Design of compact microstrip low-pass filter with

International Journal of Microwave and Wireless Technologies, page 1 of 6. doi:10.1017/S1759078715000689

# Cambridge University Press and the European Microwave Association, 2015

research paper

Design of compact microstrip low-pass filter with analytical sharpness of transition band hesam siahkamari1, ehsan heidarinezhad2, ehsan zarayeneh3, seyyed ali malakooti1, seyyed mohammad hadi mousavi2 and payam siahkamari2

A novel microstrip low-pass filter (LPF) using radial patched resonator and modified T-shaped resonators is designed to achieve ultra-wide stop-band. Also, the designed LPF has successfully addressed the problems of compactness and insertion loss, simultaneously. LC equivalent circuit of the proposed filter is calculated and equation for the sharpness in transition band is obtained based on LC equivalent circuit and transfer function. The proposed filter not only exhibits a very wide stopband of 168%, but also is able to suppress the 11th-harmonic response in conjunction with a small size of 0.147 × 0.052lg, where lg is the guided wavelength at 1.47 GHz. It is shown that the simulated results are highly consistent with the measured data. Keywords: Low-pass filter, Wide stopband, Equivalent circuit, Transfer function, Analytical sharpness Received 13 August 2014; Revised 19 March 2015; Accepted 22 March 2015

I.

INTRODUCTION

High-performance and compact-size low-pass filters (LPFs) with broad stop-band and sharp cut-off frequency are highly in demand in many communication systems, especially in wireless and mobile communications in order to suppress high-frequency harmonics [1]. In [2], a LPF using shunt openstubs at feed points of a center fed coupled-line hairpin resonator was presented. This filter had a wide stop-band, but the cut-off frequency was not amply sharp. In [3], a LPF with bended resonators and open stubs was presented so as to achieve sharp roll-off and ultra-wide stop-band, even though the structure of the filter was not symmetrical. In [4], a new transformed radial stubs (TRSs) with an extended stop-band was introduced. In [5], a new microstrip LPF with compact size and an ultra-wide stop-band using both triangular patch resonators and radial patch resonators was presented. Sharp roll-off and wide stop-band LPF based on radial split ring was presented in [6]. A compact LPF using T-shaped patches with an extended stop-band and high suppression factor (SF) was designed in [7]. In [8], a symmetrical miniaturized LPF using triangular and high-low impedance resona-

1 Electrical Engineering Department, Engineering Faculty, Razi University, Kermanshah, Iran. Phone: +989183326304 2 Department of Electrical Engineering, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran 3 Electrical Engineering Department, Islamic Azad University, South Tehran Branch, Tehran, Iran Corresponding author: H. Siahkamari Email: [email protected]

tors was introduced. A LPF using a high-impedance bended transmission line loaded by polygonal and triangular resonators was introduced for achieving a good roll-off rate and ultra-wide stop-band [9]. A novel configuration of shunt stubs and transmission line is presented to improve feature of filter like relative stopband bandwidth (RSB) size of circuit and figure of merit (FOM) in this paper. Also, the sharpness in transition band is calculated using LC equivalent circuit. The designed filter has an ultra-wide stop-band from 1.79 up to 20.58 GHz with an attenuation level better than 222 dB. The transition band is from 1.47 to 1.77 GHz with 23 and 220 dB, respectively.

II.

EQUIVALENT CIRCUIT

Figure 1(a) shows the topology of the proposed filter, comprises a radial patch resonator, modified T-shaped resonators, and rectangular shaped resonators. The proposed filter combine some resonators, each of which can generate several transmission zeros. The transmission zeros can ameliorate the sharpness in transition band or extend the breadth of stop-band. The modified T-shaped resonators are exploited to achieve sharpness in transition band and the radial patch resonator and rectangular shaped resonators are adopted to attain wide stop-band along with low insertion loss in the transition band. Moreover, the resonators can generate some poles to decrease insertion loss in passband. The LC equivalent circuit of the filter is complex. Thus, the capacitances and inductances effective at high frequencies are omitted in as much as they are not effective for calculating sharpness in transition band as well as transmission zeros at low frequency. The equivalent LC circuit of the filter is illustrated in Fig. 1(b) 1

