DESIGN OF BANDSTOP FILTERS USING DEFECTED GROUND STRUCTURES. Thesis. Submitted to. The School of Engineering of the UNIVERSITY OF DAYTON

Transcription

1 DESIGN OF BANDSTOP FILTERS USING DEFECTED GROUND STRUCTURES Thesis Submitted to The School of Engineering of the UNIVERSITY OF DAYTON In Partial Fulfillment of the Requirements for The Degree of Master of Science in Electrical Engineering By Kaushik Annam Dayton, Ohio August, 2015

2 DESIGN OF BANDSTOP FILTERS USING DEFECTED GROUND STRUCTURES Name: Annam, Kaushik APPROVED BY: Guru Subramanyam, Ph.D. Advisory Committee Chairman Department of Electrical and Computer Engineering Monish Chatterjee, Ph.D. Committee Member Department of Electrical and Computer Engineering Weisong Wang, Ph.D. Committee Member Department of Electrical and Computer Engineering John G. Weber, Ph.D. Associate Dean School of Engineering Eddy M. Rojas, Ph.D., M.A., P.E. Dean, School of Engineering ii

3 Copyright by Kaushik Annam All rights reserved 2015 iii

4 ABSTRACT DESIGN OF BANDSTOP FILTERS USING DEFECTED GROUND STRUCTURES Name: Annam, Kaushik University of Dayton Advisor: Dr. Guru Subramanyam In this thesis, modified design of band stop filters using defected ground structures have been proposed. The new proposed structures have conventional dumbbell DGS integrated with U-slot and the conventional spiral DGS integrated with U-slot both designed using microstrip lines. These structures provide high Q-factor with low insertion loss (below 1dB) in the pass band. By adding the U-slot to the conventional structures, the overall capacitance and inductance are increased which results in low resonance frequency of 1.4GHz with a notch depth of dB for dumbbell-slot when compared to 2.6 GHz with a notch depth of dB for conventional dumbbell DGS. The resonance frequency is 1.2GHz with a notch depth of db for spiral-slot when compared to 1.4GHz and a notch depth of dB for conventional spiral DGS. Sharp transition is achieved from pass band to stop band for the new proposed DGS while the DGS sizes remained iv

5 the same. The proposed designs were fabricated for a dielectric substrate with a dielectric constant, εr of 10. v

6 Dedicated to my parents and my brother vi

7 ACKNOWLEDGEMENTS First, I would like to thank Dr.Guru Subramanyam, my advisor who has been very patient and supported me since the day I have joined University of Dayton. He had always given me the freedom to work on my own pace and my own style which made me very comfortable when I was fully loaded with other tasks. I thank him for all his support and encouragement he gave me throughout my program. I would also like to thank Dr. Sunil Kumar Khah, who was a visiting professor from India. He was the one who introduced Defected Ground Structures to me, and helped me to gain good knowledge in this topic. He also helped me with learning AWR tool and introduced me to Dustin Brown while he was leaving back to India. Dustin, who is now Dr. Brown, was really the best team member I ever had in my life. He had really helped me a lot with all kinds of problems I had when I started my thesis. He never hesitated to share his knowledge with others which was really helpful for a beginner like me when I newly joined this lab. I would also like to thank Dr. Monish Chatterjee, who is like my mentor. He always helped me boost my confidence levels whenever I felt it was necessary. I still remember my first master s class Digital Communications which was taught by him in spring 2013, during the course I vii

8 got an opportunity to learn a lot from him. I would like to thank him for being one of my committee members. I would also like to thank Dr. Weisong Wang for being my committee member and reviewing my work and guiding me whenever I needed help. I would also like to thank Dr.Eunsung shin, Wang Shu, Hailing Yue, Kuan-Chan Pan, Ayesha Zaman for the support they gave me. viii

9 TABLE OF CONTENTS ABSTRACT... iv DEDICATION... vi ACKNOWLEDGEMENTS... vii LIST OF FIGURES... xiii LIST OF TABLES... xviii CHAPTER 1: INTRODUCTION Background Scope Outline... 6 CHAPTER 2: FILTERS Introduction Decibels (db) CHAPTER 3: DEFECTED GROUND STRUCTURES Introduction ix

10 3.2.1 Dumbbell DGS Arrowhead Dumbbell DGS Circular Slot Dumbbell Modified Dumbbell DGS H-Shaped DGS Spiral DGS U-Slot DGS Equivalent Circuit Models CHAPTER 4: ANALYSIS OF BASIC DEFECTED GROUND STRUCTURES Dumbbell DGS Influence of the Square Lattice Influence of the Gap Distance U-Slot DGS Length L Distance D Width of the Slot G CHAPTER 5: DESIGN AND ANALYSIS OF BAND STOP FILTERS USING NOVEL DGS Design of New Dumbbell-Slot DGS x

11 5.1.1 Dumbbell DGS for New Dumbbell-Slot DGS U-Slot for New Dumbbell-Slot DGS Equivalent Circuit Model for New Dumbbell-Slot DGS Design of New Spiral-Slot DGS Spiral DGS for New Spiral-Slot DGS Equivalent Circuit Model for New Spiral-Slot DGS Measured Results New Dumbbell-Slot DGS New Spiral-Slot DGS Redesigned Dumbbell-Slot DGS for εr of Dumbbell DGS for New Dumbbell-Slot DGS for εr of U-Slot for New Dumbbell-Slot DGS for εr of Equivalent Circuit Model for New Dumbbell-Slot DGS for εr of Measured Data of New Dumbbell-Slot DGS for εr of Redesigned Spiral-Slot DGS for εr of Spiral DGS for New Spiral-Slot DGS for εr of U-Slot for New Spiral-Slot DGS for εr of xi

12 5.10 Equivalent Circuit Model for New Spiral-Slot DGS for εr of Measured Data of New Spiral-Slot DGS for εr of CHAPTER 6: CONCLUSION AND FUTURE WORK Conclusion Future Work BIBLIOGRAPHY xii

13 LIST OF FIGURES Figure 1-1 Telephone Tower Sweden [1]... 1 Figure 1-2 The Electromagnetic Spectrum [2]... 3 Figure 1-3 Modern Telephone pole [3]... 3 Figure 1-4 WiMAX Receiver with Harmonic Separation [4]... 4 Figure 2-1 Basic Filter [5]... 8 Figure 2-2 Ideal Filter Responses [5]... 9 Figure 2-3 Practical Filter Responses [6] Figure D View of Dumbbell DGS Figure 3-2 Top View of Dumbbell DGS Figure 3-3 Frequency Response (S21, S11) of Dumbbell DGS Figure 3-4 Frequency Response (S12, S22) of Dumbbell DGS Figure 3-5 Arrowhead-Slot Dumbbell DGS Figure 3-6 Frequency Response of Arrowhead Slot DGS Figure 3-7 Circular Slot Dumbbell DGS Figure 3-8 Frequency Response of Circular Head Slot xiii

