Investigating cost-effective EMC methods

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(1)Investigating Cost-Effective EMC Methods P. Gideon Wiid Thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Engineering at the University of Stellenbosch Supervisor: Prof. H.C. Reader December 2005.

(2) i. Declaration I, the undersigned, hereby declare that the work contained in this assignment/thesis is my own original work and that I have not previously in its entirety or in part submitted it at any university for a degree.. Signature: ............................... Date: .....................................

(3) ii. Summary Due to the expensive nature of high frequency measurements in the EMC (Electromagnetic Compatability) field, more affordable methods of measurement instrumentation and environments are investigated. Different calibration methods for an Automatic Network Analyser (ANA) are evaluated against each other to determine the most cost-effective method of calibration. The mathematics for all the calibration methods are used in MATLAB programs which perform the error-calculation and correction which is usually done by the ANA software. These programs can be used to develop a simplified homebuilt ANA at reduced cost. The MATLAB program calibrations are compared to actual ANA calibrations to determine accuracy. Different measurement environments are considered as well to decide on a best compromise between cost and accuracy. To achieve this a reverberation chamber was built in which measurements were done and compared to measurements done on an Open Area Test Site. The Device Under Test was a standard radiator constructed specifically for such measurements. The development of both the radiator and the reverberation chamber are discussed and all the measurement results are considered in this thesis.. Opsomming Siende dat ho¨e-frekwensie metings in die EMV (Elektromagnetise Versoenbaarheid) veld so duur is, is meer bekostigbare metodes van metings-instrumentasie en -omgewings ondersoek. Verskillende kalibrasie metodes vir ’n Outomatiese Netwerk Analiseerder (ONA) word teenoor mekaar ge¨evalueer om die mees koste-effektiewe metode van kalibrasie te bepaal. Die wiskunde van al die kalibrasie metodes word in MATLAB programmatuur gebruik om die fout-berekeninge en -regstelling te verrig wat gewoonlik deur die ONA sagteware gedoen word. Hierdie programmatuur kan gebruik word om ’n vereenvoudigde tuisvervaardigde ONA te ontwikkel teen verminderde koste. Die MATLAB programmatuur kalibrasies word met werklike ONA kalibrasies vergelyk om akkuraatheid te bepaal. Verskillende metings-omgewings word ook oorweeg om te besluit op die beste skikking tussen koste en akkuraatheid. Om dit te verwesenlik, is ’n weerkaatsingskamer saamgestel waarin metings gedoen is en vergelyk is met metings wat op ’n Ope Area Toetsterrein gedoen is. Die toestel wat getoets is, was ’n standaard uitstraler wat spesifiek vir sulke metings gebou is. Die ontwikkeling van beide die uitstraler en die weerkaatsingskamer word bespreek en al die metings se resultate word oorweeg in hierdie tesis..

(4) iii. This thesis is dedicated to my late mother, Ina, to my father, Eben, my brothers Eben and Inus and to my Genex Cell Group..

(5) Contents 1 Introduction 1.1 Measurement Instrumentation 1.2 Instrumentation Software . . . 1.3 EMC Measurements . . . . . 1.4 Thesis Layout . . . . . . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. 2 ANA Calibration Techniques 2.1 Introduction . . . . . . . . . . . . . . . 2.2 Automatic Network Analyser or ANA . 2.3 Measurement Errors . . . . . . . . . . 2.4 12-Term Error Model . . . . . . . . . . 2.5 SOLT Calibration Procedure . . . . . . 2.6 Modelling of SOLT Standards . . . . . 2.7 Error-Calculations . . . . . . . . . . . 2.8 8-Term Error Model . . . . . . . . . . 2.9 TRL and LRM Calibration Procedure . 2.10 Modelling of TRL and LRM Standards 2.11 Error-Calculations . . . . . . . . . . .. . . . .. . . . . . . . . . . .. . . . .. . . . . . . . . . . .. . . . .. . . . . . . . . . . .. 3 ANA Calibration with MATLAB Program 3.1 Introduction . . . . . . . . . . . . . . . . . . 3.2 SOLT Calibration using MATLAB . . . . . 3.3 Comparison of Results . . . . . . . . . . . . 3.4 TRL and LRM Calibration using MATLAB 3.5 Comparison of Results . . . . . . . . . . . . 3.6 Conclusion . . . . . . . . . . . . . . . . . . .. . . . .. . . . . . . . . . . .. . . . . . .. . . . .. . . . . . . . . . . .. . . . . . .. . . . .. . . . . . . . . . . .. . . . . . .. . . . .. . . . . . . . . . . .. . . . . . .. . . . .. . . . . . . . . . . .. . . . . . .. . . . .. . . . . . . . . . . .. . . . . . .. . . . .. . . . . . . . . . . .. . . . . . .. . . . .. . . . . . . . . . . .. . . . . . .. . . . .. . . . . . . . . . . .. . . . . . .. . . . .. . . . . . . . . . . .. . . . . . .. . . . .. . . . . . . . . . . .. . . . . . .. . . . .. . . . . . . . . . . .. . . . . . .. . . . .. . . . . . . . . . . .. . . . . . .. . . . .. . . . . . . . . . . .. . . . . . .. . . . .. . . . . . . . . . . .. . . . . . .. . . . .. . . . . . . . . . . .. . . . . . .. . . . .. 1 1 2 2 3. . . . . . . . . . . .. 4 4 4 6 7 8 10 11 16 18 18 19. . . . . . .. 24 24 24 25 26 27 30. 4 Standard Radiator 31 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.2 Radiator Housing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.3 Radiator Circuitry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.

(6) CONTENTS 4.4 4.5 4.6. v. Testing the Radiator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Radiator Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36. 5 Reverberation Chamber 5.1 Introduction . . . . . . . . . . . . . 5.2 What is a Reverberation Chamber? 5.3 Layout and Design . . . . . . . . . 5.4 Calibration Background . . . . . . 5.5 Calibration Procedure . . . . . . . 5.6 Measurement Procedure . . . . . . 5.7 Results . . . . . . . . . . . . . . . . 6 OATS Measurement 6.1 Introduction . . . . . . 6.2 Test Setup . . . . . . . 6.3 Measurement Process . 6.4 Results . . . . . . . . . 6.5 Comparison of Results. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . . . .. . . . . .. . . . . . . .. . . . . .. . . . . . . .. . . . . .. . . . . . . .. . . . . .. . . . . . . .. . . . . .. . . . . . . .. . . . . .. . . . . . . .. . . . . .. . . . . . . .. . . . . .. . . . . . . .. . . . . .. . . . . . . .. . . . . .. . . . . . . .. . . . . .. . . . . . . .. . . . . .. . . . . . . .. . . . . .. . . . . . . .. . . . . .. . . . . . . .. . . . . .. . . . . . . .. . . . . .. . . . . . . .. . . . . .. . . . . . . .. . . . . .. . . . . . . .. . . . . .. . . . . . . .. . . . . .. . . . . . . .. . . . . .. . . . . . . .. 37 37 37 38 40 42 44 45. . . . . .. 47 47 47 48 50 51. 7 Conclusions and Recommendations. 53. A ANA Settings 59 A.1 Settings for SOLT Calibration . . . . . . . . . . . . . . . . . . . . . . . . . 59 A.2 Settings for TRL Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 60 B MATLAB Programs B.1 SOLT Calibration and Measurement . . . . . . . . . . . . . B.2 LRM and TRL Calibrations and Measurement . . . . . . . . B.3 LRM and TRL Calibrations and Measurement - Airline . . . B.4 LRM and TRL Calibrations and Measurement - NIST Short B.5 Reverberation Chamber Variation Calculations . . . . . . . . B.6 Reverberation Chamber Measurement Calculations . . . . . B.7 Reverberation Chamber Measurement to OATS Equivalent . B.8 OATS Measurement Calculations . . . . . . . . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. 61 61 67 72 77 81 85 88 90. C MATLAB Plots 92 C.1 MATLAB Plots for the 75mm Airline . . . . . . . . . . . . . . . . . . . . . 92 C.2 MATLAB Plots for the NIST Short . . . . . . . . . . . . . . . . . . . . . . 94 D Radiator Schematic. 95.

