1. INTRODUCTION
Microstrip filters play various roles in wireless or mobile communication systems. The demands for advanced microwave filters have been increasing other than conventional Chebyshev filters in order to meet stringent requirements from microwave systems, particularly from wireless communications systems [Reference Hong and Lancaster1]. Various methods have been used to design a lowpass filter with good specifications. In [Reference Wei, Chen, Shi, Huang and Wang2], compact lowpass filter with wide stopband using coupled-line hairpin unit has been presented. It has a bad return loss in the stopband, gradual roll-off and low attenuation level in the stopband. In [Reference Ma and Yeo3], new ultra-wide stopband lowpass filter using transformed radial stubs has been designed, but this structure does not have a good return loss in the passband and stopband. Also insertion loss in the passband is undesirable. In [Reference Wang, Cui and Zhang4, Reference Cui, Wang and Zhang5], designs of compact microstrip lowpass filters with ultra-wide stopband have been studied. In both of them, the return loss and the attenuation level in the stopband is not adequate. In [Reference Velidi and Sanyal6, Reference Karimi, Lalbakhsh and Siahkamari7], sharp roll-off lowpass filters with wide stopband have been presented. But the size of these two lowpass filters is large. In [Reference Chen and Xu8], defect ground structure resonator with two transmission zeros and in [Reference Kufa and Raida9], lowpass filter with reduced fractal defected ground structure have been presented. Their disadvantages are complex fabrication and additional radiation loss. In [Reference Kaddour10], simple periodic coplanar-waveguide structures are used to realize compact, selective, well-matched filters with reduced spurious frequency bands. In this paper, a microstrip lowpass filter with sharp roll-off, high return loss, low insertion loss, and wide stopband is designed, fabricated, and measured. The transmission lines are folded to achieve small size. Also to obtain sharp roll-off, the step impedance resonator is modified to a radial stub resonator. The proposed filter has good return loss and insertion loss in the passband with using a radial stub resonator. Furthermore, a suppressing cell with high and wide stopband is used to obtain a filter with wide stopband.
2. FILTER DESIGN
A lowpass filter consists of two main parts. These two parts are resonator and suppressing cell. The resonator is used to remove unwanted harmonics in the low frequency with an Elliptic response, and the suppressing cell is used to remove unwanted harmonics in the high frequency with a Chebyshev response. So by combining these two cells a lowpass filter with sharp roll-off and wide stopband is achieved. The main challenge in the lowpass filter design, is to improve the filter characteristics such as size, roll-off, stopband bandwidth, insertion loss, and return loss in the passband. So the design process for the proposed filter is given as follows:
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• Calculating the LC equivalent circuit and ABCD parameters of the conventional stepped impedance resonator.
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• Modifying the conventional stepped impedance resonator to achieve sharper roll-off and smaller size.
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• Changing effective parameters in the proposed resonator and studying their influences on the response.
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• Designing proper suppressing cells and adding them to the proposed structure to achieve wide stopband.
A) The conventional stepped impedance resonator
In the microstrip lines, the high impedance lines act as series inductors and the low impedance lines act as shunt capacitors [Reference Hong and Lancaster1]. Figure 1 shows the geometric structure of the conventional stepped impedance resonator with its LC equivalent circuit. In the LC equivalent circuit of the conventional stepped impedance resonator, C r and L r are the equivalent capacitance and the equivalent inductance of the resonant branch, respectively. C L is the equivalent capacitance of the lateral loaded open stub. L t is the equivalent inductance of the main transmission line.
Fig. 1. The geometric structure of the conventional stepped impedance resonator with its LC equivalent circuit.
