High performances, low cost and compact size often meet the stringent requirements of modern microwave communication systems. There have been some new technologies such as Low-temperature co-fire ferrite (LTCF), Low-temperature co-fire ceramic technology (LTCC) and some new structures such as Substrate integrates wave-guide (SIW), Photonic band gap (PBG), DGS, and so on to enhance the whole quality of system. In 1987, Yablonovitch and John proposed PBG [1, 2] which implodes and utilizes metallic ground plane, and breaks traditional microwave circuit confined design to surface components and distributions of the medium circuit plane. Consequently, there has been an increasing interest in microwave and millimeter-wave applications of PBG [3-7]. Similarly, there is another new ground plane aperture (GPA) technique which simply incorporates the microstrip line with a centered slot at the ground plane, and the use of GPA has attractive applications in 3 dB edge coupler for tight coupling and band pass filters for spurious band suppression and enhanced coupling [8, 9, 10].
PBG is a periodic structure which has been known as providing rejection of certain frequency band. However, it is difficult to use a PBG structure for the design of the microwave or millimeter-wave. components due to the difficulties of modeling. There are so many design parameters that effect on the band gap property, such as the number of lattice, lattice spacing, lattice shapes and relative volume fraction. Another problem is caused by the radiation from the periodic etched defects. Furthermore, with the introduction of a GPA below the strip, the line properties could be changed significantly as the characteristic impedance varies with the width of the GPA. Usually the GPA is considered as the basis of equivalent J-inverter circuit theory and its filtering behavior has been characterized by a closed form equation. As a technique to improve circuit performance, there are more investigations on the applications than the essence of GPA. In order to alleviate these problems Park et al.  proposed DGS which is designed by connecting two square PBG cells with a thin slot. DGS which bases on GPA focuses not only on its application but also on its own characteristics. DGS adds an extra degree of freedom in microwave circuit design and opens the door to a wide range of application. In the following years, a great lot of novel DGSs were proposed and they had become one of the most interesting areas of research owing to their extensive applicability in microwave circuits. The parameters of equivalent circuits models of DGSs were also researched and utilized to design planar circuit easily. Many passive and active microwave and millimeter devices have been developed to suppress the harmonics and realize the compact physical dimensions of circuits for the design flow of circuits with DGS comparatively simple.
2. DEFECTED GROUND STRUCTURE
DGS is an etched periodic or non-periodic cascaded configuration defect in ground of a planar transmission line (e.g., microstrip, coplanar and conductor backed coplanar wave guide) which disturbs the shield current distribution in the ground plane cause of the defect in the ground. This disturbance will change characteristics of a transmission line such as line capacitance and inductance. In a word, any defect etched in the ground plane of the microstrip can give rise to increasing effective capacitance and inductance.
2.1. Basic Structure and Transmission Characteristics
The dumbbell DGS are composed of two a × b rectangular defected areas, g × w gaps and a narrow connecting slot wide etched areas in backside metallic ground plane as shown in 1(a). This is the first DGS . 1(b) shows the S-parameters from an EM simulation of a dumbbell DGS. DGSs have the characteristics of stop-band, slow-wave effect and high impedance. DGS has more advantages than PBG as follows:
(1) The circuit area becomes relatively small without periodic structures because only a few DGS elements have the similar typical properties as the periodic structure like the stop-band characteristic.
(2) The simulated S-parameters for dumbbell DGS unit can be matched to the one-pole Butterworth-type low-pass response.
For the DGS unit, DGS pattern is simply fabricated and its equivalent circuit is easily extracted.
(3) DGS needs less circuit sizes for only a unit or a few periodic structures showing slow-wave effect. Compared with PBG, DGS is more easily to be designed and implemented and has higher precision with regular defect structures. Therefore, it is very extensive to extend its practical application to microwave circuits.
DGS has more competition than PBG in the microwave circuit with high requirement of dimension under certain craftwork conditions.