(7) List of Figures 1.1. Calvin from Bill Watterson’s Calvin and Hobbes Collection [1]. 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 2.15. Typical ANA test setup (after, [2]) . . . . . . . . . . . . . . . . . . . Simplified model of an ANA [3] . . . . . . . . . . . . . . . . . . . . . S-Parameter definition (after, [4]) . . . . . . . . . . . . . . . . . . . . 12-Term error model in forward and reverse direction (after, [2]) . . . Signal flow diagrams for the SOLT standards connected to the setup . Cross-section of Short and Open SMA standards (after, [2]) . . . . . Signal flow diagram simplifications from Pozar [6] . . . . . . . . . . . Signal flow diagram for EDF , ESF and ERF . . . . . . . . . . . . . . . Signal flow diagram for S11F . . . . . . . . . . . . . . . . . . . . . . . Signal flow diagram for S21F . . . . . . . . . . . . . . . . . . . . . . . Signal flow diagram for S12F . . . . . . . . . . . . . . . . . . . . . . . Signal flow diagram for S22F . . . . . . . . . . . . . . . . . . . . . . . 8-Term error model (after, [7]) . . . . . . . . . . . . . . . . . . . . . . Scattering transfer parameters (after, [9]) . . . . . . . . . . . . . . . . Test setup with T-Parameters . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . .. 5 6 6 7 9 10 12 13 14 14 15 15 17 19 20. 3.1 3.2 3.3. 25 26. 3.4. 20dB Attenuator magnitude measured with SOLT calibration . . . . . . . 20dB Attenuator phase measured with SOLT calibration . . . . . . . . . . 20dB Attenuator magnitude measured with SOLT, TRL and LRM calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20dB Attenuator phase measured with SOLT, TRL and LRM calibrations. 4.1 4.2 4.3. Isometric view of radiator unit [12] . . . . . . . . . . . . . . . . . . . . . . 32 Diagram for the radiator circuitry . . . . . . . . . . . . . . . . . . . . . . . 33 Radiator with loop antenna attached . . . . . . . . . . . . . . . . . . . . . 36. 5.1 5.2 5.3 5.4. Reverberation chamber layout . . . . . . . . . . Photographs showing the reverberation chamber Reverberation chamber setup for calibration . . Reverberation chamber measurement variation .. . . . . . stirrers . . . . . . . . . .. . . . .. . . . .. . . . .. . . . . . .. . . . .. . . . .. . . . .. . . . .. . . . . . . . . . . . . . . .. . . . .. . . . . . . . . . . . . . . .. . . . .. . . . .. 1. 28 29. 38 39 41 43.

(8) LIST OF FIGURES. vii. 5.5. Reverberation chamber setup for measurement . . . . . . . . . . . . . . . . 44. 6.1 6.2. OATS site at Houwteq . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Measurement setup for OATS . . . . . . . . . . . . . . . . . . . . . . . . . 49. C.1 Airline magnitude measured with SOLT, TRL and LRM calibrations . . . 92 C.2 Airline phase measured with SOLT, TRL and LRM calibrations . . . . . . 93 C.3 NIST Short measured with SOLT, TRL and LRM calibrations . . . . . . . 94 D.1 Schematic diagram for the Standard Radiator unit [12] . . . . . . . . . . . 96.

(9) List of Tables 4.1 4.2 4.3 4.4. Radiator frequencies and VR circuit power output Frequency drift for Voltage Divider circuit . . . . Frequency drift for Voltage Regulator circuit . . . Initial frequency drift when connecting batteries .. 5.1. Chamber attenuation, cable attenuations, antenna mismatch and assumed antenna efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Measurements of standard radiator . . . . . . . . . . . . . . . . . . . . . . 46. 5.2 6.1 6.2 6.3. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. 34 34 35 35. Cable and antenna attenuations, antenna gain and antenna factor . . . . . 50 OATS measurements of radiator . . . . . . . . . . . . . . . . . . . . . . . . 50 OATS measurements and reverberation chamber measurement prediction of standard radiator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51. A.1 Calibration kit values loaded onto the ANA (SOLT calibration) . . . . . . 59 A.2 Calibration kit values loaded onto the ANA (SOLT and TRL calibrations) 60.

(10) Abbreviations AF ANA dB DUT EM EMC EMI EMIR EMV LPDA LRM GHz OATS OATT ONA NIST NSA MHz SA SG SOLT TRL VD VR. Antenna Factor Automatic Network Analyser Decibel Device under Test Electromagnetic Electromagnetic Compatability Electromagnetic Interference Electromagnetic Interference Receiver Elektromagnetiese Versoenbaarheid Log-periodoc Dipole Antenna Line Reflect Match GigaHertz Open Area Test Site Ope Area Toetsterrein Outomatiese Netwerk Analiseerder National Institute of Standards and Technology Natural Site Attenuation MegaHertz Spectrum Analyser Signal Generator Short-Open-Load-Through Through-Reflect-Match Voltage Divider Voltage Regulator.

(11) Acknowledgements I would like to thank the following people for the help and support provided during the development of this thesis. All thanks and praise to the Lord God, for providing strength and determination in making this part-time thesis possible. For all the prayers and support of friends and family, especially the Genex cell group, thank you all. To Profesor Howard Reader, thank you for all the encouraging support and leadership, patience and good humour, and especially for all the late evenings dedicated to this project. You put the super in supervisor! I would also like to thank Rodney Urban and Martin Siebers for all their time and support in the HF lab, and for help with equipment setups, borrowing laptops and assisting in measurements. A further thanks is owed to Ulrich B¨ uttner and Pieter de Kok for their effort and time spent on building the reverberation chamber stirrers and setting up the motors and motor control. To Ralph Dreyer and Nick van Graan, who were always ready to help with components and service with a smile, thank you very much guys. Thanks to Professor Keith Palmer and Professor Petri Meyer as well for the use of their calibration kits. And the last thanks goes to Silulame Doyi and Fred Thomas from Houwteq, who allowed the use of the OATS and assisted with all the OATS measurements..

(12) Chapter 1 Introduction Money! Most everybody loves it, and usually nobody can have enough of it, as Calvin so humorously shows in figure 1.1. Unfortunately, more often than not, you have to have money to make money. This is also true when starting a business, especially one in the field of high frequency measurements and electromagnetic compatibility (EMC). The main focus of this thesis revolves around metrology in the EMC field. To do EMC measurements and testing, different measurement techniques or methods can be used. Unfortunately, most of these techniques and the instrumentation needed for it are extremely expensive. To enter the field of EMC, more cost-effective methods of measurement need to be investigated.. 1.1. Measurement Instrumentation. When doing EMC measurements, the first thing you need is the tools to measure with. A very versatile instrument that is commonly used for accurate high frequency measurement is an automatic network analyser (ANA). When connecting an ANA to equipment to be tested, the cables and connectors introduce errors in the measurement setup. To eliminate. Figure 1.1: Calvin from Bill Watterson’s Calvin and Hobbes Collection [1].

(13) Chapter 1 — Introduction. 2. any errors that the test equipment and cables introduce into the test setup, a calibration must be done using (quite expensive) standards which have previously determined known characteristics. The calibration is done by measuring these standards, calculating the errors from the measured values, and evaluating them against the known characteristics. It would be extremely beneficial to obtain these errors without using the expensive test equipment such as an ANA and its calibration standards. In order to explore alternatives, different calibration techniques are investigated during this thesis to obtain a method with the best balance between cost and effectiveness.. 1.2. Instrumentation Software. Keeping in mind that the ANA is a very expensive piece of instrumentation, the possibility exists to duplicate the hardware of the ANA with advanced microchip technology at a fraction of the price. If the software doing the ANA’s error-calculation and correction can be duplicated, a simplified ANA can be home-built and used to do the same measurements as the conventional ANA. The error-calculation and correction mathematics of three different calibration methods are developed in MATLAB programs for this thesis. These programs are then run in conjunction with the ANA calibrations to determine accuracy when compared to actual ANA calculations and corrections. The results are discussed in this report.. 1.3. EMC Measurements. To do really accurate EMC measurements, the environment needs to be of such a nature that no external interference can be picked up by the measurement instrumentation. The three main environments where this can be achieved are an enclosed, shielded chamber (reverberation chamber), an anechoic chamber or an open area test site (OATS). All of these have their advantages and disadvantages, but looking purely from a costperspective, the reverberation chamber definitely needs further investigation. The reverberation chamber measurement is a relatively low-cost measurement technique to determine total radiated power of the device under test (DUT). With no reverberation chamber close at hand, an existing enclosed chamber was used, adding in two mode-stirrers to create a uniform field inside the chamber. This allowed a power-measurement to be taken at almost any position inside (the working volume of) the chamber. The design and construction of the mode-stirrers for the reverberation chamber forms part of the thesis. Looking specifically at radiation testing, it was decided to build a standard radiator which could be tested on an OATS and in the reverberation chamber. Although industry standards prescribe the OATS measurement, the results of the two techniques are.