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Fig. 1. (a) Layout of the proposed resonator, (b) the LC equivalent circuit.

in which L2–L9 are inductances of high–low impedance lossless line and L1 refers to the inductance of the transmission line. Furthermore, in this figure, capacitors are the sum of equivalent capacitances of microstrip T junction (capacitors are only used) and high–low impedance lossless lines apart from C1, C5, and C8, which are the sum of equivalent capacitances of open-end and high–low impedance lossless line. The layout and LC equivalent circuit of high–low impedance lossless line, microstrip line T-junction, and open-end

are illustrated in Fig. 2. The Formulas of high–low impedance lossless line are summarized in the figure. Also, the formulas of open-end and microstrip T junction are summarized in [1] and [10], respectively. A high-impedance lossless line terminated at both ends by relatively low-impedance lines can be presented by a P-equivalent circuit, as shown in Fig. 2(a). The values of inductors and capacitors can be obtained as:   1 2p × zs × sin l , v lg

(1)

  1 1 p cs = × × tan l , v zs lg

(2)

ls =

Fig. 2. Layout and LC equivalent circuit of: (a) the high–low impedance lossless line, (b) the open-end, (c) the microstrip line T-junction.

where zs is the characteristic impedance of the line, l is the length of it, and lg is the guided wavelength at the cut-off frequency. The parameters associated with these structures are La1 ¼ 0.9 mm, La2 ¼ 2.25 mm, La3 ¼ 5.75 mm, La4 ¼ 2 mm, La5 ¼ 0.9 mm, La6 ¼ 1.1 mm, La7 ¼ 0.95 mm, La8 ¼ 4.45 mm, La9 ¼ 1.5 mm, La10 ¼ 3 mm, La11 ¼ 1.16 mm, Ra ¼ 5.2 mm, Wa1 ¼ 1 mm, Wa2 ¼ 0.55 mm, Wa3 ¼ 0.1 mm, Wa4 ¼ 4 mm, Wa5 ¼ 6.6 mm, Wa6 ¼ 0.1 mm, Wa7 ¼ 1.3 mm, and Wa8 ¼ 2.5 mm. The values of these parameters can be extracted using Fig. 2. They are tabulated in Table 1. Figure 3 shows frequency response of the proposed filter and EM and equivalent circuit simulation results of proposed filter which are in good agreement. In this section, we will look at the behavior of the main resonator by examining its transfer function. The transfer function is calculated from LC equivalent circuit, for example, sharpness in the transition band can be adjusted with transfer

design of compact microstrip lpf

Table 1. Calculated values for LC equivalent circuit (Units: C, pF; L, nH). Parameters Calculations

C1 0.2

C2 0.24

C3 0.24

C4 0.74

C5 0.95

C6 0.24

C7 1.01

C8 0.57

C9 1.27

Parameters Calculations

L1 0.6

L2 1.49

L3 3.8

L4 1.11

L5 2.8

L6 0.14

L7 0.18

L8 0.1

L9 0.48

function. r in the transfer function alludes to resistance of matching. Also note that s ¼ jv.

vo vi T

(a2 b2 cr ) ,           =  s (r + L1 s) b L2 + L3 + L2 L3 s + a L3 s (r + (L1 + L2 )s + b r + L1 + L2 + L3 s sh              × (r + L1 s) 2bc + b L2 + L3 s + L2 s 2s + L3 s + a (r + (L1 + L2 )s 2c + L3 s + b 2c + r + L1 + L2 + L3 s (3)

where a=

1 + C 1 L4 s 2 , C 1 s + C 2 s + C 1 C 2 L4 s 3

            1 + s2 C5 L5 + L6 + L7 + C4 L5 + L6 1 + C5 L7 s2 + C3 L5 1 + C4 L6 + C5 L6 + L7 s2 + C4 C5 L6 L7 s4         , b= C5 + C6 + C5 C6 L5 + L6 + L7 s2 + C4 1 + C6 L5 + L6 s2 s         1 + C5 L7 s2 + C3 1 + C6 L5 s2 1 + C4 L6 + C5 L6 + L7 s2 + C4 C5 L6 L7 s4

c=

1 + (C7 L8 + C8 (L8 + L9 ))s2 + C7 C8 L8 L9 s4 . s(C8 + C9 + C8 C9 (L8 + L9 ))s2 + C7 (1 + C9 C8 s2 )(1 + C8 L9 s2 )

