PEOPLE'S DEMOCRATIC REPUBLIC OF ALGERIA
MINISTRY OF HIGHER EDUCATION AND SCIENTFIC RESEARCH
Kasdi Merbah University of Ouargla
Faculty of New Technologies of Information and Communication
Department of Electronics and Communication
Year : ………..
Registration Number : …………
Thesis
Submitted for obtaining the Degree of
Magister in Electronics
Option:
Microwaves and Signal Processing
Title :
Presented and Submitted by :
LOUAZENE Hassiba
Submitted in :
08 June 2014
Front of the Board of Examiners composite of :
First & Last Name
Degree
Quality
University
Pr . BENATIA Djamel Prof Chairman Batna Dr . BOULAKROUNE M’Hamed MCA Supervisor Ouargla Dr . CHALLAL Mouloud MCA Co-Supervisor Boumerdes Pr . FORTAKI Tarek Prof Member Batna
Pr . BOUTTOUT Farid Prof Member B. Bouarréridj
Design, Development and Optimization Ultra
Wideband - Pass Filters bands for Wireless
Université Kasdi Merbah Ouargla
Faculté des Nouvelles Technologies de l'Information et de Communication
Département d’Electronique et de Communication
Année : ………
Numéro d enregistrement :……
Mémoire
Présenté en vue de l’obtention du diplôme de
Magister en Electronique
Option :
Micro-ondes et traitement du signal
Thème :
Présenté et soutenu Par :
LOUAZENE Hassiba
Soutenu le : 08 juin 2014
Devant le jury composé de :
Nom & Prénom
Grade
Qualité
Université
Pr . BENATIA Djamel
Prof
Président
Batna
Dr . BOULAKROUNE M’Hamed
MCA
Rapporteur
Ouargla
Dr . CHALLAL Mouloud
MCA
Co-Rapporteur
Boumerdes
Pr . FORTAKI Tarek
Prof
Examinateur
Batna
Pr . BOUTTOUT Farid
Prof
Examinateur
B. Bouarréridj
Conception, Développement et Optimisation de
Filtres Passe-bandes Ultra Large Bande pour les
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ACKNOWLEDGEMENT
All gratitude is due to “ALLAH” who guides me to
bring forth to light this thesis.
I would like to express my sincere gratitude to my
first supervisor Dr. BOULAKROUNE who accepted
to supervise me and for the help, guidance and
support. He provided me throughout the
accomplishment of this work. I am greatly indebted
to my second supervisor Dr. CHALLAL, for his
helpful guidance, suggestion and encouragement
throughout this work. I would like to thanks all
members of the board examines, particularly to
Prof .BENATIA DJAMEL and Prof. FARTAKI from
the university of Batna, Prof .BOUTTOUT FARID
from the university of B Bouaréridj Who have
Work.
Thanks to those who devoted me their time and
information. Everyone was very helpful and
enthusiastic for my thesis success. Moreover this
thesis would have not been finished without the
endless support and tolerance of my friends NINA
and djamila .
Last but not the least, it would be impossible for me
to work on this thesis
completely without the encouragement from my
family. Therefore I am greatly
appreciated for both physically and mentally
supports they gave me.
Louazene Hassiba
Dedication
First thing, I would like to dedicate my work to my
dear parents, who trusted in me when no one did,
who stood up with me in educational journey, from
day one, thank you for being such Loving and
caring
To all my lovely family: mohamed, noor , nassima,
To my cousins
To all my teachers and instructors
To all my friends and all my co-workers
To everybody took care of me even in hard
situations, thank you….
Résumé
Dans le but d' atteindre les caractéristiques suivantes: faible perte d' insertion bande atténuée et grande compacité dans les systèmes de communication sans fil ultra large bande une étude comparative est menée entre trois filtres passe bande ; deux avec DGS et un sans DGS .
Abstract
In this work a comparative study between three types of micro strip band pass filters was done. Two of them are designed with DGS and one without DGS. These filters are used in ultra wide band (UWB) communication systems. The aim of this investigation is to achieve the flowing characteristic : low insertion loss (IL) , compact size and deep stop-band.
Contribution
1. "Compact Ultra-Wide Band Bandpass Filter Design Employing Multiple-Mode Resonator and Defected Ground Structure ", submitted for publication in "Annales des Sciences et Technologie", university Kasdi Merbah of Ouargla .
2. "UWB Microstrip Bandpass Filter using Multiple-Mode Resonator and Rectangular-Shaped
DGS" , presented in International Congress on Telecommunication and Application’14 University of A.MIRA Bejaia, Algeria, 23-24 APRIL 2014.
3. "The Broadside-coupled Microstrip Structure using Open Loop Resonator DGS " , submitted in
the International Conference on Electrical Engineering and Control Applications (ICEECA2014) University of Constantine1, Algeria, November 18 - 20, 2014.
LIST OF CONTENTS
Introduction.……….. 1
References ……….……… 3
Chapter I : UWB Filters State of Art ……… 4
I.1 UWB thchnologies ……….……… 5
I.1.1 Defintion……… 5
I.1.2 Avantages ………. 5
I.1.3 Disavantage ……… 6
I.1.4 Applications………. 7
I.2 Overview of RF theory……… 8
I.2.1 Microstrip transmission line ………... 9
I.2.2 Analysis and synthesis formulas………... 11
I.2.3. Scattering parameters (S -parameters)……….. 13
I.3 Filter definition………... 15
I.3.1 Classification of filters……… 15
I.3.2 UWB Band-Pass filter ………. 16
I.3.2.1 Advantages ……… 18
I.3.2.2 Disavantages………. 18
I.3.2.3 Applications……… 18
I.4 Different types of UWB BPF………... 19
I.5 Conclusion……… 22
References………...……... 24
II.1 Passive filter theory ……… 26
II.1.1 Terms used in filters ………... 26
II.1.1.1 Insertion loss ……….…... 26
II.1.1.2 Pass band ………. 27
II.1.1.3 Cut-off frequency ……….…….27
II.1.1.4 Stop band ……….……… 27
II.1.2 Filter Types ……….. 27
II.1.2.1 Butterworth Filter……… 27
II.1.2.2 Chebyshev Filter………. 28
II.1.2.3 Bessel Filter………... 30
II.2 Filter design by the insertion loss method……….……… 31
II.3 Defected ground structure (DGS)………….………..……….. 32
II.3.1 DGS Characteristics……… 33
II.3.2 Various DGS shapes……… 33
II.3.3 Defected Ground Structures as Periodic Structures………. 34
II.3.4 Equivalent Circuits………...…… 35
II.4 UWB BPF structures based on DGS………..……… 41
II.4.1 Multiple-Mode Resonator (MMR) using DGS for UWB Systems(Structure 1)… 41 II.4.2 The Broadside-coupled microstrip Structure using DGS (Structure 2) …… 42
II.4.3 Microstrip Multi-mode Resonator and Two parallel-coupled lines at two ends (MMR)(structure 3)………..……… 43
Conclusion………..………...……… 44
References………. 45
Chapter III : Results and Discussion……….. 47
III.1 Design procedure …….………..……... 47
III.2.1 Structure 1 (UWB-BPF_1)………..………… 48
III.2.2 The Modified Structure 1 (UWB-BPF_2)………..…………. 49
III.2.2.1 Effect of the filter dimensions on the performances …….…. 50
III.2.2.2 Simulation of DGS ……… 54
III.2.2.3 Structure of the Modified Structure 1 without DGS……...….55
III.2.2.4 Comparison between Structure 1 and Modified Structure1………...…. 58
III.2.3 Structure 2 (UWB-BPF_3)……….……. 60
III.2.4 The Modified Structure 2 (UWB-BPF_4)………..……… 62
III.2.4.1 Effect of the filter dimensions on the performances ……….. 64
III.2.4.2 Simulation of DGS ……… 67
III.2.4.3 Structure of the Modified Structure 2 without DGS……….. 68
III.2.4.4 Comparison between Structure 2 and Modified Structure2………...……. 71
III.2.5 Structure 3 (UWB-BPF_5)……… 73
III.2.6 The Modified Structure 3 (UWB-BPF_6)……….………..……… 75
III.2.6.1 Effect of the filter dimensions on the performances …….…. 76
III.2.6.2 Simulation of DGS ……… 80
III.2.6.3 Structure of the Modified Structure 3 without DGS…….…. 81
III.2.6.4 Comparison between Structure 3 and Modified Structure 3……….. 83
III.3 Conclusion……….. 85
References…………..……… 87
Conclusion……….