14 Figure 3-9 Modified Dumbbell DGS Figure 3-10 Frequency Response of Modified Dumbbell Figure 3-11 H-Shaped DGS Figure 3-12 Frequency Response of H-Shape DGS Figure 3-13 Spiral DGS Figure 3-14 Frequency Response of Spiral DGS Figure 3-15 U-Slot DGS Figure 3-16 Frequency Response of U-Slot DGS Figure 3-17 LC Equivalent Circuit Model Figure 3-18 RLC Equivalent Circuit Model Figure 3-19 Equivalent Circuit Model for Multiple Band Gaps Figure 4-1 Influence of Rectangular Lattice Dimension Figure 4-2 Influence of Gap Distance Figure 4-3 Influence of Length L on Frequency Response of U-Slot Figure 4-4 Influence of Distance D on Frequency Response of U-Slot Figure 4-5 Influence of Width G on Frequency Response of U-Slot Figure D View of New Dumbbell-Slot DGS Figure 5-2 Top View of New Dumbbell-Slot DGS Figure 5-3 Frequency Response of New Dumbbell-Slot DGS xiv

15 Figure 5-4 Dumbbell for New Dumbbell-Slot DGS Figure 5-5 Frequency Response of Dumbbell DGS Figure 5-6 U-slot for New Dumbbell-Slot DGS Figure 5-7 Frequency Response of U-slot DGS Figure 5-8 Equivalent Circuit Model for New Dumbbell-Slot DGS Figure 5-9 Schematic Model vs Simulation Result of New Dumbbell-Slot DGS Figure 5-10 Variable Tuner for New Dumbbell-Slot DGS Figure D View of New Spiral-Slot DGS Figure 5-12 New Spiral-Slot DGS Figure 5-13 Frequency Response of New Spiral-Slot DGS Figure 5-14 Spiral DGS for Spiral-Slot DGS Figure 5-15 Frequency Response for Spiral DGS Figure 5-16 Equivalent Circuit Model of New Spiral-Slot DGS Figure 5-17 Schematic Model vs Simulation Result of New Spiral-Slot DGS Figure 5-18 Variable Tuner for New Spiral-Slot DGS Figure 5-19 Measured Result vs Simulated Result for New Dumbbell-Slot Figure 5-20 Measured Result vs Simulated Result for New Spiral-Slot Figure 5-21 New Dumbbell-Slot DGS for ε r of Figure 5-22 Frequency Response of New Dumbbell-Slot DGS for ε r of xv

16 Figure 5-23 Dumbbell DGS for ε r of Figure 5-24 Frequency Response of Dumbbell DGS for ε r of Figure 5-25 U-Slot for New Dumbbell-Slot DGS for ε r of Figure 5-26 Frequency Response of U-slot DGS for New Dumbbell-Slot DGS for ε r of Figure 5-27 Equivalent Circuit Model for New Dumbbell-Slot DGS for ε r of Figure 5-28 Schematic Model vs Simulation Result of New Dumbbell-Slot DGS for ε r of Figure 5-29 Variable Tuner for New Dumbbell-Slot DGS Figure 5-30 Measured Result vs Simulated Result for New Dumbbell-Slot DGS for ε r of Figure 5-31 New Spiral-Slot DGS for ε r of Figure 5-32 Frequency Response of New Spiral-Slot DGS for ε r of Figure 5-33 Spiral DGS for New Spiral-Slot DGS for ε r of Figure 5-34 Frequency Response of Spiral DGS for ε r of Figure 5-35 U-Slot for New Spiral-Slot DGS for ε r of Figure 5-36 Frequency Response of U-Slot for New Spiral-Slot DGS for ε r of Figure 5-37 Equivalent Circuit Model for New Spiral-Slot DGS Figure 5-38 Schematic Model vs Simulation Result of New Spiral-Slot DGS for ε r of xvi

17 Figure 5-39 Variable Tuner for New Spiral-Slot DGS Figure 5-40 Measured Result vs Simulated Result for New Spiral-Slot DGS for ε r of xvii

18 LIST OF TABLES Table 5-1 Comparison between Conventional DGS and New Dumbbell-Slot for ε r of Table 5-2 Comparison between Conventional DGS and New Spiral-Slot for ε r of Table 5-3 Comparison between Conventional DGS and New Dumbbell-Slot for ε r of Table 5-4 Comparison between Conventional DGS and Spiral-Slot for ε r of xviii

19 CHAPTER 1 INTRODUCTION 1.1 Background: Initially, because of the limited number of users and applications, the low end of the frequency spectrum was utilized for the development of the modern radio techniques. Figure 1-1 Telephone Tower Sweden [1] 1

20 The telephone tower shown in the above figure, served as the biggest telephone hub in Sweden [1]. It used to hold about 5000 connections. However with the increase in applications and users of RF spectrum, the spectrum became overpopulated, resulting in the interference in transmission and reception of signals. A wider bandwidth was essential for full utilization of these improvements. This forced an expansion into the higher frequencies of the frequency spectrum. Increase in the frequency meant a decrease in the wavelength, as well as an increase in problems because of the geometry of the components, as the components used in the equipment became comparable to the wavelengths used. Transmission line theory provides a solution to these problems in microwave technology. The microwaves are the alternating current signal with frequencies between 300MHz and 300GHz. These signals have the wavelengths on the order of mm and are often referred to as mm waves. The electrical wavelengths are on the order of device dimensions and because of this the phase of the voltage or the current changes significantly over the physical extent of the device. Microwave components often act as distributed elements and the lumped circuit element approximations of the circuit theory may not be valid at high RF and microwave frequencies. The figure 1-2 shows the electromagnetic spectrum which shows the location of the microwave frequency band. 2

21 Figure 1-2 The Electromagnetic Spectrum [2] RF and Microwaves have revolutionized the wireless technology. Today one can access data and voice anywhere at any time because of the RF/ Microwave technology. The figure below depicts the modern telephone pole with radio link antennas. Figure 1-3 Modern Telephone pole [3] 3

22 The radio link antenna may handle as many communication channels as the telephone pole in figure 1-1. Interference and noise are of major concern in modern communication systems. To overcome these issues filters are used. As the spectrum is limited and need to be used for many applications among many users, filters are used to select or confine signals within spectral limits. A Band stop filter with good selectivity is used to eliminate noise. One of the practical scenarios where band stop filter is used is in the WiMAX Equipment. Figure 1-4 WiMAX receiver with harmonic separation [4] The receiver equipment in non-linear measurements like measurement of WiMAX power amplifier or communication system is important to capture accurately the information of the device under test. The RF receiver tends to generate nonlinear effects in measurements. The fundamental signal and its harmonics should be within the linear dynamic range of the equipment receiver. The harmonics mostly have low power levels while the fundamental signal has high power level. To handle these extreme power levels is difficult for the receiver. When the power level difference of the fundamental signal 4

