# Potential Applications of PBG Engineered Structures in Microwave Engineering: Part I

Electromagnetic bandgap (EBG) materials are periodic structures that exhibit wide bandpass and band rejection properties at microwave frequencies. Introducing periodic perturbations such as dielectric rods, holes and patterns in waveguides and PCB substrates forms photonic bandgap (PBG) materials. As in a photonic crystal (PC), photon propagation is impeded by electrons and the electromagnetic waves in a PBG material are impeded due to the periodic discontinuities, hence creating a slow-wave structure. Currently, people are also referring to the term PBG as EBG. Due to their unique properties, EBG materials find potential applications in antennas, waveguide, amplifiers, filters, power combining, phased arrays, EMC measurements and in many microwave devices. The application of PBG engineered materials causes the suppression of surface waves.1–7 Consequently, the performance of active and passive microwave components and devices is enhanced. The use of PBGs in the ground plane of a microstrip line provides attractive features.8–11 Even the PBG engineered microstrip line itself shows excellent and attractive performance.12 PBG may have many forms due to their different lattice structures. Their behavior can be controlled with the proper choice of different lattice structures and the lattice parameters.

Recently developed uniplanar compact photonic bandgaps (UC-PBG) are very useful for different applications.13 The passband characteristic of the UC-PBG is used as a slow-wave medium, which reduces the size of electronic circuits. The deep stopband is applied to suppress spurious transmission and leakage in guiding structures such as conductor backed coplanar waveguides (CB-CPW) and striplines. The use of PBG structures in antenna design provides better performance.14–21 Due to the superior performance of EBG assisted microwave devices, research on different EBG structures (EBGS) is accelerating exponentially.

This article reviews the EBG configurations and the application of EBG engineered structures in different microwave applications. In this context, the novelty of this structure has been explored for a high Q image guide resonator useful in the design of low noise oscillators,22 microcavities for better light emitting diode (LED),22 power amplifiers,23 low pass filters,24,25,26 bandpass filters13 and mixers.25 The comparison between EBG engineered and conventional structures demonstrates the importance of EBG materials in microwave engineering. It is believed that this novel structure has opened up a new era in the development of broadband and highly efficient microwave components and devices.

EBG Configurations

EBG structures are periodic in nature, and may be realized by drilling, cutting and etching the metal or substrates. They may be formed in the ground plane or over the substrate. A recent trend is where the main element such as the transmission line is itself creating a PBG12 without having any perturbation in the ground plane. This new idea can be extended to filters, antennas and other microwave components and devices where the important issue of packaging will be minimized. The PBG configuration can be categorized, as shown in the tree structure of Figure 1. On the basis of dimensions, PBG structures may be classified as 1-D, 2-D and 3-D PBG.

Bumpy Surface

Several configurations have been reported in the literature. The first structure is made by drilling a periodic pattern of holes in the substrates27 or etching a periodic pattern of circles in the ground plane.8 A bumpy surface is shown in Figure 2. A bumpy metal sheet has a narrow surface-wave bandgap. The electric field wraps around the bumps at the upper edge of the bandgap (a) and the electric field extends across the bumps at the lower edge of the bandgap (b); hence, a slow-wave structure is achieved.

Corrugated Surface

A corrugated surface,28 shown in Figure 3, is a metal slab into which a series of vertical slots have been cut. The slots are narrow, so that many of them fit within one wavelength across the slab.

Each slot can be regarded as a parallel plate transmission line, running down into the slab and shorted at the bottom. If the slots are one quarter-wavelength deep, then the short circuit at the bottom is transformed by the length of the slots into an open circuit at the top end. Thus, the impedance at the top end is very high.6 In this situation, the surface impedance is capacitive and transverse magnetic (TM) surface waves are forbidden. Furthermore, a plane wave polarized with the electric field perpendicular to the ridges will appear to be reflected with no phase reversal.

