Wide Band Stop Response Using Interdigital Capacitor/CSRR DGS in Elliptical Microstrip Low-Pass Filter

In this paper, a compact elliptic-response microstrip low pass filter (LPF) is presented with a wide stop-band using stepped impedance resonators. With high attenuation in the stop-band, the overall size reduction of the proposed filter is achieved using a novel defected ground structure technique using an interdigital capacitor and complementary split ring resonator (CSRR). A 4.2 GHz LPF is designed and simulated on FR4 substrate and a stop band of 8.8 GHz is obtained by utilizing interdigital and complementary split ring resonator. Results further show that the use of U-shaped high impedance line on the top layer of filter enhances the stop-band bandwidth by 2.2 GHz. In the final design, the passband insertion loss is found below 0.5 dB, and –10 dB is obtained over a band from 5.06 GHz to 17.06 GHz between input and output ports. The normalized circuit size of the filter is 0.417 0.202 and the figure of merit is calculated about 55 at the cut-off frequency. These proposed LPFs have promised significant advantages in the stop-band characteristics with an acceptable roll-off rate for spurious-free communications.


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Most of these designs either suffer with low attenuation (<20 dB) range in the stop-band or have larger size. In addition, for better roll-off rate as well as compactness, an elliptical-function response is used in many LPFs which are based on several structures, such as stepped-impedance hairpin resonator [8], tapered resonator [12], slit-loaded tapered compact microstrip resonator cell [13], symmetrically loaded radial-shape patches and meandered transmission line [14], triangular patch resonators and radial patch resonators [15], symmetrically loaded triangular and high-low impedance resonators [16], P-shaped resonators [17], novel asymmetric structures for resonator and suppressor [18], wide stop-band using tri-section stepped impedance resonator [19] etc.
Recently, a microstrip low-pass filter made using a rectangular resonator and high impedance elements is reported with a wide stop-band bandwidth of 18.7fC for fC = 1.01 GHz [20]. To increase the compactness of designed filter with better harmonic control, sometime a slot is made on the ground (bottom) conductor to create extra parasitic elements. Such structure is known as a defected ground structure (DGS) [21]. Various kinds of DGS designs are proposed for different filter types and explored the desired properties like compactness [2], [22], [23], sharp rejection [24], wide stop-band [25], multi-band response [26]. In some applications, sharp transition region plays a vital role for rejection of intermodulation products and so that the roll-off rate should be analyzed for these applications [27], [28]. Also, the resonant frequency of the slot can be varied by changing the number of metal fingers which are incorporated in the slot instead of changing the size of slot [29]- [32]. Also, a square-shaped complementary split ring resonator (CSRR) filtering can be used for isolation improvement [33]. Such CSRR offers high filtering (band-rejection) capability which is generally required for coupling suppression along with compact size and ease of fabrication.In this way the search for compact filter design structure with smooth curve of group delay and wide stop-band can over to use in the extensively spread microwave and millimeter-wave systems. To achieve such ideal response, approach of combining the interdigital capacitor and CSRR DGS are used.
In the presented work, the interdigital capacitor is placed as a DGS at the bottom layer to increase the stop-band region for a fifth order elliptical low-pass filter accompanied with CSRR and a wide stop band is achieved. With optimization of interdigital/CSRR DGS on the bottom layer and U-shaped high impedance line on the top layer using in CST microwave studio, we obtained the maximum stopband of about 12 GHz (relative to -10 dB) on a physical size of only 22.22 mm × 9.5 mm including 50  feed lines.

