Design and Implementation of RF and Microwave Filters Using Transmission Lines Rethabile Khutlang A thesis submitted to the Department of Electrical Engineering, University of Cape Town, in fulfilment of the requirements for the degree of Bachelor of Science in Engineering. Cape Town, October 2006 Declaration I declare that this thesis report is my own, unaided work. It is being submitted for the degree of Bachelor of Science in Engineering at the University of Cape Town. It has not been submitted before for any degree or examination in any other university. SignatureofAuthor.................................. ............................ Cape Town 23 October 2006 i Abstract RF and Microwave filters can be implemented with transmission lines. Filters are signifi- cant RF and Microwave components. Transmission line filters can be easy to implement, depending on the type of transmission line used. The aim of this project is to develop a set of transmission line filters for students to do practical work with. There are different transmission lines due to different RF and Microwave applications. The characteristic impedance and how easy it is to incise precise lengths are two important characteristics of transmission lines; thus they are used to investigate which transmission line to use to implement filters. The first part of this project looks into which transmission line to use to erect a filter. Then the different filter design theories are reviewed. The filter design theory that allows for implementation with transmission lines is used to design the filters. Open-wire parallel lines are used to implement transmission line filters. They are the transmission lines with which it is easiest to change the characteristic impedance. The resulting filters are periodic in frequency. The open-wire lines can be used well into the 1 m wavelength region. For characteristic impedance below 100 Ohms, the performance of open-wire lines is limited. ii Acknowledgements I would like to thank my supervisor, Professor Michael Inggs, for his guidance and toler- ance throughout the extent of the project. I have benefitted immensely from his wealth of knowledge. I would also like to thank Andile Mngadi and Jonathan Ward for their availability when- ever help was needed. iii Contents Declaration i Abstract ii Acknowledgements iii 1 Introduction 1 1.1 TermsofReference ............................. 1 1.2 ReviewoftheTermsofReference . 2 1.2.1 Introduction ............................ 2 1.2.2 FunctionalCharacteristics . 2 1.2.3 InterfaceCharacteristics . 2 1.2.4 SafetyCharacteristics. 2 1.2.5 ImplementationIssues . 3 1.2.6 Timescale.............................. 3 1.2.7 TestRequirements ......................... 3 1.3 PlanofDevelopment ............................ 3 2 Literature Review 6 2.1 FilterDesignMethods ........................... 7 2.1.1 FilterDesignbytheImageMethod . 7 2.1.2 FilterDesignbytheNetworkSynthesisMethod . .. 10 2.2 TransmissionLines. ............................ 12 2.2.1 CoaxialCable ........................... 12 2.2.2 Open-WireLines .......................... 13 2.2.3 Microstrip ............................. 13 2.3 TransmissionLineStubFilters . .. 14 2.3.1 Richard’sTransformation . 14 2.3.2 KurodaIdentities . .. .. .. .. .. .. .. 15 iv 2.3.3 Non-RedundantFilterSynthesis . 15 2.4 TransmissionLineResonatorFilters . .... 15 2.4.1 ImpedanceandAdmittanceInverters . 16 2.4.2 Quarter-WaveCoupledFilters . 16 2.5 ImplementationofFilters . 17 2.5.1 Stepped-ImpedanceFilters . 17 2.5.2 WaveguideFilters . .. .. .. .. .. .. .. 17 2.5.3 FixedImpedanceCoaxialCableFilters . 17 2.5.4 Open-wireParallelLinesFilters . 21 2.6 Summary .................................. 21 3 Filter Designs 22 3.1 DesignofaLow-PassFilter . 23 3.2 DesignofaHigh-PassFilter . 25 3.3 DesignofaBand-PassFilter . 27 3.4 DesignofaBand-StopFilter . 29 3.5 Conversion of Lumped-Elements to Distributed Elements ........ 31 3.5.1 Low-passFilter .......................... 31 3.5.2 High-PassFilter .......................... 32 3.5.3 Band-PassFilter .......................... 33 3.5.4 Band-StopFilter .......................... 33 3.6 Summary .................................. 33 4 Implementation of Filters 35 4.1 ImplementationoftheLow-PassFilter . ... 35 4.2 ImplementationoftheHigh-PassFilter . .... 37 4.3 Implementation of the Band-Pass and Band-Stop Filters . ........ 37 4.4 TranslationoftheFilterImpedance . ... 37 4.4.1 TheBalun ............................. 37 4.4.2 CoaxialCable ........................... 38 4.4.3 Connectors ............................. 38 4.5 Summary .................................. 39 5 Testing 40 5.1 E5071BNetworkVectorAnalyserCalibration . ..... 40 5.2 Low-PassFilterTest ............................ 42 5.3 TheHigh-PassFilterTest . 44 5.4 DiscussionofResults ............................ 