Metal Pad or High Impedance Surface

A more effective and compact approach, which makes use of a triangular or square lattice of metal pads connected to ground with vias, has been recently proposed2,6 and can be applied to enhance the gain of planar antennas. These structures are the first realization of planar compact electromagnetic crystals with a complete stopband in the microwave range. This type of textured structure with a triangular lattice of hexagonal metal plates that provides high impedance surface is shown in Figure 4.

Planar PBG

The periodic structures are etched in the ground plane. They may be of different forms on the basis of a lattice structure,10 which may be square, triangular, rectangular, honeycomb, etc. The shapes of the unit cell10,29 may also be square, rectangular, circular, triangular and sinusoidal, etc. A continuous research effort is being made to develop different PBG structures to obtain the required performance. Planar slow-wave structures and low leaky conductor-backed coplanar waveguide using a UC-PBG substrate (Figure 5) have recently been presented.16 In a UC-PBG, vias are not used. Advantages of this crystal are its simple and low cost configuration compatible with MMICs. The UC-PBG structure is a two-dimensional periodic lattice pattern on a conductor-backed dielectric substrate. The unit cell of the PBG lattice consists of square pads and narrow branches, which have an inductive behavior that is further enhanced by insets.

The PBG structure forms a distributed LC network with specific resonant frequencies. At these frequencies, the periodic loading becomes an open circuit and an equivalent magnetic surface is created. Very recently, a new simplified UC-PBG has been proposed by S.K. Sharma and L. Shafai.30 It reduces cost with better performance in antenna applications.

The authors have proposed a ring PBG structure24 that is a potential candidate for more freedom because of its extra aspect ratio characteristics. By changing the aspect ratio of the structure, the bandgap and bandwidth can be controlled. A recent contribution of the authors31 includes the concept of non-uniform distribution of PBGs to be used as a low pass filter (LPF) with improved performance. The authors also propose non-uniform ring PBGs by which the passband ripple is dramatically suppressed both at higher and lower frequencies.

Thus far, different PBG configurations have been presented. The following sections highlight the revolutionary possibilities afforded by PBG integration in RF and microwave electronics.

Microwave Applications of EBG

PBG engineered structures find many applications in microwave components and devices due to the unique properties. To realize microwave filters, mixers, antennas, power amplifiers and phased arrays, etc., the stopband and passband created by the PBG structures play a vital role. After a comprehensive literature review, the applications of EBGs have been categorized, as shown in Figure 6.

Low Noise Oscillator Design

Y. Qian, et al.22 offer the design of PBG engineered passive and active components. Application of a high Q image guide resonator results in a low noise oscillator. The defected mode concept in PBG structures has been utilized here. The schematic of a high Q resonator based on PBG defect-effect in an image guide is shown in Figure 7, where a is the period of the 1-D lattice of grooves. It is interesting to note that a stopband for wave propagation is achieved when Bragg’s condition24 is satisfied. On the other hand, a sharp high Q defected mode can be obtained when a cavity is formed in the middle of the PBG lattice with a length l. A modulated Gaussian pulse outside the PBG grooves excites the image guide. In this case, 8.255 GHz is obtained as the peak frequency for transmission.

An experimental investigation is needed for the design of a proper coupling scheme to launch and measure the image guide mode. A microstrip-fed Yagi-Uda slot array is used in the design of an efficient transition (as shown in Figure 8) that is used for the measurement of “S-parameters.” It can be seen from the result shown in Figure 9 that the peak frequency is 8.276 GHz, which is excellent (only 0.25 percent error). A reasonably high value of unloaded Qu of 697 is measured. In a low noise oscillator design, this type of image guide resonator is a potential component to provide a relatively pure spectrum. Figure 10 shows how the resonator is used to realize a low noise oscillator. The resonator provides an output power level of 8.5 dBm after subtracting the coaxial cable loss. A noise level of approximately –102 dBc/Hz at 100 kHz offset is obtained. The image guide resonator is used in the feedback loop of a cascaded amplifier.