2.2. DGS Unit
There have been two research aspects for adequately utilizing the unique performance of DGS: DGS unit and periodic DGS. A variety of slot geometries etched in the microstrip line ground plane have been reported in the literature [12-16]. In 2, it is shown that a variety of attached area shapes including spiral head, arrowhead-slot and “H” shape slots and so on. There also have been more complex DGSs so as to improve the circuit performance shown in 2, such as: a square open-loop with a slot in middle section, open-loop dumbbell and interdigital DGS. The new DGS unit could control the two transmission zeros near the pass-band edges and easily control the frequency of the slot by changing the length of the metal fingers [17, 18].
The use of a bent microstrip line does not significantly change the frequency behavior that remains as for the straight DGS microstrip line. The bending technique leads to a 2D configuration, in which the microstrip line presents multiple bends, following a similar structure as that of a meander line. This configuration has a broad stopband and allows a large number of periods in a reasonable circuit area. New proposed DGS unit has some advantages than dumbbell DGS:
(1) A higher slow wave factor and more compact circuit. The circuit area of filter using “H” shape slots is much smaller about 26.3% than using dumbbell DGS .
(2) A narrow width stopband and deeper rejection.
(3) A slightly larger external Q.
To compare the transfer characteristics of the U-slot DGS with that of the conventional DGS, the spiral-shaped DGS and U-slot DGS are designed to provide the same resonance frequency. Q factor of the spiral DGS is 7.478(3 dB bandwidth of 0.39 GHz), while the U-slot DGS provides a high-Q factor of 36.05 (3 dB bandwidth is 0.081 GHz) .
In a word, more and more new DGSs are proposed which bring a great convenience to the design of microwave circuit to realize various passive and active device compact structures and to suppress the harmonics.
2.3. Periodic DGS
Periodic structures such as PBG and DGS for planar transmission lines have drawn a wide interest for their extensive applicabilities in antennas and microwave circuits. Transmission lines with a periodic structure have a finite pass and rejection band as low-pass filters. The increased slow-wave effect and the additional equivalent components are important properties of periodic structure that can be realized and the circuit sizes can be reduced using these properties. Periodic means repetition of the physics structure. By cascading DGS resonant cells in the ground plane the depth and bandwidth of the stopband for the proposed DGS circuit are inclined to depend on the number of period. Period DGSs care about parameters including the shape of unit DGS, distance between two DGS units and the distribution of the different DGSs. As shown in 3, by now there are two types of periodic DGS: one is (a) horizontally periodic DGS(HPDGS), the other is (b)vertically periodic DGS(VPDGS) [21-23].
The prominent feature of the proposed structure is possible to organize the periodicity along the vertical direction as well as the horizontal direction. It is named as VPDGS. On the other hand, the conventional DGS for planar transmission lines have the only HPDGS with serially cascading structure along the transmission direction.
HPDGS initially is produced for enlarging the stopband of frequency response curve. Few uniform square-patterned defects form a periodic DGS for planar circuit, which provides excellent stopband and slowwave characteristics. They have been reported and used in oscillators and amplifiers [23-26]. Nonuniform circular-patterned DGSs using the function distribution compared with the previous periodic DGSs are proposed. They have a compensated microstrip line and the dimensions of the square defects are varied proportionally to relative amplitudes distribution of the exponential function e1/n distribution (n denotes the positive integer), or Chebyshev, [ln (10)]1/n distribution,C1/n distribution and so on. VPDGS produces much higher slowwave factor than HPDGS. The increased slow-wave factor means the longer electrical length for the same physical length. As an application example, a size-reduced amplifier was designed by inserting VPDGS into the matching network. Two series microstrip lines in input and output matching networks of the amplifier were reduced to 38.5% and 44.4% of the original lengths, respectively .
3. EQUIVALENT CIRCUITS OF DGS
Design and analysis are two challenges for DGS. The commercially available EM solvers is the main resource to design and analyze DGS.
To apply the proposed DGS section to a practical circuit design example, it is necessary to extract the equivalent circuit parameters.