Figure 4(a) shows the structure of modified T-shaped resonators. The equivalent LC circuit of the modified T-shaped resonators is shown in Fig. 4(b). In Fig. 4(c), frequency responses of the proposed filter and modified T-shaped resonators are compared with one another. It can be seen that the steep sharpness in transition band is generated by modified T-shaped resonators. Hence, in this paper, we utilized LC model and transfer function of modified T-shaped resonators for the calculation and enhancement of the sharpness in transition band because the transfer function can be calculated by the LC model. Furthermore, we have calculated the frequency

of pole and zero (they are seen in Fig. 4(c)) through the transfer function. The sharpness is equated to zero frequency minus pole frequency. The formula of sharpness is summarized here. The formula of sharpness is used to achieve the best sharpness in transition band. For instance, the sharpness can be changed and improved by altering L3. L3 changes by altering La3 and Wa3. As a result, the sharpness is simply adjustable. For example, if L3 was 4.8, 4.3, and 3.8 nH, La3 will be 6.25, 6, and 5.75, respectively. Therefore, sharpness (f20 db 2 f3 db) will be 0.48, 0.45, and 0.4 GHz and choosing suitable dimension for designing a suitable sharpness is simple.

   r  √     − + 1+ −3 3dL1 L2 (2L1 +L2 )−d 2 L22 r 2   3L 1  ⎛ ⎞ ⎛ ⎞1/3 3 3 3   2 2 2 2 3 −36d L L r +9d L L r −2d L r 2 2    1 2 2    ⎜ 3 22/3 dL L ⎝  ⎠ ⎟  3  2  ⎜ 1 2 ⎟ 3 3 2 L2 r 2 + −36d 2 L2 L2 r +9d 2 L L r −2d 3 L r 3  ⎜ ⎟ + 4 3dL L ( 2L +L )−d 2 1 2 1 2 1 2 2 1 2  ⎜ ⎟  ⎜ ⎟ sharpness ≈  ⎜ ⎟ ⎛ ⎞1/3 ⎟ , ⎜ 2 2 2 2 3 3 3 3 L L r +9d L L r −2d L r −36d 1 2 ⎜ 1 2 2 ⎟  √ ⎝  1  ⎠ ⎠   1− −3 ⎝   − 1/3   3    2   6 2 dL1 L2 + 4 3dL1 L2 (2L1 +L2 )−d 2 L22 r 2 + −36d 2 L21 L22 r +9d 2 L1 L32 r −2d 3 L32 r 3     1     −    L5 (C3 +C4 +C5 )+L6 (C4 +C5 )+C5 L7 (4)

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Fig. 3. EM and equivalent circuit simulation results of the proposed filter.

where 7 d = C4 + C5 + 3C6 + C3 . 6 Figure 4(c) shows frequency response of modified T-shaped resonators, but the structure does not have a suitable stop-band. To increase stop-band, a strong transmission zero is generated by the radial patch resonator and it is incorporated into the modified T-shaped resonators. Figure 5(a) shows the structure of radial resonator and its equivalent LC circuit and frequency response are shown in Figs 5(b) and 5(c). The transfer function of radial patch resonator is computed to achieve the transmission zero of radial patch resonator.

Fig. 4. (a) Layout of the T-shaped resonators, (b) LC equivalent circuit of the T-shaped resonators, (c) frequency responses of the proposed filter and T-shaped resonators.

vo −(r(1 + C7 L8 s2 + C8 L8 + C8 L9 s2 + C7 C8 L8 L9 s4 )) , =  vi rad. (r(1 + La s)(C7 s + C8 s + C7 C9 L8 s3 + C8 C9 L8 s3 + C7 C8 L9 s3 + C7 C8 C9 L8 L9 s5 ).   2(1 + C7 L8 s2 + C8 L8 S2 + C8 L9 s2 + C7 C8 L8 L9 s4 ) × r + La s + C 7 s + C 8 s + C 9 s + C 7 C 9 L8 s 3 + C 8 C 9 L8 s 3 + C 7 C 8 L9 s 3 + C 8 C 9 L 9 s 3 + C 7 C 8 C 9 L8 L 9 s 5

(5)

where L a = L 1 + L2 + L 3 . The transmission zero can be calculated by equation (5)       2   −(1/C L ) − (1/C L ) − (1/C L ) − −4C C L L + C L + C L + C L C L L /C 7 8 7 9 8 9 7 8 8 9 7 8 8 8 8 9 7 8 8 9     . √ Fz =   2 2p      

The location of transmission zeros can easily be changed. For example, the location of transmission zeros is related to L7 in Fig. 5(b) and L7 changes by altering Wa2 in Fig. 1(a). Also, Wa2 has the direct relevance with the location of transmission zero.