Enhanced Spontaneous Emission Led by Microcavities

PBG based microcavities22 provide an LED with enhanced spontaneous emission. In the terahertz frequency range, the PBG-based microcavities are outstanding candidates to achieve single mode, small volume resonators. These types of cavities are used to enhance spontaneous emission and to increase the efficiency of an LED. In Figure 11, a high dielectric slab resides on a substrate with a much lower value of dielectric constant so that the electromagnetic energy of the guided modes is confined inside the high dielectric constant slab.

The dispersion diagram of a transverse electric (TE) like mode, shown in Figure 12, is for t/a = 0.33 and r/a = 0.40, where t is the thickness of the substrate, r is the radius of a circular-patterned EBGS and a is the inter-element distance. A bandgap for the guided propagation is found in the range of 0.33c/a to 0.4c/a only for TE-like modes, where c is the velocity of light.

Defects realized by adding an appropriate volume of dielectric material are necessary to support highly localized electromagnetic modes, whose frequency will fall within the range of the forbidden gap of the two-dimensional crystal. The energy of these modes cannot couple to the guided modes of the slab; it resides around the defect, which acts as a microcavity. In the design of light emitting diodes, it is an excellent component where the energy is confined in the active region of the LED. Three configurations are shown in Figure 13, where the minimum effective volume is about 2, in units of (λ/2h)3, for all configurations. Y. Qian, et al.22 suggest that this value is expected to achieve a five-fold spontaneous emission enhancement. The smallest possible EM mode volume in a dielectric cavity has been previously documented.23 The performance of PBG-based microcavities to provide enhanced emission of LED is shown in the figure.

Suppression of LO Leakage in a Mixer

A conventional low pass filter (LPF) needs many stages to reject the LO leakage. However, a UC-PBG-structured filter can be used to suppress this leakage in a mixer, as shown in Figure 14. The UC-PBG filter25 is placed at the drain side to extract IF output as well as to reject the LO leakage. Figure 15 shows the comparison of conversion gain and LO leakage between a PBG assisted mixer and a conventional mixer. The graph shows that the LO power has been injected into the drain more efficiently from the increase in conversion gain from 1 to 1.5 dB at lower levels when using the PBG filter. It is very clear that the PBG mixer suppresses the LO leakage by more than 10 dB.

Broadband High Efficiency Power Amplifier

The achievement of broadband harmonic tuning is typically cumbersome for active integrated antenna amplifiers and for power amplifiers in general. The technique of using a periodic structure is actually well suited for a narrow band. Thus, additional harmonic filtering is required that necessitates larger transmission stopbands. These types of larger stopband filters can be achieved with the use of PBG ground plane. The proposed PBG ground plane for microstrip lines32 provides low loss, slow-wave propagation at lower frequencies and a wide distinctive stopband as the frequency increases.9,26 The implementation of a PBG ground plane in power amplifiers results in intrinsic, broadband harmonic suppression without any stub or filtering element. In the design of broadband power amplifiers the PBG periodic structure is integrated with a slot antenna, where it is used to tune the second harmonic. The measured input impedance of the slot antenna with a microstrip feed is shown in Figure 16. It has been mentioned by V. Radisic, et al.32 that the measured power added efficiency (PAE) is better than 50 percent over an 8 percent bandwidth (3.7 to 4.0 GHz) with second harmonic tuning only. When a combined approach,32 where a microstrip patch with shorting pins is used to tune the second harmonic and the periodic structure is used to tune out the third harmonic for a class AB power amplifier, the PAE is 61 percent with an output power of 21.9 dBm.

