH is chosen to be implemented using the meander line. Hence, we can control their size and hence confirm the filter size requirements since these two elements are the biggest size elements. The Equations (8) and (9) were solved numerically where the initial values in the solving algorithm were adjusted using the pre-calculated values from initial design step employing the image method.

It is worth to mention that based on the above design steps and given that we designed the proposed dual passband filter as a narrow passband, we can control the filter amplitude within the passband without extra design equations. However, for wide band filters, we can zoom in the passbands by designing the three passbands by adding three more equations for insertion loss values at the filter center frequency. For example, for zero insertion loss at center frequencies, this can be adjusted as

(10)

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Also, it is worth to mention that the proposed filter is based on using the π G-NRI TL which, as proved, is capable of introducing up to five passbands controlled by eight loading/parasitic work.[[26]] For the sake of compactness, we designed the filter to be dual band and hence we had solved six nonlinear equations for six unknown elements.

Finally, the obtained designed values have been optimized using circuit modeling based on two consideration, first to achieve the wanted filter specification illustrated in the beginning of this section and second the ability to realize. The final lumped values are examined using circuit modeling, full wave simulation, and experimental measurements as will be explained in next sections.

The proposed CPW dual-band filter layout is shown in Figure 4(a) and its fabricated photo is shown in Figure 4(b). As can be seen, the filter is designed employing only one cell of the π-GNRI TL. The equivalent circuit for the proposed filter is shown in Figure 1. The lumped components in the equivalent circuit model are designed using distributed strip/meander line inductors and inter digital capacitors. The mapping between the filter realized layout in Figure 3 and the equivalent circuit mode in Figure 1 can be explained as follow. A series of six fingers interdigital capacitor represents the series capacitor (CS). Two parallel meandered lines are used to represent the parallel inductance (LSH) parallel with the capacitance (CSH) in the series branch. The shunt inductor (LHS) is represented by a straight strip element connected series with a ten finger interdigital capacitor (CHS) which is connected to the ground. The other shunt straight segment represents a shunt inductor (LHH). The series interdigital capacitor is 4 mm length, whereas the parallel interdigital capacitor is 2.9 mm length. The meander line branch length is 2 mm. The two shunt strip lengths are 3.9 and 1.3 mm. All other strip/gab length/width in the structure is 0.2 mm.

Graph: Figure 4. (a) The circuit layout of the proposed dual-band CPW π-generalized NRI filter with (50 Ω) terminals, (b) The fabricated dual-band CPW π-generalized NRI TL filter.

The proposed filter was designed using Roger RT6010 substrate with dielectric constant, εr = 10.2 and thickness, h = 0.625 mm. Two CPW feeding TLs of length = 3 mm and tapered width to 50 Ω width at ends to enhance the matching. The employed inter digital capacitors and meander line inductors realizations were designed using the mathematical empirical formulas in [[28]]. Some fine optimization steps have been carried out using both circuit modeling and electromagnetic full wave simulations for best filter performance results.

The dispersion diagram obtained from the calculated designed lumped elements based on the filter circuit model, using the designed image method parameters, is shown in Figure 5. As shown in Figure 5, there are two passbands. The first band is extending from 0.78 to 0.85 GHz, whereas the second band is extending from 1.34 to 1.46 GHz. The circuit model shown in Figure 1 is simulated employing the same lumped element values used in plotting the dispersion diagram in Figure 5 using the commercial advanced design system simulator and the simulated scattering parameter magnitudes are plotted in Figure 6. As shown in Figure 6, the passband message concluded using the simulated equivalent circuit model confirms the aforementioned results of the image method but with slight shifting in the frequencies. That is because the image method is based on using periodic analysis while only one cell is used in the circuit modeling and only one unit cell will be realized. However, as mentioned before, the image method is not the final design step and it is used only as an initial design.

Graph: Figure 5. The dispersion diagram for the circuit model of the dual-band filter, CS = 0.8 pF, LS = 6.7 nH, LSH = 4.5 nH, CSH = 1 pF, LHS = 0.6 nH, CHS = 1 pF, LHH = 10 nH, and CHH = 1.77 pF.

Graph: Figure 6. The simulated S-parameters magnitudes for circuit model for the proposed dual-band filter.

For design validation, the proposed designed CPW π-G-NRI TL filter structure shown in Figure 3 has been tested using electromagnetic full wave simulations and experimental measurements. The full wave simulated scattering parameter magnitudes (employing commercial full wave simulator (HFSS)) are shown in Figure 7, compared to the full wave simulated scattering parameter magnitudes (employing the commercial full wave (CST) simulator). Both two simulations confirm the dual passband of the filter. There are discrepancies between the two simulation results from the cutoff frequencies point and its relation to this obtained from the circuit model simulation in Figure 6. However, these shifts do not change the main contribution of the dual-band operation of the proposed filter.

Graph: Figure 7. The HFSS simulated and CST simulated S-parameters magnitudes of the proposed dual-band filter.

According to CST results, the filter exhibits 18 and 28 dB return loss within the first and second passbands, respectively, and 1 and 0.6 dB insertion loss within the first and second passbands, respectively.

The effective relative permittivity and permeability of the proposed dual-band filter has been extracted based on the simulated S-parameters magnitudes [[30]] and are plotted in Figure 8(a) and (b), respectively. As shown in the figure, both permittivity and permeability are negative within the first passband and positive within the second passband. Otherwise, they are one positive and one negative which supports our claim from the dispersion diagram in Figure 2 that the filter exhibits NRI within the first pass-band and positive refractive index within the second passband.

Graph: Figure 8. The effective relative (a) permittivity and (b) permeability, of the proposed dual-band filter based on the HFSS simulated S-parameters magnitudes.

The final step in verifying our proposed filter performance was the practical measurements. This was done by measuring its scattering parameter magnitudes using vector network analyzer. The measured scattering parameter magnitudes are shown in Figure 9. As shown in the figure, the measured two passbands have almost 1.2 dB insertion loss and at minimum 17 dB return loss. Moreover, the measured transmission coefficient (S21) and reflection coefficient (S11) in the stopband separating the twopass bands are about −11 dB. The first passband is between 0.79 and 0.85 GHz with center frequency 0.82 GHz and the second passband is between 1.38 and 1.56 GHz with center frequency 1.48 GHz. Compared to the simulated circuit model, we can claim that there is good matching in both level and cutoff frequencies. On the other hand, compared to full wave simulation, we can claim that there is reasonable agreement between measurement and HFSS/CST results.

Graph: Figure 9. The measured transmission S-parameters magnitudes of the proposed dual-band filter.

Finally, for the sake of comparison, the proposed filter is 0.2λg length at the first passband and 0.36λg length at the second passband which makes it ultra compact compared to many compact introduced filters. For example, the filter introduced in [[31]] is 0.33λg length at the first passband and the filter introduced in [[32]] which is 0.39λg length at the first passband.

A dual-band CPW metamaterial filter based on generalized NRI TL is presented. The filter analytical design, circuit model, electromagnetic full wave simulations, and experimental measurements are introduced. All results have good agreement between each other. The proposed filter has two passbands from 0.78 to 0.85 GHz (11%) and the second band is from 1.38 to 1.56 GHz (12.1%). The insertion loss at the two band center frequencies is almost 1 dB. The filter is 0.2λg length at the first passband which is up to 50% size reduction compared to similar filters in literature.

The authors did not have any commercial interest in any of the materials used in this study.