88List of Figures
I.1 Spatial Capacity Comparison……….……… 6
I.2 EM Spectrum………. 8
I.3 Microstrip Transmission lines………... 10
I.4 Two port network………... 13
I.5 (a) Low-Pass Filter, (b) High-Pass Filter, (c) - Band-Pass Filter and (d) Band-Stop Filter……….. 15
I.6 Schematic of UWB band-pass filters using 3 λg/4 parallel-coupled line resonators……. 17
I.7 Schematics of UWB band-pass filters with five short-circuited stubs……… 17
I.8 The schematic of a microstrip multi-mode resonator (MMR) and two parallel-coupled lines at two ends………. 20
I.9 The schematic of a CPW MMR………. 20
I.10 The schematic of the proposed broadside-coupled microstrip-CPW structure , (a) top view, (b) bottom view……… 21
I.11 Evolution of the proposed composite BPF……… 21
II.1 Attenuation curves for Butterworth low-pass prototype……… 28
II.2 Attenuation curves for Chebyshev low-pass prototype with 0.01-dB ripple……… 29
II.3 Attenuation curves for Chebyshev low-pass prototype with 0.1-dB ripple……….. 30
II.4 Attenuation curves for Bessel low-pass prototypes………... 31
II.5 The first DGS unit: (a) Dumbbell DGS unit, (b) Simulated S-parameters for dumbbell DGS unit……… 33
II.6 Different types of DGS: (a) spiral head (b) arrow-head slot (c) “H” shape slot (d) square open-loop with a slot in middle section (e) open loop dumbbell (f) inter-digital DGS (a) A dumbbell shaped DGS etched in the ground plane of a microstrip line…… 33
II.7 (a) with periodic uniform distribution, (b) binomial distribution, (c) exponential
distribution……….. 34
II.8 Periodic DGS : HP-DGS……… 35
II.9 Periodic DGS : VP-DGS……… 35
II.10 Conventional design and analysis method of DGS………... 36
II.11 LC equivalent circuit: (a) equivalent circuit of the dumbbell DGS circuit, (b) Butterworth-type one-pole prototype LPF circuit………. 37
II.12 RLC equivalent circuit for unit DGS……… 38
II.13 π shaped equivalent circuit for unit DGS: (a) equivalent circuit, (b) π shaped circuit…. 39 II.14 New design and analysis method of DGS: (a) analysis method of DGS, (b) equivalent-circuit model of unit cell DGS……….. 40
II.15 (a) The layout of the structure 1 (b) the schematic of the top view(c) the schematic of bottom view……… 41
II.16 (a) The layout of the structure 2 (b) the schematic of the top view(c) the schematic of bottom view……… 43
II.17 The layout of the structure 3……….. 44
III.1 Magnitudes of S21 and S11 of Structure 1………. 49
III.2 (a) Layout of the Modified Structure 1 (b) Top view and, (c) Bottom view……….. 50
III.3 Magnitude of S21 of the Modified Structure 1 for different L1………. 51
III.4 Magnitude of S21 of the Modified Structure 1 for different L2……… 52
III.5 Magnitude of S21 of the Modified Structure 1 for different W1……….. 53
III.6 Magnitude of S21 of the Modified Structure 1 for different S……… 53
III.7 Layout of DGS unit for Modified Structure 1……….. 54
III.8 Magnitude of S21 and S11 of DGS of the Modified Structure 1………. 54
III.9 Layout of the Modified Structure 1 without DGS……… 55
III.10 Magnitude of S21 and S11 of the Modified Structure 1 without DGS……… 55
III.11 Magnitude of S21 and S11 of the Modified Structure 1……….. 56
III.12 Current distribution (a) at 7.35 GHz, (b) at 0.9 GHz and, (c) at 14.9 GHz……….. 57
III.13 (a) Comparison between S21 parameters from UWB BPFs ,(b) Comparison between S11 parameters from UWB BPFs……… 58
III.14 Magnitude of S21 and S11 of structure 2……… 60
III.15 (a) the layout of the Modified Structure 2 (b) the schematic of the top view(c) the schematic of bottom view……….. 61
III.16 Magnitude of S21 of the Modified Structure 2 for different L1……… 62
III.18 Magnitude of S21 of the Modified Structure 2 for different L4………. 64
III.19 Magnitude of S21 of the Modified Structure 2 for different L3……… 65
III.20 Magnitude of S21 of the Modified Structure 2 for different W3……… 66
III.21 Layout of DGS for the Modified Structure 2……… 67
III.22 Magnitude of S21 and S11 of DGS units of the Modified Structure 2……… 68
III.23 Layout of the Modified Structure 2 without DGS………. 68
III.24 Magnitude of S21 and S11 of the Modified Structure 2 without DGS………. 68
III.25 Magnitude of S21 and S11 of the Modified Structure 2……….. 70
III.26 Current distribution (a) at 6.7 GHz, (b) at 1.7 GHz and, (c) at 11.7 GHz……… 71
III.27 (a) Comparison between S21 parameters from UWB BPFs ,(b) Comparison between S11 parameters from UWB BPFs……… 72
III.28 Magnitude of S21 and S11 of structure 3………. 74
III.29 (a) the layout of the Modified Structure 3 (b) the schematic of the top view(c) the schematic of bottom view……….. 75
III.30 Magnitude of S21 of the Modified Structure 3 for different L1……… 76
III.31 Magnitude of S21 of the Modified Structure 3 for different W1………. 77
III.32 Magnitude of S21 of the Modified Structure 3 for different S………. 78
III.33 Magnitude of S21 of the Modified Structure 3 for different Lc………. 79
III.34 Layout of DGS unit for the Modified Structure 3……… 80
III.35 Magnitude of S21 and S11 of DGS units………. 80
III.36 Layout of the Modifed Structure 3 without DGS……….. 81
III.37 Magnitude of S21 and S11 of the Modified Structure 3 Without DGS……… 81
III.38 Magnitude of S21 and S11 of the Modified Structure 3………. 82
III.39 Current distribution (a) at 6.85 GHz, (b) at 0.4 GHz and, (c) at 13.1 GHz……… 83
III.40 (a) Comparison between S21 parameters from UWB BPFs ,(b) Comparison between S11 parameters from UWB BPFs……… 84
List of Tables
I.1 Radio Frequency Bands………..……... 9
I.2 Simulation results for state of the art of UWB filter………...…... 22
III.1 Dimension (in mm) for the Structure 1……….………. 48