Efficient Transmitter Front-ends Integrated with EBG

The tuning of second and third harmonics provides an efficient power amplifier. C.Y. Hang, et al.33 show a comparison between an amplifier assisted with a PBG microstrip line at the output, and a reference amplifier with a standard 50 Ω microstrip line of identical length. The measured and simulated PAE versus input power for the PBG and reference amplifier at 3.6 GHz are shown in Figure 17.

Comparing these results with the reference amplifier, it is seen that the PBG engineered RF amplifier provides a 10 percent improvement in PAE and a 1.3 dB increase in output power. The maximum measured PAE is 65 percent at an output power of 25.5 dBm for the PBG amplifier. It has also been reported33 that the PAE is better than 50 percent from 3.32 to 3.62 GHz (8 percent BW) for the PBG engineered RF amplifier and from 3.5 to 3.6 GHz (4 percent BW) for the reference. The PBG structure provides a 37 dB additional suppression for the second harmonic and at least 30 dB for the third harmonic. It is expected that the implementation of the entire system on a PBG ground plane may lead to a very compact, high performance power amplifier for a wide range of wireless and microwave amplifiers.

Low Pass Filters

The UC-PBG structure25 is used in the ground plane of a low pass filter (LPF), as shown in Figure 18. A small portion of the 50 Ω feed line is placed on a perforated ground plane (UC-PBG plane), the remaining being on the solid ground plane. A Duroid 6010 substrate is used with εr = 10.2 and a thickness of 25 mils. The width of the 50 Ω microstrip line is 24 mils. The simulation results show the wider stopband above 6 GHz and S21 is found to be below –30 dB over a wide frequency range. Within the stopband range, the return loss, S11, is found to be approximately 0 dB, which indicates very little radiation loss and ensures the PBG property. The simulation results are shown in Figure 19. It is noted that a stepped-impedance LPF with seven reactive elements has been chosen.34

Measurement results for both the PBG filter and a reference filter have also been shown. Important findings from the comparison between the PBG assisted filter and the conventional filter include: the maximum attenuation is increased from 20 to 58 dB due to inclusion of EBGS; the spurious passband is completely suppressed; the passband loss is comparable to the conventional LPF; the application of a PBG structure maintains the matching conditions and does not increase the conductor loss.

Non-uniform PBG Assisted LPF

The authors describe31 a microstrip line on non-uniform EBGS as a low pass filter. In this article a novel EBGS is proposed in the form of non-uniform distributions of circular and annular ring patterns to investigate any improvement over the conventional uniform circular-patterned EBGS. Two distributions, Binomial35 and Chebyshev polynomials,36 as applied to antenna array synthesis, are used to taper the dimensions of the etched circular and annular ring patterned EBG units on the ground plane of a standard microstrip transmission line. While the uniform distribution of the circular-patterned EBGS8 is hindered with high passband ripples near the cut-off frequency, the non-uniform distributions in the forms of binomial and Chebyshev polynomials yield superior performances by suppressing passband ripples and producing a distinct wide stopband. The novelty of the proposition is that binomial and Chebyshev polynomials are exploited to control the LPF response and selectivity. Hence, the filter synthesis is substantially relaxed in the present approach. Also, the level of the passband return loss, selectivity and the ripples can be controlled with the side-lobe level (SLL) index of the Chebyshev polynomial. Since the passband ripple height increases with the filling factor, the uniform circular-patterned PBG limits the wideband applications. Using the non-uniform distribution of PBG patterns, both passband ripple and stop bandwidth problems are alleviated and the selectivity of the stopband of planar PBGs increases.

