A compact low insertion loss bandpass filter based on meandered self-coupled ring resonator

The traditional structure of dual mode bandpass filter is formed by a circular or rectangular resonator, which causes excessive circuit areas to be occupied. A 5.2 GHz bandpass filter, based on the triple-branch self-coupled ring resonator, is designed to achieve most essential features such as low insertion loss, compact size, and wide stopband. The coupling of each coupled branch introduces the evenand odd-mode perturbation, which produce sharp bandpass and wide stopband responses due to the generation of band-edge transmission zeros. The simulation and measurement in this paper are respectively verified by using IE3D electromagnetic simulator and Agilent’s HP8722C network analyzer. Experimental results show that the filter has 19.2% bandwidth centered at 5.2 GHz, 1.2 dB insertion loss, 25 dB stopband rejection from 6 to 9 GHz. Moreover, the circuit size in this paper has been down to 9×6 mm and can be applied to communication of microwave applications.


Introduction
The component of passive circuit, such as the filter occupying the largest percentage of communication system structure, is more important to preserve high performance and reduce the electronic circuit size.Many researches of dual-mode bandpass filter have been proposed in papers [1][2][3][4][5][6][7][8][9].
The bandpass filters based on the dual-mode ring resonator was first analyzed by Wolff [1].Some papers proposed dual mode ring resonator bandpass filters by using step-impedance or ring resonators with different perturbation schemes [2][3][4].The perturbation element is a plus to or cut from the resonator, and it is also viewed as capacitive or inductive [5].One of the methods is the investigation of designing a compact, low insertion loss and sharp rejection by cascaded dual mode ring resonator [6].Furthermore, dual-mode microstrip filters are highly attractive for radio frequency systems because their sizes are compact and easy to fabricate [7].By adding open stubs symmetrically on ring resonator, the dual mode filter is realized [8].
However, there is a novel distributed perturbation by self-coupled segments of the ring resonator, which brings the easier implementation scheme [9].In this paper, the ring resonator is based on the theory of a selfcoupled, simple bandpass filter with low insertion loss and the compact size designed, which showed the easy structure and narrow bandwidth with two transmission zeros near the passband.This filter of 5.2 GHz band is designed.The measurement results show good consensus with simulation.

Filter design
The traditional structure of dual mode bandpass filter is shown in Fig. 1.Generally, the filter structure is formed by a circular or rectangular resonator, which causes excessive circuit areas to be occupied.To make up for the disadvantage, the ring resonator was bended in this study to achieve the goal of saving the filter size.

Schematic of proposed bandpass filter
Unlike those studies in the past using the perturbation approach, the ring resonator with coupling method is applied to cause the even and odd mode to be separated, and to achieve resonance effects.Thus, the filter offers an advantage of a simpler circuit layout and is easier to be implemented.The schematic types of the proposed self-coupled bandpass filter with input and output ports are shown in Fig. 2. The proposed bandpass filter is composed of self-coupled ring resonator with parallel-DOI: 10.1051/matecconf/201712300016 ICPMMT 2017 coupled input and output networks.The self-coupled ring includes a central coupled branch and two other coupled branches, connected at both ends of the central coupled branch.An intuitive way to understand this selfcoupled ring resonator is the meandering of the conventional circular ring resonator such that the ring size can be considerably miniaturized.Different from the lumped perturbation of the conventional ring resonator, the distributed coupling of the proposed ring resonator provides the mode perturbation between even and odd modes.

Resonance conditions
In Fig. 2, the layout discontinuity effect of both coupled sections are neglected, with the structure of the ring resonator symmetric to line AB , and the even-odd mode theory applied to analyze the resonance mode characteristics.Fig. 3(a) and (b) show that the equivalent even-mode, odd-mode circuits, the even-mode and oddmode resonance conditions can be derived from equation ( 1)-( 6) and ignore the coupling support effect on both sides of the bent section.Two coupled sections at ends have the same parameters: the electrical length of 1 , the coupling coefficient of 1 c , and the characteristic impedance 1 Z .The central coupled section has the electrical length of 2 , the coupling coefficient of 2 c , and the characteristic impedance of 2 Z .The equation derived is shown as below.The equivalent even circuit of dual-mode ring resonator is shown in Fig. 3 (a).By calculating the input impedance of the even mode, the even mode resonates when Z Be = .On the other hand, the input admittance of the even mode Y Be =0.Similarly, The equivalent odd circuit of dual-mode ring resonator is shown in Fig. 3 (b), and the input impedance vanishes when the odd mode resonates, The odd mode resonance condition is obtained as Where Under the even-odd mode resonant frequency re f and ro f , the 1e , 2e , 1o and 2o are the electrical lengths corresponding to the physical lengths 1 and 2 respectively.Thus, the resonance frequency condition is obtained as r r e r o f f f .Since the complicated form of equation ( 1)-( 6) is difficult to obtain the analytic solution, we use the graphic expression for analyzing the effect of the evenmode and odd-mode resonant frequencies with the impedance ratio and coupling coefficients.

