**2.4 Increment of bandwidth and roll-off factor of lowpass filter by circular split ring DGS**

Another technique is proposed here to increase the stopband, which involves the combination of a third-order lowpass filter (LPF) with bandstop filters. The first step is to design a microstrip elliptic function lowpass filter to develop this filter. The

**Figure 37.** *Photographic view of the bottom plane of the Split-ring DGS with Open-stub.*

**Figure 38.** *Comparison of the simulated and measured s-parameter results.*

**Figure 39.** *Measured phase responses.*

elliptic filter is chosen due to its sharper cutoff rate for a given number of reactive elements [4]. The bandstop responses are obtained by split ring type DGS units of different sizes. The main purpose of these DGS units is to increase the bandwidth of the rejection band.

#### *2.4.1 Analysis of different LC elements and parameters*

The L-C element values, scaled to *Z*<sup>0</sup> and *fc* are determined by the following equations (Eqs. (9) and (10)):

$$L\_i = \frac{1}{2\pi f\_c} Z\_{\mathbb{Q}} \mathbf{g}\_{Li} \tag{9}$$

$$\mathbf{C}\_{i} = \frac{1}{2\pi f\_{c}} \frac{1}{Z\_{0}} \mathbf{g}\_{Ci} \tag{10}$$

The element values of the third-order elliptic function lowpass prototype are given in **Table 6**, with corresponding L-C values derived from the above equations. All the inductors are realized using high impedance lines with characteristic impedance *Z*0*<sup>L</sup>* = 93 Ohms, whereas all the capacitances are realized using low impedance lines with characteristic impedance *Z*0*<sup>C</sup>* = 14 Ohms. **Table 7** lists all relevant microstrip design parameters calculated using the microstrip design equations [10]. Corresponding design parameters are substituted from **Tables 6** and **7** in the following equations (Eqs. (11) and (12)) to realize the initial physical lengths of the high and low impedance lines and are listed in **Table 8**. The layout of this third-order elliptic function LPF with the design dimension is given in **Figure 40**.


#### **Table 6.**

*LPF prototype elements values and L-C element values for third-order elliptic function LPF.*


#### **Table 7.**

*Microstrip design parameters for the elliptic function LPF with a dielectric constant of the substrate 3.2 and substrate height = 0.79 mm.*


**Table 8.**

*Initial physical lengths of the corresponding L-C parameters.*

#### **Figure 40.**

*Schematic diagram of the lowpass filter using open-ended T-shaped stub.*

$$dl\_{Li} = \frac{\lambda\_{\rm gl} \left(f\_c\right)}{2\pi} \sin^{-1} \left(2\pi f\_c \frac{L\_i}{Z\_{0c}}\right) \tag{11}$$

$$d\_{\rm Ci} = \frac{\lambda\_{\rm gC} \left(f\_c\right)}{2\pi} \sin^{-1} \left(2\pi f\_c Z\_{0c} \mathbf{C}\_i\right) \tag{12}$$

#### *2.4.2 Simulated result of the third order elliptic filter*

The MoM based EM simulation verifies the design, and the simulated frequency response is illustrated in **Figure 41**. It is clear from the simulation that the upper stopband of the LPF is relatively poor, about 820 MHz at a –15 dB attenuation level. The sharpness factor is 34.7 dB/GHz, with cutoff frequency and pole frequency being 3.3 GHz and 4.5 GHz, respectively.

#### *2.4.3 Bandwidth improvement by DGS units*

This third-order elliptic function LPF is then modified by the four split ringshaped DGS structures. The four DGS units are of different sizes and are distributed in two concentric sets. Each of these sets is constructed by a pair of split ring DGS units and placed on two sides of the LPF. This modified LPF layout is given in **Figure 42**. The dimension of the split ring DGS are:- the inner radius of the smaller split ring DGS placed at the left-hand side, r1 = 3 mm, the outer radius of the smaller split ring DGS placed at the left-hand side r1' = 3.3 mm, the inner radius of the bigger split ring

**Figure 41.** *S-parameter response of the open-ended T-shaped stub.*

*Filter Designs Based on Defected Ground Structures DOI: http://dx.doi.org/10.5772/intechopen.103065*

#### **Figure 42.**

*Schematic diagram of the lowpass filter using open-ended split ring DGS sections and T-shaped stub.*

DGS placed at the left-hand side r2 = 4.3 mm, the outer radius of the smaller split ring DGS placed at the left-hand side r2' = 4.6 mm, the inner radius of the smaller split ring DGS placed at the right-hand side r3 = 2.7 mm, the outer radius of the smaller split ring DGS placed at the right-hand side r3'= 3 mm, the inner radius of the bigger split ring DGS placed at the right-hand side r4 = 3.7 mm, the outer radius of the bigger split ring DGS placed at the right-hand side r4' = 4.1 mm, the distance between two sets of DGS units, L = 15 mm, the slot widths of the four DGS units are same and are given by, g1= 0.3 mm, the split gaps of the DGS units are also alike and are referred to as, g2 = 0.2 mm.

#### *2.4.4 Simulated result of the modified third order elliptic filter with DGSs*

The design is simulated, and the corresponding simulated response is shown in **Figure 43**. It is evident from the response that the filter's stopband is increased, and – 15 dB bandwidth is obtained as 2.7 GHz. The proposed filter exhibit four transmission zeros responsible for four DGS units. These pole frequencies occur at 3.1 GHz, 3.9

#### **Figure 43.**

*S-parameter response of the lowpass filter using double unit split ring DGS sections and Open-ended T-shaped stub.*

**Figure 44.** *Photographic view of the fabricated prototype top plane.*

**Figure 45.** *Photographic view of the fabricated prototype bottom plane.*

*Filter Designs Based on Defected Ground Structures DOI: http://dx.doi.org/10.5772/intechopen.103065*

**Figure 46.** *Comparison of the simulated and measured S-parameter result.*

**Figure 47.** *Comparison of the simulated and measured phase response.*

GHz, 4.7 GHz, and 5.2 GHz. The filter's cutoff frequency is obtained at 2.89 GHz with an insertion loss of less than 0.5 dB. The maximum rejection level of the stop-band is 16.3 dB, and the sharpness factor is increased to 100.9 dB/GHz. Therefore the proposed filter provides greater bandwidth and sharper roll-off factor by applying the four split ring-shaped DGS units.

#### *2.4.5 Measured result of the modified third order elliptic filter with DGSs*

The fabricated prototype verifies the simulated response, and a photograph of the fabricated layout is shown in **Figures 44** and **45**. There is good agreement between simulated and measured results, plotted in **Figures 46** and **47**, showing the variation of simulated and measured phase response with the frequency.
