диафрагмированные волноводные фильтры / 2a4347b3-f170-4ec5-be26-a2a242f534dc

With the rapid development of wireless communication technology, high-performance miniaturized RF circuits are becoming more complicated, and more functions and signals

are being packed into a small, tight space, resulting in

a significant level of electromagnetic (EM) interference and signal crosstalk. In modern wireless communication systems, a higher signal-to-noise ratio is desirable and can be attained using differential signals and circuits. Using the differential technique, commonmode (CM) interference is rejected, enhancing signal

transparency. Thus, lots of attention has been drawn to differential/balanced circuits, owing to their advantages over traditional single-ended circuits, such as immunity to interference, high reliability, considerable output power, harmonic suppression, and so on [1]. Corresponding to this trend, differential topologies have been used to design basic and key devices for RF front-end systems, such as filters [2], [3], power dividers [4], antennas [5], [6], and active components [7].

Dielectric resonators (DRs) have also been extensively applied in modern wireless communication systems, such as cellular base stations, satellite payloads, and various styles of antennas, due to advantages including a high unloaded quality factor (Qu),

significant power capacity, low cost, superior temperature stability, easy excitation, and so on. Pioneering research on DRs began during the 1960s, and the work has continued to the present [8]–[19].

Driven by these trends, the combination of DRs and differential technology has become a hot-topic research area. In a differentially fed DR, differential excitation provides a pair of identical amplitude and out-of-phase signals to feed the DR, exciting the modes with out-of-phase field distributions but not stimulating those with in-phase field distributions. The modes that appear in a differentially fed DR keep the same EM fields as their eigenmodes. This valuable characteristic simplifies the creation of applications of differentially fed DRs [20].

As early as the 1970s, it was possible to realize a differential DR filter (DRF) using a pair of simple baluns [21]. Unfor-

tunately, this approach resulted in a large physical size, design complexity, instability, and additional loss from the cascade connection. In contrast, a differential DRF that uses a direct method can obtain better performance, such as lower insertion loss, narrower bandwidth, and higher passband selectivity, when compared with traditional single-ended filters, regardless of whether they employ a printed circuit board [22], [23], low-temperature cofired ceramic [24], [25], or substrate integrated waveguide [26], [27].

Additionally, during the past three decades, DR antennas (DRAs) have received widespread attention

July 2020

for their compact size, high efficiency, and wider bandwidth compared to patch antennas. Various differentially fed antennas have been studied, not only for their compatibility with differential circuits but also for their relatively low cross polarization [5]. Chair et al. [28] proposed a differential, 3D, J-shaped, probe-excited DRA with high isolation between ports for dual polarization applications. The research group of Leung, City University of Hong Kong, has explored DRs in differential applications in depth, and two kinds of differentially fed rectangular DRAs were introduced in [29] and [30], respectively. Finally, recently, several differentially fed DRAs using the method in [21] have been presented [31]–[33].

In this article, the resonant modes of cylindrical and rectangular DRs—the most popular DRs in both academia and industry—are introduced and investigated. Based on these findings, a differential feeding mechanism for the dominant modes is presented, and types of differential applications in DRFs and DRAs are summarized to illustrate the theory behind differentially fed DRs.

Basic Properties of a DR

To calculate the resonant frequency of a DR, the basic idea is to describe the field of the resonant mode and ensure that it satisfies the continuity of the tangential field on the boundary [8]. Figure 1 shows two typical structures of isolated DRs [a rectangular DR in Figure 1(a) and a cylindrical one in Figure 1(b)]. If the relative permittivity is high enough, the surfaces of the DR can be considered perfect magnetic walls. Thus, (1) is the only condition that the modes of a DR should satisfy:

where Ev represents the electric field (E-field) intensity and nv denotes the normal vector to the surface of the DR. This ideal magnetic wall method can calculate the resonant frequency of higher-order modes with a small

Figure 1. The structures of isolated DRs. The (a) rectangular DR and (b) cylindrical DR.

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margin of error. However, when it is used to calculate the RF of lower-order modes, the error can exceed 10%. Improved calculation methods for lower-order modes, including the dielectric waveguide mode (DWM) method [9], can reduce this error.