The ABCD parameters of the conventional resonator are calculated as follows:
$$A = \displaystyle{{1 - \omega ^2 ((L_t + L_r ) + (C_r + 2C_L ))} \over {1 - \omega ^2 L_r (C_r + 2C_L )}},$$
$$B = \displaystyle{{2j\omega L_t - j\omega ^3 L_t (L_t + 2L_r )(C_r + 2C_L )} \over {1 - \omega ^2 L_r (C_r + 2C_L )}},$$
$$C = \displaystyle{{j\omega (C_r + 2C_L )} \over {1 - \omega ^2 L_r (C_r + 2C_L )}},$$
$$D = \displaystyle{{1 - \omega ^2 (L_t + L_L )(C_r + 2C_L )} \over {1 - \omega ^2 L_r (C_r + 2C_L )}},$$
Now we can extract S parameters from ABCD parameters as shown:
$$\eqalign{& \hskip-2pt S_{11} = S_{22}, \cr &\hskip10pt = \displaystyle{{ - j\omega ^3L_t(L_t + 2L_r)(C_r + 2C_L) + 2j\omega L_t - j\omega Z_0(C_r \!+ 2C_L)} \over \matrix{2Z_0 - 2\omega ^2Z_0(L_t + L_r)(C_r + 2C_L) - j\omega ^3L_t(L_t + 2L_r) \hfill \cr\quad (C_r + 2C_L) + 2j\omega L_t + j\omega Z_0^2 (C_r + C_L) \hfill} }} $$
$$\eqalign{& S_{12} = S_{21} \cr &\quad = \displaystyle{{2Z_0 - 2\omega ^2Z_0L_r(C_r + 2C_L)} \over \matrix{2Z_0 - 2\omega ^2Z_0(L_t + L_r)(C_r + 2C_L)- j\omega ^3L_t(L_t + 2L_r) \hfill \cr\quad (C_r + 2C_L) + 2j\omega L_t + j\omega Z_0^2 (C_r + C_L) \hfill} }.} $$
Based on the calculated S parameters, it is clear that the first transmission zero is depending on L r , Cr , and C L . By S 21 = 0 the transmission zero is equal to:
$$f_Z = \displaystyle{1 \over {2 \times \pi \times \sqrt {L_r \times (C_r + 2C_L )}}}. $$
So by increasing C L the transmission zero moves to the cut-off frequency, which results in sharper roll-off.
B) The proposed resonator
To achieve sharper roll-off and smaller size, the modified radial stub resonator based on the conventional stepped impedance resonator is presented as shown in Fig. 2(b). The roll-off rate of the proposed resonator is 65.38 and the roll-off rate of the conventional resonator is 51.51, so improvement of the roll-off rate is about 26.5 %. The proposed modified radial stub resonator and its frequency response are shown in Figs 2(b) and 2(c), respectively. Figure 2(c) shows, the proposed resonator has sharper roll-off. Another parameter relevant to the performance of the proposed resonator is the slow wave factor (SWF). The SWF is given by [Reference Zhang11] as:
$$SWF = \displaystyle{{\lambda _0 \Delta \theta} \over {360d}} + \sqrt {\varepsilon _{eff}}, $$
where d is the physical length of the microstrip line, λ 0 is the guided wavelength, Δθ is the phase difference between the conventional microstrip line and the proposed resonator, and ε eff is the effective microstrip permittivity. The variation of the SWF versus frequency is shown in Fig. 2(d). Compared with the conventional stepped impedance resonator, the proposed resonator increases the SWF by 50% at 1.19 GHz.
Fig. 2. (a) The conventional resonator. (b) The proposed resonator. (c) The frequency response of the conventional stepped impedance resonator and the proposed resonator. (d) SWF of the proposed resonator.
C) Effective parameters
Equation (7) shows, the effective parameters are L and W r . The frequency response of the proposed resonator with different values of the L and W r are shown in Figs 3(a) and (b), respectively. Figure 3(a) shows, the transmission zero will be moved to lower frequencies, by increasing L from 0.1 to 0.5 mm with step of 0.2 mm, which results in sharper roll-off. Also the transmission zero will be moved to higher frequencies, by decreasing W r from 3.5 to 2.5 mm with step of 0.5 mm. This decrement results in gradual frequency response of the proposed resonator.
Fig. 3. (a) The frequency response of the proposed resonator with different values of the L. (b) The frequency response of the proposed resonator with different values of the W r.
D) Suppressing cell design
To extend the stopband, extra sections should be added to the proposed structure as shown in Fig. 4(a), which results in size increment. To achieve the smaller size, the transmission lines are folded as shown in Fig. 4(b). The bended microstrip line is modeled by an equivalent T-network, as shown in Fig. 4(c). The disadvantage of using folded lines is additional capacitance, which is added to the structure. The additional capacitance is so small that the S 21 curves in Fig. 4(d) are nearly the same, and its effects on suppression levels can be neglected.
Fig. 4. (a) The prototype suppressing cells. (b) The proposed suppressing cells. (c) Equivalent circuit of the bended microstrip line. (d) The frequency response of the prototype and proposed suppressing cells.
Closed-form expressions for evaluation of capacitance and inductance of the equivalent T-network are presented in [Reference Hong and Lancaster1]. These proposed suppressing cells suppress the harmonics in the frequency range of 4.6–20 GHz as shown in Fig. 4(d). To have a LPF with a wide stopband, sharp roll-off and good passband performance, the proposed suppressing cell and the proposed resonator are combined as shown in Fig. 5(a).
Fig. 5. (a) The proposed filter. (b) Photograph of the proposed filter. (c) Measured and simulated results of the proposed filter. (d) Group delay of the proposed filter.