II. 5 TH ORDER HIGH LOW ELLIPTICAL LPF (HL-ELPF)
Design of a 5 th order HL-ELPF is accomplished using two capacitive low-impedance elements and three inductive high-impedance elements. Filter specifications are chosen as a cut-off frequency (fC) of 4 GHz, maximum stop-band insertion loss of 30 dB, 100 Ω and 20 Ω as high and low impedances, respectively and a FR4 material is taken as a substrate which has a dielectric constant (r) of 4.5 and thickness of 1.5 mm along with copper layer thickness of 35 µm.
For the 5 th order LPF design, the values of inductance (Li) and capacitor (Ci) can be obtained from the immittance ( ) values using the following equations [2], [21].
For high-impedance line, For low-impedance line, So, the physical lengths of these lines are obtained as follows [2], [21], For high-impedance transmission line length, For low-impedance transmission line length, The schematic of the HL-ELPF is shown in Figure 1 and details with dimensions are given in Table I for filter designed using FR4 substrate, where g0 and g6 represent the source and load sections included for matching purpose.  As we can see from Table I, a combination of high and low-impedance lines can be used to realized L2/C1 and L4/C2 resonators [1], [2], which offers high reflections due to unwanted reactance and susceptance at their junctions, respectively. In addition, these combinations will have a large size [2].
To realize the shunt connected series L-C for a three-pole symmetric stepped impedance LPF with the elliptic reponse, the low impedance lines (C's) are connected in series with high impedance CPW line (L's) as DGS to ground plane [34].In order to make a symmetrical structure, initially the following approximation formula is used to estimate a single transmission line for L2/C1 and L4/C2 resonators [2].
where 2 represents a "compensated" susceptance formed by the line elements L2 and C1, and Δ 123 represents an unwanted total equivalent susceptance due to the first three inductive line elements (L1, L2 and L3) [2].
We estimated the dimensions of low impedance lines (C's) to represent the shunt connected series L-C using equation (7) Similar approach has been applied for the line elements L4 and C2 to be realized with a single transmission line. The approximate lengths of all sections are given in Table I. An HL-ELPF with these dimensions is designed on Computer Simulation Technology (CST) software as shown in Figure 2(a) where top layer is synthesized for the symmetrical filter. The optimized dimensions (width W's and length L's) are given in Table I. This complete LPF design has dimensions of 25.59 mm × 11.6 mm. 499 As can be seen in Figure 2(b), the cut-off frequency (fC) is obtained as 4.22 GHz and in the passband centered at 2 GHz, the maximum return loss (RL) is 18 dB and the insertion loss (IL) is 0.41 dB. The bandwidth of stop-band is obtained from 5.1 to 11.2 GHz i.e. 6.1 GHz corresponding to 10 dB attenuation.

A. Simulation of HL-ELPF with slot and interdigital capacitor DGS
For an improvement in the stop-band, we introduced a simple rectangular shape slot as a defected ground structure (DGS) just below the three high-impedance lines of top layer [3]. On the bottom layer, the two side slots are made of size of 4.90 mm width  3.70 mm length whereas the center slot has the size of 4.90 mm width  5.60 mm as illustrated in Figure 3   In respect to the equivalent circuit shown in Figure 3(c), the input impedance Zin of the bottom layer is modeled using the lumped elements [35,36] as given in the equation (8), The values of equivalent lumped elements are obtained as: L1=L2=L4=L5= 6.12 nH, L3=9.26 nH, C1=C3= 0.0297 pF, C2=0.0196 pF. These lumped values provide the resonant frequencies of 11.8 GHz and 11.814 GHz, respectively due to first (and third) and second resonators. So, as the slot dimensions generated the resonant frequencies of about 11.8 GHz, the reflections are found to increase at 11.2 GHz and beyond. So, in 11.8 to 14.25 GHz range, the S21 response is flattened to about -7dB. Consequently, stop-band BW increases to 6.8 GHz, as shown in  As the width of the metal finger is directly related to the capacitance of the IDC so, the increment of width of the capacitor leads to decrease in the equivalent capacitance. If the number of fingers is increased with keeping width of the fingers and space between fingers constant, then capacitance of IDC increases with corresponding decrease in the quality factor. With increasing space between the fingers, then the capacitive effect of the IDC is increased. The similar effect can also be observed on the equivalent inductance of the bottom layer. Equivalent circuit of IDC suggested the extension of stop-band by higher capacitance or reduced inductance as IDC is a multi-conductor structure with passband and stop-bands [37]. With the equivalent circuit model as shown in Figure 5(c) [35,36,38], the input impedance formula as shown in equation (9) is obtained as,  these values the small transmission at 11.8 GHz is possible due to the center (second) slot and beyond it, the side IDCs support the non-transmission of higher frequency. The simulated responses of Design 3 and Design 4 are given in Figure 6(a) and (b), respectively.
As the values of inductance and capacitance generated in the side slots have offered a passband around 11.8 GHz and afterwards the stop-band with minor change in fC (4.255 GHz), IL and RL in pass band as can be seen in Figure 6(a). This modification has slightly decreased the BW of stop-band to 6.5 GHz due to a transmission peak of -7 dB at 11.8 GHz due to first and third slots. For the second modification on the bottom layer as in Figure 5(b), the stop-band BW is further reduced to 6.1 GHz with a resonance peak at 11.5 GHz (shown in Figure 6b). However, the reflections are higher beyond this frequency due to two side IDCs till the negative reflection peak at 13.9 GHz. Miniaturization of IDC beyond above mentioned dimensions is difficult, which restricts shifting of passband and stopband towards higher frequency. So, if the peak at 11.8 GHz can be addressed by other means, the increase in stop-band BW is possible.