(14) Chapter 1 — Introduction. 3. compared to each other to determine to what level the reverberation measurement can be trusted for pre-compliance testing. Due to the fact that worst radiation is measured on the OATS and total radiated power is measured in the reverberation chamber, it is difficult to get a precise correlation between the two. If necessary, an institution such as NIST (National Institute of Standards and Technology) can be approached to verify the results.. 1.4. Thesis Layout. To explain the background of ANA calibration, chapter 2 of this report takes a closer look at the theory and mathematics of different calibration techniques. The 12-term error model is explained and the modelling of the short-open-load-through (SOLT) calibration standards are given. The derivation of the equations that are used for the error-calculation and correction are explained. Using the 8-term error model, the correlation between through-reflect-line (TRL), line-reflect-match (LRM) and SOLT calibration standards are shown. This is followed by an explanation of the mathematics used in the error-calculation and correction for both TRL and LRM calibration methods. Chapter 3 shows how the mathematics is used in MATLAB programs (Appendices) which simulates the error-calculation and correction that is done by the ANA’s software. Three different calibrations and various measurements were done on the ANA, downloading all the raw data to be used in the MATLAB software. Two standards from a verification kit, as well as a short standard (whose characteristics were carefully determined by NIST), were measured. The resulting MATLAB program calibrated measurements are compared to the actual ANA SOLT and ANA TRL calibrated measurements on magnitude and phase plots and discussed at the end of the chapter. The layout design and reasoning behind the building of a standard radiator for testing in the various test environments is explained in chapter 4. In chapter 5 the design and building of mode-stirrers for a reverberation chamber are discussed. The calibration and evaluation of the chamber, as well as the reverberation chamber measurement of the standard radiator, are shown. Chapter 6 deals with an OATS measurement of the standard radiator. The test results of all the standard radiator measurements, viz. the OATS and the reverberation chamber measurement OATS equivalent predictions are then compared. Conclusions and recommendations can be found in chapter 7, followed by the bibliography. ANA calibration settings, the MATLAB program code for the calibration procedures, as well as MATLAB programs for the reverberation chamber measurement and OATS measurement calculations, are shown in the Appendix..

(15) Chapter 2 ANA Calibration Techniques 2.1. Introduction. For an EMC consultant, an ANA is a very useful tool which can be used for many measurements, eg. measuring attenuation and frequency response of cables, determining reflection coefficients, gain and efficiency of antennas, as well as the calibration of transducers such as current probes. The problem is that an ANA is currently priced at betwen R500000 and R1 million. To overcome this budgetary constraint, a RF/IF Gain Phase Detector chip is available on the market at a price of around R1000. This chip could be utilised to perform the duties of the ANA hardware, but the ANA software has to be linked to the chip in a practical way. MATLAB was identified as a possible program solution, due to its strong mathematical ability and its versatility. For calibration of such a simplified home-built ANA, cost-effective calibration standards are also needed. To do a thorough investigation into these possibilities, different calibration techniques as well as the ANA calibration software needed to be clearly understood. In this chapter an overview is given of an ANA and two error models for the ANA are discussed, namely the 12-term and the 8-term error model. From these models different calibration techniques are explained and the mathematical equations used by the ANA software to do the error-calculation and correction are derived. The standards that are used during calibration are also mathematically modelled in order to use in MATLAB programs.. 2.2. Automatic Network Analyser or ANA. An automatic network analyser (ANA) as in figure 2.1 is a two-port measurement device for accurate measurements over a wide frequency range. When doing measurements on a device under test (DUT), the cables used as well as the port connections introduce errors due to reflections and coupling, which do not form part of the DUT. Thus to eliminate.

(16) Chapter 2 — ANA Calibration Techniques. 5. Figure 2.1: Typical ANA test setup (after, [2]) these errors from the test setup, standards with known characteristics are connected and measurements are made. These measurement values are used by the ANA together with the known characteristics loaded onto the ANA to calculate the errors. The measured values are then adapted by the ANA to eliminate the errors and only reflect the true measurement values of the DUT. This elimination of the errors is called calibration. In figure 2.2 a simplified model of an ANA is shown. From the RF IN signal the ANA is set for either the forward or the reverse direction, shifting the excitation between port 1 and port 2. Attenuators keep the signal to a manageable level to not damage the test equipment. The directional couplers ensure propagation of the signal in only the specified directions. In other words if the signal is coming from port one to the device under test (DUT), any reflected signal will go via the directional coupler to the mixer at b1 . The forward-going signal through the directional coupler will terminate in a perfectly matched load with no reflections (theoretically). The reflected signal and signal going through the DUT are measured at b1 and b2 respectively, whereas the ingoing signal is read at a1 for this example. At a2 no signal should be measured, as no input was given through port 2. These measurements are then used by the ANA software and presented on the screen in whichever format is selected. The signal flow between the two ports can more clearly be shown by the scattering or S-parameter defenition as in figure 2.3. The S-parameters of any two-port, S11 , S12 , S21 and S22 are defined as: . . .  . . b S S12   a1   1  =  11 b2 S11 S12 a2. (2.1). From equation 2.1 it can be seen that S11 and S22 are the reflected signals for ports 1 and.

(17) Chapter 2 — ANA Calibration Techniques. 6. Figure 2.2: Simplified model of an ANA [3] 2 respectively (called the reflection coefficients), and that S21 is the signal going through from port 1 to port 2 and S12 from port 2 to port 1 (called transmission coefficients). The most common format for power-measurements is set to dB magnitude and phase respectively. Plots for measurements done later in this thesis are also shown in this format.. 2.3. Measurement Errors. Measurement errors occur in any high frequency measurement, adding uncertainty to the results. The two main categories of errors are random errors and systematic errors.. Figure 2.3: S-Parameter definition (after, [4]).

(18) Chapter 2 — ANA Calibration Techniques. 7. Figure 2.4: 12-Term error model in forward and reverse direction (after, [2]) Random errors are caused by noise, temperature or physical changes in the test setup, and they are non-repeatable measurement variations. Systematic errors, however, are repeatable measurement variations in the test setup that the ANA can measure. The cables in a test setup, as well as the terminations, can cause leakage and mismatch signals. Other errors that can occur are isolation characteristics between the reference and test signal paths, and system frequency response. These errors can be better explained by error-models, as will be discussed in the following sections.. 2.4. 12-Term Error Model. The 12-term error model in figure 2.4 shows the signal flow diagram in the forward and reverse directions for a DUT connected to the two ports of an ANA. The S-parameters S11 , S12 , S21 and S22 show the characteristics of the DUT, which is what is wanted as the end-result. The first systematic errors encountered are the Directivity errors (EDF and EDR ), which are introduced due to directional coupler imperfections. A real directional device does not perfectly separate the forward and reverse signals. A small amount of the incident signal will appear at the coupled output due to leakage, and unwanted reflections can result from the termination into an imperfect match. Another contributory factor can be due to reflections from the ANA or cable adapters..

(19) Chapter 2 — ANA Calibration Techniques. 8. The next systematic errors encountered with reflection measurements are Source Match errors (ESF and ESR ). These error signals appear at the system test input due to the inability of the source to maintain constant power at the test device input, as well as adapter and cable mismatches and losses encountered by the reflected signal. Frequency Response or Reflection Tracking errors (ET F and ET R ) are test setup variations in magnitude and phase with frequency, including signal separation devices, test cables, adapters, and variation in frequency response between the reference and test channels. The Load Match errors (ELF and ELR ) are similar to the Source Match errors, but are due to imperfect termination of the DUT at the output port. These errors are also dependent on the transmission coefficients S21 and S12 . When doing transmission measurements, a significant error is the Transmission or Reflection Tracking error (ERF and ERR ), a similar type of error as reflection tracking, but dependent on DUT input and output impedances, in other words imperfect matches at ports 1 and 2. Lastly the Isolation or Crosstalk errors (EXF and EXR ) are caused by leakage between the system test and reference channels.. 2.5. SOLT Calibration Procedure. For high frequency measurements at low power levels, done with an ANA, calibration is necessary to ensure that all the possible systematic errors mentioned in section 2.4 are eliminated, giving the true measurement of the DUT. Various methods of ANA calibration are commonly found in literature. One of these methods used especially for coaxial test setups, is a SOLT calibration. The SOLT stands for Short-Open-Load-Through, which are the four standards used for the calibration. All the characteristics of these four standards are known and loaded onto the ANA. This is used to give accurate descriptions of the standards’ reflection and transmission coefficients. Before the DUT is connected to the ANA for measurement, the setup is done using low-loss cables. Care is taken to clean all connectors and standards, ensuring that there are no possibilities of high resistance connections due to dirt or grime in between the contact planes. All the connections are tightened with a torque wrench (usually provided with a calibration kit) to a specified torque. This causes the contact planes of the connectors to be tightly and firmly pressed together, preventing any unwanted reflections. With the setup ready, all four the SOLT standards are connected to the cables one by one to determine the errors from section 2.4. In total twelve measurements are made to determine the errors: Measuring raw reflection responses at both ports (S11 and S22 ) of the short, open.