III.2 Simulated result of the Modified Structure 1 for different values of L1……….. 51
III.3 Simulated result of the Modified Structure 1 for Different L2……….………… 52
III.4 Simulated result of the Modified Structure 1 for Different W1……….... 53
III.5 Simulated result of the Modified structure 1 for Different S……….. 54
III.6 Dimensions (in mm) for the Modified Structure 1…..………... 56
III.7 Comparison of BPFs performances……….….. 59
III.8 Dimensions (in mm ) for the Structure 2……… 59
III.9 Simulated result of the Modified Structure 2 for Different length L1……… 63
III.10 Simulated result of the Modified Structure 2 for Different length L3………...…. 64
III.11 Simulated result of the Modified Structure 2 for Different length L4……… 65
III.12 Simulated result of the Modified Structure 2 for Different gap width g………. 66
III.13 Simulated result of the Modified Structure 2 for Different width W3………. 67
III.14 Dimensions (in mm) for the Modified Structure 2….……… 70
III.15 Comparison of BPFs performances………... 73
III.16 Dimensions (in mm) for the Structure 3………...……….. 73
III.17 Simulated result of the Modified Structure 3 for Different L1……….. 77
III.18 Simulated result of The Modified Structure 3 for Different W1………... 78
III.19 Simulated result of the Modified Structure 3 for Different slot width S……….…. 79
III.20 Simulated result of the Modified Structure 3 for Different length Lc………. 80
III.21 Dimensions (in mm) for the Modified Structure 3………. 82
III.22 Comparison of BPFs performances……… 85
VIII
LIST OF ABBREVIATIONS
BPF :Band pass filter BSF: Band-Stop Filter BRF: Band Reject Filter BW: bandwidth
CPW: Coplanar waveguide CE: Consumer electronics DGS :Defected ground structure EM :Electromagnetic
FCC: Federal Communications Commission FBW: Fractional bandwidth
GPS: Global Positioning System HPF: High-Pass Filter
HP-DGS: Horizontally periodic DGS
IEEE: Institute of Electrical and Electronics Engineers IL: Insertion loss
ISM: Dispositifs industriels, scientifiques and médicaux . LPF: Low pass filter
MMR: Multiple-mode resonator P-DGS: Periodic DGS
RADAR: Radio Detection And Ranging RF: Radio frequency
RFID: Radio frequency identification RL: Return loss
VP-DGS: Vertically periodic defected ground structure. VSWR: Voltage standing wave ratio
UWB: Ultra wide band
WLAN: Wireless local area networks WPAN: Wireless Personal Access Network
IX
List of Symbols
B :Channel Banwidth (HZ)
C : Maximum channel capacity(bits/sec) S : Signal power(watts) N : Noise power(watts) Lc : Coupling length F : Frequency ω : Angular frequency fo : Central frequency fc : Cutoff frequency L: Inductance C: Capacitance R :Resistance
ԑr.: Relative dielectric constant of the material
ԑe : Effective dielectric constant
h : Substrate height
tan (δ) : Loss tangent of the substrate Zo : Characteristic impedance
λo : Wave length in free space
λg : Wavelength in the guided medium E : Electric field
H : Magnetic field
µ : Permeability of the medium c : Velocity of light in free space P : Polarisation
n : Medium refractive index k : Wave number
Introduction
Ultra Wideband (UWB) is defined in terms of a transmission from an antenna for which the emitted signal bandwidth exceeds the smaller of 500 MHz or 20% of the center frequency. UWB communications transmit in a way that does not interfere principally with other more traditional ''narrow band'' and continuous carrier wave uses in the same frequency band [1]. In an UWB wireless communication system, the UWB filter plays an important role in ensuring the radiation of the system. A lot of researchers have been engaged in developing the components in UWB wireless system to use the unlicensed band of 3.1~10.6 GHz [2]. Various structures of band pass filters (BPFs) with specified passbands are therefore required to progress in UWB technology. Such structures may include Defected Ground Structure (DGS). Defected ground structures improve different characteristics of many microwave devices [3]. They have great important on bandgap effect, slow wave effect and high characteristic impedance, hence they provide high performance, compact size and low cost for the precise requirements of modern microwave communication systems. Extensive works have been carried out to achieve UWB characteristics in the filter performance [4].
This work reports the study and design of three types of microstrip BPFs, two filter based on DGS and one filter without DGS technique for UWB applications whith Compact BPF using Defected Ground Structure for UWB Systems, Compact UWB BPF Using Microstrip-open loop DGS Simplified Structure and UWB BPF Using Multiple-Mode Resonator. Filters characteristics along with a comparative study of different types of BPFs are presented.
overview of filter , UWB BPF and different type of UWB BPF
Chapter 2 investigates Passive filter theory and the DGS technique and three types of microstrip UWB BPFs, two based on DGS are presented. One of the UWB BPF structure without DGS is also presented in this chapter.
Chapter 3 presents the results and discussion of the studied UWB BPFs.
References
[1] Xuemin, (Sherman)Shen,Mohsen Guizani,Robert Caiming Qiu,Tho Le-Ngoc," ULTRA-WIDEBAND WIRELESS COMMUNICATIONS AND NETWORKS", 2006 John Wiley & Sons.PP
[2] Federal Communications Commission, “Revision of part 15 of the commission’s rules regarding ultra-wideband transmission systems,” Tech.Rep., ET-Docket 98–153, FCC02–48, Apr. 2002.PP
[3] Shao Ying HUANG, Yee Hui LEE" Development of Ultra-wideband (UWB) Filters",.