In most situations, transverse electric (TE) mode TE11d is the dominant mode of the rectangular DR [Figure 1(a)], and it is the most widely used. Therefore, the TE mode will be used as an example of the DWM method in this article. According to the DWM method, the isolated DR is placed in a perfect magnetic conductor wall waveguide, which is composed by infinitely extending the four faces of the DR in the z direction, as shown in Figure 2(a). The fields of the TE mode can be expressed as the following:

In the dielectric region, a standing wave exists at resonance. In the air region, the field exhibits an

exponential decay since the resonance is below the cutoff of the waveguide, so f(z) in (2) can be expressed as

The resonant frequency can be calculated by the continuity of the tangential field on the boundary surface.

However, in many practical applications, DRs are placed on a substrate and in a metal cavity. Thus, the influence of the substrate, ground plane, and top cover should be taken into account [34]. The improved DWM is shown in Figure 3, where the infinite magnetic wall waveguide is sealed by two perfect electric conductor (PEC) walls. To describe the effect of additional conditions, a hyperbolic function is used to replace the exponential function so that f(z) can be expressed as

As for the cylindrical DR, most CMs are the TE01d and a hybrid EM (HEM) one, HEM11d, as shown in Figure 4(a) and (b). Their resonant frequencies can also be calculated using the improved DWM method, illustrated in Figure 4(c). Its field can be described as

where p is the region index. The radial propagation constant of the mode is fixed by a magnetic wall at t = r, and the mode can be solved as

for the TE01d mode and

can be excited by a differential port pair. Based on (9), to achieve strong differential coupling using a differential electric current source (such as a differential probe pair), the source should be located in an area with strong E fields in the operating mode or modes. On the other hand, when using a differential magnetic current source (such as an aperture with a microstrip line fed by a differential port), the source should be located in an area with strong H fields, according to (10). For a mixed coupling, the port locations do not follow these principles, and transmission zeros for DRFs or radiation nulls for DRAs can be achieved.

Differentially Fed DRFs

for the HEM11d mode. The separation constants can be obtained as

In the application of cylindrical DRs, the TE01d mode is always used to constitute filters, and the HEM11d mode is always used to design antennas [35].

To utilize DRs for filters or antennas, energy must be coupled into or out of the resonators through one or more ports. A number of excitation methods have been proposed for DRs, such as a coaxial probe, aperture coupling with a microstrip line or coaxial line, a

Some high-performance differential DRFs have been designed based on the preceding principles. Because the differential port pair can be treated as one port (equivalent to a single-ended one) in the synthesis of the differential filter, the design method of these DRFs is similar to traditional single-ended architectures, relying on extracting the external quality factor Qde and coupling coefficient kd.

During the early 1970s [21], T.D. Iveland realized a three-order DRF dealing with differential signals, as shown in Figure 5(a). Iveland’s DRF differs only slightly from the traditional four-port differential devices because it is still a single-ended two-port filter. The differential signal is obtained by means of a simple balun based on a delay line. According to Ampere’s right-hand rule, a pair of differential feeding microstrips can be used to drive the dominant TE11d mode of the rectangular DR because the H-field distribution introduced by the differential feeding

x

(a)

–h1

E-Field Amplitude

(b)

According to these two equations, only the modes with out-of-phase field distributions

Figure 3. The DWM model for the rectangular DR with a substrate, ground plane, and top cover. The (a) structure and (b) field amplitude in the z direction.

microstrips is consistent with that of a TE11d mode. The motivation for differentially feeding the rectangular DR is to acquire stronger coupling for the TE11d mode. As a result, the measured insertion loss is only 0.5 dB, as illustrated in Figure 5(b).

Based on the traditional single-ended feeding structure for driving a TE01d-mode ring-shaped DR, a pair of differential feeding probes can be constructed by

adding a symmetric probe, as in Figure 6. Similarly, according to Ampere’s right-hand screw rule, the H-field distribution introduced by the currents on the differential feeding probes placed face to face is consistent with that of a TE01d mode. Thus, the dominant TE01d mode can be excited by the antiphase currents in the differential feeding structure. Using this structure, a novel differential filter based on a TE01d-mode

ring-shaped DR is proposed. The filter, which would be useful in many industrial applications [20], is shown in Figure 7; it combines low insertion loss (0.4 dB), good CM suppression (> 40 dB), and a simple design procedure.

The major drawback of DRFs is their inferior spurious characteristics, which are caused by a crowded mode chart: undesirable modes are in close proximity to both the desired dominant mode and each other. As is well known, a spurious-free region up to the second

(b)

DR_H

c

or third harmonics is usually required for most communication systems. Accordingly, much effort has been spent on improving the spurious performance of the DRF (i.e., by widening the upper stopband). Introducing a hole at the center of the DR can improve the separation between the dominant mode and higher-order ones, but the stopband extension is limited.

