Keywords

1 Introduction

The design of UWB devices such as filters is required in the UWB systems used in microwave and other similar applications. To miniaturize a system, the devices inside the system must also be miniaturized. Metamaterials (MTMs) concept was involved as the key to solve this problem. The basic properties of MTMs were proposed theoretically by V.G. Veselago at the end of 1967, representing the first MTM with negative media properties of permittivity (εr) and permeability (µr) [1]. The design of the UWB planar filters and some other relevant devices using CSRRs [2] has actually taken a great advantage of the new compact designs [3]. The MTM components have thus become powerful elements in microwave technology due to their sub-wavelength dimensions [4]. The CSRRs are thereby etched in the lower plane of the microstrip to remove the undesired frequency spurious band [5].

In the last decades, several techniques for the design of UWB filters based on MTM components have been witnessed [6]. Whereby, a microstrip of UWB-BPF centered at 3.4 GHz with 4.8 GHz bandwidth has been introduced. The insertion loss (S21) of this filter was less than 0.9 dB and the return losses (S11) were better than 10 dB [7]. Furthermore, the design analysis of an UWB filter based on CRLH-TL concept has been delineated in Refs. [8–10]. From a different perspective, Gil et al. in [11] presented the design of CRLH-TL based on CSRRs and interdigital capacitors (IDCs) with transmission bandwidth of 7.5 GHz for UWB applications in the interval (3.1–10.6) GHz. The device has had a relatively small size and reasonable performance. Further presented, fabricated, and measured was a four-cell CRLH-UWB filter based on defected ground structure (DGS) and microstrip IDC. In addition, an UWB filter with passband range (3.2–7.5) GHz and insertion loss of less than 0.5 dB has also been achieved [12]. Within a different approach, an UWB filter combining a conventional bandpass characteristic, and negative permittivity (εr) MTM made of CSRRs was presented. Hereby, a new technique to improve the matching between the host TL and the CSRRs was proposed. The filter has had bandwidth of 8.4 GHz, an insertion loss of less than 1 dB and a 22 dB rejection at 5.4 GHz [13]. Moreover, a simplified left-handed transmission line (LH-TL) structure-based UWB-BPF has been proposed. The filter has thereby had a return loss of higher than 12 dB, and the group delay was approximately 0.25 ns at the pertinent bandpass interval [14].

From another corner, an UWB filter using fractal shape or CSRRs structures etched in the ground plane as a DGS and series capacitive gap in the upper conductor was fabricated and tested. The insertion loss was better than 1.5 dB except at high frequencies and the bandwidth of the 10 dB return loss was 128 % [15]. Besides, a compact UWB-BPF based on open circuited lines planted in a DGS was proposed. The equivalent circuit model of this filter with notch implementation was also presented. In this filter the insertion loss was whereby less than 1 dB throughout the passband range of (3.1–10.6) GHz with 7.5 GHz bandwidth and the group delay in the passband interval was less than 0.2 ns except for the notched band [16]. On the other hand, the process of adding capacitive cross coupling to the conventional CRLH structure has led to control the phase shift in the right-handed passband. A compact UWB-BPF with good selectivity, low insertion loss of less than 1.35 dB, rejection level of higher than 20 dB at the stopband range of (11.95–16) GHz, and flat group delay across the passband was thereby obtained [17]. Another attempt in the field exhibited the design procedure of a compact BPF in UHF CRLH-TL. The CRLH-TL was utilized to miniaturize the overall size up to 80 % at 0.61 GHz and reject higher ordered harmonics up to 4th order [18]. From a different corner, a compact UWB-BPF using single unit cell CRLH-TL was designed. It operated from (4–9.5) GHz with S21 < −1.5 dB, and reduced total size up to 7 % [19]. Ahmed Reja et al. in March 2014 was manifested a study about the effect of adding MTM components on the conventional microstrip in the LPF design [20]. They have further upgraded their efforts in the same year through developing new UWB-BPFs based on tuning forks (TFs) shape and CSRRs [21].

This paper presents an UWB-BPF based on CRLH-TL. The ID-TLs and CSRRs are both used to miniaturize the filter size and for appreciable performance in microwave filters design. In addition, to improve the performance more and more, the closed rectangular rings have been connected to input and output ports of the filter. All those components contribute together in order to get MTM media that has negative index of refraction (n) by which the device has been miniaturized. This paper complements the work of the last-mentioned two other earlier works in the field [20, 21].

2 Microwave Frequency Description

The microwave frequency band description is listed in Table 1. The concentration in this work on a range of microwave frequencies has been restricted to cover U to C bands of frequencies for pragmatic technical reasons. Some of its applications are illustrated in Table 2.