[4] L. H. Weng, Y. C. Guo, X. W. Shi, and X. Q. Chen ,"AN OVERVIEW ON DEFECTED GROUND STRUCTURE", Progress In Electromagnetics Research B, Vol. 7, PP,173–189, 2008.
State of the Art
I.1 UWB technologies ……….……….... 5
I.2 Overview of RF theory………...…….. 8
I.3 Filter definition………..……… 15
I.4 Different type of UWB BPF ………..………...… 19
Chapter I
State of the Art
Ultra-Wideband (UWB) technology has received great interest due to its important roles in recent communication and sensor applications. The systems designed for UWB communications transmit data over a wide spectrum of frequency bands with very low power at very high rates[1]. Ever since the release of unlicensed basis on UWB devices (range of 3.1–10.6GHz), several works have been carried out to ensure the technology performance. A band-pass filter is a key component in development of UWB systems. The former filter is designed in such a way that signal bandwidth (BW) is 500MHz or a fractional bandwidth (FBW) larger than 20 percent at all times of transmission[2]. Designing UWB BPF is mostly based in improving filter performance and overcoming some narrowband shortcomings. Various methods and structures are being used to develop these UWB filters. Depending on the additional technologies, there are several ways of designing UWB filters. Some of the designs may include standard lumped element (L-C) filter, combination of low-pass and high-low-pass filters, hybrid microstrip-defected ground structure, hairpin-comb filter, notched band filter and so on.
Once a filter is designed, there are some associating factors to be counted for the improvement of the filter performance. UWB filters have several applications in different communication systems. In RF/Microwave, scattering parameters are among the important factors for understanding some signals characteristics.
This chapter presents a brief description of UWB technologies, an overview of RF theory and UWB band pass filters descriptions.
I.1
UWB technologies
I.1.1 Definition
On February 14, 2002 the FCC released a report that officially allocated spectral space for UWB technology. This allocation was strictly to define and restrict the radio frequency (RF) emissions of this technology and bandwidth to allow coexistence. The minimum bandwidth of UWB as defined by the FCC must follow one of the two constraints listed below [3].
The minimum bandwidth must occupy more than 20% of the center frequency. The minimum bandwidth must exceed 500 MHz.
The total bandwidth that could be occupied as defined by the FCC is from 3.1 GHz to 10.6 GHz. This covers a total span of 7.5 GHz. The power regulations for this technology were also strictly defined to allow coexistence. The max power emitted must be under ‐41.3 dBm/MHz. This is equivalent to 0.5 mW of average continuous power transmission across the full 7.5 GHz bandwidth (3.1‐10.6 GHz) [4].
I.1.2 Advantages
The main advantage that UWB has over other current wireless technology (Wi-Fi, Bluetooth) is bandwidth. Shannon’s channel capacity equation shown in Equation( I.1) below describes the absolute maximum data rate a channel can transmit [5]. The equation shows that capacity “C” increases linearly with bandwidth, “B”, while it increases only logarithmically with the signal to noise ratio “S/N”. Thus, it is easier to send data faster in a communication system (increase its capacity) by increasing the bandwidth rather than the transmitted signal power.
= B. log 1 + (I. 1)
where:
C = Maximum channel capacity (bits/sec) B = Channel Bandwidth (HZ)
S = Signal power (watts) N = Noise power (watts)
UWB has a total bandwidth of 7.5 GHz which is unique. This provides the capability for expansion in the number of devices used simultaneously, that other wireless communication standards do not have. UWB is projected at having upwards of 6 devices working simultaneously at 480 Mb/s within a range of 10 m, which is unheard of in today’s wireless
communications [6]. UWB has the potential to revolutionize the consumer electronics industry. When looking at the spatial capacity measurements of different wireless standards, this puts UWB way out front. Spatial capacity in this case is measured in terms of bits/sec/square‐meter.
Figure.I.1 shows the special capacity comparison between Bluetooth v1.2 and 802.11
wireless standards [6].
However, with every advantage there are disadvantages and challenges. UWB as a technology still has some hurdles to overcome before it is fully realized for production [7].
Figure. I. 1 : Spatial Capacity Comparison
I.1.3 Disadvantages
a) Potential interference to and from existing systems
FCC has defined as power masks (emission masks) to give extra protection from a UWB device at frequencies containing the existing 2.4 GHz ISM band that is used by current wireless local area networks such as IEEE 802.11 and wireless personal area networks like Bluetooth. Most of the time, the resulting UWB signal is below the noise floor of many receivers, due to the wide distribution of signal energy in bandwidth.
The amount of interference at an UWB receiver due to a narrow band transmitter depends on the antennas used and their orientation. Use of direct sequence or time hopping spread spectrum modulation makes it possible to mask out a powerful narrowband interfere without significantly impacting the UWB receiver’s ability to process the desired signal [8].
b) Not supporting super resolution beam forming
A beam is formed by phasing different antennas so that the combined signal’s carrier is coherent when sent to or received from, a particular direction. The theory of beam forming and super-resolution beam forming is based on phase relationships among sinusoidal waveforms and does not apply directly to pulse based UWB systems.
c) Complex signal processing required
For narrowband systems that use carrier frequency, Frequency-division multiplexing is very straight forward and the development of a narrowband device need only consider the band of frequencies directly affecting itself and minimizing interference to out-of-band systems by emission control techniques like filtering and wave shaping. For carrierless transmission and reception, every narrowband signal in the vicinity is a potential interferer and also every other carrierless system. So any carrierless system has to rely on relatively complex and sophisticated signal processing techniques to recover data from the noisy environment.
d) Produces a large number of multipath components
A large number of multi-paths exist because of the reflective environment, and they are observable in case of a UWB signal because of the picoseconds precision of the UWB signal, the multi-paths do not overlap in time and therefore, do not interfere or cancel out.
e) Pulse coding of signals require relatively long synchronization times
Since picoseconds precision pulses are used in UWB, the time for a transmitter and receiver to achieve bit synchronization can be as high as a few milliseconds. Hence the channel acquisition time is very high which can significantly affect performance especially for intermittent communications [8].
I.1.4 Applications
The motivation for discussing UWB technology comes from its applications and the advantages it offers over other narrowband technologies. Some of the current and future applications of UWB technology are [8] [9][10]:
a) In Wireless Communication Systems:
2. Roadside information stations that can be deployed where the messages may contain weather reports, road conditions, construction information and emergency assistance communication.
