Tuning the Resonance Frequency and Miniaturization of a Novel Microstrip Bandpass Filter

In this paper, a compact microstrip bandpass filter is designed using two open loop resonators. In order to obtain a tunable bandpass response with low insertion loss, two stubs are loaded inside them. The design process is based on obtaining the input admittance. Then, using the input admittance, a method is presented to control the resonance frequency and miniaturization simultaneously. The obtained insertion loss and the return loss at the resonance frequency are 0.1 dB and 19.7 dB respectively. To verify the design method, the proposed filter is fabricated and measured. The measured results are in good agreement with the simulated results.

, parallel-coupled lines (Moradian et. al. 2009;Othman et. al. 2013;Fathelbab et. al. 2005;Kuan et. al. 2010) and quarter/half wavelength resonators (Li et. al. 2010;Deng et. al. 2010) have been used.Also, several approaches on suppressing harmonics have been proposed (Kang et. al. 2010;Wang et. al. 2008;Chen et. al. 2009;Cheng et. al. 2014;Wu et. al. 2017).In Zhang et. al. (2012), three open loop resonators are used to design a bandpass filter with a high selectivity.However, it has an undesired fractional bandwidth.The common weakness of these reported filters is their large sizes and large insertion losses.In Moradian et. al. (2009) a third-order bandpass filter is proposed to attenuate the harmonics.In Kuan et. al. (2010), the parallel coupled lines and step impedance resonators are used to design a microstrip bandpass filter.A microstrip bandpass filter operating at 1.78 GHz with suppressed harmonics up to 6.2 GHz is presented in Li et. al. (2010).But this filter has a large return loss.In Kang et. al. (2010), a ringbalun bandpass filter has been proposed to attenuate the harmonics up to 12 GHz.In Wang et. al. (2008), coupled ring resonators have been utilized to design a bandpass filter with a complex structure, while using a complex structure leads to hard fabrication.In Chen et. al. (2009), various types of bandpass filters have been introduced utilizing cross coupled resonators to suppress the second harmonic.Nevertheless, their stop bands are narrow.In Cheng et. al. (2014), the inductive-coupled stepped-impedance quarter-wavelength resonators are used to design a microstrip bandpass filter with an undesired insertion loss.A dualmode microstrip bandpass filter operating at 1.67 GHz has been introduced in Lu et.al. (2017), which has a narrow fractional bandwidth and large area.
A microstrip bandpass filter with high return loss has been designed in Guan et. al. (2017).In this filter, a triangular cell has been coupled to the step impedance feed structures that results in improving the bandwidth.
Then, a method is proposed for miniaturizing and tuning the resonance frequency simultaneously.Using this method, the shapes and dimensions of the internal stubs can be determined as well as the resonance frequency.Next, a simple tunable bandpass filter is presented using two proposed resonators to solve the problems of previous works in terms of large implementation area and large insertion loss.In addition, the harmonics are attenuated reasonably and fractional bandwidth and selectivity are improved.Finally, the effect of changing the dimensions on the frequency response is investigated.

Filter Design
An open loop resonator is shown in Fig. 1a.A large size simple step impedance cell is loaded inside the proposed resonator to control the resonance frequency.The electrical lengths θi are used to obtain the input admittance, where i=1, 2, 3, s.An LC equivalent circuit of the proposed resonator is shown in Fig. 1b, where C and L are the capacitors and inductors of the bends respectively.The parameters Cg and Cp present the gap capacitors.The parameters of La, Lb, Lc, Le, Lf and Lg are the inductors of the stubs with the physical lengths la, lb, lc, le, lf, and lg respectively.Co is the capacitor of the open end, which its position is subsequent the loaded step.Cs, LS1 and LS2 are the capacitance and inductance of the step impedance cell.The input admittance from the open end of θ1 can be written as follows: where θs is the total electrical length of the step impedance cell, Y is the admittance of the step impedance cell and open loop resonator.For the even mode, when, Yin=0, the resonance condition is obtained from: So the resonance condition can be tuned by adjusting θ1, θ2, and θ3 while θs is fixed.The electrical length has a direct relation with the physical length.Therefore, the resonance frequency can be controlled by adjusting the loop and step impedance open stub dimensions.
When the electrical length θs is maximum, then from θs= ls β (where β is propagation constant) ls must be maximum.Therefore, by choosing a maximum value for ls, (from Equation 2 and also from θs= ls β) tan(θs) is increased and the total of tan(θ1)+ tan(θ2)+ tan(θ3) is decreased (tan(θ1)+ tan(θ2)+ tan(θ3) is minimum).Under this condition θ1, θ2, and θ3 are small values.Therefore, (from θ3=(la+ lg+ lf) β, θ2= lcβ and θ1= leβ) the open loop dimensions consisting of la, lb, lc, le, lf, and lg are decreased.This is a method to decrease the resonator size and adjust the resonance frequency simultaneously.
As a total result of above discussion, a method to control the resonance frequency and miniaturization is obtained by the following steps: In the first step, a resonator is selected which some stubs are loaded inside it.In the second step, the main resonator size is decreased and the dimensions of stubs are increased, so that the desired resonance frequency can be obtained.In the proposed resonator (Fig. 1a), the physical lengths la, lb, lc, le, lg and lf must be smaller while the internal stub length must be larger.Therefore, the inductors La, Lb, Lc, Le, Lg and Lf can be smaller and LS2 or/and LS1 can be larger.
According to Equation (2), in some cases, there is a degree of freedom to control the resonance frequency so that we have to use the optimization method.Therefore, in order to obtain a compact size at the target resonance frequency, the additional optimization is performed.
In order to design a bandpass filter as shown in Fig. 2a, two open loop resonators consisting of different step impedance cells are used.The loops are connected together using mix coupling.The coupling structure consists of three coupled lines with different widths, which are used to attenuate the harmonics.The feed structures with the step impedance forms are added to the input and output ports to decrease the insertion loss without size increment.The simulated and measured frequency responses of the propose filter are shown in Fig. 2b.According to the above discussion, the resonance frequency can be controlled by adjusting the physical lengths of open loops while the internal stubs have a maximum size.Therefore, a method to control the resonance frequency is changing of the lengths (L3, L9) or/and (L4 , L11).
The frequency response as a function of L3, L9, L4 and L11 are shown in Fig. 3a and Fig. 3b.Figures 3a and 3b depict the loop size changing effect on the resonance frequency.When the loops are large, the resonance frequency is shifted to the left.When the loops are small, the resonance frequency moves to the right.A photograph of the fabricated filter is shown in Fig. 3c.

Results
The  insertion loss is obtained, while the harmonics are attenuated from 2.16 to 7.1GHz with a maximum attenuation level of -19.5dB.In addition, the resonance frequency is tuned by calculation of the input admittance

Figure 3 .
Figure 3. (a) Frequency response as a function of L3 and L9 , (b) Frequency response as a function of L4 and L11 , (c) a photograph of the fabricated filter.

Table 2 .
proposed filter is simulated by Advanced Design System (ADS) full wave EM simulator.In the Table2, IL, RL, and FBW are the insertion loss, return loss, and fractional bandwidth respectively.

Table 1 .
The dimensions of proposed structure (in mm).

Table 2 .
Comparison between the proposed filter and previous works.