In order to derive the equivalent circuit parameters of DGS unit at the reference plane, the S-parameters vs.frequency should be calculated by full-wave electromagnetic (EM)-simulation to explain the cutoff and attenuation pole characterstics of the DGS section. The circuit parameters for the derived equivalent circuit can be extracted from the simulation result which can be fit for the one-pole Butterworth-type low-pass response. The full-wave analysis does not give any physical insight of the operating principle of DGS. The follow flow chart in 4 shows the conventional design and analysis methods of DGSs.
The full-wave solver is used to find the S-parameters vs. frequency behavior of the DGS. The disadvantage of this method is that there is no direct correlation between the physical dimensions of DGS and the equivalent LC parameters. The derived performance of DGS is not fully predictable until the optimized solutions are achieved through trial and error iterative process. Hence the conventional methods as reported in the open literature [11, 27-31, 36] are time consuming and may not lead to optimum design.
At present, DGS can be equivalent by three types of equivalent circuits: (1) LC and RLC equivalent circuits, (2) π shaped equivalent circuit, (3) quasi-static equivalent circuit.
3.1. LC and RLC Equivalent Circuits
The equivalent circuit of the DGS and one-pole Butterworth prototype of the LPF are given in 5. The rectangular parts of dumbbell DGS increase route length of current and the effective inductance
The slot part accumulates charge and increases the effective capacitor of the microstrip line. Two rectangular defected areas and one connecting slot correspond to the equivalently added inductance (L) and capacitance (C), respectively. Accordingly, a resonance occurs at a certain frequency because of the parallel L-C circuit. Inversely, it is intuitively known that the equivalent circuit includes a pair of parallel inductor-capacitor form the resonant phenomenon in the S-parameter. As the etched area of the unit lattice increases, the effective series inductance increase and increasing the series inductance gives rise to a lower cutoff frequency. When the etched gap distance increases, the effective capacitance decreases so that the attenuation pole location moves up to higher frequency.
In order to match DGS to Butterworth low-pass filter reactance values of both circuits are equal at the cutoff frequency. So L and C are derived as follows:
where, ω0 is the resonance angular frequency of the parallel LC resonator.
where f0 and fc are resonance (attenuation pole) and cutoff frequency which can be obtained from EM simulation results. The characteristics of most of DGS are similar to dumbbell DGS, so they could be discussed by one-pole Butterworth low-pass filter too. Furthermore, radiation effects are more or less neglected. DGS unit can be modeled most efficiently by a parallel R, L, and C resonant circuit connected to transmission liens at its both sides as shown in 6. This resistance corresponds to the radiation, conductor and dielectric losses in the defect. From EM simulations or measurements for a given DGS, the equivalent R, L, and C values are obtained from the expression in .
The size of DGS is determined by accurate curve-fitting results for equivalent-circuit elements to correspond exactly to the required inductance.
3.2. π Shaped Equivalent Circuits
However, it is very difficult to implement the DGS circuits for the purposed of the harmonic termination to satisfy simultaneously the excellent pass band and stop band characteristics. More accurate equivalent circuit models than the LC and RLC equivalent circuit were proposed, such as π shaped equivalent circuit shown in 7.
Considered the phase influence of DGS, Park proposed π shaped equivalent which simulates both amplitude vs. frequency and phase vs. frequency characteristics. The S-parameters vs. frequency curve of π shaped equivalent is more anatomized than LC and RLC equivalents, but its circuit is more complex and the parameters is so many that the equivalent is difficult to extract. π shaped equivalent circuit is much suitable to the exigent precision of circuit design. The ABCD parameters for the unit cell will be obtained using the expression as follows:
The full-wave analysis is very involving and does not give any physical insight of the operating principle of the DGS.
3.3. Quasi-static Equivalent Circuit
Different from the two types of equivalent circuits mentioned above, a quasi-static equivalent circuit model of a dumbbell DGS is developed which is directly derived from the physical dimensions of dumbbell
This overcomes the limitation of report full-wave analysis by developing the equivalent circuit model. This approach gives a comprehensive understanding of the physical principle of DGS including how the DGS creates bandstop and bandpass responses and which dimensions play the most vital role to create the distinct performance. At present, the equivalent circuits are mostly concerned about influences of the addition of DGS such as radiation, or an equivalent circuit corresponded to a new DGS. Because different DGS has different characteristic, different equivalent circuits are not formed uniform circuit model and mathematics theory for the moment. Thus, the optimization based on an equivalent circuit network is highly desirable to design and evolve this kind of circuit configuration.