3. Automotive in-car services like real time video for directions and passenger entertainment, or download driving directions from PDA for use by onboard navigation system
4. Short range voice, data and video applications
5. Military communications on board helicopters and aircrafts which would otherwise have too many interfering multipath components.
b) In Radars
6. Ground penetrating radar
7. Vehicular Radars used for collision avoidance/detection and sensing road conditions 8. Through wall imaging used for rescue, security and medical applications
9. Identification tags 10. Radar security fence
c) In Precision Location Tracking
11. In container inventory systems : RFID 12. GPS.
13. Localization in search and rescue efforts [10]
I.2 Overview of RF theory
Input current to an antenna results to an electromagnetic (EM) field suitable for wireless broadcasting and communication systems. The generated fields occupy certain ranges of frequencies and therefore their corresponding names.
Radio frequency (RF) field ranges from 3 kHz to about 300GHz. There are some other waves corresponding to their frequency ranges below and above RF range. Figure.I.2 shows a complete EM spectrum.
Sound RF light Harmful radiation
3kHz 300GHz
RF field provides various applications in communication systems. Cordless and cellular telephone, radio and television broadcast stations, satellite communications systems, and two-way radio services all operate in the RF spectrum. RF spectrum is subdivided into different ranges or bands, each band represent an increase of frequency of magnitude 10 times higher than the one below it. The RF bands are shown in Table.I.1.
Description Abbreviation Frequency
Very low Frequency VLF 3 to 30 KHz
Low Frequency LF 30 to 300 KHz
Medium Frequency MF 300 to 3000KHz
High Frequency HF 3 to 30 MHz
Very high Frequency VHF 30 to 300 MHz
Ultra-high Frequency UHF 300 to 300MHz
Super high Frequency SHF 3 to 30 GHz
Extremely high Frequency EHF 30 to 300 GHz
Table I.1: Radio Frequency Bands [11]
The SHF and EHF bands are often referred to as the microwave spectrum. From the RF bands, UWB systems (3.1–10.6GHz) lie in SHF. There are several ways of transmitting RF signals. These ways somewhat depend on which band the signals are situated. In microwave frequency spectrum, signal can be transmitted using microstrip line and other ways.
I.2.1 Microstrip transmission line
Microstrip transmission line is the most popular and used planar transmission line in Radio frequency RF applications, exploited for designing certain components like filter, coupler and transformer. The wave type propagating in this transmission line is a quasi-TEM wave. The microstrip transmission line consists of metallic strip of width W and the thickness t, metallic
ground and between us dielectrics substrate constant of thickness
ɦ
as shown in the Figure. I.3.The characteristic impedance of the line is determined by width W, thickness t and dielectrics substrate constant .
Figure.I.3: microstrip transmission lines.
Microstrip lines can be used in the manufacturing of some microwave components; therefore UWB filters can be made from them. Due to some suitable features, microsrtip line is widely used (regardless of low power handling capacity) in the transmission of microwave frequency signals. The features may include:
• Its simple geometry.
• Small size and low cost.
• Absence of difficulties in devices integration and mass production.
• Good repeatability and reproducibility.
The use of the normal conductors may result to microstrip losses. In designing microstrip lines, some parameters have to be well defined. Due to field lines between the conducting strip and the ground plane being not restrained entirely in the substrate, the propagating mode along the strip is not purely transverse EM (TEM) but quasi-TEM. In analyzing microstrip lines, characteristic impedance (Zo) of the line is an important factor.
effective relative dielectric constant (εeff). Latter parameter defines the intermediate relation
of dielectric constant of the medium and that of air (εo).
I.2.2. Analysis and synthesis formulas
Different equations have been established in determining characteristic impedance (Zo) of
the line. The following are the important parameters for microstrip designs with 1% accuracy [12]. + = h W W h Z eff o 4 8 ln 60
ε
Ω (I.2) where: − + + − + + = − 2 2 1 1 04 . 0 12 1 2 1 2 1 h W W h r r effε
ε
ε
for ≤1 h W or + + + = 444 . 1 ln 667 . 0 393 . 1 120 h W h W Z eff oε
π
Ω (I.3) where: 2 1 12 1 2 1 2 1 − + − + + = W h r r effε
ε
ε
for ≥1 h WSince the values of Zo depend on
h W
, synthesis formulas are given out depending on
characteristic impedance (Zo) with its associating conditions [12]:
1 exp 4 1 8 exp − ′ − ′ = H H h W (I.4) where:
(
)
+ + − + + = ′ π ε π ε ε ε 4 ln 1 2 ln 1 1 2 1 9 . 119 1 2 Z H r r r r o (I.5) Again if (Zo >[
63−2εr]
Ω) then 2 4 ln 1 2 ln 1 1 2 1 1 2 1 − + + − ′ − + =π
ε
π
ε
ε
ε
ε
r r r r eff H (I.6)where H′is given in equation (1.4)
Also when Zo <
(
44−2εr)
i.e. for wide strips, then(
) (
)
[
]
(
)
− + − − + − − − = r r r d d d h Wε
πε
ε
π
ε ε ε 517 . 0 293 . 0 1 ln 1 1 2 ln 1 2 (I.7) where: r o Z dε
π
ε 2 95 . 59 = 555 . 0 10 1 2 1 2 1 − + − + + = W h r r eff ε ε ε (I.8) when Z is firstly known; o
(
0.109 0.004) (
[
log10)
1]
96 . 0 + − + − = o r r r eff Z ε ε ε ε (I.9) From the above equations, the characteristic impedance (Zo) of a microstrip depends onwidth (W), thickness (h) and effective relative dielectric constant (εeff).In the above
every moment in designing a microstrip with new characteristic impedance (Zo), the change
in phase velocity or wavelength of wave has to be counted. Note that this is not a case in coaxial cable or stripline designs.
I.2.3 Scattering parameters (S-parameters)
In the field of RF and microwave engineering, the S–parameters are commonly used for characterizing networks. S-parameters are such like other parameters (Y, Z, H and T parameters) except that they are commonly used in higher frequency designs. In higher frequency, some setbacks arise resulting to other parameters (Y, H, Z and T) difficult to be treated. Such problems may include:
• Lack of equipment to read total voltages and currents at all ports.
• Short and open circuits are difficult to achieve.