23 and the harmonics is larger than the dynamic range, the result can be either one of the two a) Only the fundamental signal is obtained and the harmonics cannot be captured by the receiver. b) Only the harmonics are captured by suppressing the fundamental signal this can be due to the compression point of the equipment of the receiver itself. In order to solve this problem the fundamental signal is separated by harmonics. The fundamental signal goes to the band pass filter and the harmonics with lower power level below go through the band stop to avoid the fundamental signal entering the harmonic channel. High performance of the band stop filter is very important, including large depth of rejection. 1.2 Scope: This thesis introduces designs of band stop filters using Defected Ground Structures (DGS). These are microstrip transmission line based structures showing a better Q-factor with low insertion loss can be achieved at low frequencies using DGS. The simulation and measured results are shown in chapter 5 and a fairly decent match is observed. However some attention is needed towards the fabrication of the devices. Our group in the past few years has been investigating the possibility of using BST thin film varactor technology to come up with various tunable devices like filters, Inductors, resonators and antennas etc. Our group is pursuing design of bandstop and bandpass filters using coplanar waveguide (CPW) structures. 5

24 1.3 Outline: Chapter 1 gives insight to RF and Microwave communication engineering, and how it s evolved over the past 100 years. It also discuss the significance of the band stop filters in wireless applications. Properties and significance of filters are discussed in chapter 2. In chapter 3 Defected Ground Structures are introduced. Different defects and their effects are discussed based on simulation results. The analysis of the basic Defected Ground Structures is given in chapter 4. Then modified Defected Ground Structures for band stop filter designs are proposed and the analysis is made on the basis of the simulation and measured results in chapter 5. Conclusions and future work are presented in chapter 6. 6

25 CHAPTER 2 FILTERS 2.1 Introduction: In today s advanced world, we are totally dependent on electronic gadgets such as, a mobile phone for communication and many more. Filters play an important role in these applications. If we track the history, filters were playing a key role in telecommunications and wireless communications prior to World War II. They were developed and practiced by many researchers such as Richards, Darlington, and Sykes etc. [2] Filters in general can be defined as a two port network with energy storage elements like inductors, capacitors and transmission lines. These are used to obtain frequency dependent characteristics i.e. transmitting required signals in the pass band and rejecting or attenuating in the stop band. These kind of characteristics can be obtained using different combinations of capacitors and inductors. A capacitor blocks DC and lower frequencies while allowing higher frequencies to pass through it, on the other hand inductor plays quite opposite to capacitor by blocking higher frequencies and allowing low frequencies to pass through it. 7

26 With these reciprocal elements one can achieve different configurations, basically four different kinds of filters; a) Low Pass Filter (LPF): This filter allows all the frequencies below cutoff frequency fc to pass through and blocks or attenuates all other frequencies. b) High Pass Filter (HPF): This filter allows all the frequencies above cutoff frequency fc to pass through while blocking others. c) Band Stop Filter (BSF): This kind of filter is also called as notch filter. It blocks a band of frequencies which is determined by upper and lower cutoff frequencies and allows all other frequencies. Hence the name band stop filter. d) Band Pass Filter (BPF): This filter works quite opposite to BSF, allowing a band of frequencies determined by the upper and lower cutoff frequencies and rejecting all other frequencies. Figure 2-1 Basic Filter [5] The figure above shows a basic filter and its transfer function is given by: T(s) = Y(s) / X(s) 8

27 The main objective of these filters is to block or reject the noise entering into the circuitry and keeping the signals confined to determined band of frequencies. The figure below shows the ideal and practical responses of all basic kind of filters. Figure 2-2 Ideal filter responses [5] The figure 2-2 shows ideal filter responses. It is not possible in real life to achieve such an ideal filter response. A design is said to be best when its frequency response is close to ideal frequency response. Practical filter frequency response is shown in figure

28 Figure 2-3 Practical Filter Responses [6] Filters are widely used in wireless communications, satellite communications, radar systems, telecommunications and many other military and commercial applications. With all these applications filters have many stringent requirements to meet as to fulfill requirements. Frequency selectivity, size, weight, reliability and performance at various environments are some of the key factors for the filters. With the recent advancements, filters can be designed as lumped element or distributed element circuits based on the requirements. They can also be made tunable with the novel materials and fabrication technologies which adds more flexibility. These include Microelectromechanical system 10

29 (MEMS), Ferroelectrics, High-Temperature super conductors (HTS), Low- Temperature co-fired ceramics (LTCC), Liquid Crystal Polymers (LCP), Monolithic microwave integrated circuits (MMIC) and Defected Grounded Structures (DGS) etc. [8]. 2.2 Decibels (db): For those who design filters, Decibel (db) is the important parameter to know. It is used to express the power ratio in logarithmic unit. Power Ratio (db) = 10 log10 P2 P1 If P2 P2 = 1000, then P1 P1 (db)=30 db. Where P2, P1 are the powers being compared. Having decibel logarithmic, the size of the numbers are reduced greatly to express large ratios. Another advantage of decibel being logarithmic is that the ratios can be turned upside down by simply changing the sign of a ratio in db. If 1000 = 30 db then = -30 db. 11

30 CHAPTER 3 DEFECTED GROUND STRUCTURES 3.1 Introduction: Electromagnetic Band Gap (EBG) structures like photonic band gap (PBG) structures are periodic structures which have defects in the ground plane. PBG s initially were researched mostly in the optical frequencies. The concept of PBGs can be applied to wide range of frequencies. They are used in many applications like lasers, antennas and other devices. PBG s can provide band gap characteristics with periodic defects in the ground plane [9]- [13]. PBG s are difficult to use for microwave and millimeter wave components. This is mainly due to difficulties in modeling. And moreover the radiation from the periodic defects was another concern [14]. A defected ground structure (DGS) is similar to that of photonic band gap structures which have defects in the metallic ground plane. The concept of DGS is one that has attracted many researchers because of the increasing demand of the microwave and millimeter wave applications. Park et.al.[14] have proposed DGS by introducing a thin slot in between the two square shaped PBG cells. 12

31 As mentioned the DGS has a defect that is etched on the uniform ground plane which alters the uniformity of the ground plane, thus called Defected Ground Structure. This etched defect in the ground plane disturbs the shielding current distribution, which alters and rise the inductance and capacitance of the line [15]. The shielding current distribution depends on the shape and dimensions of the defect and the band gap property relies on many design parameters such as lattice shape, lattice spacing, and number of lattice [14]. First DGS was proposed in 1999, later many researchers have proposed alternate designs that has boosted the applicability s of DGS. The main advantage of DGS over PBG is the circuit area, for DGS the circuit area is relatively very small when compared to PBG as few DGS elements can achieve similar parameters as periodic PBG and can show slow-wave effect[14] - [15]. Another advantage of DGS is by cascading the unit cell we can achieve deeper and steeper stop band depending on the number of cells. The cascading can be in both horizontal and vertical direction but with the conventional planar transmission line, vertical cascading is not possible. Cascading has to be done along the transmission line direction [15]. The etched section of DGS increases the series inductance which in turn increases the reactance of the microstrip with increase in frequency. This gives a start for the rejection of certain frequency range. The attenuation pole location is provided by the series inductance in parallel with the capacitance. This acts like a parallel LC resonator. The unwanted surface waves, leakage 13

