Modelling an RF Converter in Matlab

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(1)Institutionen f¨ or systemteknik Department of Electrical Engineering. Examensarbete. Modelling an RF Converter in Matlab Mattias Hjorth och Bj¨ orn Hvittfeldt LiTH-ISY-EX-3260-2002 13 februari 2002. Department of Electrical Engineering Linköping University SE-581 83 Linköping, Sweden. Linköpings tekniska högskola Institutionen för systemteknik 581 83 Linköping.

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(3) Modelling an RF Converter in Matlab Examensarbete utf¨ ort i datatransmission vid Link¨ opings tekniska h¨ ogskola av Mattias Hjorth och Bj¨ orn Hvittfeldt Reg. nr: LiTH-ISY-EX-3260-2002. Abstract Radar warning systems are life saving equipment in modern fighter aircraft. It is therefore vital that the system can tell the difference between a threat (genuine frequency) and a false signal (spurious frequency). This thesis presents a model aimed at predicting the frequencies and other parameters in the RF converter of the radar warning system. The components of the RF converter have been studied, measured, and modelled. The modelling tool has been the Simulink toolbox for Matlab. Extreme accuracy has been sacrificed in order to make the model easy to use for the working engineer. Instead, this model presents a rough estimate of some of the most important properties of the radar warning system with just a few data sheet figures as input. The simulation results are satisfactory as a whole. Simulink is the limiting factor in the implementation of the model. Significantly improved results can probably be obtained by working in another software environment. Key words: Radar warning receiver, Spurious frequencies, Model, Simulink, Matlab, Mixer, Amplifier, Filter. Supervisor: Examiner:. Simon Germishuizen Ulf Henriksson Link¨ oping, February 13, 2002.

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(5) Avdelning, institution Division, department. Datum Date. Data Transmission Department of Electrical Engineering. February 13, 2002. Språk Language. Rapporttyp Report category. ❑ Svenska/Swedish x Engelska/English ❑ ❑ ______________. ❑ x ❑ ❑ ❑ ❑ ❑. Licentiatavhandling Examensarbete C-uppsats D-uppsats Övrig rapport _______________. URL för elektronisk version URL for electronic version. ISBN. ISRN. LiTH-ISY-EX-3260-2002 ISSN. Serietitel och serienummer Title of series, numbering. http://www.ep.liu.se/ Titel Title. Modellering av en radarvarningsmottagare i Matlab Modelling an RF Converter in Matlab Författare Authors. Mattias Hjorth and Björn Hvittfeldt. Sammanfattning Abstract. Radar warning systems are life saving equipment in modern fighter aircraft. It is therefore vital that the system can tell the difference between a threat (genuine frequency) and a false signal (spurious frequency). This thesis presents a model aimed at predicting the frequencies and other parameters in the RF converter of the radar warning system. The components of the RF converter have been studied, measured, and modelled. The modelling tool has been the Simulink toolbox for Matlab. Extreme accuracy has been sacrificed in order to make the model easy to use for the working engineer. Instead, this model presents a rough estimate of some of the most important properties of the radar warning system with just a few data sheet figures as input. The simulation results are satisfactory as a whole. Simulink is the limiting factor in the implementation of the model. Significantly improved results can probably be obtained by working in another software environment.. Nyckelord Key words. Radar warning receiver, Spurious frequencies, Model, Simulink, Matlab, Mixer, Amplifier, Filter.

(6) c 2002 Mattias Hjorth and Bj¨. orn Hvittfeldt. The publishers will keep this document online on the Internet—or its possible replacement—for a considerable time from the date of publication barring exceptional circumstances. The online availability of the document implies a permanent permission for anyone to read, to download, to print out single copies for your own use and to use it unchanged for any non-commercial research and educational purpose. Subsequent transfers of copyright cannot revoke this permission. All other uses of the document are conditional on the consent of the copyright owner. The publisher has taken technical and administrative measures to assure authenticity, security and accessibility. According to intellectual property law the author has the right to be mentioned when his work is accessed as described above and to be protected against infringement. For additional information about the Link¨ oping University Electronic Press and its procedures for publication and for assurance of document integrity, please refer to its WWW home page http://www.ep.liu.se/. This report was typeset on a pc using the MikTEX distribution of LATEX 2ε with WinEdt as text editor. The layout uses the fancyhdr package, the book class with changes to the paper size, and sans serif typeface for headers. The PDF output was created with pdfLATEX and the graphics in XFig. Printed in Sweden by UniTryck, Link¨ oping 2002. The cover was printed on Calorit 160 g, and the body on Multicopy 80 g..