B. Simulation of HL-ELPF with IDC/CSRR
To achieve stop frequency as 11.  Figure 7(c) [33,38], where IDC is presented by a series RLC resonator with two shunt capacitors and mirrored CSRR is by two shunt LC resonators. The equivalent input impedance formula as shown in equation (11).   In the simulation response of this design shown in Figure 8, the maximum RL of 16 dB and IL of 0.42 dB are obtained at 2.9 GHz i.e. ripples in passband are shifted. Although fC increases to 4.34 GHz due to CSRR, significant increase in stop-band BW is also noticed from 6.5 GHz to 8.8 GHz (i.e.

-14 GHz
). This happened due to increment of characteristic impedance by insertion of CSRR which slightly changes the resonant frequency of the overall filter structure as discussed above and the quality factor is also observed to reduce. The further rejection of band from 11.8 GHz to 14 GHz is observed due to CSRRs on the both side slots, which resulted in the wide stopband.

IV. SIMULATION OF HL-ELPF WITH U-SHAPED LINE AND IDC/CSRR
In order to address the compactness of filter, top layer is modified by inserting a U-shaped highimpedance line in place of the straight line as reported in [5]. On top layer of this filter, dimensions of low-impedance line are kept unchanged and on the bottom layer, IDC/CSRR DGS of Figure 7(b) is placed as shown in Figure 9(a). Also to mitigate the problems of parasitic capacitance due to reflections and accumulation of charges at the corners of U-shaped lines, a 50% mittering is performed with the dimension of 0.42 mm at the corners in all three U-shaped lines, which is shown in Figure 9(b) keeping the same bottom layer (as in Figure 7b). Lumped equivalent model of its bottom layer is same as mentioned in Figure 7 which basically depends on loss tangent of the material. Roll-off factor of the filter is also found to be increased upto 6.145 dB/GHz due to insertion of DGS elements as more number of elements increases the order of the overall filter i. e. sharpness as noticed after simulation. Here two attenuation poles are obtained at 8.484 GHz and 12.51 GHz due to variation of inductance lengths. Also, one resonance peak of -7.85 dB in S11 is observed at 14.82 GHz. The overall dimension of the filter is reduced to 22.22 mm  9.5 mm i.e. by 28.89% compared to the original design of Figure 2(a). Similar response is observed for HL-ELPF with mitered U-shaped line, which is shown in Figure 10(b) except a peak of -8.35 dB in S11 at 14.88 GHz. However, the advantage of this Design 7 is BW of 12.0 GHz for stop-band corresponding to 10 dB attenuation. The characteristics of low-pass filter designs reported in this work are summarized in Table II as discussed in this section and previous section. The LPF performance parameters like, roll-off rate (β), relative stop-band (RSB) bandwidth for -20 dB return loss, normalized circuit size (NCS), and figureof-merit (FOM) are calculated from the known relations [9,18] and comparison of last three designs is given in Table III.As given in Table III, the performances of Design 6 and Design 7 are comparable to the earlier reported filters [8,19,21,31]. In addition, the proposed filters in this work achieved wide stop-band of 8.15 GHz with high attenuation (> -20 dB) in the stop-band with the compact circuit size.