3. RESULTS AND DISCUSSION
The proposed structure is implemented on an RT/Duriod 5880 substrate with ε r = 2.2, thickness = 15 mil, and loss tangent = 0.0009. A photograph of the fabricated filter and the measured and simulated results are shown in Fig. 5(b) and (c), respectively. The proposed filter is simulated using ADS software, and the measurements are done using an HP8757A network analyzer. The cut-off frequency of the proposed filter is at 1.19 GHz. The transition band is approximately 0.2 GHz from 1.19 to 1.39 GHz with corresponding attenuation levels of 3–20 dB, respectively. The stopband is from 1.39 to 19 GHz with the rejection level higher than 20 dB. The insertion loss and return loss in the passband from DC to 0.8 GHz are better than 0.26 and 14 dB, respectively. Figure 5(d) shows the proposed filter has a flat group delay, and the maximum variation of the group delay is 0.4 ns. Table 1 shows the performance comparison between the proposed filter and the references. The figure-of-merit (FOM) is defined as [Reference Karimi, Lalbakhsh and Siahkamari7, Reference Afzali, Karkhanehchi and Karimi12]:
$$FOM = \displaystyle{{\xi \times RSB \times SF} \over {NCS \times AF}},$$
where ξ is the roll-off rate, RSB is the relative stopband, SF is the suppression factor, NCS is the normalized circuit size, and AF is the architecture factor which are presented in [Reference Karimi, Lalbakhsh and Siahkamari7, Reference Afzali, Karkhanehchi and Karimi12]. When comparing the selectivity of filters with different cut-off frequencies, it is better that the roll-off rate is normalized to the cut-off frequency so relative roll-off rate (ξ′) is given as:
$$\xi \hskip1pt {\rm ^{\prime}} = \displaystyle{{\alpha _{max} - \alpha _{min}} \over {f_s - f_c}} \times \displaystyle{1 \over {f_c}},$$
where α max and α min are the 20 and 3 dB attenuation points, respectively. f c is the 3 dB cut-off frequency, and f s is the 20 dB stopband frequency. Also return loss (RL) and insertion loss (IL) in the passband are the important parameters in filters, but these parameters are not included in the FOM, so overall FOM (OFOM) with considering RL, IL, and relative roll-off rate (ξ′) is presented as:
$$OFOM = \displaystyle{{\xi\hskip1pt ^{\prime} \times RSB \times SF} \over {NCS \times AF}} \times \displaystyle{{RL_{({\rm dB})}} \over {IL_{({\rm dB})}}} \times 10^{ - 3}. $$
Table 1. Performance comparison of the proposed filter with the references.
As shown in Table 1, we can observe that the proposed filter has the highest OFOM.
4. CONCLUSION
A microstrip lowpass filter with wide stopband and sharp roll-off is presented. The proposed filter consists of a modified radial stub resonator, which is cascaded by four suppressing cells. The results indicate that the proposed filter has many desirable features such as, low insertion loss in the passband, sharp roll-off, and wide stopband. There is a good agreement between the measured and the simulated results. The proposed filter is suitable for wireless communication systems.
ACKNOWLEDGEMENT
The authors would like to thank the Kermanshah Branch, Islamic Azad University, for the support of this research project.
Mohsen Hayati received the B.E. in Electronics and Communication Engineering from Nagarjuna University, India, in 1985, and the M.E. and Ph.D. in Electronics Engineering from Delhi University, Delhi, India, in 1987 and 1992, respectively. He joined the Electrical Engineering Department, Razi University, Kermanshah, Iran, as an Assistant Professor in 1993. Currently, he is a professor with the Electrical Engineering Department, Kermanshah Branch, Islamic Azad University as well as Faculty of Engineering, Razi University. He has published more than 170 papers in international and domestic journals and conferences. His current research interests include microwave and millimeter wave devices and circuits, application of computational intelligence, artificial neural networks, fuzzy systems, neuro-fuzzy systems, electronic circuit synthesis, modeling, and simulations.
Mehrnaz Khodadoost received the B.Sc. in Electronics Engineering from the Islamic Azad University of Kermanshah, Iran in 2009. She is currently working toward the M.Sc. degree in Electrical Engineering in Razi University. Her research interests include design and analysis of the microwave circuits, microstrip filters, and couplers.
Hamed Abbasi was born in Kermanshah, Iran in 1987. He received the B.Sc. in Electronics Engineering from the Islamic Azad University of Kermanshah, Iran in 2008 and received the M.Sc. degree in Electrical Engineering from the Razi University, Kermanshah, Iran in July 2012. He is currently working toward the Ph.D. degree in Electrical Engineering at Razi University. His research interests include design and analysis of the microwave circuits, power amplifiers, low noise amplifier (LNA), microstrip filters, couplers, and antennas.
