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IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGIES, VOL. 32, NO. 2, JUNE 2009 273

Microwave Bandstop Filters Using Novel Artificial Periodic Substrate Electromagnetic

Band Gap StructuresFelix D. Mbairi, Member, IEEE, and Hjalmar Hesselbom

Abstract—Novel microwave and millimeterwave (mm-wave) bandstop filters using artificial periodic substrate electromagnetic bandgap (EBG) are investigated in this paper. Three types of microstrip structures using periodically modified trace width, patterned dielectric substrate, and periodically modified ground plane are treated, respectively. By periodically modifying either the width of the conductor trace, the substrate height, or the dielectric constant of a standard microstrip transmission line, it has been possible to design microwave bandstop filter functions with wide stopband characteristics and reduced size, compared to conventional microwave/RF filter structures. Commercial electronic design automation (EDA) and computational electro- magnetic tools such as Agilent’s advanced design system (ADS) and CST Microwave Studio are used in the design and simulations of these filter structures. The effects of the physical parameters of the structures on the filter characteristic are studied. The design procedure and simulation results are described and possible applications of these filter structures are discussed in this paper. A particularly wide stopband is achieved by the circuits presented in this paper, which use only a few cell elements. A significant performance improvement of microstrip patch antenna has been observed by implementing one of the presented EBG periodic substrate structures.

Index Terms—Bandstop filter (BSF), electromagnetic bandgap (EBG), microstrip, microwave, millimeterwave (mm-wave), pho- tonic bandgap (PBG), -parameters.

I. INTRODUCTION

ITH the increasing trend towards miniaturization and the perpetual quest for higher performance circuits, new

methods and techniques of making smaller size electronics de-vices with better performance are of great importance.

The interest in periodic substrate electromagnetic bandgap (EBG) and defected ground structures (DGS) for microwave

and millimeterwave (mm-wave) applications has much in-

Manuscript received November 29, 2006; revised February 06, 2009. Cur- rent version published July 22, 2009. This work was supported in part by Mid Sweden University, ITM. This work was recommended for publication by As- sociate Editor L.-T. Hwang upon evaluation of the reviewers comments.

F. D. Mbairi was with the Department of Microelectronics and Infor- mation Technology, Royal Institute of Technology (KTH), Electrum 229, SE-164 40 Sweden. He is now with UMG/PHEE/Mobile Internet Plat- form Engineering, Intel Corporation, Hillsboro, OR 97124 USA (e-mail: felix.d.mbairi@intel.com).

H. Hesselbom was with the Department of Electronic Production, Mid Sweden University, ITM, Campus Östersund, SE 831 25, Sweden. He is now with the Hesselbom Innovation & Development HB, 141 38 Huddinge, Sweden (e-mail: hjalmar@ hesselbom-id.com).

Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TCAPT.2009.2018833

creased these recent years, due to the unique properties and advantages of improved performance, slow-wave property, size reduction, etc., related to these concepts. EBG Bragg grating and DGS structures have been successfully applied to many microwave components and devices such as planar transmission lines, filters, couplers, antennas, mixers, power amplifiers, etc., showing attractive features (e.g., slow-wave effects, harmonics suppression, wideband characteristics, circuit size reduction, performance enhancement). Various sorts of periodic structures exhibiting these characteristics have been investigated and developed by several authors [1]–[12].

Microwave/RF filters play a major role in communication systems where they are widely used to eliminate unwanted signal frequencies while permitting good transmission of the desired frequencies.

In this paper, another concept of EBG structures based on pe- riodical modification of the microstrip line impedance is pre- sented which preserves the uniformity of the conductor backing and thus does not suffer enclosure or packaging problems. Three types of BSF using simple microstrip periodic structures and providing small size, large bandwidth, and great stopband re- jection characteristics are described. The three structures are formed by periodically modifying the signal trace width, the thickness of the ground/reference plane (or the substrate height), and by periodically varying the substrate dielectric constant, re- spectively. A microstrip patch antenna using the patterned di- electric substrate configuration has been shown to suppress har- monic components and enhance bandwidth.

Agilent’s commercial software package advanced design system (ADS) is used to design and simulate these structures. The frequency characteristics of the proposed EBG microstrip structures are investigated by full-wave electromagnetic sim- ulations using microwave studio (MWS), a finite-difference time-domain (FDTD) software from CST Corporation. The ef- fects of the physical parameters on the filter characteristics are studied for the structure with periodically modified substrate heights, showing the possibilities of optimizing its frequency response.

In the next paragraphs, an overview of the EBG concept is presented, followed by the design theory and analysis of the three filter structures, as well as the simulation results and discussions.

II. PBG/EBG CONCEPT

The concept of photonic bandgap was originally developed in the optical domain [13] and describes the selective

propagation

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274 IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGIES, VOL. 32, NO. 2, JUNE 2009

Fig. 1. Schematics of a type of Bragg grating, where a shallow corrugation is created on the top surface of a structure. is the Bragg grating period.

of electromagnetic waves (light) in a periodic structure. Such a structure presents some allowed frequency regions (bands) where the electromagnetic (EM) waves can propagate, and some forbidden band or bandgap in which no wave propagation is permitted. The term “bandgap” is borrowed from solid-state physics and refers to a forbidden region in a crystal structure, where wave propagation is not allowed. The terminology is in- herited from the theory of electron and hole propagation in crys- tals. In the forbidden frequency band, incident waves at var- ious directions interfere destructively and thus are unable to propagate.