(6)

III. SIMULATION AND EXPRIMENTAL RESULTS

Figure 6 shows the results of simulation and measurement. Simulated and measured results are obtained by an

design of compact microstrip lpf

Fig. 7. Photograph of the proposed filter.

For comparison, Table 2 provides a summary of some LPF performances based on several specifications defined in [6]. As shown in the Table 2, the presented filter demonstrates much higher FOM (41389) than the quoted filters. The following paragraphs define some relevant parameters. Sharp roll-off (j) is a parameter for defining sharpness in transition band. Fig. 5. (a) Layout of the radial patch resonator, (b) LC equivalent circuit of the radial patch resonator, (c) frequency responses of layout and LC equivalent circuit of the radial patch resonator.

EM-simulator advanced design system (ADS) and Agilent network analyzer N5230A, respectively. Evidently, return loss and insertion loss are better than 13.1 and 0.4 dB from DC to 1.3 GHz, respectively. The results exhibit that the stopband with 22 dB as a reference is from 1.8 up to 20.6 GHz and the sharpness in transition band is roughly 0.269 GHz (1.474– 1.906 GHz with 23 and 240 dB, respectively). Figure 7 shows the photograph of the presented filter fabricated on a substrate with a relative dielectric constant 1r ¼ 2.2, thickness h ¼ 15 mil, and loss tangent tand ¼ 0.0009 (RT/duroid 5880). The size of the fabricated LPF is about 22 × 7.75 mm2, which corresponds to an electrical size of 0.147 × 0.052 lg, where lg is the guided wavelength at 1.47 GHz.

j=

amax − amin (dB/GHz), fs − fc

(7)

where amax is the 40 dB attenuation point, amin is the 3 dB attenuation point, fs is the 40 dB stop-band frequency, and fc is the 3 dB cut-off frequency. TheRSB is given by: RSB =

stop-band bandwidth . stop-band center frequency

(8)

The SF is based on the stop-band bandwidth. For example, the stop-band bandwidth is referred to 22 dB suppression, thus the corresponding SF is defined as 2.2. A higher suppression corresponds to a greater SF. The normalized circuit size (NCS) is calculated by: NCS =

physical size (length × width) , l2g

(9)

where lg is the guided wavelength at 3 dB cut-off frequency. The architecture factor (AF) can be recognized as the circuit Table 2. Performance comparison among published filters and presented one.

Fig. 6. Simulated and measured performance of the LPF.

Reference

Roll-off

RSB

SF

NCS

[2] [3] [4] [5] [6] [7] [8] [9] This work

95 202 62 36 94.9 46 257 178.9 85.6

1.4 1.65 1.72 1.32 1.6 1.37 1.57 1.73 1.68

2 2 3 1.5 2.3 2 1.5 2 2.2

0.214 × 0.104 0.290 × 0.124 0.310 × 0.240 0.079 × 0.079 0.104 × 0.123 0.220 × 0.137 0.108 × 0.145 0.168 × 0.138 0.147 × 0.052

AF

FOM

1 1 1 1 1 1 1 1 1

11951 19951 4430 11543 27292 4182 38747 26912 41389

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hesam siahkamari et al.

complexity factor, which is: FOM =

IV.

1 × RSB × SF . NCS × AF

(10)

CONCLUSION

A novel microstrip LPF with small size and ultra-wide stopband is presented. In this paper, sharpness, transmission zero, and transfer function have been calculated and examined. The presented filter has a very high FOM of 41389. Considering all these good properties, the proposed LPF is applicable in modern communication systems.