(20) Chapter 2 — ANA Calibration Techniques. 9. Figure 2.5: Signal flow diagrams for the SOLT standards connected to the setup and load standards give the Directivity errors in both directions, forward and reverse (EDF and EDR respectively), the Source match errors (ESF and ESR ) and the Reflection Tracking errors (ERF and ERR ). With the load still connected, measuring transmission parameters (S21 and S12 ) gives the Isolation terms (EXF and EXR ). Finally, connecting the through standard and measuring all four S-parameters gives the remaining four errors, namely Load match and Transmission Tracking in both directions (ELF , ELR and ET F and ET R ). In theory, this gives twelve measurements for twelve unknowns, and it is possible through mathematics to determine all twelve unknowns. After the measurements of all four standards are completed, the ANA calculates the errors and the calibration is done. For any further measurements, all systematic errors will be eliminated and a true measurement of the DUT in that setup will be given. A method for calculating all the errors is found from DeGroot [5]. It gives a good summary for the mathematical modelling of the standards and the use of these models and calculated errors to correct the measurement so that the error-terms are eliminated. The modelling of the standards is explained in the following section..

(21) 10. Chapter 2 — ANA Calibration Techniques. Figure 2.6: Cross-section of Short and Open SMA standards (after, [2]). 2.6. Modelling of SOLT Standards. A calibration kit is made up of standards to which an ANA setup is calibrated. All the characteristics of the standards are known and loaded onto the ANA. To attemp to do a calibration off-line in a MATLAB program, these standards have to be very accurately modelled. Approximations are made for the four standards used for calibration, the short, open, load and through standards. From [2] and [5] the common coaxial descriptions for the standards gives the open as an effective capacitance Cef f , the short as an effective inductance Lef f and the load as a single resistance value Zload . The short and open can be seen as in fig 2.6. The effective capacitance of a coaxial open can be described using a polynomial in frequency (f ): Cef f = C0 + C1 f + C2 f 2 + C3 f 3. (2.2). where C0 −C3 are coefficients with units F , F/Hz, F/Hz 2 and F/Hz 3 respectively. These values are known from the standards’ descriptions (as provided with each calibration kit). Similarly the effective inductance of a coaxial short can be described as: Lef f = L0 + L1 f + L2 f 2 + L3 f 3. (2.3). where L0 − L3 are coefficients with units H, H/Hz, H/Hz 2 and H/Hz 3 respectively..

(22) Chapter 2 — ANA Calibration Techniques. 11. Using these known values the reflection coefficients Γopen , Γshort and Γload , can be calculated from DeGroot [5] to give: Γopen =. 1 − jωCef f Z0 −2γl e 1 + jωCef f Z0. (2.4). Γshort =. jωLef f − Z0 −2γl e jωLef f + Z0. (2.5). Γload =. Zload − Z0 Zload + Z0. (2.6). with γl = αl + jβl =. rof f set q f ∗ 10−9 + jωtd 2cZ0. (2.7). where ω is the angular frequency, c is the speed of light and rof f set is the offset loss. The term td is the offset loss time for the open or short standard, which models the phase delay. It should be noted that these models are approximations as dispersion is not taken into account. The through is taken to have no delay and zero length. This gives a scattering matrix S T of: . . . . T S T S12 0 1   = S =  11 T T S21 S22 1 0 T. (2.8). These modelled values are used in the calculations in the following section to determine the error coefficients and error correction of measured data.. 2.7. Error-Calculations. With the standards modelled and known, the mathematics for error-calculation and correction can be addressed. With help from De Groot [5], the following error-calculations were done by a signal flow diagram approach, using Pozar’s [6] signal flow diagram simplification in figure 2.7. When the three known standard terminations short, open and load, with their known reflection responses (Γshort , Γopen , Γload ) are connected to the ANA, and their reflection responses (a0 /b0 ), namely Γs m , Γo m and Γl m are measured, it can be seen from the signal flow diagram in fihure 2.8 that the errors EDF , ESF and ERF can be calculated from the following equations: EDF + Γshort Γs EDF + Γopen Γo. m ESF m ESF. − ∆EΓshort = Γs − ∆EΓopen = Γo. m. m. (2.9) (2.10).

(23) 12. Chapter 2 — ANA Calibration Techniques. Figure 2.7: Signal flow diagram simplifications from Pozar [6] EDF + Γload Γl. m ESF. − ∆EΓload = Γl. (2.11). m. where ∆E = EDF ESF − ERF. (2.12). Rewriting equations (2.9), (2.10) and (2.11) in matrix form, shows the solutions to the errors EDF , ESF and ERF :     . EDF ESF ∆E. . .      =  . 1 Γopen Γo m −Γopen 1 Γshort Γs m −Γshort 1 Γload Γl m −Γload. −1     .    . Γo m Γs m Γl m.     . (2.13). with ERF = EDF EF − ∆E. (2.14). The same can be done in the reverse direction to obtain the solutions to the errors EDR , ESR and ERR :     . EDR ESR ∆E 0. . .      =  . 1 Γopen Γo m −Γopen 1 Γshort Γs m −Γshort 1 Γload Γl m −Γload. −1     .    . Γo m Γs m Γl m.     . (2.15).

(24) 13. Chapter 2 — ANA Calibration Techniques. Figure 2.8: Signal flow diagram for EDF , ESF and ERF with ∆E 0 = EDR ESR − ERR. (2.16). giving ERR = EDR ER − ∆E 0 With the load connected to ports 1 and 2, measuring reflection responses S21l and S12l m (b0 /a3 ) the isolation terms EXF and EXR can directly be obtained:. (2.17) m. (b3 /a0 ). EXF = S21l. m. (2.18). EXR = S12l. m. (2.19). When connecting the two ports with the through standard, the remaining four error coefficients can be determined from the measured through S-parameters: S11thru m (b0 /a0 ), S21thru m (b3 /a0 ), S12thru m (b0 /a3 ) and S22thru m (b3 /a3 ). From the signal flow diagrams in figures 2.9, 2.10, 2.11 and 2.12 (using Pozar’s [6] signal flow diagram simplification) in the forward direction, the following equations can be obtained: S11F = EDF +. T ERF S11 T 1 − ESF S11. (2.20).

(25) Chapter 2 — ANA Calibration Techniques. Figure 2.9: Signal flow diagram for S11F. Figure 2.10: Signal flow diagram for S21F. 14.

(26) Chapter 2 — ANA Calibration Techniques. 15. Figure 2.11: Signal flow diagram for S12F. Figure 2.12: Signal flow diagram for S22F. S21F =. T S21 T 1 − ESF S11. (2.21). S12F =. T ERF S12 T 1 − ESF S11. (2.22). T S22F = S22 +. T T ESF S21 S12 T 1 − ESF S11. (2.23). and doing the same for the reverse direction: T S11R = S11 +. T T ESR S21 S12 T 1 − ESR S22. (2.24). S21R =. T ERR S21 T 1 − ESR S22. (2.25). S12R =. T S12 T 1 − ESR S22. (2.26). S22R = EDR +. T ERR S22 T 1 − ESR S22. (2.27).

