A novel wide stopband coplanar stripline low-pass filter

　　1 Introduction

　　Coplanar stripline (CPS) is a coplanar transmission line proposed in the 1970s. Due to its simple structure, it is easy to bridge active and passive two-port devices, avoiding the process troubles caused by perforation. At the same time, CPS is insensitive to dielectric thickness, has small parasitic effects caused by discontinuous structures, and has low losses during high-frequency electromagnetic wave propagation. Therefore, it is widely used in feed networks and microwave circuits, such as printed dipole antennas, filters, couplers, resonators, and amplifiers.

　　In the rectenna system, the low-pass filter is required to allow the fundamental wave to pass through and effectively block the second and third harmonics to improve the conversion efficiency of the rectenna system. Therefore, in the rectenna system, a low-pass filter with a wide stopband and low loss is more practical. The CPS bandpass filter and bandstop filter used in the rectenna system in the literature have an insertion loss simulation of -0.3dB at the operating frequency, and the stopband bandwidth with an attenuation of less than -10dB is about 6GHz, which effectively suppresses the second harmonic, but the third harmonic suppression performance is greater than -5dB, and the size is large.

　　According to the analysis of the discontinuous structure characteristics of CPS, the half-wavelength T-type open-circuit branches and open-ring resonant circuits are equivalent to series LC circuits, which produce transmission zeros and realize stopband characteristics. In order to reduce the volume of the filter, slots on the microstrip line also have stopband characteristics. Therefore, by adding T-type branches and T-type slot resonances inside and outside the transmission line, high-order harmonics can be well suppressed, and the design of a wide stopband low-pass filter can be realized.

　　This paper proposes a new type of open-loop CPS resonator and analyzes its lumped element equivalent circuit diagram. Based on the open-loop structure resonator, a third-order CPS low-pass filter is designed, which has the characteristics of small size, small loss in the passband, and wide stopband bandwidth. It effectively suppresses the second and third harmonics and can be applied to RF front-end and rectenna systems.

　　2 Coplanar Stripline (CPS) Structure

　　The CPS structure has a dielectric plate of finite size, as shown in Figure 1. According to the CPS transmission line theory, as the gap S increases, the total loss of the CPS becomes smaller and smaller, while its characteristic impedance becomes larger and larger. In other words, a CPS structure with a high characteristic impedance corresponds to a smaller transmission loss [3]. In order to obtain a higher diode conversion efficiency, the CPS needs to have the characteristics of low loss and high characteristic impedance.

　　Figure 1 Coplanar stripline structure

　　The dielectric plate used in the CPS structure low-pass filter designed in this paper has a relative dielectric constant of 2.55, a thickness of 0.8mm, and a copper coating thickness of 0.035mm. According to the full-wave simulation software IE3D analysis, when the line width W and spacing S of the parallel transmission lines are 0.6mm and 0.4mm respectively, the characteristic impedance Z0 of CPS is 172ohm.

　　3 Design of CPS low-pass filter

　　3.1 CPS open-ring resonator

　　The open-loop CPS resonator proposed in this paper has a structure and an equivalent circuit as shown in Figure 2, which is realized by a resonant open loop with a length of λg/2. According to the analysis of the discontinuity structure characteristics, the open loop with a circumference of λg/2 is equivalent to the inductor Lp, the spacing g1 between the open loop and the transmission line is equivalent to the coupling capacitor cp1, and the symmetrical open loop spacing g2 is equivalent to the coupling capacitor cp2. Then, the open loop structure shown in Figure 2 can be equivalent to a series LC circuit. The equivalent series resonant circuit is connected in parallel between the transmission lines to generate a transmission zero point and realize the stopband characteristics.

　　In Figure 2, the length of the open loop is 7.4mm, the line width is 0.4mm, the gap spacing g1 and g2 are both 0.4mm, the resonant frequency is 9.4GHz, and the frequency characteristics are shown in Figure 3(a). The minimum S21 in the passband is -0.068dB, and S21 reaches -31.8dB at a frequency of 9.4GHz. According to the IE3D simulation curve Figure 3(b) analysis, when the gap S, g1, and g2 increase, the insertion loss in the passband gradually decreases, and the resonant frequency shifts to high frequency. This is mainly because the coupling capacitance between the ring and the transmission line and the symmetrical ring decreases, the resonant frequency increases, and the resonant Q value increases.

　　Figure 2 CPS open-ring resonator

　　Figure 3(a) Frequency response characteristics of CPS open-loop structure

　　Figure 3(b) The frequency response of the CPS open-loop structure changes with g2

　　3.2 CPS open-ring resonator with T-branch

　　In order to enhance the depth and width of the stopband, a pair of half-wavelength T-type resonators are added to the above open-ring resonator, and its structure and equivalent circuit are shown in Figure 4. The half-wavelength T branch is equivalent to the inductor L'p, and the gap g3 between the T branch and the transmission line is equivalent to the coupling capacitor C'p. Then the T-type open circuit structure and the open circuit ring are equivalent to two series LC resonant circuits, which achieve the purpose of increasing the second harmonic attenuation by generating two transmission zeros. The length of the T branch is 6.6mm, and the length of the open ring is 7mm. The frequency characteristics are shown in Figure 5. Two resonance points are generated at 9.8GHz and 13.6GHz, and S21 is -24.5dB and -37dB respectively, which widens the stopband.

　　Figure 4 Open-loop resonant structure with T-branch

　　Figure 5 Frequency response characteristics of the open-loop resonant structure of the T-branch. 　　Since the bandwidth for suppressing the second and third harmonics is relatively wide, slots are opened on the CPS parallel transmission line, which can be equivalent to a series LC circuit. By generating a transmission zero point, the third harmonic can be further suppressed without increasing the volume.

　　3.3 Third-order CPS low-pass filter design

　　A third-order CPS low-pass filter is designed using the above open-loop structure (Figure 2) and composite structure (Figure 4), and its structure and equivalent circuit are shown in Figure 6. The dimensions of W and S are the above CPS dimensions, L1=5.6mm, L2=3.7mm, and L3=3.5mm.

　　Figure 6: Third-order CPS low-pass filter

　　The S11 and S21 frequency response curves of the third-order CPS low-pass filter with T-branch obtained by IE3D software simulation are shown in Figure 7. At 5.8 GHz, 11.6 GHz and 17.4 GHz, S21 is -0.095 dB, -25.1 dB and -13 dB respectively, which effectively blocks the second harmonic.

　　Figure 7 Frequency characteristics of third-order CPS low-pass filter

　　In order to better suppress the third harmonic, a T-slot is opened on the W line width, and its structure and equivalent circuit diagram are shown in Figure 8. Among them, L4=4.3mm, and the slot width is 0.4mm. The simulation curve is shown in Figure 9, which well suppresses the third harmonic. The S parameters of the fundamental frequency, second harmonic, and third harmonic are listed in Table 1.

　　Figure 8 Improved third-order CPS low-pass filter

　　Figure 9 Improved third-order CPS low-pass filter

　　Table 1 Frequency response characteristics of the improved third-order CPS low-pass filter

　　5 Conclusion

　　Based on the basic CPS circuit theory, this paper designs a third-order CPS low-pass filter operating at 5.8GHz. Its size is 25mm *7.6mm, the minimum insertion loss in the passband is -0.08dB, the 3dB cutoff frequency is 7.7GHz, and the absolute bandwidth with attenuation less than -15dB is 10.3GHz, which effectively suppresses the second and third harmonics.