32 and spurious signals can be suppressed with stopband characteristics of DGS. The reactance of capacitance is decreased with the increase in frequency. DGS can provide sharp selectivity at cutoff frequency and excellent performance in terms of spurious signals in stop band and ripples in pass band [15].Using DGS we can suppress harmonics too. Many researchers have combined DGS with new materials to achieve special characteristics like tunability and more. In [16] a filter is designed using DGS and LTCC and moreover Substrate integrated waveguide (SIW) was adopted and combined with DGS in [17]. The LC equivalent components of DGS causes slow wave effect which is one of the most important advantages of DGS. The transmission line with DGS when compared to conventional lines has higher impedance and slow wave factor [15]. With these properties the circuit sizes can be reduced. DGS can be applied to microwave oscillators, microwave couplers (to increase the coupling), microwave filters, microwave amplifiers etc. DGS is also used in microstrip antenna design for different applications such as antenna size reduction, cross polarization reduction and harmonic suppressions. DGS is also used in beam steering of antenna performance. The impedance of a conventional microstrip line was limited to around 100 ohms ~ 130 ohms which was a serious problem. This is overcome by using DGS in the metallic ground plane, which leads to raise in the impedance of the microstrip line more than 200 ohms [15]. In [15] 1:6 unequal Wilkinson power divider was proposed which was designed using DGS. In this power divider 14

33 the microstrip line of characteristic impedance 208 ohms could be achieved by using a rectangular block defect. One can also use this advantage of high characteristic impedance in digital systems. 3.2 Different Defected Ground Structures: Dumbbell DGS: Dumbbell DGS is the first that was proposed. Dal Ahn et.al. [14] has presented a dumbbell DGS. It is composed of two a x b rectangular defected areas, and a narrow connecting slot width g etched in the metallic ground plane. This structure can provide band gap characteristics and the equivalent circuit was derived using 3-D field analysis method. The band gap effect was explained by the extracted parameters and network analysis theory. The etched defect has narrow and wide areas in the ground plane. Figure3-1 shows the 3-D view of the dumbbell defect in the backside of the metallic ground plane. From the 3-D view we can clearly see defect made in the metallic ground plane, and in figure 3-2 the top view of the dumbbell DGS is shown. 15

34 Figure D View of Dumbbell DGS Figure 3-2 Top View of Dumbbell DGS 16

35 Unlike PBG, this DGS could provide cutoff frequency and attenuation pole location with only one unit cell. There was no need of periodic array like in PBG. DGS section increases the effective permittivity of the microstrip that in turn increases the effective inductance that causes the cutoff frequency. The etched gap underneath conductor introduces capacitance. The combination of both capacitance and inductance has generated the attenuation pole-location. The figure below shows the simulated s-parameters for the dumbbell DGS. Figure 3-3 Frequency response (S21,S11) of Dumbbell DGS 17

36 Figure 3-4 Frequency response (S12, S22) of Dumbbell DGS From the above figures 3-3 and 3-4 we can see that, the structure is symmetric. S22 is similar to S11 and S21 to that of S12. The notch depth of - 28 db was achieved and the Q-factor is poor Arrowhead Dumbbell DGS: In [18] Adel B. Adbel-Rahman et.al. examined DGS geometries on the basis of performance. In this paper, it is also stated that a 3-pole low pass filter with arrowhead DGS has 67% of the length of a conventional 3-pole LPF. A good comparison between different slot heads of the dumbbell DGS is made. The arrowhead slot area can be used to control inductance whereas the thin slot that is used to connect two arrowhead slots can be used to control the capacitance. This is similar to that of the conventional dumbbell where the rectangular slot is responsible for inductance. It is also stated that the separation distance between the slots has impact on the inductance and 18

37 capacitance. The cutoff frequency fc and the attenuation pole frequency fo can be controlled by various dimensions of DGS. Figure 3-5 Arrowhead-slot Dumbbell DGS The Length of arrowhead slot has less influence on fc but the distance between the two arrowheads has good influence on capacitance. When compared to other dumbbell shaped DGS arrowhead has sharp cutoff. Figure 3-6 shows the frequency response of the arrowhead slot DGS. 19

38 Figure 3-6 Frequency response of Arrowhead slot DGS From the figure above we can see that the attenuation pole frequency for arrow head is at 3.7GHz. When compared to different dumbbell slot heads, arrowhead for the same area shows better sharpness with the cutoff and the stop band is improved as well. The shape of the slot head plays a significant role on the band stop characteristics of the filter. The slot heads are the major source of radiation when compared to other dumbbell slots arrow head slot has less radiation Circular Slot Dumbbell: In [18] Adel B. Abdel-Rahman et. al. has discussed on circular shaped slot dumbbell. For this defect the radius r of the circular slot shows strong influence on inductance than capacitance, moreover r shows control over the cutoff frequency fc than on the attenuation pole frequency fo which helps to change inductance with a small change in the attenuation pole frequency. 20

39 Figure 3-7 Circular Slot Dumbbell DGS Figure 3-7 shows the circular slot dumbbell DGS. Even for this defect structure the separation between two slots heads has the similar impact on cutoff frequency and attenuation pole frequency. In fact it has higher impact on inductance and capacitance. The more the separation between the slots, the closer the cutoff frequency and attenuation pole frequency. This improves the sharpness of the transition. All the dumbbell defects have similar kind of circuit model. Figure 3-8 shows the frequency response of the circular slot dumbbell. 21

40 Figure 3-8 Frequency response of Circular Head Slot It is not fair to compare all three head slots with this simulation result as they are not on equal scale. However, arrowhead slot has sharp frequency response than that of square head slot dumbbell and circular head slot Modified Dumbbell DGS: This defect was proposed by Amr M.E. Satwat et. al. [19] on coplanar waveguide, for convenience I have redrawn on to microstrip transmission line and simulated. This modification gives the freedom to tune the rejection frequency unlike the conventional dumbbell shaped defect. This is done using reconfiguration technique. This technique allows the control over the DGS equivalent model. The modification does not alter the symmetry, so leaving us with the same symmetric conditions of that of the conventional DGS. It is mentioned that 19% tunability of the central frequency is achieved with this modification [19]. The equivalent circuit model depends on the DGS. In this 22

41 paper the relationship between the model and the DGS symmetry is formulated. This defect is similar to that of the dumbbell, except that a strip of width t is removed around the circumference of the square keeping metal patch inside rather than removing as shown in figure 3-9. Figure 3-9 Modified Dumbbell DGS The square patch plays a key role to achieve the tunability. Any device for example a varactor, one of its terminal can be connected to the patch the other to the ground. It is easy to apply bias to the patch to control the operation. Tunability can also be achieved using thin films like BST. 23

42 Figure 3-10 Frequency response of Modified Dumbbell The figure shows the simulated s-parameters of the modified DGS. The frequency response is almost similar to that of the dumbbell DGS, but this DGS can be made tunable H-Shaped DGS: Mrinal Kanti Mandal and Subrata Sanyal have proposed a novel defected ground structure in [20]. This DGS is a compact structure and it was reported that this DGS is 26.3% compact lengthwise than other reported structures [20]. It also shows sharper transition knee. This defect has its main slot underneath the microstrip line and the ends join to H shaped slots. All these slots are etched on the metallic ground plane of the microstrip line. Figure 3-11 shows the H-Shaped DGS for microstrip transmission line. 24