Table 1 Description of microwave frequency band
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Table 2 Part of microwave frequencies and some of its applications
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3 CRLH-TL Circuit Model

In this work, an UWB-BPF is designed based on CRLH-TLs concept. CSRRs etched in the ground plane and ID-TLs printed on the upper side of microstrip line are introduced to satisfy the necessity of the filter design. The equivalent circuits of the CRLH-TL are shown in Fig. 1a [8], b [4], and c [22]. The filter takes on bandpass property under the balanced case and illustrates the series resonance (ωs)- and the shunt resonance (ωp)-angular frequencies as

$$\omega_{s} = \frac{1}{{\sqrt {C_{L} L_{R} } }}\;\;\; \text{rad/s}\;,\;\;\;\; \omega_{p} = \frac{1}{{\sqrt {C_{R} L_{L} } }} \;\;\;\; \text{rad/s}$$
(1)
Fig. 1
figure 1

CRLH-TL equivalent circuits. a Unit cell. b T-circuit model. c Pi-circuit model

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The center frequency (f o) of the passband is expressed as [8] as

$$f_{o} = \sqrt {f_{cL} \cdot f_{cR} } = \frac{1}{{2\pi \cdot {\sqrt[4]{{L_{R} C_{R} L_{L} C_{L} }}}}}$$
(2)

where, f CL, f CR are the high- and low-cutoff frequencies of pure left hand (LH)-TL and pure right hand (RH)-TL, respectively. LR, CR, LL and CL are the RH and LH inductances and capacitances respectively. To get UWB filter, LL, CL must be as large as possible while LR, CR as small as possible in case of CRLH-TL.

4 Components of the Proposed UWB Filter Design

4.1 CSRRs Structure

CSRRs are interesting particles introduced by Falcone et al. in [23] and J. D. Baena et al. in 2005 [24]. The topology of the CSRR unit cell coupled with TL and its equivalent circuit are illustrated in Fig. 2. The CSRRs components were presented to produce a negative effective permittivity (εr) at resonance frequency depending on its dimensions. CSRRs elements are etching in the ground plane of the microstrip line as a defected ground structure (DGS) without any extra space added, and hence, it is effective for miniaturizing microwave devices. The equivalent circuit model of CSRRs loaded TLs and their equivalent values of the pertinent intrinsic inductances and capacitances can be calculated using methods which are delineated in [24]. It is essential that both the insertion loss and return loss ought to be improved if this structure were to be integrated into the UWB filter design.

Fig. 2
figure 2

CSRR unit cell, a topology, b equivalent circuit model

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The calculations were performed to obtain the relative effective permittivity (εr) from the scattering parameters (S21 and S11) of the proposed CSRR MTMs [25, 26]. The simulation results of the structure can be obtained using high frequency structure simulator (HFSS). Three cells of CSRRs with 0.1 mm gap between them were used. The optimized dimensions of CSRRs structure have been set to overcome the tail in the upper side of response curve and to get reduction in size of the design. The parameters in Table 3 manifest that the rings achieved sharp cutoff beyond 6.0 GHz to limit the width of band into 5.6 GHz, with center frequency (f o) of 3.2 GHz.

Table 3 Characteristics of CSRRS
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4.2 Interdigital (ID) Coupled Lines Structure

The generalized model of the single ID coupled lines structure and its equivalent circuit are illustrated in Fig. 3. The geometry of an n-number of fingers of interdigital line (nID) described with finger width (W), finger length (l) and the spacing between two adjacent fingers (S). The space (S) in ID coupled lines taken as small as possible (practically ≥ 0.1 mm) to get high matching and coupling. The dimensions of this structure are chosen with respect to the required frequency (f o).

Fig. 3
figure 3

Proposed ID coupled lines, a topology of generalized model, b equivalent circuit model, c auxiliary equivalent circuit model

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To calculate the circuit parameters shown in Fig. 3b; Ls (very small and can be neglected), Cs, and Cp, firstly, the S-parameters of the ID coupled lines are determined using computer aided design (CAD). After that, S-parameters are converted into admittance parameters (Y) and impedance parameters (Z), using standard conversion formulae as shown in the equivalent circuit in Fig. 3c. Finally, the parameters of ID coupled lines equivalent circuit are obtained [8].

The capacitance of ID line shape is given as follows [27].

$$C_{ID} \left( {pF} \right) = \frac{{\varepsilon_{eff} .\left( {n_{ID} - 1} \right).l.K(k)}}{{18\uppi.10^{-3} . K^{\prime}(k)}}$$
(3)

The value of effective permittivity (εeff) in case of W/h < 1 is expressed in (4) while the approximated value is the first part of (5) and mainly it depends on dielectric constant (εr).