In S-parameters treatment, matched loads are used. S-parameters of a network are all about power and provide a visual physical interpretation of the transmission and reflection performance of the device. Those parameters provide a matrix which describes the features of complex network as a simple one. The matrix elements depend on a network ports. Consider a two ports network:
Port 1 Port 2
a1 a2
b1 b2
Figure.I.4: Two port network [12]
a1 and a2 as incident waves and b1 and b2 as reflected waves, the waves equations of the
network is given below [12]:
= + (I.10) = + (I. 11)
Two port network
In matrix form:
=
1 2 12 22 11 21 1 2 a a s s s s b bThe matrix elements S11, S12, S21, and S22 are the scattering parameters or the
S-parameters. Assuming that each port is terminated by characteristic impedance (Z0); then
Forward Reflection Coefficient;
1 1 11 a b s = 0 2= a
Forward Transmission Coefficient;
2 1 12 a b s = 0 1= a
Reverse Transmission Coefficient;
1 2 21 a b s = 0 2= a
Reverse Reflection Coefficient;
2 2 22 a b s = 0 1= a
S-matrix is given by:
=
12 22 11 21 s s s ss
(I.12)N-port network contains a N2 coefficients (scattering parameters), each one representing a possible input-output path.
Scattering parameters in RF and microwave field can represent various network features such as gain, return loss (RL), voltage standing wave ratio (VSWR), insertion loss (IL), stability and so on. The S-parameters are vector quantities but usually their magnitudes are useful in communication systems. From S-parameters, some RF/Microwave field features are given below.
IL
( )
dB = −20log10 s21 (I.13) RL( )
dB =−20log10s11 (I.14)I.3 Filter definition
The filters are important components in the Transmitter/Receiver system. Frequency-selective or filter circuits pass to the output only those input signals that are in a desired range of frequencies (called pass band). The amplitude of signals outside this range of frequencies (called stop band) is reduced (ideally reduced to zero).
I.3.1 Classification of filters
There are four main classes of filters:
1. Low-Pass Filter (LPF): a low-pass filter passes low frequency signals, and rejects
signals at frequencies above the filter's cutoff frequency ( C).
2. High-Pass Filter (HPF): The opposite of the low-pass is the high-pass filter, which
rejects signals below its cutoff frequency ( C).
3. Band-Pass Filter (BPF): a band pass filter allows signals with a range of
frequencies( , ). (pass band) to pass through and attenuates signals with frequencies outside this range.
4. Band-Stop Filter (BSF) or Band Reject Filter (BRF): a filter with effectively the
opposite function of the band-pass is the band-reject or notch filter .
Figure. I.5 : (a) Low-Pass Filter, (b) High-Pass Filter, (c) Pass Filter and, (d)
In this report, we will focus in the UWB band pass filters.
I.3.2 UWB Band-Pass Filter
After the release of UWB, band-pass filters with a pass band of the same frequency range (3.1 GHz - 10.6 GHz, a fractional bandwidth of 110 %) were challenges for conventional filters design.
Before mid 2003, the bandwidth of the pass band for band-pass filters was extended from 40% to 70% . These filters are named broad band-pass filters. They were not covering the whole UWB frequency range yet. In [3:13], a band-pass filter covering the whole UWB frequency range with a fractional bandwidth of 110% was realized by fabrication signal lines on a lossy composite substrate. A successful transmission of the UWB pulse signal was demonstrated using the proposed band-pass filter. This is one of the early reported filters that possess an ultra-wide pass band. However, it has a high insertion loss in the pass band due to the lossy substrate.
In 2004, a ring resonator with a stub was proposed which shows a bandwidth of 86.6% . A band-pass filter covering the whole UWB frequency band was a challenge for microwave filter designers and researchers in that period of time.
In 2005 , There are mainly four types of structures that are able to realize an ultra-wide passband.
In 2006 , microstrip multiple-mode resonator (MMR) based on UWB band-pass filters are proposed with improvement in the rejection of the upper stop-band. It has been done by introducing interdigital microstrip coupled lines at the two sides of the MMR. A high-pass filter consisting of a transmission line with two embedded U-shaped slots is cascaded with a low-pass filter which is a dumbbell-shaped defected ground structure array in the ground plane, to obtain a pass band from 3 GHz to 10.9 GHz . With novel high-pass and low-pass structures, the band-pass filter obtains a wider bandwidth than the filter taking a similar approach in 2005. With regards to the UWB band-pass filters design by cascading a high-pass and a low-pass filter, a systematic consistent and analytical method was proposed. There are a good number of new structures proposed that exhibit an ultra-wide pass band.
Figure.I.6: UWB band-pass filter schematic using 3 λ ⁄ parallel-coupled line resonators [13]. 4
In [13:13] , 3 λ ⁄ parallel-coupled line resonators shown in Figure.I.6 are used to realize a 4 pass band from 3 GHz to 10 GHz. With the introduction of lumped components to a microstrip line, a miniaturized UWB BPF with a length of 0.18λg was realized at a fractional bandwidth of 127% at a center frequency of 6.5 GHz . The small physical size is attributed to the lumped components used. A broadside coupled line in suspended substrate stripline can also be used to realize an UWB band-pass filter. A filter with short-circuited stubs could give rise to a UWB band-pass filter.
Figure.I.7: Schematics of UWB band-pass filters with five short-circuited stubs [13].
Figure.I.7 shows a filter with five short-circuited stubs arranged to realize a bandpass filters
with a bandwidth of 110% .
In 2007 , UWB band-pass filters with a notch stop-band from 5 GHz to 6 GHz for filtering the wireless local-area network (WLAN) is a new topic branched out in this area. Additional components are introduced providing the notch stop-band at the desired frequency. In [17:13], an embedded open-circuit stub was proposed providing a sharp notch stop-band. It
is integrated into a UWB band-pass filter providing the stop-band from 5 GHz to 6 GHz. A stub is introduced in the broadside-coupled microstrip-CPW structure to generate a notch stop-band at WLAN frequency range.
I.3.2.1 Advantages
UWB band-pass filters have been considered and developed to make up a UWB pass band with 110 % fractional bandwidth at 6.85 GHz. Recently the UWB has been developed and applied widely. There are several advantages for UWB radio system, such as transmitting higher data rates, needing lower transmit power, and simplifying the error control coding. In such a system, an UWB filter is one of the key components, which should exhibit a wide bandwidth with low insertion loss over the whole band. In order to meet the FCC limit, good selectivity at both lower and higher frequency ends and flat group-delay response over the whole band are required [13].
I.3.2.2
Disadvantages
Band-pass filters with a pass band of the same frequency range (3.1 GHz - 10.6 GHz, a fractional bandwidth of 110%) were challenges for conventional filters design.
Lumped-element filter design is generally unpopular due to the difficulty of its use at microwave frequencies along with the limitations of lumped-element values. Hence, conventional microstrip filters being a popular choice [13].
I.3.2.3
Applicationsa) WPAN (Wireless Personal Access Network)
– Desktop and Laptop PCs
– Printers, scanners, storage devices, etc
– Connectivity to mobile and consumer electronics (CE )devices – MP3, games, video
– Cameras, DVD, PVR, HDTV
b) Personal connectivity
– Positioning, geo-location ,localization, high multipath environments,obscured environments
– Communications :high multipath environments ,short range high data rate low probability of intercept/ interference
– Radar/ Sensor : MIR (motion detector, range-finder, etc.), Military and Commercial [10].