(27) 16. Chapter 2 — ANA Calibration Techniques. From equations (2.20 to 2.27), the remaining four errors can be determined as follows: ELF =. ET F = ET R = ELR =. S11thru m − S11F S22F (S11thru m − S11F ) + S21F S12F (S21thru. m. (S12thru. m. (2.28). − EXF )(1 − ELF S22F ) S21F. (2.29). − EXR )(1 − ELR S11R ) S12R. (2.30). S22R − S22thru m S11R (S22thru m − S22R ) + S21R S12R. (2.31). The corrected S-parameters can then be calculated using the 12 error-terms as follows: S11. b1 = = a1. S21 =. S12. b2 = a1. b1 = = a2. S22 =. b2 = a2. . S11M −EDF ERF. h. 1+. . S22M −EDR ERR. . i. ESR − ELF. . S21M −EXF ET F. . S12M −EXR ET R. . (2.32). D . S21M −EXF ET F. h. 1+. . S22M −EDR ERR. . i. (ESR − ELF ). (2.33). D . S12M −EXR ET R. h. 1+. . S11M −EDF ERF. . i. (ESF − ELR ). (2.34). D . S22M −EDR ERR. h. 1+. . S11M −EDF ERF. . i. ESF − ELR. . S21M −EXF ET F. D. . S12M −EXR ET R. . (2.35). where S11M − EDF S22M − EDR D = 1+ ESF 1 + ESR ERF ERR S12M − EXR S21M − EXF ELF ELR − ET F ET R . . . . . . . (2.36). Equations (2.13 to 2.36) gives a complete set of calculations for a MATLAB program to do error-calculation and correction using raw data downloaded from an actual SOLT calibration on an ANA.. 2.8. 8-Term Error Model. TRL calibration helps with difficulties when measuring and calibrating in microstrip or other non-coaxial transmission media. Producing distinct impedance standards for noncoaxial transmission media is extremely difficult, so an alternative calibration approach had to be investigated. For a TRL calibration, less standards are used and less measurements are necessary. From two sets of two-port measurements for a short piece of.

(28) Chapter 2 — ANA Calibration Techniques. 17. Figure 2.13: 8-Term error model (after, [7]) transmission line and a direct through connection, as well as two reflection measurements for (any) reflect standard, the full 12-term error model can be determined. Two assumptions are made for the test setup to attain the 8-term error-model, which is used to describe the errors for the TRL calibration. Firstly the Isolation terms are omitted from the 12-term error-model (assuming no cross-talk between the two ports) and secondly the two ANA ports are assumed to be identical. This means that figure 2.4 can be reduced to have only 8 error terms as can be seen in figure 2.13. The relationship between the 12-term error-model and the 8-term error model can be shown in the following equations:. e10 e01 = ERF. (2.37). e00 = EDF. (2.38). e11 = ESF , ELR. (2.39). e10 e32 = ET F. (2.40). e23 e33 = ERR. (2.41). e33 = EDR. (2.42). e22 = ESR , ELF. (2.43). e01 e23 = ET R. (2.44) (2.45). This implies that these eight errors can be determined by drawing up eight equations with eight unknowns. However, because a balanced system is assumed for the TRL and LRM procedures, a Switching term must be calculated to compensate for Source and Load Match differences in the two directions. The Isolation errors can also be measured with this calibration in the same manner as the full two-port calibration, adding two measurements. With.

(29) Chapter 2 — ANA Calibration Techniques. 18. the Switching term and the Isolation errors known, all the errors for the twelve-term error-model can be determined.. 2.9. TRL and LRM Calibration Procedure. Although TRL calibration is mainly used for measurements in non-coaxial media, it can be used for coaxial measurements as well. With a coaxial TRL or LRM calibration, only three standards are used for each. These are Through-Reflect-Line and Line-ReflectMatch respectively. The LRM calibration is just a variation of the TRL method, but the same principles for error-calculation and correction can be used. As with section 2.5, special care is taken to clean all connections and to ensure that every connection of the standards and cables are correctly torqued. The TRL standards’ characteristics are loaded onto the ANA and the definitions have to be placed in the correct positions within the ANA memory. For the TRL calibration procedure on an ANA, ten measurements are made which combines to determine the 8 errors. The procedure is quite simple and the steps are easily followed from the ANA prompts. Two additional measurements have to be made, however, to attain the isolation errors. Only then can all the errors of the twelve-term error model be calculated. When the reflect standards are connected, one at each port, their reflection coefficients (S11 and S22 ) are measured. The through is not actually a standard, but a direct connection between male and female connectors of the cables. All four S-parameters are measured for the through, as with the line standard. Because a perfectly balanced system is assumed, additional calculations have to be done during the line and thru standard measurements. The ratio of the incident signals at a0 and a3 are measured to determine the switching term. This ratio enables the e11 and e22 error terms to be modified to produce the Source Match (ESF and ESR ) and Load Match errors (ELF and ELR ). An Isolation measurement can be done by connecting the SOLT match standard and measuring the transmission S-parameters (S21 and S12 ). With that the full two-port TRL calibration on the ANA is finished, and the error-calculation and correction will be done.. 2.10. Modelling of TRL and LRM Standards. The same descriptions for the through, reflect (short or open) and match (load) from the SOLT kit are used as in section 2.6, namely equations (2.4 to 2.8). The through is just a straight connection between the male and female cables that are used. A short or an open standard as used in the SOLT calibration can be used for the reflect standard. Lastly for the match, the male and female load standards can be used..

(30) Chapter 2 — ANA Calibration Techniques. 19. Figure 2.14: Scattering transfer parameters (after, [9]) Any short piece of transmission line for which the characteristic impedance and precise physical length is known, can be used for the coaxial line standard. A 94.75ps airline from a verification standards kit was used for this thesis. The airline’s description, SLine can be modelled by the following equation: . SLine = . 0 e−γl. . e−γl  0. (2.46). rof f set td + jωtd 2ZOf f set. (2.47). with γl = αl + βl ≈ and ZOf f set = Z0 + j. rof f set td 2ω. (2.48). where ω is the angular frequency, td is the time delay (directly proportional to the length), rof f set is the offset loss and ZOf f set is the offset characteristic impedance. Another option was open regarding the reflect and match standards. Off-the-shelf male and female short and load standards were taken to NIST and carefully measured across a wide frequency range. Their characteristics were downloaded and saved on file. This enabled the use of their actual characteristic values instead of modelled values.. 2.11. Error-Calculations. One of the most widely known papers on TRL calibration is Engen and Hoer [8], which explains all the theory behind the TRL method. A more recent approach was however found from Rytting [7], which uses matrix algebra to do the error-calculations and corrections for any of the TRL methods, including LRM. The decision was taken to use this approach because of the small difference between the calculations for the TRL and the LRM methods..

(31) 20. Chapter 2 — ANA Calibration Techniques. Figure 2.15: Test setup with T-Parameters To get a bit of background understanding, the definition of Scattering Transfer Parameters will first be discussed as taken from Carson [9]. The T -parameters, T11 , T12 , T21 and T22 are defined with the help of figure 2.14 by the following equation: . . .  . . b T T12   a2   1  =  11 a1 T11 T12 b2. (2.49). where a1 and a2 are the inputs and b1 and b2 are the outputs. When equations (2.49) and (2.1) are combined, the correlation between S-parameters and T -parameters are given by: . . . . T T12  1  −∆ S11   11 = S21 −S22 1 T11 T12. (2.50). with ∆ = S11 S22 − S12 S21. (2.51). Using equation (2.50) to convert the 8-term error-model diagram (figure 2.13) to Tparameters as shown in the test setup diagram of figure 2.15, the following equation can be derived: . TM. . . . 1  −∆X e00  1  −∆Y e22  = TDU T e10 −e11 1 e32 −e33 1. (2.52). where TM is the measured T-parameters and ∆X and ∆Y are defined as: ∆X = e00 e11 − e10 e01. (2.53). ∆Y = e22 e33 − e32 e23. (2.54). and.