$$\varepsilon_{eff} = \frac{{\varepsilon_{r} + 1}}{2} + \frac{{\varepsilon_{r} - 1}}{2}\left[ {\frac{1}{{\sqrt {1 + \frac{12h}{W}} }} + 0.04\left( {1 - \frac{W}{h}} \right)^{2} } \right]$$
(4)
$$k = tan^{2} \left( {\frac{{W.\uppi}}{4(W + S)}} \right) , \;\;\; k^{\prime} = \sqrt {1 - k^{2} }$$
(5)
$$\frac{K(k)}{{K^{\prime}(k)}} = \frac{\uppi}{{{ \ln }\left[ {2\frac{{1 + \sqrt {k^{\prime}} }}{{1 - \sqrt {k^{\prime}} }}} \right]}}$$
(6)

K(k) and K′(k) are the complete elliptic integral of the first kind and its complement. l is the length of each finger. The approximate formula (7) is commonly used to quickly approach the inductance (with presence of the ground stub) in case of the interdigital line (LID). The substrate height (h) and thickness metallization (t) are the requested value for this calculation.

$$L_{ID} \left( {nH} \right) = 2l \times 10^{ - 4} \left[ {\ln \left( {\frac{l}{W + t}} \right) + 1.193 + \frac{{0.224\left( {W + t} \right)}}{l}} \right].K_{g}$$
(7)
$$K_{g} = 0.57 - 0.145\ln \left( \frac{W}{h} \right)$$
(8)

The design dimensions are W = 0.2 mm, S = 0.035 mm, and l = 9.5 mm, which are smaller than quarter wavelength account for strong capacitive coupling to achieve the UWB filtering. Whereas, the input and output ports formed as rectangular closed rings with 0.2 mm width.

5 Simulation Results of UWB-BPF

In this work, the design is applied on the Rogers RT-duroid 5880 substrate that has εr of 2.2, substrate height (h) of 0.5 mm. The HFSS has been used as assistant tool for simulation, and the important detailed results were the transmission (S21)- and reflection (S11)-coefficients. From scattering parameters details, the group delay (τd), voltage standing wave ratios (VSWRs), and quality factor (Q) have been calculated using the formulae below. The group delay (τd) is hereby given as in [20].

$$\tau_{\text{d}} = \frac{{{\text{d}}\emptyset_{21} }}{{{\text{d}}\upomega}}\;\;\;\;{ \text{s} }$$
(9)
$$VSWR_{1} = \frac{{1 + \left| {S_{11} } \right|}}{{1 - \left| {S_{11} } \right|}} , \;\;\; VSWR_{2} = \frac{{1 + \left| {S_{22} } \right|}}{{1 - \left| {S_{22} } \right|}}$$
(10)
$$Q = \frac{{f_{o} }}{BW}$$
(11)

where Ø21 is the phase angle of S21 in radians, ω is the angular frequency in radians per second and BW is the bandwidth in GHz.

The possibility of designing UWB filters operating in microwave frequencies region is available. The UWB-BPF design presented is shown in Fig. 4; having four fingers in each side in opposite direction in the upper plane of a microstrip line. These fingers are connected to the closed rectangular rings terminated with the input and output ports. Every ring has external dimensions of 1.8 mm × 3 mm and strip width equal to 0.2 mm.

Fig. 4
figure 4

Geometric design of UWB-BPF

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The process of etching three unit cells of CSRRs in the ground plane of the microstrip line is essentially useful to overcome the tail of transmission response. The overall external dimensions of the design is 17 mm × 4.3 mm. The variations of S-parameters and phase response for this filter are shown in Figs. 5 and 6, respectively. The maximum attenuation of |S11| is approximately 33 dB at 1.4 GHz. The bandwidth of bandpass is equal to 5.6 GHz starting from 0.4 to 6 GHz. The group delay and VSWRs are shown in Figs. 7 and 8, respectively. The group delay variation is nearly constant and equal to 0.15 ns in passband interval except at 2.1 GHz, while the VSWRs are smaller than 2 in passband interval.

Fig. 5
figure 5

Frequency response of UWB filter

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Fig. 6
figure 6

The phase of UWB filter

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Fig. 7
figure 7

Group delay of UWB filter

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Fig. 8
figure 8

VSWRs of UWB filter

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6 Comparison with Other Works

A comparison between this work with some other works in [21, 28, 29] of UWB filters related to resonance frequency (f o), bandwidth (BW), length of device (l), insertion loss (S21), return loss (S11), and quality factor (Q) are listed in Table 4. The approximate miniaturization in the presented design is 53 % compared to the design in [28]. The roll-off has sharp cutoff in this design better than other designs.

Table 4 Comparison between different UWB filters design
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7 Conclusion

A new idea for designing an UWB microwave MTM filter using ID couple lines and CSRRs components is presented. This design has been achieved and improved into wideband width equal to 5.6 GHz at 3.2 GHz resonance frequency. The design achieved flat insertion loss of lesser than 1 dB and return loss better than 12 dB. The stopband roll-off has very sharp slope in the upper cutoff frequency. The miniaturization of the filter with controllable bandwidth has been achieved depending on CSRRs dimensions. The BPF performance has been simulated and optimized depending on finite element method (FEM).