I.4
Different types of UWB BPF
The filter operating bandwidth lies on a UWB frequency range (3.1–10.6GHz). UWB signals must have bandwidths of greater than 500 MHz or a fractional bandwidth larger than 20 percent at all times of transmission. Fractional bandwidth is a factor used to classify signals as narrowband, wideband, or ultra-wideband and is defined by the ratio of bandwidth at -10 dB points to center frequency shows this relationship[14].
= ×100oo c f BW FBW (I.15) where BW = fh − fl and 2 l h c f f f = +
With f and h f as the highest and lowest cutoff frequencies (at the -10 dB point) of a l
UWB pulse spectrum, respectively.
Here is the classification of signals based on their fractional bandwidth [14]:
FBW < 1% Narrowband
1% < FBW < 20% Wideband
FBW > 20% Ultra-wideband
There are mainly four types of structures that are able to realize an ultra-wide pass band. They are described briefly as follows:
1. Microstrip multi-mode resonator and two parallel-coupled lines at two ends as shown in Figure.I.8 . It consists of a microstrip multi-mode resonator (MMR) and a parallel-coupled line at each end of the network. The MMR has two identical high-impedance sections with a length of quarter guided wavelength at two sides and a low-impedance section with a length of half guided wavelength in the middle. The MMR in the filter generates first and third resonant mode at the edges of the UWB pass band. The parallel-coupled lines are modified to obtain the ultra-wide pass band. This could be done by adjusting the coupling length, Lc .
Figure. I.8: The schematic of a microstrip multi-mode resonator (MMR) and two
parallel-coupled lines at two ends [5:13].
2. CPW MMR as shown in Figure.I.9 This type of structure consists of a CPW MMR on one side and a microstrip input and output on the other side . The CPW MMR is responsible for generating the first and third resonant mode for the UWB pass band, which is similar to a microstrip MMR in [5:13]. Its geometry can be varied.
Figure.I.9: The schematic of a CPW MMR in [6:13].
3. The third type of filter which is also able to have a fractional bandwidth of 110% is the coupled microstrip-CPW structure as shown in Figure.I.10. There is a broadside-coupled microstrip line on one side of the substrate (see Figure. I. 10 (a)) and an open-end CPW on the other side of the substrate (see Figure.I.10 (b)). The length of the coupled line equals to λg/2 in order to obtain a 110% bandwidth.
Figure.I.10: The schematic of the proposed broadside-coupled microstrip-CPW structure in
[7:13], (a) top view, (b) bottom view.
4. The last type of filter that has a bandwidth as high as around 100% is the combination of a high-pass filter and a pass filter is shown in Figure.I.11. A stepped-impedance low-pass filter is embedded into a high-low-pass filter with quarter-wavelength short-circuited stubs, achieving a pass-band from 3 GHz to 10 GHz. Figure.I.11 shows the configurations of a directly cascaded BPF and the proposed composite BPF. Obviously, the latter uses an area much less than the former. Both BPFs consist of a hi-Z, low-Z LPF and an HPF structure designed with shunt quarterwave short-circuited stubs separated with λ ⁄4 sections, acting as impedance inverters. The variable λ is the guided wavelength at a proper frequency # which
will be addressed shortly[15].
The performances of the reported design are summarized in Table.I.2. Ref Substrate paramet ers Center frequency (GHz) Dimension (mm²) Insertion loss (dB) Return loss (dB) Bandwidth (GHz) [16] ε% =9.9 h=0.5mm 6.45 15x12 < 2 <10 7.5 [17] ε% =10.8 h=1.27m m 6.85 16x1.08 <2 <10 7.5 [18] ε% =4.4 h=1.6mm 7.9 26.2x 2.7 0.46 <10 9 [12] ε% = 9.6 h=0.8mm 5.76 5.4x 0.2 < 1.6 < 13 9
Table.I.2: Simulation results for state of the art of UWB filter.
W and L are respectively the width and the length of the filter, whereas h is a thickness and
ε% is a dielectric constant.
I.5 Conclusion
In this chapter, an UWB technology and an overview of RF theory have been discussed. UWB promises high data rate at the unlicensed band, which will make more multimedia applications possible. UWB also provides an inherent security because of its low power. Different UWB-BPFs types have been briefly presented in this chapter. It has shown that in Table.I.2 . The filter in [16] has high insertion loss with moderate bandwidth and center frequency compared to the other studied filters. Also this type of filter occupies a little bit much area and less return loss with respect to the other studied filters. The filter in
[17] has moderate center frequency and bandwidth with high losses (insertion and return loss) comparing to other studied filters. Also filter in [17] occupies average area compared to the rest of the studied filters.
The filter in [18] has less return loss and occupies a much area this filter has high center frequency and bandwidth. In [12] filter has a wider passband with high return loss. Also the studied filter has less center frequency and occupies little area compared to the rest.
References
[1] Xuemin, (Sherman)Shen,Mohsen Guizani,Robert Caiming Qiu,Tho Le-Ngoc,," ULTRA-WIDEBAND WIRELESS COMMUNICATIONS AND NETWORKS", 2006 John Wiley & Sons.
[2] Shao Ying HUANG, Yee Hui LEE" Development of Ultra-wideband (UWB) Filters",.
[3] Aiello, Robert, and Anuj Batra. Ultra Wideband Systems: Technologies and Applications.Burlington, MA: Elsevier Inc, 2006.
[4] Green, Evan R., and Sumit Roy. System Architectures for High‐Rate Ultra‐Wideband
Communication Systems: a Review of Recent Developments. Intel Corporation. Hillsbro, OR: Intel Labs, 2004. 06 Feb. 2007 http://www.intel.com/technology/comms/uwb/download/W241_Paper.pdf>.
[5] Kerry Lacanette, , "A Basic Introduction to Filters Active, Passive,and Switched-Capacitor ",National Semiconductor Application Note 779, April 1991 .
[6] Foerster, Jeff, Evan Green, Srinivasa Somayazulu, and David Leeper. Ultra‐Wideband
Technology for Short‐ or Medium‐Range Wireless Communications. Intel Architecture Labs. Intel Corporation, 2001. 2 Feb. 2007
[7] Jarrod Cook,Nathan Gove," UltraWideband Research and Implementation" ,Senior Capstone Project 2007
[8] Ashima Gupta and Prasant Mohapatra, "A Survey on Ultra Wide Band Medium Access Control Schemes",aricle, A Survey on UWB Medium Access Control Schemes.
[9] J. Reed, R. M. Buerhrer and D. Mckinstry. Introduction to UWB: Impulse Radio for Radar and Wireless Communications. GM Briefing, August 2002.