The PBG concept has been widely used in the optical area to create periodically modified structures (e.g., optical waveguide, filter, and coupler structures, with periodic array of grating pat- terns atop a dielectric or semiconductor layer), where the elec- tromagnetic waves propagation is frequency selective, creating additional features in the characteristics of the structures other than their conventional functions. Recently, the PBG concept has been extended to microwave and mm-wave applications, under the terminology EBG. PBG or EBG structures are based on Bragg grating condition. The term “Bragg grating” refers to an optical device created by periodically modulating the refrac- tive index (structural corrugation) in an optical waveguide (see Fig. 1), thereby reflecting light in multiples of narrow wave- length ranges while transmitting all other wavelengths. This ability to selectively reflect certain wavelength is attractive for a wide range of filtering applications in optical telecommunica- tions (optical filters, fiber Bragg gratings applications, etc.).

For the Bragg-grating-based filters, the operating frequency is determined by the spatial grating period (or Bragg period) , according to the Bragg condition given by (1) and (3) for optical waveguide devices, and (2) and (4) for electromagnetic devices

(1)

where is the free space wavelength, is the effective index of refraction of the guiding dielectric structure, and is an in- teger representing the order of the Bragg grating. The refractive index is related to the dielectric constant by

, where is the permittivity of free space. is

the wave- length of light inside the dielectric material.The Bragg condition can also be expressed in terms of the

propagation constant as

(2)

where is the phase constant in the length direction of period- icity .

The Bragg grating acts as a 1-D diffraction grating which re- flects electromagnetic waves from the forward-travelling mode into the backward travelling mode.

According to the Bragg condition, in order for constructive interference to occur between reflected light (waves), the path difference between reflected light (waves) from subsequent grating periods must be an integral number of wavelength. Equations (1) and (2) represent the Bragg condition for a th-order Bragg grating.

For , (1) and (2) become

(3)

(4)

which are the conditions for a first-order Bragg grating. The path difference is precisely one wavelength, and the grating period is one half of the wavelength. This corresponds to the strongest reflection or diffraction efficiency. Only a first-order and 1-D Bragg

grating is considered in this work. Higher order Bragg gratings provide a substantially larger grating pitch, which simplifies the fabrication process.

By changing the pitch, the number of cells, or the modulation depth of the grating across the length of the device, it is possible to shape its spectral or frequency response.

III. DESIGN THEORY/CONCEPT

Many conventional microwave devices, for example, filters, transformers, couplers, etc., use alternating sections of different characteristic impedances (known as stepped impedance) to easily implement their functions. In this paper, a periodic imple- mentation of this feature is used to create distinctive bandstop filter characteristics. Three configurations of microstrip EBG bandstop filters are presented. The three structures are based on periodic modification of the characteristic impedance of the microstrip transmission line, using Bragg grating conditions.

The characteristic impedance of a standard microstrip trans- mission line is given in [14] by

(5)

where is the relative dielectric constant of the substrate ma- terial used, is the substrate height, is the thickness of the conductor trace, and is the trace width. As there are four variable parameters in this relation, four options are possible for changing using only one of these parameters (for simplicity).

A. By Changing the Conductor Trace Width ( ), and Maintaining the Other Parameters Constant

This results in a stepped impedance like structure shown in Fig. 2(a), often used in the literature for nonperiodic filter struc- tures (e.g., stepped impedance low-pass filter) [15]. In combina- tion with an EBG Bragg grating, this type of

structure can pro- duce a very wide stopband characteristic, as illustrated in Fig. 6.

As estruturas da fig. 2 foram implementadas usando Agilent ADS. Os circuitos são modelados por repetir periodicamente (quatro vezes) uma ligação em cascata de duas linhas de transmissão e TL_2 Tl_1, de diferentes impedâncias características Z01 e Z02 respectivamente. Por razões de simetria e na outra para coincidir com as portas de entrada e de saída, um outro elemento Z01 foi adicionada no final das estruturas.

A condição de Bragg (4) sugere que o período ᴧ deve ser igual a um meio comprimento de onda para a frequência de criação, isto é,

Onde lambida0 é o comprimento de onda na faixa de rejeição f_0 frequência central

Com Epsolon_reff sendo constante dieléctrica efetiva da microfita, dada pelas expressões de forma fechada:

Onde F

Os passos de grade delta_l_1 e delta_l_2 podem ser escolhidos para ser igual em comprimentos físicos ou em comprimentos elétricos (atrasos iguais), ou de comprimentos diferentes (por um período constante) em todos os casos. Um comprimento elétrico igual entre as duas secções TL_1 (delta_l_1 de comprimento físico) e TL_2 (delta_l_2 de comprimento físico) implica.