Figure 20 shows two different varieties — a uniform and non-uniform circular-patterned planar PBG on microstrip substrates. As can be seen in the figure, the uniform and the non-uniform circular patterns are etched with a period a on the ground plane of standard microstrip transmission lines to form a PBG engineered microstrip transmission line. The important design parameters to achieve a stopband characteristic are the period a and the filling factor r/a. For the uniform circular-patterned PBG, the circles are of the same radius r and period a. For non-uniform patterned PBGs, the central elements have the largest radii of r0 and the radii of the adjacent circles decrease proportionally to the amplitude coefficients of the polynomials. For a Chebyshev distribution, the area of the PBG patterns will vary proportionally to the coefficients of the polynomial for a particular side-lobe level (voltage ratio). Here, two distinct relationships between amplitudes of the coefficients of the polynomials and the physical dimensions of the PBG circles are proposed — the polynomial coefficient’s amplitudes are proportional to the radius of the PBG circle (r), called Type 1, and the polynomial coefficient’s amplitudes are proportional to the area of the PBG circle (πr2), called Type 2. The tapering of the physical dimensions of the PBGs for both types 1 and 2 follows the coefficients of the polynomial taking the central elements as the reference. The period and the filling factor (r/a) of the PBG line determine the dimensions (radius) of the central PBG elements. The improved performance of the proposed model is shown in Tables 1 and 2. The S-parameter performance for uniform and Chebyshev distribution is shown in Figures 21 and 22. The ripple free transmission with a distinct and wider stopband can be seen.

Compact Microstrip Bandpass Filters

Conventional parallel-coupled bandpass filters (BPF) need extra filters to suppress spurious transmission that results in the increase of insertion loss. The use of extra filters can be avoided by applying PBG to obtain a compact microstrip BPF with intrinsic spurious rejection. The well-matched microstrip on the UC-PBG ground plane is suited as a low loss transmission line. Generated spurious passbands at higher harmonics can be suppressed with the aid of PBGs as they provide a wide and deep stopband. The physical length of the filter circuit is reduced as well due to the slow-wave effect of the UC-PBG structure. Figure 23 shows the schematic of a microstrip BPF on the UC-PBG ground.

The literature34 describes the standard design procedures for a parallel-coupled BPF. The design requirements include:13 centre frequency, f0 = 6 GHz, W1 = 17 mils, W2 = 21 mils, G1 = 8 mils, G2 = 28 mils. The width of the microstrip feed lines = 24 mils (corresponding to 50 Ω transmission line), the number of coupling sections = 4, and a 0.5 dB equal-ripple response. The physical length of the coupled-line sections (L1 and L2) = 145 mils. This length is 20 percent shorter than that of a conventional quarter-wavelength line. The performance comparison with a conventional BPF is shown in Figure 24.

At the frequencies of 12 and 17 GHz, the transmission coefficients of a conventional BPF are seen to be –10 and –5 dB, respectively. On the other hand, the UC-PBG filter provides a spurious suppression of 30 to 40 dB.

Although the lengths of the microstrip resonators have been scaled according to the slow-wave factor, the coupling gaps remain the same, which results in an increased fractional bandwidth (21.6 percent) at 6 GHz center frequency. Like for a conventional BPF, the coupling coefficients can be optimized to improve the bandpass characteristics of the PBG engineered BPF. Including the effect of two SMA connectors, the minimum insertion loss of the PBG filter is found to be 1.9 dB at 6.39 GHz. The passband loss is comparable to that of a conventional BPF.

Recently the authors proposed37 a binomial distribution of PBGs for harmonic suppression. The geometry of the BPF is the same as described in Yang, et al.13 The only difference is that circular PBGs have been used where their radii have been calculated as per a binomial distribution. The geometry and results are shown in Figure 25.

From the result it can be seen that the second harmonic is significantly suppressed by more than –40 dB and the return loss performance as well as the insertion loss at fundamental frequency is improved for the case of binomial distribution of PBGs. The third harmonic is totally suppressed.

