Dielectric-Loaded Miniaturized Cavity Bandpass Filter with Improved Power Capacity

Abstract

A novel design method of dielectric-loaded miniaturized cavity bandpass filter is presented in this paper. The proposed cavity resonator is filled with dielectric material to improve power capacity, while realizing the miniaturization of the filter. To validate our proposal, a bandpass filter with a center frequency of 1475 MHz and bandwidth of 90 MHz is designed, fabricated, and measured. The measured insertion loss is ≤0.49 dB and return loss is ≥20 dB in 1430 MHz~1520 MHz. The measured upper stopband rejection is greater than 48.5 dB in 1575 MHz~2700 MHz. The measured results are in good agreement with the simulation, which verifies the effectiveness and practicability of the method. The metal cavity bandpass filter, filled with dielectric material, is reduced by 25% in the thickness direction and its power capacity is increased by 45.8%.

1. Introduction

As an important passive device, filters are widely used in 5G wireless communication systems, satellite navigation, radar detection, electronic countermeasures and other fields [1,2,3,4,5,6]. Filter performance is often directly related to the performance of the whole RF transceiver system. With the development and application of modern wireless communication technology, limited spectrum resources are becoming increasingly crowded and precious with higher requirements for high performance; therefore, the miniaturization [7,8,9,10,11,12] and high power [13,14,15,16] of filters are put forward. The main function of bandpass filters is to allow useful signals to pass through with low loss, while suppressing useless stray signals. Miniaturization has always been one of the hot directions of filters. Based on the research status of filters [17], the current miniaturization technologies of cavity filters mainly include the following: (1) loading technology [18,19,20], such as resonator capacitor loading, lumped element loading and high permittivity ceramic material loading, etc.; (2) multi-mode resonator technology [21,22,23,24,25] that, in a resonant cavity, motivates two or more resonant modes simultaneously; (3) spiral resonator [26], short circuit branch [27], slow wave structure [8] and other technologies are used to realize the miniaturization of filters. Generally, as the size of filter decreases, the power capacity of the filter will also decrease. Therefore, it is very important to consider power capacity [28] while considering the miniaturization of filters.

First, by introducing dielectric material to fill the metal coaxial resonator, the loading capacitance value is increased, the miniaturization of the filter is realized, and the maximum breakdown electric field of resonator is also increased. Second, a Generalized Chebyshev filter is designed and fabricated. Third, a theoretical analysis of the power capacity is given. Finally, the measured results are listed.

2. Dielectric-Loaded Metal Resonator

Capacitance loading is one of the methods used to miniaturize a metal cavity filter, especially in low frequency bands where the corresponding size of the resonator is larger. The usual method makes a resonator with a loaded resonant plate structure and the loaded plate and top surface of the resonator forms a large capacitance, so as to achieve the purpose of miniaturization. The capacitance effect can be analyzed using the parallel plate capacitor formula. A parallel plate capacitor is shown in Figure 1.

$$C=\frac{{\epsilon }_r{\epsilon }_{0}S}{4\pi kd}$$

(1)

It should be noted that ${\epsilon }_r$ is the relative permittivity, and ${\epsilon }_r$ of air is 1.0. According to Equation (1) of the parallel plate capacitor, the value of capacitance C increases when the relative permittivity increases. For the resonator, the larger the capacitance between the loaded plate and top surface of resonator, the lower the resonant frequency. Therefore, if the size of the resonator is kept unchanged and the air between the surface of the resonator plate and top surface of the resonator is replaced by dielectric materials with higher permittivity, the resonant frequency can be lower, so as to achieve the purpose of miniaturization. As shown in Figure 2b, the dielectric-loaded resonator has a single cavity size of φ16 $\times$ H13 mm. Its single cavity resonant frequency is shown in

Table 1. Relationship between permittivity and resonant frequency.

Relative Permittivity ${\epsilon }_r$	1.0	2.1	10
Resonant Frequency f (MHz)	1726.9	1472.3	1008.4

, using dielectric materials with different relative permittivity. As can be observed from Table 1, the larger the permittivity of the loading medium, the lower the resonant frequency of resonator. The ceramic materials with high permittivity can achieve lower resonant frequency without changing the size of the resonant cavity. Therefore, we can achieve the goal of filter miniaturization by loading the metal resonator with dielectric material. From the analysis of the dielectric-loaded resonator, we can use a dielectric-loaded resonator to miniaturize a cavity filter. ir="LTR">1008.4