(32) Chapter 2 — ANA Calibration Techniques. 21. Equation (2.52) can be rewritten to link the error-terms to the inputs and outputs of the test setup as follows: . . .  . . b 1  −∆X e00   b1   0  = e10 −e11 1 a0 a1. (2.55). and . . .  . . b 1  −∆Y e22   b3   2  = e32 a2 −e33 1 a3. (2.56). If SM is the measured S-parameters at the ANA ports and S is the actual S-parameters of the DUT, the inputs and outputs can also be shown as follows: . . . . h i b a  0  = SM  0  b3 a3. (2.57). and . . . . h i−1 a b  1  = S  1  a2 b2. (2.58). To be able to link the error-terms to the measured S-parameters as well as the actual DUT S-parameters, equations (2.55) and (2.56) were combined by Rytting [7] according to the test setup inputs and outputs to give the following equation: . . b.  0     b3       ···       a0   . a3. . 0  −∆X   0 −k∆Y    =  ··· ···    −e11 . 0. 0 e22.    .. . e00 0  b 1    ..     . 0 ke33   b2        ··· ···  · · ·      ..   a  . 1 0   1    .. a 2 . 0 k. (2.59). where k is defined as: k=. e10 e23. (2.60). With this definition of the errors, two terms from the 8-term error-model (namely e01 and e23 ) were normalised to 1 and another normalising term, k, was introduced. To compensate for the two error-terms that are left out, a switching term calculation has to be done as well. The switch error arises from the fact that the ANA signal generator is electronically switched from port one to port two during the measurement process. The switch paths are not identical and this slight imbalance is described through the switching term. This error term can only be removed on analysers where four independent channels are available. To calculate the switching term, the ratio between the ANA measurement.

(33) 22. Chapter 2 — ANA Calibration Techniques. signals at b0 and b3 is taken. In other words, for the raw S-parameters of the direct through connection, T hru T hru swf = S21 /S12. (2.61). forms the switching term for the forward direction and T hru T hru swr = S12 /S21. (2.62). for the reverse direction. The measured transmission S-parameters of the DUT are then corrected for the switching terms as follows: S21M c = swf S21M. (2.63). and S12M c = swr S12M. (2.64). where S21M c and S12M c are the corrected measured transmission S-parameters. To ease the mathematics and close the link between the error-terms and the measured and actual DUT S-parameters, 4 error matrices T1 , T2 , T3 and T4 , are defined from equation (2.59) by grouping the error terms:           . b0 b3 ··· a0 a3. .       T1     =  ···     T3 . .. . T2   ···    .. . T4.           . b1 b2 ··· a1 a2.           . (2.65). If equation (2.57) replaces the b0 and b3 in equation (2.65) and equation (2.58) replaces the a1 and a2 , a linear equation can be formed: T1 S + T2 − SM c T3 S − SM c T4 = 0. (2.66). where SM c is the switch-term corrected measured S-parameters of the DUT and S is the actual S-parameters of the DUT. This equation expanded in matrix format is used in the MATLAB program code to determine the seven error-terms:  . . S.  11M   0    S21M c . 0. . 1 S S. 11 11M      0 S12 S11M   =    0 S11 S21M c   . 0 S12 S21M c. −S11 −S12 0 0. 0 0 0 1. S21 S12M c 0 0 S22 S12M c 0 −S12cM S21 S22M −S21 0 S22 S22M −S22 −S22M.                        . e00 e11 ∆X ke33 ke22 k∆Y k.          (2.67)       .

(34) Chapter 2 — ANA Calibration Techniques. 23. The error-calculation is done using this equation. By rewriting equation (2.66) to get S in terms of the T-error matrices and the measured SM c, it can be used to do the error-correction: S = (T1 − SM c T3 )−1 (SM c T4 − T2 ). (2.68). The only error-terms that are not addressed with this mathematics are the isolation errors. It was, however, found through actual ANA calibrations, that with the isolation included or omitted, the measured values differ by a relatively small margin (less than 0.01dB). Taking the raw measurements of the standards from the ANA and putting them through these equations in MATLAB gives the error-corrected measurements. For TRL all four S-parameter measurements of the Through standard, two measurements of the Reflect and two measurements for the Line standard are used in the calculations. In the case of the LRM, all S-parameter measurements for the Line, two measurements for the Reflect and two measurements for the Match are used in the program code..

(35) Chapter 3 ANA Calibration with MATLAB Program 3.1. Introduction. Having developed all the mathematics to be used for the calibrations, it had to be compiled in a format which could interface with the ANA for testing. It was decided to use MATLAB due to its strong mathematical ability and the interface programming already developed. Another advantage was the plotting functions which enabled the results of the ANA calibrations to be visually compared to those of the MATLAB programs. Different devices were measured for all the different calibrations and the resulting S-parameters’ magnitude and phase were plotted against frequency.. 3.2. SOLT Calibration using MATLAB. A setup was done on the ANA using phase-stable cables, one with female termination, and the other one, male. A careful SOLT calibration was done using the procedure as set out in section 2.5. The details of the actual ANA setup as well as the parameters used in the programming can be found in appendix A.1. After the calibration was done, a 20dB attenuator from a Verification Kit was connected as DUT and all its S-parameters were measured and downloaded to file. With those values saved, the error-correction on the ANA was turned off to get raw measurements of the 20dB attenuator (which included the systematic errors of the setup). Keeping the correction turned off, all the necessary standards’ S-parameters were also measured and downloaded. For both the through and load standards, all the S-parameters were downloaded, while only the reflection S-parameters were downloaded for the short and open standards. Having obtained all the raw data, the MATLAB program was compiled, the first.

(36) Chapter 3 — ANA Calibration with MATLAB Program. 25. Figure 3.1: 20dB Attenuator magnitude measured with SOLT calibration command being to load all the data from the files. The models for the standards were calculated afterwards (from section 2.6) and, together with the measured data, used in the mathematics of section 2.7 to calculate the errors. The calculated errors were then used together with the raw measurement of the 20dB attenuator to do the error-correction. The final program-corrected data was plotted (for all the S-parameters in magnitude and phase) against the actual ANA corrected measurement of the attenuator. The program code can be found in appenix B.1.. 3.3. Comparison of Results. The resulting MATLAB plots in figures 3.1 and 3.2 show that the program-corrected measurement values agree well with the ANA corrected measurement values. Figure 3.1 shows a maximum deviation between the ANA corrected and the Program corrected S21 and S12 magnitude of 0.03dB from 45MHz to 16GHz. The deviance in magnitude for S11 and S22 begins at 0.5dB at 45MHz and goes to 5dB in the GHz-range. Due to the.

(37) Chapter 3 — ANA Calibration with MATLAB Program. 26. Figure 3.2: 20dB Attenuator phase measured with SOLT calibration reflection measurement being closer to the noise floor at around -40dB, a bigger variation can be expected. The phase plots show the same results, with figure 3.2 not showing more than 2 degrees variation for S11 and S22 for the whole frequency range up to 10GHz. The apparent large difference at 45MHz for S22 is due to a 180 degree shift in the ANA display. The actual measurement is at 181.5 degrees, but the ANA only displays between 180 degrees and 0 degrees. For the phase plots of S21 and S12 the largest difference was 0.2 degrees.. 3.4. TRL and LRM Calibration using MATLAB. Again a careful SOLT calibration was done similar to section 3.2, the only difference being that sliding loads were also used as standard Three different devices were then measured with the correction turned on, namely the 20dB attenuator from the previous measurements, a 75mm airline and a NIST measured short. All the data were downloaded and saved on file..

(38) Chapter 3 — ANA Calibration with MATLAB Program. 27. Afterwards a TRL calibration was done on the ANA, using the direct through connection, 94.75ps delay for the line and SOLT short standards as reflect. An optimal line length is a quarter wavelength or 90 degrees insertion phase in the middle of the frequency span. The insertion phase will, however, vary with frequency. From [11] the difference between the insertion phase of the line standard and thru standard must be between 20 and 160 degrees, as measurement uncertainty will increase significantly beyond these boundaries. The frequencies at which these limits are reached for the line and thru standards used were calculated to be at 586 MHz and 4.69 GHz. The ANA setting details and parameters used for the program code are shown in appendix A.2. The LRM is not a standard option on the ANA calibration menu, therefore the LRM could only be done offline by the program. With the TRL calibration error-correction turned on, all three devices were measured again and the data downloaded. To obtain the data for the programs to use, the correction was turned off and all three devices’ raw measurements downloaded. With the correction still turned off, the raw measurements were made of the standards to be used, namely the direct through connection, the delay line and the NIST measured short and match standards. All the measurement values were downloaded to be used in the offline TRL and LRM calibrations. The MATLAB program included both the TRL and LRM procedures, because of the small difference in the mathematics. The first step was to download all the data again, together with the short and match standards’ actual characteristics, which were carefully measured at NIST. Secondly the models of the standards were calculated from section 2.10 and used together with the raw measured data to calculate the errors as per section 2.11 for both the TRL and LRM. With the calculated errors, the correction could be done (also from section 2.11) for all three devices that were measured. The program-corrected data was then plotted against the ANA corrected measurements for the SOLT and TRL calibrations for all three devices.. 3.5. Comparison of Results. Figures 3.3 and 3.4 show good agreement between the program-corrected measurement values and the ANA corrected measurement values. From figure 3.3 it can be seen that the maximum difference between the ANA corrected and the program corrected S21 and S12 magnitude is 0.015dB from 586 MHz up to 4.69 GHz. For the magnitude of S11 and S22 , an interesting observation can be made. S11 for the ANA SOLT and program LRM values agree to within 0.02db and to 0.3dB from 586MHz to 4.69 GHz, while the ANA TRL and program TRL agree to between 0.2dB and 1.1dB over the frequency range. The two sets, however, differ with up to 2.2dB, and have the least variation of 0.4dB between 2GHz and 4GHz. The S22 have even less variation, 0.018dB to 0.2dB between ANA SOLT and.