43 Figure 3-11 H-Shaped DGS From the above figure, the main slot which is underneath the microstrip line contributes to the increase of the effective capacitance while the H-slots that are connected to the main slots give inductive loading. Attenuation pole and cutoff frequency can be achieved with a unit cell. This prevents periodicity that reduces the overall circuit size. A parallel resonance circuit with transmission line in series can be used to represent this defect [20]. This defect has better Q-factor and deeper rejection when compared to the conventional dumbbell DGS. The figure 3-12 shows the simulated frequency response of H-Shaped DGS. 25

44 Figure 3-12 Frequency response of H-Shape DGS The H-shape DGS has symmetric properties. All these defects discussed till now can provide a stop band characteristics but the low Q-factor is not useful for notch or band stop filter. Spiral and u-slot defects give higher Q-factor and band rejection properties than that of the conventional DGS Spiral DGS: Jong-sik Lim et.al.[21] presented a spiral defected ground structure on CPW. Microstrip form of the spiral DGS is shown in figure One of the important characteristics of spiral defect is that its shunt-inductance and slowwave effects increases rapidly [21]. This defect has more number of degrees of freedom which yields flexibility in achieving the required frequency response by varying the dimensions. 26

45 Figure 3-13 Spiral DGS In figure 3-13 the spiral DGS has a rectangular loop. It can also be circular and octagonal etc. Spiral DGS is smaller in dimension for the similar frequency response when compared to the conventional dumbbell DGS and modified DGS as this spiral defect has increased inductance and slow-wave effects. 27

46 Figure 3-14 Frequency response of Spiral DGS In figure 3-14 we can clearly see that spiral DGS gives a steep cutoff characteristics when compared to dumbbell DGS, and it has improved Q- factor when compared to conventional DGS U-Slot DGS: A novel U-slot shaped DGS bandstop filter on microstrip line has been proposed by Duk-Jae Woo et.al. [22]. This defect is proposed on the microstrip line. The Q-factor has been improved when compared to conventional DGS and with the simple shape this defect provides steeper rejection characteristics. One advantage of U-slot is that it has flat pass band i.e. the insertion loss is low. The U-slot defect is right underneath the microstrip line. This defect uses very less ground plane when compared to other DGS. In this paper another slot based defect called V-Slot is proposed. It is stated in [22] that when 3 U-slot DGS are cascaded it provided Q of 38.6, 28

47 which is pretty good Q-value but makes the overall size of the device large. It is also stated that Q-factor for a single U-slot DGS is 16.5 in [22], which is better when compared to conventional dumbbell shaped and spiral shaped DGS. The figure 3-15 shows the U-slot DGS for microstrip line. Figure 3-15 U-Slot DGS From the above figure it can be seen that two slots of length L and width g underneath the microstrip line are connected to another slot of width c making a U-shape defect. This gives 3 degrees of freedom like slot width, slot length and the distance between two slots. These can used to control the frequency response, Q-factor and reflection bandwidth. We look more on how the characteristics change with varying different parameters in the next 29

48 chapter. A comparison is made in [22] that the Q-factor of the spiral shaped DGS was about whereas the U-slot DGS has which is very high when compared. From figure 3-16 the frequency response characteristics of U-slot are shown, it can be seen from this figure that the u-slot has very steep rejection characteristics. Figure 3-16 Frequency Response of U-Slot DGS 3.3 Equivalent Circuit Models: Typically the equivalent circuit model for DGS can be of 3 types: 1) LC & RLC equivalent circuits 2) π shaped equivalent circuits 3) Quasi-static equivalent circuits 30

49 It can also be any other type of circuit depending on the defect size and shape. In [14] it has been stated that frequently in many cases DGS section can be replaced by parallel LC resonator. But in order to implement this equivalent circuit we need to extract the parameters. Figure 3-17 LC equivalent circuit model [14] From the attenuation pole location of the frequency response characteristics we can extract the parallel capacitance value of the DGS for a unit dimension, which is the resonance frequency of parallel LC. For the proposed DGS the reactance value can be given as XLC = 1 ω o C( ω o ω ω ω ) Where ωo is the resonance angular frequency and the L & C values are given as: C = ω c Z o g 1 1 ω o 2 ω c 2 L = 1 4π 2 f o 2 C 31

50 Where Zo Scaled impedance level of the in/out terminal ports. g1- prototype value of the Butterworth type low pass filter. fo attenuation pole location frequency A better circuit parameters extraction method for dumbbell shaped DGS is presented in [23]. These equations contain S11 &S21 as extraction parameters. LC equivalent circuit not always can provide exact response. In this paper LCR based equivalent circuit parameter extraction method proposed, to get a better frequency response of the DGS. Figure 3-18 RLC equivalent circuit model [23] C= ω c 2Z o (ω o 2 ω c 2 ) ; L = 1 ω o 2 C R (S11 (ω)) = 2Z o 1 S11 (ω) 2 (2 Z o(ωc 1 )) ω 2 1 L...(a) 32

51 R (S21 (ω)) = 2Z o S21 (ω) 2 1 S21 (ω) 2+ [ S21 (ω) 2 1 S21 (ω) 2] 4Z o 2 (ω 1 ω )2...(b) Where ωo angular resonance frequency ωc 3-dB cutoff angular frequency Zo - Characteristic impedance of microstrip line S11(ω) input reflection coefficient of the equivalent circuit network S21(ω) forward transmission coefficient of the equivalent circuit network. Equation (a) and (b) are dependent of frequency in other words they are a function of frequency. But we want R which is independent of frequency. Assuming the DGS as a single pole lowpass, the loss resistance is given by R11 = 2 Z o S 11 (ω o ) 1 S 11 (ω o ) ωo - Resonance frequency of DGS. R using S21 R21 = 2Zo 1 S 21 (ω o ) S 21 (ω o ) The resistance R11 is different from R21. R11 gives good match with S11 but gives rise to an error term in S21. Therefore the R is given as R = R 11+R 21 2 This gives a better accuracy. 33

52 In [24] Jia-sheng Hong et.al. presented circuit model for DGS that has multiple band gaps or stop bands in the frequency response. With the help of full-wave EM simulations the circuit parameters can be easily extracted. The circuit consists of lumped elements. This model can be used for modeling over a wide range of DGS for a wide bandwidth. This model can be stable for any planar transmission line such as microstrip transmission line and coplanar waveguide etc. Many circuit models using slot lines also been presented in [21], [22]. But for slot line the effective dielectric constant and the characteristic impedance are both frequency-dependent which requires accurate models. To overcome this a new circuit model is proposed in this paper which can be used as a more general circuit model for many DGS. The figure below shows the circuit model : Figure 3-19 Equivalent circuit model for multiple band gaps [24] Ci = 1 Z o 1 4 π f 3dB i ; Li = 1 (2πf oi ) 2 C i Cp = - 1 2πf t X 21 ; Lsi = X ii X 21 2πf t + L i ( f t f oi ) 2 1 for i= 1, 2 34