3. Design of Generalized Chebyshev Filter

The generalized Chebyshev filter response can be set to the pole position in the stopband arbitrarily and is more flexible than the ordinary Chebyshev filter response. The response of the generalized Chebyshev filter can produce isoripple characteristics in the passband, and its characteristic response curve is similar to that of the elliptic function. The amplitude of its transmission function can be expressed as Equation (2), ch(x) represents the hyperbolic cosine function in Equations (3) and (4) and x_i is the intermediate variable in Equation (5).

$${\left|s_{21}\left(j\omega \right)\right|}^2=\frac{1}{1+{\epsilon }^2{C}_N^2\left(\omega \right)}$$

(2)

$$C_N\left(\omega \right)=\mathrm{ch}\left[{{\displaystyle \sum }}_{i=1}^N{\mathrm{ch}}^{-1}\left(x_i\right)\right]$$

(3)

$$\mathrm{ch}\left(x\right)=\frac{e^x+e^{-x}}{2}$$

(4)

$$x_i=\frac{\omega -1/{\omega }_{pi}}{1-\omega /{\omega }_{pi}}$$

(5)

A fourth-order, two-zeros cross-coupled bandpass filter is designed by using dielectric-loaded metal resonators. The topology is shown in Figure 3.

After comprehensive theoretical evaluation of a generalized Chebyshev filter [29,30,31,32,33,34,35,36,37], it can be concluded that the delay of the group is 4.63 ns, and the two transmission zeros are 1584 MHz and 1643 MHz, respectively. The coupling matrix is shown in Figure 4. The corresponding circuit model and filter response suggested in the AWR circuit software are shown in Figure 5.

If the conventional capacitive-loaded metal resonator in Figure 2a is adopted, the single cavity size is 17.5 × 17.5 × 16.3 mm³ and the resonance frequency of 1475 MHz is achieved. In addition, for the dielectric plate material using Telfon (${\epsilon }_r=2.1$), the diameter of resonator base is φ4 mm, the size of the single cavity is 17.5 × 17.5 × 13 mm³, the resonance frequency of 1475 MHz is achieved and the resonator height is reduced by about 25%. A schematic diagram of the metal resonant disk and dielectric disk is shown in Figure 6. The structure of the metal resonant plate and dielectric plate is shown in Figure 7.

After co-simulation optimization of AWR and HFSS software, the height of the connector is 5.1 mm, and the height of each resonator is 6.87 mm, 6.90 mm, 6.82 mm and 6.80 mm, respectively. The simulation results are shown in Figure 5, where the return loss is 22 dB and the suppression of out-of-band is ≥45 dB at 1575 MHz~2700 MHz.

4. Theory of Filter Power Capacity

In a resonant cavity, the distribution of the electromagnetic field is related to the structure of the cavity. If the electric field distribution in the cavity is expressed as Equation (6), Emax is the electric field amplitude of the maximum electric field point in the cavity, $\overrightarrow{f}\left(x,y,z\right)$ is the distribution function of electric field in the cavity and its maximum amplitude equals 1.0.

$$\overrightarrow{E}=E_{\mathrm{Max}}\ast \overrightarrow{f}\left(x,y,z\right)$$

(6)

$${\left|\overrightarrow{f}\left(x,y,z\right)\right|}_{\mathrm{Max}}=1$$

(7)

The value of E_Max is related to the excitation power of the cavity and the distribution function $\overrightarrow{f}\left(x,y,z\right)$ is independent of the excitation power. In the cavity, the energy storage of the electric field is listed as Equation (8).

$$W_{\mathrm{Max}}=\frac{{\epsilon }_0}{2}{{\displaystyle \int }}_V^{ }\overrightarrow{E}·\overrightarrow{E^{\ast }}dV=E_{\mathrm{Max}}^2·\left(\frac{{\epsilon }_0}{2}{{\displaystyle \int }}_V^{ }\overrightarrow{f}\left(x,y,z\right)·\overrightarrow{f^{\ast }}\left(x,y,z\right)dV\right)=\frac{1}{{\zeta }^2}{E}_{\mathrm{Max}}^2$$

(8)

$$\zeta =\frac{E_{\mathrm{Max}}}{\sqrt{W_{\mathrm{Max}}}}=\frac{1}{\sqrt{\frac{{\epsilon }_0}{2}{{\displaystyle \int }}_V^{ }\overrightarrow{f }\left(x,y,z\right)·\overrightarrow{f^{\ast }}\left(x,y,z\right)dV}}$$

(9)