(7) Preface As much as this report has meant hard work for us, it has also been an experience far beyond what we had expected when we first decided that we should do our final thesis together. During our time at Link¨ oping University, we have discovered that we complete each other in the way we work and think. Mattias is the hands-on guy, who tries new ideas and never reads the user manual before springing into action. Björn is the methodical type, who reads the book from cover to cover. Our year together at LinTek in 1998–1999 made us realise that we would actually stand each other during the creation of a final thesis. We set our target high, and decided to do our thesis together, in a country with a warm climate, and with an English speaking population. Australia was the first country on our list, since Saab has a subsidiary there. We had no success. After that, South Africa emerged as a possible candidate. Our contacts went from Saab headquarters in Linköping, via Saab Avionics in J¨ arf¨ alla, to Avitronics in South Africa. Once the initial contact had been made, things went fast. Before we knew it, we had landed on Johannesburg International. Doing our thesis at Avitronics has given us many moments to remember. First of all of course, we have worked hard to realise the report you are now reading. But in our spare time, we have also taken the opportunity to experience South Africa. We will remember the scenery, the weather, the shopping, the crime, and the poverty. But above all, we will remember the people. Friendly, curious, and helpful, they helped making our stay a memory for life. Thank you! mattias hjorth mattias@hjorth.info bj¨ orn hvittfeldt bjorn@hvittfeldt.com. v.

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(9) Acknowledgments The authors would like to express their gratitude towards the following people (in alphabetical order) for their assistance and support during our work on this report. Besides these specific individuals we would like to thank all employees at Avitronics for their hospitality. Nico van Dalen Nicklas Forsberg Simon Germishuizen Fredrik Gustafsson Bjo ¨rn Henriksson Ulf Henriksson Dave Howie Monica Kjellander Daniel Lindeque Merenchia Louw Rose Mahashe Denis Milton Thinus Neethling Alenka Rosenqvist Johan S¨ afholm Anton Snyman. Matlab wiz at the Signal Processing Lab. For helpful feedback on the report. Our supervisor. For invaluable (and quick!) help on some Matlab issues. For sending us to South Africa. Our examiner. For getting us started and supplying us with the necessary papers, books, and components. Without Monica, this thesis would not have been possible. For being an excellent office neighbour, library, and host at a number of social events. Our main contact at Avitronics, words are not enough to express our gratitude. For that excellent coffee. Always with a smile on his face and a working knowledge in many areas. For helping us with amplifier and filter measurements. For that initial contact with Saab in Järfälla. For helpful feedback on the report. Another guy who knows his components, and who also provided a daily translation of the phrase of the day.. vii.

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(11) Contents Preface. v. Acknowledgments 1 Introduction 1.1 Background . . . . . . . . . 1.2 Problem Identification . . . 1.3 The Thesis . . . . . . . . . 1.3.1 Purpose . . . . . . . 1.4 Methods . . . . . . . . . . . 1.4.1 Method Weaknesses 1.5 Thesis Outline . . . . . . .. vii. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. 1 1 1 1 2 2 2 2. 2 Radar Warning Receivers 2.1 Overview of Radar Warning Receivers 2.2 Components . . . . . . . . . . . . . . . 2.2.1 The RF Converter . . . . . . . 2.2.2 The Synthesiser and LO Units 2.2.3 The DSP Unit . . . . . . . . . 2.2.4 The Controller . . . . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. 5 5 5 5 6 6 7. 3 Theory and Measurements of the RF Converter 3.1 RF Converter Outline . . . . . . . . . . . . . . . . 3.1.1 Signals . . . . . . . . . . . . . . . . . . . . . 3.1.2 Noise Figure . . . . . . . . . . . . . . . . . 3.1.3 Spurious Free Dynamic Range . . . . . . . 3.1.4 Voltage Standing Wave Ratio . . . . . . . . 3.2 Mixer Theory . . . . . . . . . . . . . . . . . . . . . 3.2.1 Conversion Loss . . . . . . . . . . . . . . . 3.2.2 Noise Figure . . . . . . . . . . . . . . . . . 3.2.3 Intermodulation . . . . . . . . . . . . . . . 3.2.4 Isolation Port-to-Port . . . . . . . . . . . . 3.2.5 Conversion Compression Point . . . . . . . 3.3 Mixer Measurements . . . . . . . . . . . . . . . . . 3.4 Amplifier Theory . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . . .. 9 9 9 10 10 11 12 13 14 14 14 14 15 15. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. ix.