PBG Filter without Packaging Problem

Different types of PBG filters are very good candidates to offer passband and stopband properties. Normally the PBG structure is etched in the ground plane. Packaging of microwave circuits severely degrades the performance of the PBGs. T. Akaline, et al.38 recently proposed a structure to mitigate the packaging problem. The influence of the back shield has been addressed here; the casing embeds the circuit when the filter is integrated in the microwave systems. Figure 26 shows a photograph of the ground plane of a periodically etched microstrip PBG-type filter. The hole radius is 3.525 mm and the period is 14.1 mm. The worst performance due to the shielding effect is also shown. Two patterned PBG structures have resulted in the improvement against the degraded performance due to the back shield. In this case the top pattern is formed via a printed technology with five successive high and low impedance sections having a width of 0.4 and 0.8 mm, respectively. The back plate is etched with two holes of radius 3.5 mm with period of 14.1 mm. The holes are under the high impedance sections. The total length is 35.3 mm. The better performance achieved with the two-sided PBG filter is noticeable.

D. Nesic, et al.29 reported a unique PBG structure very recently, where sinusoidal variations of the characteristic impedance have been implemented by a sinusoidally shaped microstrip line on the substrate. No etching in the ground plane was required. The problem of packaging does not appear. It provides an alternative solution to the packaging problem in PBG engineered components and devices. The schematic of the line, along with the result, is shown in Figure 27.

Q. Xue, et al.12 describe a new microstrip transmission line where a PBG structure has been incorporated on the transmission line itself. It consists of a regular 50 Ω line with six periodic perforations. An increased series inductance is obtained from the narrowed lines on both sides of the perforation while an increase of shunt capacitance results from the two edges of the perforation across the width of the microstrip line. Two mirrored triangles are introduced to increase the shunt capacitance and series inductance further and to achieve a tunable cell of the transmission parameters. Two narrow connecting strips connect the triangles to the narrow portions of the microstrip line. The perturbed transmission line and the unit cell are shown in Figure 28. Remarkable additional shunt capacitance is obtained from the gaps between the triangle edges and the end edges of the perforation. The connecting lines and the triangles form a resonant component for enhancing the bandstop phenomena.

The S-parameter’s performance is shown in Figure 29. A stopband between 6.5 to 8.5 GHz is found and the bandwidth of the stopband is more than 25 percent. The phase changes faster at frequencies near the edges of the stopband indicating a slow-wave characteristic. The novel achievement of this structure is the elimination of the dependence of the propagation constant on the orientation and location of the transmission line with respect to the axes of the periodicity of the PBG ground plane.

Conclusion

In the first part of this two-part article, the basic PBG configurations and application of PBG structures in enhancing the performance of microwave devices and components have been reviewed. The focus has been on the performance of PBG assisted low noise oscillators, PBG-based microcavities, suppressing the LO leakage in mixers for broadband harmonic tuning, high efficiency power amplifiers, and LPFs and BPFs. The following beneficial points are noted:

- An excellent image guide resonator is achieved by inclusion of PBGs, useful in low noise oscillator design.
- PBG-assisted microcavities provide enhanced spontaneous emission and increase the efficiency of an LED.
- It can be seen that a PBG-based mixer suppresses LO leakage by more than 10 dB.
- An amplifier with perturbed ground plane with PBGs results in intrinsic broadband harmonic suppression without any stub or filtering element. The PAE is also increased.
- In case of LPFs, it can be seen that the PBGs provide more attenuation, complete suppression of spurious transmission without excess conductor loss. The non-uniform PBGs with binomial and Chebyshev distribution provide better performance in terms of ripple height in the passband, selectivity and wider stopband.
- The use of UC-PBGS in a conventional BPF suppresses the second and third harmonics significantly.
- The proposed non-uniform PBGs with binomial distribution is also very useful in suppressing the harmonics in a bandpass filter.
- The packaging issues in implementing PBGs in RF and microwave circuits have also been addressed. Three varieties of PBGs are presented that can alleviate the conventional packaging issues in HMIC and MMIC multilayered configurations.

Thus, the PBG structures find many potential applications in microwave components and devices to enhance their overall performance. In the next part of the article, PBG applications in waveguides, antennas and phased arrays will be presented.

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