(39) Chapter 3 — ANA Calibration with MATLAB Program. 28. program LRM, and between 0.03dB and 0.85dB for the two TRL corrections. The same difference can be seen between the two sets as with S11 , differing with about 2.1dB. From 3GHz to 5GHz the sliding loads were used in the calibration, but only for the program LRM and ANA SOLT. This difference can be seen in S21 and S12 magnitude where the two sets slightly diverge again. The reason is that the sliding load is well-defined at higher frequencies, thus the drop in reflection response. In figure 3.4 for S11 and S22 phase, the difference between the plots show the same characteristics as with the magnitude plots. The SOLT and LRM agree within 1 degree and the TRL corrections between 1 degree and 3.5 degrees, except at 586MHz, where the difference is about 7 degrees. For the phase plots of S21 and S12 the largest difference was 0.2 degrees.. Figure 3.3: 20dB Attenuator magnitude measured with SOLT, TRL and LRM calibrations The plots for the other devices that were measured for comparison were moved to the appendix due to the volume of data that needed to be presented. The plots for the airline and short are shown in sections C.1 and C.2. The airline magnitude plots of figure C.1.

(40) Chapter 3 — ANA Calibration with MATLAB Program. 29. Figure 3.4: 20dB Attenuator phase measured with SOLT, TRL and LRM calibrations show S21 and S12 differences of only 0.015dB to 0.1dB. The reflection values, namely S11 and S22 , directly give the load match and source match errors. This yields valuable information on the symmetry of the system after calibration, and on residual errors. The phases have the same characteristics in figure C.2, with 0.3 degrees difference for S21 and S12 , but a lot of noise on S11 and S22 . The plots of the NIST short measurements can be seen in figure C.3. The NIST short is measured as verification against program calibrations which were done with the NIST short as standard. An ANA SOLT corrected measurement of the short is included, and the values as given by NIST are compared to the measurements as well. The NIST values agree 100% with the program corrected measurements, but have a maximum difference of 0.017dB to 0.04dB for magnitude and 1 degree for phase from the ANA SOLT corrected measurement of the short standards. This can be attributed to the fact that other reflect standards were used for the SOLT calibration..

(41) Chapter 3 — ANA Calibration with MATLAB Program. 3.6. 30. Conclusion. From this experiment of rigorous measurements, it was shown that the ANA software can be successfully duplicated in MATLAB format. The SOLT program corrected measurements agree well with the actual SOLT ANA corrected measurements. The LRM program correction shows good agreement to the actual SOLT calibration as well. The TRL program corrected measurements show good agreement to the actual TRL ANA corrected measurements, and both have good agreement to the SOLT calibration. Considering the results for all the different DUT’s and keeping in mind that the hardware for a simplified home-built ANA is available, this means a cost-effective alternative is possible. Comparing the different programs, all three can be deemed to show good results. The major difference between the three methods lies in the standards used. The SOLT relies upon a high quality match standard and the LRM makes use of a well-defined match standard. The TRL in these experiments makes use of only one line reference, whereas multiline TRL calibrations would yield better results. For both LRM and TRL, one less standard is needed compared to the SOLT, giving a potential cost-saving. The most significant implication for the LRM calibration, however, is in acquiring the characteristics of the match standard. For this experiment, the relevant standards for LRM and TRL were bought at lower cost than actual calibration kit standards, and were measured at NIST. The characteristics have to be measured only once, very carefully, and then it can be used for LRM and TRL calibration. Thus a carefull measurement at either a University laboratory or any accredited laboratory will suffice, implicating a once-off investment for any EMC consultant. Another possible advantage of the LRM and TRL calibrations are that it takes less time than a full SOLT calibration, showing benefits for time and money..

(42) Chapter 4 Standard Radiator 4.1. Introduction. If an EMC consultant succeeds in acquiring cost-effective measurement instrumentation, which could include a hand-held electromagnetic interference receiver (EMIR) or a homebuilt ANA, the following logical requirement would be to have an evaluation space to do measurements. The more commonly used measurement environments include anechoic chambers and open area test sites, which are both expensive to set up. A reverberation chamber, however, could be less costly to set up, and has certain benefits above the other environments, eg. the environment is shielded from external interference. It was decided to construct and evaluate a reverberation chamber against one of the more commonly used environments. Due to limited information on regulations with regard to reverberation chambers, the decision was taken to do the evaluation for EMC radiation testing, as enough information is available on radiation testing on an OATS as well as ways of linking a reverberation chamber measurement to an OATS measurement. For the purpose of the evaluation, a standard radiator was adapted as a DUT which could be measured in both an OATS and a reverberation chamber. Because EMC radiation compliance testing allows limits of up to 6 dB for in and out-of-phase reflections from unknown groundplanes, it was decided to keep the design of the radiator as simple as possible.. 4.2. Radiator Housing. The basic requirement for the standard radiator was to radiate at certain fixed frequencies dictated by the test environments. For the reverberation chamber a lower limit of 500MHz was set and for the OATS the upper limit was 1GHz. Furthermore, the radiator was constructed as a sealed box on which different antennas could be interchanged. An undergraduate student, Rowan Youell, had already constructed such a radiator [12], and it was decided to modify the circuitry of that unit to fit the requirements of this.

(43) Chapter 4 — Standard Radiator. 32. Figure 4.1: Isometric view of radiator unit [12] experiment. The unit was constructed from double-sided PCB board having dimensions of 0.4m x 0.15m x 0.08m. The sides and bottom of the box were soldered together and sealed with conductive adhesive metallic tape, but the lid was made to be removeable, should the circuitry need to be changed. When measurements are made, the lid must be sealed again with the metallic tape to ensure that no leakage currents can escape and that all emissions are radiated only by a specified antenna. This antenna can be attached to the BNC connector fitted at the top of the unit. The slot opening on the side was not used for this thesis. An isometric view of the radiator box is shown in figure 4.1. The power of the unit is provided by two 9V batteries which are housed in a separate shielded chamber in the lid. A schematic diagram for the unit can be found in figure D.1 in appendix D.. 4.3. Radiator Circuitry. A diagram for the radiator circuitry can be seen in figure 4.2. A supply voltage of 18V, given by two 9V batteries, is regulated by a Voltage Regulator (VR) chip down to 15V. The VR then gives a stable supply to a Voltage Controlled Oscillator (VCO) and a.

(44) Chapter 4 — Standard Radiator. 33. Figure 4.2: Diagram for the radiator circuitry high frequency Operational Amplifier (Op-amp). The VCO gives a voltage dependant frequency range from 500MHz to 1GHz. The Op-amp is set to amplify the signal to the supply rails to deliver a square-wave output with harmonics in the frequency domain. The input to the VCO comes from two VRs supplying 5V and 12V respectively (these two voltages were chosen because the chips were readily available from the store). The input to the VCO can be switched between the two VR’s with a toggle switch at the side of the box. The output from the Op-amp was also made to switch between a slot opening radiation and the BNC connector. For this thesis the slot was not used and it was sealed with metallic tape. Thus the output only goes to the BNC connector to which any antenna with a BNC connector could be attached. A light emitting diode (LED) is included right after the 15V VR to show when the batteries are going low. If the LED is not burning, the batteries have dropped below the 15V supply for the VR and should be replaced. The two antennas that were used with the radiator unit previously by Rowan Youell, were used for this experiment as well. They were a 400mm monopole antenna and a 75mm radius loop antenna, both with BNC connectors.. 4.4. Testing the Radiator. The unit was connected to a spectrum analyser to determine at which frequencies it was radiating. Initially the input circuit to the VCO consisted of a Voltage Divider (VD) made up of resistors. After frequency drift problems, this was replaced with the VR input circuits. For the two different circuits, the following frequencies, as well as the power output of the VR circuit at the BNC connector, were recorded: For the VD circuit, there was a very small voltage drift due to resistor tolerances,.