53 Where Zo - Characteristic impedance of the transmission line f01, f02 1 st and 2 nd resonating frequencies. ft Transit frequency f 3dB 1-3- db bandwidth at f01 f 3dB 2 3-dB bandwidth at f02 X11, X22, and X21 Imaginary parameters of 3 Z-parameters at ft The two LC resonators are to represent the 2 notches or stop bands. The two LC resonators are connected with a T-network. The interaction between the two LC resonators is represented by T-network. The first resonator dominates below the transit frequency ft and the second resonator dominates above the transit frequency ft. 35

54 CHAPTER 4 ANALYSIS OF BASIC DEFECTED GROUND STRUCTURES In the previous chapter basic DGS structures and their frequency responses were discussed. In this chapter the effects of the physical dimensions such as their size and shape on their frequency responses are discussed. 4.1 Dumbbell DGS: As seen in the previous chapter in figure 3-2 the dumbbell DGS has narrow and wide etched areas. These defects increase the effective inductance and capacitance of the transmission line. The rectangular patch a x b with the physical dimension of 260 x 150 mil and the gap width g of 20 mil was discussed in the previous chapter Influence of the Square Lattice: The frequency responses for different rectangular etched areas are shown in the figure 4-1. In order to investigate the influence of the rectangular lattice dimension, the rectangular etch area has been varied. It is simulated for 2 different dimensions of 260 x 150 and 300 x 170 keeping the etched gap width g under the conductor line constant. The rectangular etch increases 36

55 the series inductance to the microstrip line. The increased series inductance gives rise to lower cutoff frequencies. The attenuation pole can be explained by the parallel capacitance with the series inductance. Therefore the attenuation pole location becomes lower with increase of series inductance. Figure 4-1 Influence of rectangular lattice dimension From the figure 4-1 we can see attenuation poles in the simulation result. These occurred because of the parallel capacitance and the series inductance. In this case the capacitance was constant as the etched gap g was kept constant. As the series inductance increase the resonance frequency decreases [14]. 37

56 4.1.2 Influence of the Gap Distance: The effect of gap g on the frequency response is analyzed by keeping the rectangular area constant. In the present case we have kept the rectangular etched area at 260 x 150 mil. The gap distance g is taken as 20 mil and 30 mil. As the rectangular etched areas are constant the effective series inductance is also constant. Since the series inductance is constant, there would be no change in the cutoff frequency though the gap distance is varied. This shows the gap etched underneath the conductor line does not affect the series inductance. The change in the gap distance only affects the effective capacitance. If the gap distance is increased then the capacitance is reduced then the attenuation pole location moves upto higher frequency. The figure 4-2 shows the effects of variation in the gap distance. Figure 4-2 Influence of gap distance 38

57 4.2 U-Slot DGS: The U-Slot as discussed in the previous chapter 3-15, has two slots of width g along the transmission line in the ground plane. These two slot are connected with another slot of width c. The length of the two slots are denoted by L. And the two slots are separated by a distance d Length L: By keeping the values d = 60 mil and c = g = 15 mil, and varying the length L (330 mil and 410 mil) we observe that when the length L increases, the stopband bandwidth and the resonance frequency decreases. This is because the length of the slot increases the inductance and the capacitance. The Q is not affected by the change in the slot length. Figure 4-3 Influence of length L on frequency response of U-slot 39

58 4.2.2 Distance D: The values of L= 350 mil and g=c= 15 mil, are kept constant and the distance between two slots is varied (30 mil and 50 mil). When distance between two slots D is reduced Q-factor is increased. Decrease in D increases the capacitance. Figure 4-4 shows the variations of the distance between two slots. And if the distance is increased the Q-factor is reduced and gives less capacitance. Figure 4-4 Influence of distance D on frequency response of U-slot Width of the Slot G: To investigate the effect of the slot width G on the frequency response, the slot dimensions L=350 mil, d=40 mil, and c= 15 mil, are kept constant. The width of the G is varied (20 mil and 30 mil) and the figure 4-5 shows the frequency response for the influence of the width of the slot G. 40

59 Figure 4-5 Influence of width G on frequency response of U-slot When the slot width grows, the equivalent capacitance decreases and the equivalent inductance increases, the resonance frequency slowly decreases due to the increase in inductance. The Q-factor increases as the slot width decreases. This is because when the slot width decreases capacitance increases, this increase in capacitance causes the increase in Q- factor [22]. 41

60 CHAPTER 5 DESIGN AND ANALYSIS OF BAND STOP FILTERS USING NOVEL DGS In this section the new design simulations, measurement results and analysis of the band stop filters are discussed. As mentioned before the new band stop filter is designed using microstrip transmission lines. AWR Axiem (version 10.08r) simulation tool was used. 5.1 Design of New Dumbbell-Slot DGS: Some of the major challenges for a filter especially for a band reject filter is to achieve lower resonance frequencies in the frequency spectrum with having a deeper rejection, sharp cutoff, low insertion loss and also providing high Q-factor with small size and low cost. Many researchers have proposed many kinds of filters using different technologies, but always a tradeoff with some of the parameters. In this thesis a defected ground structure based band stop filter is proposed. Some of the defected ground structures presented in chapter 3, did not meet all the requirements. A new design to meet all the stringent requirements are presented in this chapter. To have a high Q-factor with deeper rejection for a band rejection filters is very much necessary when the desired signal is closely located to the unwanted signal in the frequency 42

61 spectrum. The characteristics of the conventional DGS like dumbbell, spiral shaped and the U-slot are not satisfactory in the application of deep narrow band rejection. U-slot can provide better Q-factor but however it cannot provide deeper rejection of signal with considerable dimensions. Cascading a unit cell can give a deeper rejection however it increases the overall size of the circuit. Cascading is not a good option when size is a factor. The only option left with the system level engineer is to try new designs. Defects can be in any shape. Different shapes causes different changes in the transmission line characteristics and yields different responses. Now the main aim is to get highest possible capacitance and inductance within the small shape and size to achieve better results. The new design has the dumbbell defect etched in the metallic ground plane with a U-slot underneath the microstrip line. Figure 5-1 shows the new Dumbbell-Slot defected ground structure. One can say this design is a better way of utilizing the ground plane for defected ground structures. This design is for the substrate thickness of 62 mil and relative permittivity of 5. The line width was chosen for the characteristic impedance of 50-Ω microstrip line. 43

62 Figure D View of new Dumbbell-Slot DGS Figure 5-2 Top View of new Dumbbell-Slot DGS 44

63 Figure 5-3 Frequency response of new Dumbbell-Slot DGS Figure 5-3 shows the frequency response of the new Dumbbell-Slot defect. The new defect gives more inductance and the capacitance for the given area. As mentioned an etched defect in the metallic ground plane disturbs the shielding current and increases the effective inductance and capacitance. The rectangular patch in the ground plane increases the length for the current which increases the effective inductance. The defect is comparable to the wavelength so there will be a potential drop, as the slot underneath accumulates charge and thus increasing the effective capacitance. The dumbbell and U-slot both are simulated with the same shapes and sizes and a comparison of new dumbbell-slot DGS with the dumbbell and U-slot defects is made later in this section. 45