Impedance ratio effect Z
A case about c 1 =0.2 and c 2 =0.2 is plotted in Fig. 4 and it shows the dependence of mode resonant frequencies with respect to the impedance ratio of Z with several characteristics as below.1) When impedance ratio Z = 1, the even-and oddmode resonant frequency are not separated.2) When impedance ratio Z < 1, the odd-mode resonant is lower than the even-mode and has the inductive perturbation feature.3) When impedance ratio Z > 1, the odd-mode resonant frequency is higher than the even-mode and the type is in a capacitive perturbation state.4) The geometric average resonant frequency,  .There are several characteristics as below.1) When the coupling coefficient increases, the resonant frequency will increase at any impedance ratio.

Characteristics of Coupling Coefficient
ICPMMT 2017 2) When Z < 1, the resonant frequency will increase following the incremental impedance ratio in the any coupling coefficient.3) When Z > 1, the the resonant frequency will decrease following the incremental impedance ratio in the any coupling coefficient.4) When Z = 1, it shows the highest resonant frequency.

Transmission zeros analysis
The main advantage of the ring resonator filter is generating two transmission zeros near the passband.
Because there are two transmission paths between the input and output ports, therefore when the current of the two paths is offset each other at the output, the transmission zeroes on both sides of the passband are generated.In this way, Y-parameter matrix method (Admittance Matrix Method) is used to facilitate the analysis of transmission zero generation.
Ignoring the discontinuous effect of the circuit branch bending, as shown in Fig. 6, the entire resonator can be disassembled into a parallel coupling line with electrical length 1 / 2 , impedance Z 1 and a parallel coupling line with electrical length 2 , impedance Z 2 .In Fig. 7, the equations ( 7) to ( 12) are the formulas for the parallel coupling microstrip Y parameter of the four ports and the two ports.Further, the formulas ( 7) to (12) are converted into the following formulas (13) to (18) using the relationship between the coupling coefficient and the impedance.

Here
By using the formulas (13) to (18), we can solve the position of transmission zero in Fig. 6.The transitive formula is shown in equation ( 19), and when Y 21 is zero, the transmission zero is generated.
And within the formula (19), DOI: 10.1051/matecconf/201712300016 ICPMMT 2017 cot , 1 The complicated form of (19) makes it difficult to obtain the analytic solutions in calculation.Then we turn to the graphic expression of 21 Y for analyzing the effects of the impedance ratio Z and input-output separation length IO [9].8, it can be found that there is no transmission zero on both sides of the fundamental frequency passband when the inductive coupling Z < 1.When Z > 1 is capacitively coupled, two transmission zeros are generated on both sides of the passband and a transmission zero occurs near the second passband.When Z = 1, the transmission zero will occur near the base band, destroying the passband characteristics.

Experimential results
Following the theoretical analysis in section 2, in this paper, the coupling coefficients 1 , the characteristic impedance Z 1 is 109Ω, Z 2 is 61.5Ω, and the impedance ratio Z =1.77.Moreover, the relative dimensions of the resonator is equivalent to W 2 = 1.2 mm, W 1 = 0.3 mm, W t =0.2 mm, L 1 =8.5 mm, L 2 =4.5 mm, g 2 = 0.6 mm, g 1 = 0.6 mm, and g t =0.2 mm.This filter is fabricated on the substrate with a relative dielectric constant of 3.38, with loss tangent being 0.0025 and thickness being 0.762 mm.The actual photograph of 5.2GHz self-coupled bandpass filter is shown in Fig. 10.The size of self-coupled bandpass filter is 9 x 6 mm 2 .On the other hand, the circuit size is relatively 54% of the size to the traditional uniform ring case.DOI: 10.1051/matecconf/201712300016 ICPMMT 2017 The simulation and measurement are respectively verified by using IE3D electromagnetic simulator and Agilent's HP8722C network analyzer [10].Fig. 11 shows the simulated and measured results.Finally, there is very good consensus between the measured and simulated results in this paper that within 5-5.4 GHz, the measurement return loss is greater than 22 dB and measurement insertion loss is less than 1.2 dB and this condition improves the response of passband.The measured 3-dB bandwidth is about 19.2% at the center frequency of 5.2 GHz.The filter has three transmission zeros close to the passband at 4.39 GHz, 6.42 GHz and 7.58 GHz, which produces sharp bandpass and wide stopband response.

Conclusion
A 5.2 GHz dual-mode bandpass filter has been proposed in this study by using self-coupled ring resonator for small size, low insertion loss, wide stopband and it is easy to implement.The proposed filter size is 9 x 6 mm 2 , three transmission zeros are close to the passband at 4.39 GHz, 6.42 GHz and 7.58 GHz, and the 3-dB bandwidth is about 19.2% from 4.75 GHz to 5.73 GHz, and insertion loss is less than 1.2 dB at center frequency 5.2 GHz.A good consensus has been reached in this study by simulation and measurement showing highly valuable application of proposed bandpass filter in wireless communications.

Fig. 3 .
Fig. 3. Equivalent even and odd-mode circuit of dual-mode ring resonator.

Fig. 5 (
Fig. 5 (a) and (b) are the relative resonant frequency between coupling coefficient C 1 and C 2 for different impedance ratios under the 38 2

Fig. 8
Fig. 8 is the coupling coefficient with 1 C and 2 C being

Fig. 9 2 C
Fig.9 is the normalized frequency of Y 21 relationship diagram showing when the coupling coefficient 1 C and

Fig. 8 .
Fig. 8. Z ratio of the normalization frequency of Y 21 relationship diagram.

Fig. 9 .
Fig. 9. shows the Y 21 relationship diagram difference between the input and output ports at the normalized frequency.