(45) 34. Chapter 4 — Standard Radiator VD Voltage. Frequency. VR Voltage. Frequency. Power Output. 2V. 521.7 MHz. 5V. 645.9 MHz. -11.1 dBm. 8V. 781.5 MHz. 12 V. 933.7 MHz. -9.5 dBm. Table 4.1: Radiator frequencies and VR circuit power output. causing a significant drift in frequency. For the VCO the frequency range of 500MHz to 1GHz is given by an input signal of 1V to 16V. This implies that a change of 31kHz can be found for a 1mV change in voltage. With the resistors’ tolerances in the voltage divider circuit, the voltage kept drifting with an average of 45kHz per minute (see table 4.2). This presented a problem, seeing that the bandwidth (BW) for the frequency measurement was set on 120kHz. Within a half-minute measurement time, the peak could drift beyond the center-frequency for which the EMI receiver was set. Time Elapsed. Frequency. Drift. -. 521.79 MHz. -. 1 min. 521.74 MHz. 50 kHz. 1 min. 521.72 MHz. 20 kHz. 1 min. 521.70 MHz. 20 kHz. -. 781.64 MHz. -. 1 min. 781.57 MHz. 70 kHz. 2 min. 781.47 MHz 100 kHz. 1 min. 781.41 MHz. 60 kHz. Table 4.2: Frequency drift for Voltage Divider circuit. The decision was then taken to replace the VD circuit with VRs to stabilise the input voltages to the VCO. The frequency drift was measured again and found to be (on average) 31kHz per minute at 933MHz and 4.5kHz per minute at 645MHz, as can be seen in table 4.3. One important observation was made when connecting the batteries. The initial drift of the frequency was much more significant in the first two minutes. Table 4.4 shows the amount of drift within the first two minutes, but then it stabilises after that time. A possible reason could be due to the temperature change within the circuitry when connecting the batteries. The VR chips and the VCO first have to reach their operating temperature before their outputs stabilise. This makes it important to give the radiator time to warm up before measurements are taken, and to check the frequency on regular intervals between measurements..

(46) 35. Chapter 4 — Standard Radiator Time Elapsed. Frequency. Drift. -. 933.395 MHz. -. 30 sec. 933.377 MHz. 18 kHz. 30 sec. 933.362 MHz. 15 kHz. 30 sec. 933.345 MHz. 17 kHz. 30 sec. 933.333 MHz. 12 kHz. -. 645.970 MHz. -. 30 sec. 645.968 MHz. 2 kHz. 30 sec. 645.965 MHz. 3 kHz. 30 sec. 645.963 MHz. 2 kHz. 30 sec. 645.965 MHz. 2 kHz. Table 4.3: Frequency drift for Voltage Regulator circuit Time Elapsed. Frequency. Drift. -. 645.700 MHz. -. 30 sec. 645.390 MHz. 310 kHz. 30 sec. 645.270 MHz. 120 kHz. 30 sec. 645.200 MHz. 70 kHz. 30 sec. 645.203 MHz. 3 kHz. 30 sec. 645.202 MHz. 1 kHz. 30 sec. 645.200 MHz. 2 kHz. Table 4.4: Initial frequency drift when connecting batteries. 4.5. Radiator Antennas. To have a controlled radiation pattern, two antennas, namely a loop antenna and a monopole antenna, were used. They were attached to the BNC connector of the radiator for both the reverberation chamber and the OATS measurements. A photograph of the radiator unit with the loop antenna attached is shown in figure 4.3. These antennas were not evaluated to determine their efficiency, but their worst case directivity was taken as 1.76 dB for an ideal monopole and 1.76 dB for the loop antenna [13]..

(47) Chapter 4 — Standard Radiator. 36. Figure 4.3: Radiator with loop antenna attached. 4.6. Conclusion. The standard radiator was working and ready for measurement in a reverberation chamber and on an OATS. In a reverberation chamber, a total radiated power measurement is made of the radiator. On an OATS, however, the voltage is measured (in one direction only) from a distance of 10 meters. The voltage measurement on the OATS is used to calculate the radiated E-field at the receiving antenna (10 metres from the radiator). To be able to compare the two measurements, it was decided to use the reverberation chamber power measurement to make a prediction of an OATS equivalent E-field measurement. Detail on how this was done is explained in the following chapters..

(48) Chapter 5 Reverberation Chamber 5.1. Introduction. The four types of EMC testing on electronic equipment are usually for diagnostics, precompliance, full compliance and production [14]. For this thesis the focus is mainly on pre-compliance testing, as an EMC consulting service. This serves as a check before products go for expensive radiated emission and immunity testing for full compliance to regulations. Currently these tests are mainly done in an anechoic chamber or on an OATS. These environments are costly to set up, therefore the latest option for precompliance testing, namely the reverberation chamber, was chosen to be investigated. The reverberation chamber option for radiation and immunity testing is much more versatile in setting up, is not weather-dependent and a chamber can be constructed in nearly any business site, depending on the size required. For the purpose of this investigation, only the radiation testing was considered.. 5.2. What is a Reverberation Chamber?. Some of the pioneering research on reverberation chambers started in 1976 [15]. Initial intent of the research was for the purpose of shielding effectiveness of cables, connectors and enclosures. The scope of work was later expanded to include susceptibility testing of electronic equipment, immunity testing and emmissions testing. A reverberation chamber is an electrically large, highly conductive enclosed cavity or chamber used to conduct high frequency electromagnetic (EM) measurements on electronic equipment [16], [17]. The chamber can be any size required, depending on the size of the DUT to be tested and the measurement frequencies. The main difference to any other enclosed chamber used for EM measurements, is that the reverberation chamber has a large rotating metallic reflector or stirrer inside the test chamber. The purpose of the stirrer is to change the positions of the maximums (or modes) in the electromagnetic.

(49) Chapter 5 — Reverberation Chamber. 38. field throughout the chamber over one revolution of the stirrer. This produces a field that, when averaged over one revolution, is homogeneous, as the maximum modes obtained within the chamber are independent of position [18]. The resulting measurement is a total-radiated power measurement of the DUT. Some of the advantages of the reverberation chamber are that measurements can be taken over a wide frequency range inside a screened environment, and that total-radiated power measurements can be made anywhere inside a large working volume inside the chamber, due to an isotropic and uniform test environment. Disadvantages, however, are that the measurement needs to be averaged over many stirrer positions and that regulation on reverberation chambers are not readily available in current standards [16], [19], [20].. 5.3. Layout and Design. The decision was taken to use an existing enclosed chamber with dimensions 2.455m x 2.475m x 3.720m = 22.4m3 . All the chamber needed were the stirrers. To retain a large working volume inside the chamber, it was decided to put two smaller stirrers inside the chamber rather than one large stirrer, giving more attention to placement [21].. Figure 5.1: Reverberation chamber layout From [17] the working volume of a reverberation chamber is defined as being a distance of λ/3 from the chamber walls and from any antenna, stirrer or other object at the lowest frequency of operation. This ensures a free space in which the uniform field can be measured. To keep this as large as possible, one stirrer was placed vertically in the corner.

(50) Chapter 5 — Reverberation Chamber. 39. closest to the door, and the other horizontally across the chamber at the side opposite to the door. Figure 5.1 shows the layout of the chamber. From various sources [16], [22], [15], the only requirements for the paddles were to be as large as possible and arbitrarily shaped. This gave a wide berth of designs and options. The largest constraint, however, was to limit the size to allow a large enough working volume, but be large enough to give sufficient reflections in all directions through one revolution. From [16], the minimum frequency that could be used for the volume of the chamber is 300MHz. This would imply that the working volume would be λ/3 = 330mm from any object or wall. It was decided to place four aluminium plates on each stirrer, keeping the chamber dimensions and working volume constraints in mind. The four plates’ dimensions were limited to 950mm x 950mm, placed at 145 degrees to a carbon-fibre axis and oriented at 90 degrees to neighbouring plates, but not touching each other. The photographs in figure 5.2 show how the design was implemented.. Figure 5.2: Photographs showing the reverberation chamber stirrers The stirrers are driven by stepper motors and can be controlled by computer to either step or turn continuously at a speed of up to 2 revolutions per minute. The need for a stepper motor was justified by the two methods for measurement operation in a.

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