64 5.1.1 Dumbbell DGS for New Dumbbell-Slot DGS: Figure 5-4 Dumbbell for new Dumbbell-Slot DGS Figure 5-5 Frequency response of Dumbbell DGS 46

65 From the figure 5-5 which shows the frequency response of the dumbbell defect, the dumbbell DGS is resonating at 3.5GHz with a notch depth of db. Figure 5-5 shows both S21 and S11 for the dumbbell DGS U-Slot for New Dumbbell-Slot DGS: Figure 5-6 U-slot for new Dumbbell-Slot DGS 47

66 Figure 5-7 Frequency response of U-slot DGS The frequency response of U-slot is shown in the figure 5-7. It is resonating at 4.1 GHz and has a notch depth of db. Though it has better Q-factor, the notch depth is the limiting factor for the U-slot. When compared to the responses of the individual cases, the new DGS has highly improved characteristics in the aspects of size, Q-factor and also has deep rejection characteristics. As mentioned before deep rejection characteristics can be achieved by periodic structures. However the full-wave EM simulations is time consuming due to the increased size. Q-factor for a parallel resonance circuit is directly proportional to C L [22]. The dumbbell rectangular etched area introduces L which leads to less Q for the new proposed DGS when compared to U-slot alone. The attenuation pole location for the new design is at 2.2 GHz whereas for the dumbbell it is at 48

67 3.5 GHz and U-slot at 4.1 GHz which is approximately 50% higher resonance frequency. This is because the new design has more inductance and capacitance. f = 1 2π lc And the Q-factor is given by Q = f c f c1 f c2 Where fc is the center frequency, fc1 is the cutoff frequency at -10dB, fc2 is the cutoff frequency at -10 db. The sharpness factor fo/fc determines the sharpness of the transition. From the frequency characteristics of the new design it is calculated that the fo/fc ratio is equal to By this it can be said that the new DGS has very sharp transition knee. Moreover the new design has low insertion loss in the pass band and deep attenuation in the stop band. 5.2 Equivalent Circuit Model for New Dumbbell-Slot DGS: The RF performance of the new proposed filter DGS can be modeled using lumped elements. In general the DGS section can be modeled by parallel LC resonator circuit for many applications. But by considering the losses into account it can be efficiently modeled by parallel RLC resonant circuit. The resistance is due to different losses like conductor, dielectric and 49

68 radiation losses. And the resistance to the ground represents the substrate losses. Figure 5-8 Equivalent circuit model for new Dumbbell-Slot DGS Figure 5-8 shows the equivalent circuit diagram. The two ports on both ends are terminated by 50 ohms. The defect is modeled as parallel RLC. The shunt resistor (resistor to the ground) represents the substrate material losses. The two resonating circuits are for the two attenuation pole locations, the first RLC circuit is for the 1 st attenuation pole located at 2.2GHz and the second RLC circuit is for the harmonic at 6.8GHz. To model additional harmonics, more RLC circuits are needed to match attenuation poles. Here the first two attenuation pole locations are matched. 50

69 Figure 5-9 Schematic model vs simulation result of new Dumbbell-Slot DGS The frequency response of the equivalent circuit is shown in figure 5-9. It can be seen that it matches very well with the simulation results. The circuit parameters were extracted using AWR tool which provides a variable tuner to fine tune the parameters. The values of the first RLC circuit is L1= 2.18nH, C1= 2.4 pf, R1 = 4200 ohms. For the second tank circuit L2 =0.289 nh, C2= 1.88 pf, R2= 670 ohm and the resistor R3= 1000 ohms gives the substrate leakage value. 51

70 Figure 5-10 Variable Tuner for new Dumbbell- Slot DGS Table 5-1 Comparison between conventional DGS and new Dumbbell-Slot for ε r of 5 DGS Resonating Depth of Q(-10dB) Frequency(GHz) Notch(dB) Dumbbell U-slot New Dumbbell Slot The Q-factor calculated depends on the center frequency, the new Dumbbell-Slot DGS has a less center frequency when compared Dumbbell and U-slot which gives a less Q-factor when compared. In actual practice the Q factor gives the sharpness of the notch, which is an important parameter for 52

71 the filters. For the new Dumbbell-Slot DGS sharpness factor is about 1.25 which is considered to be very sharp. 5.3 Design of New Spiral-Slot DGS: Spiral DGS itself has better Q than dumbbell and show good rejection band characteristics. The new concept of inserting the slot underneath the microstrip line was applied to the spiral defect and it showed convincing results. One of the major problems with the spiral defect is that it produces lot of harmonics and these harmonics are sufficiently dominant. One of our group members is working on the suppression of harmonics. Figure D View of new Spiral-Slot DGS 53

72 Figure 5-12 New Spiral-Slot DGS Figure 5-13 Frequency response of new Spiral-Slot DGS 54

73 It can be seen from figure that the harmonics are quite dominant. The new Spiral-Slot DGS provides even lower resonance frequency of 1.8 GHz with improved Q-factor than spiral and deeper rejection than spiral and U-slot. The line width was chosen to be the characteristic impedance of 50-Ω microstrip line for simulations. The spiral and U-slot are simulated and the responses are compared with new Spiral-Slot DGS with the same dimensions used in the new design Spiral DGS for New Spiral-Slot DGS: Figure 5-14 Spiral DGS for Spiral-Slot DGS 55

74 Figure 5-15 Frequency response for Spiral DGS The U-slot with the same dimensions as in figure 5-6 is used for the simulation. From the frequency responses we can see that the new spiral-slot has its resonating frequency at 1.8 GHz with attenuation pole location at db. While the spiral has its resonating frequency at 2GHz with attenuation pole location at dB. With the U-slot the new Spiral-Slot has good rejection and at lower frequencies. Clearly, the new Spiral-Slot DGS shows better response than the single Spiral or U-slot DGS. The harmonics especially the fundamental harmonic from the spiral is dominating in the Spiral DGS. This can be overcome by adjusting the dimensions, as different sizes and shapes give different frequency responses. 56

75 5.4 Equivalent Circuit Model for New Spiral-Slot DGS: The equivalent circuit for the new Spiral-Slot DGS is modeled as parallel RLC, similar to as like the new dumbbell-slot. The two ports on both ends are terminated by 50 ohms. The defect is modeled as parallel RLC. The circuit model matches very well with the simulation results. Figure 5-16 Equivalent circuit model of new Spiral-Slot DGS 57

76 Figure 5-17 Schematic model vs simulation result of new Spiral-Slot DGS From the frequency response we can see that the schematic model match well with the simulation result. Only the resonance frequency and the fundamental harmonic are matched. We can match higher order harmonics by adding more parallel RLC circuits. From the circuit it was extracted as L1= 1.74 nh, C1= 4.5 pf, R1= 4000 ohm, and for the second tank circuit L2= 0.088nH, C2= 18.9 pf, R2= 170 ohms, R3 = 1000 ohm. As mentioned the resistance R3 is to represent the substrate leakage. 58