[10] Young Man Kim,"Ultra Wide Band (UWB) Technology and Applications". Nest Group , The Ohio State University July 2003
[11] James D. Taylor, “Ultra-wideband radar overview”.
[12] Kai Chang," RF and Microwave Wireless Systems", John Wiley &Sons, Inc .New York, 2000.
[13] Shao Ying Huang, Yee Hui Lee," Development of Ultra-wideband (UWB) Filters",Nanyang Technological University, S2-B4c-17, Communication Research Laboratory, 50 Nanyang Drive, Nanyang,Technological University, Singapore 639798, shaoyingh@pmail .ntu.edu.sg
[14] Kihc, Özgehan, “Defected Ground Structure And its Applications To Microwave Devices And Antenna Feed Networks,” M.Sc. Department of Electrical and Electronics Engineering , Sept 2010
[15] Ching-Luh Hsu1, Fu-Chieh Hsu and Jen-Tsai Kuo," Microstrip Bandpass Filters for Ultra-Wideband (UWB) Wireless Communications", IEEE, 2005.
[16] S. X. Han, W. Tang, G. Y. Fu," A Compact Planar Ultra-wideband Bandpass Filter using Cross-coupling SIR and Defected Ground Structure",RIEST, University of Electronic Science and Technology of China, Chengdu, mail_sxhan@163.com,611731, China
[17] Lei Zhu, Sheng Sun, and Wolfgang Menzel," Ultra-Wideband (UWB) Bandpass Filters Using Multiple-Mode Resonator", IEEE,Microwave and Wirelless components letrrers, , VOL. 15, NO. 11, Nov 2005.
[18] Neelamegam , Nakkeeran , Thirumalaivasan," Development of Compact Bandpass Filter using Defected Ground Structure for UWB Systems",International journal of Microwaves Applicationes ,Vol 2, No.1, January – February 2013.
UWB Band-pass Filters
II.1 Passive filter theory ………..……….... 26 II.2 Filter design by the insertion loss method ……….…...…….. 31 II.3 Defected ground structure (DGS)……… 32 II.4 UWB BPF structures based on DGS ………..…..………...… 41 II.5 Conclusion……….. 44
Chapter II
UWB Band-pass Filters
With the enlarging application of filters in wireless communication, different techniques have been used to develop these UWB filters. Lumped-element filter design is generally unpopular because of the difficulty of its use at microwave frequencies along with the limitations of lumped-element values. Designers needed a new method and structure to make low insertion loss and good agreement between simulated and experimental results. Introducing Defected ground structure (DGS) technique is one of the key to achieve the best performances [1] -[2].
In this chapter, a passive filter theory, an overview on DGS and UWB BPF structures based on DGS are presented.
II.1
Passive filter theory
II.1.1
Terms used in filters
II.1.1.1 Insertion loss
ideally, a perfect filter would introduce no power loss in the passband. It would have zero insertion loss. But in reality we have to expect a certain amount of power loss associated with the filter. The insertion loss quantifies how much below the 0dB line the power amplitude response drops [3].
Being P the input power from the source, P the power delivered to the load and Γ the reflection coefficient looking into the filter.
II.1.1.2 Pass band
Pass band is the band of frequencies that is allowed to pass through a filter. Pass band is equal to the frequency range for which the filter insertion loss is less than a specified value.
II.1.1.3 Cut-off frequency
Cut-off frequencyis the frequency at which the filter insertion loss is equal to 3 dB.
II.1.1.4 Stop band
Stop band is equal to the frequency range at which the filter insertion loss is greater than a specified value.
II.1.2
Filter Types
Three basic filter types such as Butterworth, Chebyshev, and Bessel are considered here in this section. Depending on the filter specification, one filter type may be preferred to the others one.
II.1.2.1
Butterworth Filter
Butterworth filters are most frequently used to obtain a filter response without ripple, flat pass band, and reasonable attenuation slope. The attenuation of a Butterworth filter is given by
A = 10log 1 + ω ! II. 2
where ω is the cut-off frequency and n is the order of the filter.
Figure. II.1 shows typical attenuation curves for a Butterworth low-pass prototype. These
curves are quite useful in providing quickly the minimum order required to achieve a specified attenuation. For Butterworth low-pass filters with source and load resistors being 1
Ω each, the reactance of the k-th element in the ladder is given by :
Figure. II.1: Attenuation curves for Butterworth low-pass prototype[4]
For Butterworth low-pass prototypes with different source and load resistors, the required component values are available for look up from tables. As an example,Table.A.1 lists the normalized values for Butterworth low-pass prototypes of order 2 to 4 for different ratios of the load and source resistors. Note that the top circuit topology corresponds to a given ratio of R, R- whereas the bottom topology is used for a given ratio of R R,- .
II.1.2.2
Chebyshev Filter
Chebyshev filters are in general better than Butterworth because of its larger attenuation. However, non-zero ripple in the pass band exists.
The attenuation of a Chebyshev filter is given by
A./ = 10log 1 + 01C13K 4! II. 4
where is the cut-off frequency, N is the order of the filter, C 678
89:is the Chebyshev
polynominal to the order n evaluated at a frequency of 78
89 , ε and K are constants defined as
0 = ;10<=>-?@− 1 II. 5
with L./ being the ripple in dB, cosh and acosh being the hyperpolic cosine and inverse hyperbolic cosine functions, respectively. It may be helpful to be reminded that
cosh M =NOPN1QO (II.7) a cosh X = ln 6X ± Sx1− 1: II. 8
The Chebyshev polynomials for the order N being 1 to 7 is listed in Table .A.2 and can be used to estimate the attenuation of the filter response using the above equations. However, it is typically much more convenient to use attenuation curves to estimate the attenuation for a given filter order or the minimum order for some specified attenuation .The attenuation curves for Chebyshev low-pass filters with 0.01-dB and 0.1-dB ripples are plotted in Figure.II.2 and
Figure. II.3, respectively. Table .A.3 lists the normalized values for Chebyshev low-pass
prototypes for 0.1-dB ripple of order 2 to 4 for different ratios of the load and source resistors.
Figure. II.3: Attenuation curves for Chebyshev low-pass prototype with 0.1-dB ripple [4]
II.1.2.3
Bessel Filter
Bessel filters are in general more preferred to Butterworth and Chebyshev because of its constant group delay or linear phase response. However, the attenuation is not good. For frequencies < 2ω , the attenuation of a Bessel filter can be approximated by :
A./ = 3 3ω 4 1
II. 9
For frequencies > 2ω , the attenuation of a Bessel filter can be estimated as 20 dB per decade.
The attenuation curves that can be conveniently used for design Bessel low-pass prototypes are shown in Figure. II.4 The normalized values for the components in a Bessel low-pass filters are listed in Table .A.4.