After the cavity structure is fixed, $\zeta$ is a constant in Equation (9), which indicates that the square of the maximum electric field has a linear relationship with the energy storage. Equation (10) can be used to calculate the proportionality coefficient between the excitation power of the filter port and the maximum energy storage of the resonant cavity.

$$\eta =W_{\mathrm{Max}}/P_{in}$$

(10)

Combining Equations (9) and (10), Equation (11) can be obtained.

$$E_{\mathrm{Max}}=\zeta ·\sqrt{\eta ·P_{in}}$$

(11)

If the maximum electric field (E_Max) in the resonator is less than the breakdown field E_p, the filter is safe. Conversely, if the maximum electric field (E_max) in the resonant cavity is greater than the air breakdown field E_p, the filter will be broken down. When E_Max = E_p, the power capacity of the filter can be obtained from Equation (12).

$$P_{\mathrm{Max}}=\frac{1}{\eta }{\left(\frac{E_p}{\zeta }\right)}^2$$

(12)

Combined with the above filter power capacity calculation theory, the power capacities of the two kinds of resonators are compared and analyzed in CST software, respectively, according to the two kinds of resonator structures, as shown in Figure 2, with the same resonator cavity size and resonant frequency.

As can be observed from the single-cavity simulation results in Figure 8, the resonant frequencies of the metal coaxial resonator and the dielectric-loaded resonator are both around 1375 MHz, and the values of $\zeta$ in the two resonators obtained from the simulation are ${\zeta }_1=2.461\ast e^9$ V/m and ${\zeta }_2=2.038\ast e^9$ V/m. According to the filter power capacity calculation formula (12), the power capacity ratio of the two resonators can be obtained. In other words, the power capacity of the dielectric-loaded resonator is improved by 45.8%, compared with that of the common metal coaxial resonator.

5. Experimental Results of Dielectric-Loaded Miniaturized Cavity Bandpass Filter

The 1475 MHz dielectric-loaded bandpass filter was fabricated and measured. Figure 9 is a photograph of the fabricated bandpass filter. Figure 10 is the measured results with Agilent Technologies PNA network analyzer (N5222A). Within the passband of 1430 MHz~1520 MHz, the return loss is ≥20 dB. The insertion loss of 1430 MHz and 1520 MHz is 0.27 dB and 0.49 dB, respectively. In 1575 MHz~2700 MHz, the suppression of out-of-band is greater than or equal to 48.5 dB. The measured results are in good agreement with the simulation.

Table 2. Comparison of the proposed filter performances with related published works.

Ref.	${\mathit{f}}_0$ (GHz)	Filter Order	Size $({\mathit{\lambda }}_{\mathit{g}}\times {\mathit{\lambda }}_{\mathit{g}})$	IL 1 (dB)	RL 2 (dB)	FBW 3	GD 4 (ns)
[33]	1.684	none	0.21 × 0.63	1.3	22	4.00%	none
[34]	1.000	none	0.59 × 0.32	3	10	30.00%	none
[35]	2.600	3	0.16 × 0.09	1.8	25	3.00%	none
[38]	4.500	2	0.28 × 0.09	3.0	10.0	60.00%	≤0.4
[36]	3.350	2	0.12 × 0.09	2.4	20.0	5.97%	≤2.5
[39]	2.450	2	0.15 × 0.13	2.4	20.0	1.63%	none
This work	1.475	4	0.19 × 0.08	0.49	20.0	6.10%	≤21.3

¹ insertion loss, ² return loss, ³ functional bandwidth, ⁴ group delay.

summarizes the performance comparison between the related work and the proposed filter. We can conclude from this table that the contributions of this work are not only its new design method, but also its good filter performance.

6. Conclusions

In this paper, a novel dielectric-loaded miniaturized cavity bandpass filter is presented. The filter has a miniaturized size and higher power capacity. By introducing a dielectric-loaded resonator structure on the basis of the conventional capacitive-loaded metal resonator, the miniaturization of the filter was realized. The measured results are in good agreement with the simulation, which verifies the validity and practicability of the miniaturization method with the dielectric-loaded resonator. Compared with the usual metal-cavity coaxial bandpass filter, the metal cavity bandpass filter loaded with dielectric material (Telfon) reduces by 25% in the thickness direction under the same electrical specifications and power capacity can be increased by 45.8%. The measured insertion loss is ≤0.49 dB and return loss is ≥20 dB in 1430 MHz~1520 MHz. The measured upper stopband rejection is greater than 48.5 dB in 1575 MHz~2700 MHz. Finally, the miniaturized advantage and high-power capacity of the filter makes it suitable for wireless communication.