77 Figure 5-18 Variable Tuner for new Spiral- Slot DGS Table 5-2 Comparison between conventional DGS and new Spiral-Slot for ε r of 5 DGS Resonating Depth of the Q(-10dB) frequency(ghz) notch(db) Spiral U-slot New Spiral Slot 59

78 5.5 Measured Results: New Dumbbell-Slot DGS: Figure 5-19 Measured result vs simulated result for new Dumbbell-Slot From the figure we can see that the results match pretty well, but the harmonic is slightly off by approximately 0.7 GHz in frequency. The resonant frequency for the measured result is at GHz with attenuation pole location at db while the simulated is at 2.2 GHz with attenuation pole location at db. 60

79 5.5.2 New Spiral-Slot DGS: Figure 5-20 Measured result vs simulated result for New Spiral-Slot From the frequency response clearly it can be seen that the measured results match well with the simulated results. But there is slight shift in the harmonics, in fact the fundamental harmonic is dominating and its attenuation pole location is at db. The design was designed and simulated for dielectric constant of 5 and the thickness of 62 mil. But due to the unavailability of the PCB boards of dielectric constant of 5 and 62 mil thick the devices were fabricated on TMM-10 boards that has the dielectric constant of approximately 10 and the thickness of 50 mil. Though the designs were simulated for a dielectric constant of 5 and 62 mil thick substrate, the simulation results match well with the measured 61

80 results on 50 mil thick TMM10 substrate. The results of redesigned circuits for TMM10 are presented in the next section. 5.6 Redesigned Dumbbell-Slot DGS for εr of 10: This time the new Dumbbell-Slot, Dumbbell, U-slot are redesigned for 10 dielectric and 50 mil thick. The width of the microstrip line is adjusted to get 50 ohms. Figure 5-21 New Dumbbell-Slot DGS for ε r of 10 All the sizes of the defects are readjusted to the new requirements. For dumbbell the same dimensions are used as in the previous case. 62

81 Figure 5-22 Frequency response of new Dumbbell-Slot DGS for ε r of 10 The frequency response shown in figure 5-22 has improved performance than that of the frequency response shown in the figure 5-3. The increase in the dielectric and the changes in the U-slot dimensions have increased capacitance which improved the Q-factor. The redesigned structure has low resonating frequency of 1.4 GHz with a notch depth of db. Similar to the previous case an attempt to compare the new Dumbbell-Slot with the Dumbbell and U-slot defects is made for εr of

82 5.6.1 Dumbbell DGS for New Dumbbell-Slot DGS for εr of 10: Figure 5-23 Dumbbell DGS for ε r of 10 Figure 5-24 Frequency response of Dumbbell DGS for ε r of 10 64

83 5.6.2 U-slot for New Dumbbell-Slot DGS for εr of 10: Figure 5-25 U-Slot for new Dumbbell-Slot DGS for ε r of 10 Figure 5-26 Frequency response of U-slot for New Dumbbell-Slot DGS for ε r of 10 65

84 From the responses above, the new Dumbbell-Slot DGS provides better frequency response than the Dumbbell and U-slot alone. The new Dumbbell-Slot has its resonating frequency at 1.4GHz with attenuation pole location at db. While the Dumbbell itself have resonating frequency at 2.6 GHz and the attenuation pole location at db. When it is compared to U-Slot its resonating frequency is about 2.8 GHz and attenuation pole location at db. This can be seen that the new Dumbbell-Slot DGS has improved characteristics when compared individually even for TMM10 dielectric. In the next section an equivalent circuit model for the new Dumbbell-Slot for the dielectric constant of 10 is given. 5.7 Equivalent Circuit Model for new Dumbbell-Slot DGS for εr of 10: Figure 5-27 Equivalent circuit model for new Dumbbell-Slot DGS for ε r of 10 66

85 Figure 5-28 Schematic model vs simulation result of new Dumbbell-Slot DGS for ε r of 10 The circuit model is same as the model used for εr of 5 substrate. The frequency response of the equivalent circuit is shown in figure It can be seen that it matches very well with the simulation results. The extracted values for the first RLC circuit is L= 2.58 nh, C= 5.01 pf, R= 5500 ohms. For the second tank circuit L=0.28 nh, C= 4.05 pf, R= 470 ohms and the substrate leakage resistance being R=1000 ohms. 67

86 Figure 5-29 Variable Tuner for new Dumbbell- Slot DGS Table 5-3 Comparison between conventional DGS and new Dumbbell-Slot for ε r of 10 DGS Resonating Depth of Q(-10dB) Frequency(GHz) Notch(dB) Dumbbell U-slot New Dumbbell Slot 68

87 5.8 Measured Data of New Dumbbell-Slot for εr of 10: Figure 5-30 Measured result vs simulation result for new Dumbbell-Slot DGS for ε r of 10 From the figure we can clearly see that the shift in the resonance frequency and the attenuation pole location is because of the dielectric mismatch. The simulation result has resonance at 1.4 GHz with attenuation pole location at db while the measured result has resonance at GHz with attenuation pole location of db. A shift in the resonance of harmonics is also seen. To confirm the measurement spiral-slot is also redesigned for 50 mil thick TMM10 substrate. 69

88 5.9 Redesigned Spiral-Slot DGS for εr of 10: Figure 5-31 New Spiral-Slot DGS for ε r of 10 Figure 5-32 Frequency response of new Spiral-Slot DGS for ε r of 10 70

89 is made. Similarly a comparison with the Spiral and U-slot frequency responses Spiral DGS for New Spiral-Slot DGS for εr of 10: Figure 5-33 Spiral DGS for new Spiral-Slot DGS for ε r of 10 Figure 5-34 Frequency response of Spiral DGS for ε r of 10 71

90 5.9.2 U-Slot for New Spiral-Slot DGS for εr of 10: Figure 5-35 U-slot for new Spiral-Slot DGS for ε r of 10 Figure 5-36 Frequency response of U-slot for new Spiral-Slot DGS for ε r of 10 72

91 5.10 Equivalent Circuit Model for New Spiral-Slot DGS for εr of 10: Figure 5-37 Equivalent circuit model for new Spiral-Slot DGS Figure 5-38 Schematic model vs simulation result of new Spiral-Slot DGS for ε r of 10 73

92 From the frequency response we can see that the schematic model matched well with the simulation result. Only the resonance frequency is matched and as mentioned the harmonics can be matched using more tank circuits. From the circuit it was extracted as L1= 2.4 nh, C1= 7.31 pf, R1= 5332 ohm and the substrate leakage value of R3 = 1000 ohm. Figure 5-39 Variable Tuner for New Spiral- Slot DGS Table 5-4 Comparison between conventional DGS and new Spiral-Slot for ε r of 10 DGS Resonating Depth of the Q(-10dB) frequency(ghz) notch(db) Spiral U-slot New Spiral-Slot