Nishikawa et al. presented a quarter-cut DR that can further improve the spurious performance of the resultant filter, but the design becomes too complicated [37]. Alternatively, mixing the DR with a metallic coaxial resonator (CR) can enhance the spurious performance significantly [38]. A high-performance differential bandpass filter using a hybrid ring-shaped DR and CR has also been proposed, where the metallic CR is inserted between the two DRs [39]. By utilizing the advantage of the large frequency space between the fundamental mode and lowest-frequency harmonic mode of the CR, the fundamental mode of the CR and the dominant mode of the DR can be designed to have the same frequency, enabling them to be magnetically coupled to construct a DM passband.

Conversely, the other harmonic modes of the DR cannot be transmitted through the CR. As a result, a differential filter [39] with good performance (i.e., spurious free with wideband CM suppression) can be constructed through the structure in Figure 8. This

–140

1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4

Frequency (GHz)

(b)

Figure 8. The differential filter with the combination of a DR and CR [39]. The (a) layout and (b) frequency response.

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However, the volume of these filters is relatively large because the employed DRs behave as singlemode resonators. It is natural, then, that the size limitations of single-mode resonators, combined with the ever-increasing demand for high performance and miniaturization of wireless systems, is driving the exploration of dualand multimode DRs in differential DRFs. Based on an analysis of the single rectangular DR, a dual-mode cross-shaped DR can be constructed that is composed of two identical rectangular DRs [40]. This cross-shaped DR is configured with a pair of orthogonal modes with the same resonant frequency. Thus, the cross-shaped DR provides dual-mode operation, facilitating the realization of a dual-mode filter.

Due to the inherent EM properties of the rectangular DR, the dominant TE11d mode of each rectangular DR can be differentially excited by a pair of feeding probes located at the DRs’ two sides, yielding the design of a corresponding differential dual-mode DRF. Due to the inherent advantages of dual-mode DRs, the designed differential filter shown in Figure 9 not only has a good DM response but also realizes the miniaturization, with a size of 0.267 × 0.267 × 0.314 m0.

b

d

r

Microstrip Lines

Substrate Ground Plane

(a)

180°

(–x) (+x)

E Plane (xz Plane)

Differentially Fed

cylindrical DRAs, respectively (Figure 10). It is clear that the E fields of the modes are odd and symmetrical whether the DR is mounted on the ground plane or substrate. Traditionally, single-ended feeding schemes, such as a coaxial probe, coupling slot, microstrip line, coplanar waveguide, conformal strip, dielectric image guide, or metallic waveguide, can asymmetrically excite the dominant modes. But for a differentially fed DRA, there are fewer exciting methods because we often place an additional feeding structure in the symmetrical position to simultaneously excite the modes. Differential excitation

cial shapes [28], and so on. The first three excitation methods are perhaps more attractive than other feeding schemes because they are convenient for direct integration of the antenna with a microwave circuit and they avoid the need to

drill holes in the DR. Moreover, impedance matching can be achieved very easily by simply varying the sizes of the conformal strips or coupling aperture. With the dominant mode excited, the DRA radiates like a magnetic dipole, with its maximum radiation fields normal to the ground plane [44].

An example is the differential aperture-coupled rectangular DRA with a microstrip feed line [29] given in Figure 11(c). The DWM [9] has been widely used to evaluate the resonant frequencies of rectangular DRAs. Although it cannot provide exact solutions, the model is generally accurate enough for practical

antenna designs. According to the DWM, the DRA in [29] is designed to cover the widely used 2.4-GHz band.

A comparison of radiation patterns between singleand differentially fed rectangular DRAs is presented in Figure 12. The calculated cross-polarized field of the differentially fed DRA is vanishingly small for both the E and H planes, but that of the single-fed DRA is

configuration of the differential rectangular, hollow DRA with an underlaid rat race in [30].

Relatively low cross-polarized fields are also achieved in frequency-tunable, differentially fed, rectangular DRAs. In [43], a frequency-tunable, differentially fed, rectangular DRA loaded by chip capacitors or chip varactors is proposed, with a good match and

y

Sdd11 (dB)

–30 1.8 2 2.2 2.4 2.6

Frequency (GHz)

(a)

Frequency (GHz)

(b)