46 v 6 Conclusions and Recommendations 49 6.1 Conclusions................................. 49 6.2 Recommendations.............................. 49 vi List of Figures 2.1 L-sectionNetwork.[1,page56] . 7 2.2 Constant-khalfsection.[1,page62]. .... 8 2.3 m-derivedhalfsection.[1,page64] . ... 9 2.4 Atwoportnetwork.............................. 18 2.5 TheSmithChart. .............................. 20 3.1 Powerlossratioofthelow-passprototype. ..... 23 3.2 Lumpedelementslow-passfilterprototype. ..... 24 3.3 Simulatedlow-passfiltercircuit. .... 24 3.4 SimulationResultsforthelow-passfilter. ...... 25 3.5 Lumpedelementshigh-passfilterprototype. ..... 25 3.6 Simulatedhigh-passfiltercircuit. .... 26 3.7 Simulationresultsforahigh-passfilter. ...... 27 3.8 Lumpedelementsband-passfilterprototype. ..... 28 3.9 Simulatedcircuitforaband-passfilter. ..... 28 3.10 Simulationresultsforaband-passfilter. ....... 29 3.11 Lumpedelementsband-stopfilterprototype. ...... 30 3.12 Simulatedcircuitforaband-stopfilter. ....... 30 3.13 Simulationresultsforaband-stopfilter. ....... 31 3.14 Inductors andcapacitors converted to series and shunt stubs. ....... 32 3.15 Seriesstubsconvertedtoshuntstubs. ..... 32 4.1 Open-wirelinelow-passfilter. .. 36 4.2 Transformers connected back-to-back and coaxial cable. ......... 38 4.3 Transformers connected to the low-pass filter. ....... 39 5.1 Thetestsetup. ............................... 40 5.2 Theplotof S11................................ 41 5.3 Theplotof S21................................ 42 5.4 Magnituderesponseofthelow-passfilter. ..... 43 vii 5.5 Phaseresponseofthelow-passfilter. ... 43 5.6 Groupdelayofthelow-passfilter. .. 44 5.7 Magnituderesponseforahigh-passfilter. ..... 45 5.8 Phaseresponseofthehigh-passfilter. .... 45 5.9 Groupdelayofahigh-passfilter. 46 1 a....................................... 53 2 b....................................... 53 3 c....................................... 54 4 d....................................... 54 viii List of Tables 3.1 Characteristicimpedanceoftheresonators. ....... 33 4.1 Centre-to-centre spacing of sections of low-pass filter. .......... 36 ix Chapter 1 Introduction This report describes the design and implementation of RF and Microwave transmission line filters. The reason for the initiation of the project is to increase practical work for the fourth year electrical engineering course: "RF and Microwave Systems" (EEE 4086F) at the University of Cape Town. The course has adequate theory but still has to increase the portion of its practical work. Filters are amongst the most common RF and Microwave components. Their function is intuitively easy, for instance a low-pass filter should pass low frequency signals. It is easy to figure out that the characteristic of merit is frequency. Because of their importance, there is an immense amount of theory dedicated to the design of filters. Students learn about some of the filter design theory in the fourth year course, consequently it is a good idea to consolidate the theory with some practical work. The theory required for the design and implementation of the RF and Microwave filters has been gathered from relevant books, the Internet and discussions with members of the radar research group at the University of Cape Town. The main constraint on the project has been time. 1.1 Terms of Reference The terms of reference of this thesis are as follows: Investigate which transmission lines can be used to implement RF and Microwave • filters. Determine which filter types can be built using the transmission lines. • Design and implement the filters using the transmission lines and connectors. The • design can be with the aid of the Smith Chart. In the designs, include the effects of the stray capacitance of the connectors. • Test the designed filters. • 1 Prepare an appendix that forms a practical, as the work carried out in this project is • to form practical work for students. 1.2 Review of the Terms of Reference 1.2.1 Introduction The Requirements Review clarifies what work the thesis entails. The project involves the design and implementation, thus the aim is to finally submit a set of working filters. The first part of the project is researching which transmission lines to use in the implementa- tion of RF and Microwave filters. The second part is the implementation of filters. 1.2.2 Functional Characteristics The most common RF and Microwave filters are the low-pass, high-pass, band-pass and band-stop filters. Quarter-wave resonators, shunt stubs, stepped impedance, comb-line and inter-digital are some of the forms of implementing transmission line filters. Filters pass the signals in their pass-band and attenuate signals in their stop-band. The atten- uation of the signals in the stop-band depends on the characteristic design of