REFERENCES [1] Hong, J.S.; Lancaster, M.J.: Microstrip Filters for RF/Microwave Applications, John Wiley & Sons, Inc., 2001. [2] Vamsi, K.V.; Subrata, S.: Sharp roll-off lowpass filter with wide stopband using stub-loaded coupled-line hairpin unit. IEEE Microw. Wireless Compon. Lett., 21 (6) (2011), 301–303. [3] Karimi, G.; Lalbakhsh, A.; Siahkamari, H.: Design of sharp roll-off lowpass filter with ultra wide stopband. IEEE Microw. Wireless Compon. Lett., 23 (6) (2013), 303–305. [4] Kaixue, M.; Kiat, S.Y.: New ultra-wide stopband low-pass filter using transformed radial stubs. IEEE Trans. Microw. Theory. Tech., 59 (3) (2011), 604–611. [5] Wang, J.; Xu, L.-J.; Zhao, S.; Guo, Y.-X.; Wu, W.: Compact quasi-elliptic microstrip lowpass filter with wide stopband. IET Electron. Lett., 46 (20) (2010), 1384–1385. [6] Hayati, M.; Asadbeigi, H.; Sheikhi, A.: Microstrip lowpass filter with high and wide rejection band. Electron. Lett, 48 (19) (2012), 1217–1219. [7] Sariri, H., Rahmani, Z., Lalbakhsh, A., Majidifar, S.: Compact LPF using T-shaped resonator. Frequenz, 67 (1–2) (2013), 17–20. [8] Wang, J.P.; Ge, L.; Guo, Y.-X.; Wu, W.: Miniaturised microstrip lowpass filter with broad stopband and sharp roll-off. Electron. Lett., 46 (8) (2010), 573–575. [9] Hayati, M.; Abdipour, A.; Abdipour, A.: Compact microstrip lowpass filter with sharp roll-off and ultra-wide stop-band. Electron. Lett., 49 (18) (2013), 1159–1160. [10] Wadell, B.C.: Transmission Line Design Handbook, British library cataloguing in publishing data, 1991.

Hesam Siahkamari was born in Kermanshah, Iran in 1988. He received his B.Sc. degree in Electronic Engineering in 2010 from Islamic Azad University, Kermanshah, Iran and M.Sc. degree in Electronic Engineering in 2013 from Razi University, Kermanshah, Iran. His current research interest includes RF/ Microwave circuit design.

Ehsan Heidarinezhad was born in Kermanshah, Iran, in 1986. He received his B.S. degree in Electronics Engineering from Islamic Azad University, Kermanshah Branch, Kermanshah, Iran, in 2009, and his M.S. degree in Electrical Engineering from the Islamic Azad University, Science and Research, Kermanshah Branch, Kermanshah, Iran, in 2014. His current research interest includes RF/Microwave circuit design. Ehsan Zarayeneh was born in Kermanshah, Iran in 1987. He received his B.S. degree in Electronics Engineering in 2011 from Islamic Azad University, Toyserkan Branch, Hamedan, Iran and he received his M.S. degree in Electronics Engineering from Islamic Azad University, South Tehran Branch in 2014, Tehran, Iran. His current research interest includes RF/Microwave circuit design. Seyyed Ali Malakooti was born in Tehran Province, Tehran, Iran, in 1987. He received his B.S. and M.S. degrees in Electrical Engineering from Razi University, Kermanshah, Iran, in 2010 and 2013, respectively. In 2015, he joined Unishare Robotic Co., Kermanshah, Iran. His current research interests include design of microstrip antennas, multi-band passive microwave components, and digital-integrated circuits. Seyyed Mohammad Hadi Mousavi was born in Kermanshah, Iran, in 1990. He received his B.S. degree in 2012 from Islamic Azad University and the M.S. degree from Islamic Azad University, Science and Research Branch, Kermanshah, Iran, in 2014, all in Communication Engineering. His research interests include high-frequency circuits and Microstrip circuit design. Payam Siahkamari was born in Kermanshah, Iran in 1991. He received his B.Sc. degree in Electronic Engineering in 2015 from Islamic Azad University, Kermanshah, Iran and he is now pursuing his M.Sc. degree from Islamic Azad University, Science and Research Branch, Kermanshah, Iran. His current research interest includes RF/Microwave circuit design.