4. APPLICATION IN MICROWAVE CIRCUIT
There are widely applications in active and passive devices useful for compact design. Since each DGS provides its own distinctive characteristics depending on the geometries, such circuit functionalities as filtering unwanted signals and tuning high-order harmonics can easily be accomplished by means of placing required DGS patterns, which correspond to the desired circuit operations without increasing circuit complexity.
4.1. Stopband Effects
DGS, which is realized by etching off a defected pattern or periodic sturctures from the backside metallic ground plane, has been known as providing rejection of certain frequency band, namely, bandgap effects. The stopband is useful to suppress the unwanted surface waves, spurious and leakage transmission. Therefore, a direct application of such frequency selective characteristics in microwave filters is becoming a hotspot research recently. As 9 shown, the Hilbert curve ring (HCR) DGS lowpass filter achieves a quite steep rejection property, a low in-band insertion less of below 0.5 dB and a high outband suppression of more than 33 dB in a wide frequency rang .
DGS provides excellent performances in terms of ripples in the passband, sharp-selectivity at the cut-off frequency and spurious free wide stopband. There have two types of filter design using DGS: one is directly using the frequency-selectivity chrematistic of DGS to design filters [31-34], the other is using DGS on the conventional microstrip filters so as to improve performance [35-39]. The second search concerns exploitation both on the conductor plane of the microstrip and the ground plane which is the most investigation hotspot in recent years. Several improvements are obtained using DGS in the metallic ground plane for the response of filter. These improvements summarize as follows:
(1) More transition sharpness,
(2) Suppressing higher harmonic,
(3) Achieving broader stopband responses,
(4) Improving the stopband and passband characteristics. Some DGS also tries to combine new material and new technology to design filters.
For example, a filter is designed based on DGS and LTCC . There also adopts SIW combined with the concept of DGS .
4.2. Slow-Wave Effect
One of the most important advantages of DGS is the slow-wave effect which is caused by the equivalent LC components. The transmission lines with DGS have much higher impedance and increased slow-wave factor than conventional lines. So the circuit size can be reduced with these properties, such as microwave amplifiers and Rat-race hybrid couplers . Furthermore, DGS could be used in broadband couplers. In 10, DGS Doherty power amplifier (DDA) could reduce the circuit size effectively by the negligible insertion loss, excellent harmonic termination characteristic and slow-wave effect .
Compared with the conventional Doherty power amplifier (CDA), the radios of the reduced lengths to CDA are 71% at the carrier amplifier output and 62% at the peaking amplifier output. Another attractive application of the DGSs is in the beam steering of a phased array antenna. DGS also can improve the performance of the antenna, restrain harmonious and reduce the mutual coupling of antenna array by suppressing the surface waves [44, 45].
4.3. High Characteristic Impedance
It is a serious problem for conventional microstrip line case that the generally accepted impedance is limited to realize is around 100 ∼
130 Ω. By adopting DGS on the ground plane is possible to increase the equivalent inductance L highly, and to decrease the equivalent C at the same time, and finally to raise the impedance of the microstrip line more than 200 Ω. For example, 11 shows layout of the proposed 1:6 unequal Wilkinson power divider that has been designed adopting DGS and a microstrip line with 208Ω of characteristic impedance has been realized using a simple rectangular-shaped DGS . The high characteristic impedance of DGS may also be used in digital systems (interconnects).
In this paper, the evolutions of DGS from conventional PBGs are reported. The basic conceptions and transmission characteristics of DGS are introduced and the equivalent circuit models of varieties of DGS units are also presented. DGS has simple structure, equivalent LC circuit model, and potentially great applicability to design RF circuit. Various designs in HMIC and MMIC have been investigated to yield better performance in terms of passband width, ripple free transmission and wider stopband.
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