(12) CONTENTS. . . . . . . . . . . . .. . . . . . . . . . . . .. 16 16 17 18 18 19 19 19 19 20 20 20. 4 Implementation of the RF Converter Model 4.1 The Aim of the Model . . . . . . . . . . . . . . . . . . . . 4.2 Earlier Work . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Earlier Mixer Work . . . . . . . . . . . . . . . . . 4.2.2 Earlier Amplifier Work . . . . . . . . . . . . . . . . 4.2.3 Earlier Filter Work . . . . . . . . . . . . . . . . . . 4.3 What Tool to Use . . . . . . . . . . . . . . . . . . . . . . 4.3.1 The Simulink Block Structure . . . . . . . . . . . . 4.4 Mixer Implementation . . . . . . . . . . . . . . . . . . . . 4.4.1 Intermediate Frequency and Spurious Components 4.4.2 Suppression . . . . . . . . . . . . . . . . . . . . . . 4.4.3 Noise . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Mixer Validation . . . . . . . . . . . . . . . . . . . . . . . 4.6 Amplifier Implementation . . . . . . . . . . . . . . . . . . 4.6.1 Noise . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.2 Amplification . . . . . . . . . . . . . . . . . . . . . 4.6.3 Harmonics . . . . . . . . . . . . . . . . . . . . . . . 4.6.4 Saturation . . . . . . . . . . . . . . . . . . . . . . . 4.7 Amplifier Validation . . . . . . . . . . . . . . . . . . . . . 4.8 Filter Implementation . . . . . . . . . . . . . . . . . . . . 4.8.1 Frequency Response . . . . . . . . . . . . . . . . . 4.8.2 Noise . . . . . . . . . . . . . . . . . . . . . . . . . 4.9 Filter Validation . . . . . . . . . . . . . . . . . . . . . . . 4.10 Model Implementation . . . . . . . . . . . . . . . . . . . . 4.11 Model Validation . . . . . . . . . . . . . . . . . . . . . . . 4.11.1 Improvements . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . .. 23 23 23 24 24 24 25 26 26 27 28 28 32 33 33 33 33 35 35 37 37 37 38 38 40 41. 5 Conclusions and Possible Enhancements 5.1 Achievements . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Recommended Improvements . . . . . . . . . . . . . . . . .. 47 47 48. 3.5 3.6. 3.7. x. 3.4.1 Saturation and Clipping . . . . . . . . . . . 3.4.2 Linear Gain and 1 dB Compression Point . 3.4.3 Two-Tone Third-Order Intercept Point . . . 3.4.4 One-Tone Second-Harmonic Intercept Point Amplifier Measurements . . . . . . . . . . . . . . . Filter Theory . . . . . . . . . . . . . . . . . . . . . 3.6.1 Noise Figure . . . . . . . . . . . . . . . . . 3.6.2 Cutoff Frequencies and Filter Bandwidth . 3.6.3 Ripple . . . . . . . . . . . . . . . . . . . . . 3.6.4 Insertion Loss . . . . . . . . . . . . . . . . . 3.6.5 Frequency Responses . . . . . . . . . . . . . Filter Measurements . . . . . . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . ..

(13) CONTENTS. Appendices A Measurement data A.1 Mixer Measurements . . . . . . . . . . . . . . . . . . . . . .. 49 49. References. 51. Index. 53. xi.

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(15) Chapter 1. Introduction 1.1. Background. Avitronics is owned 51% by the Grintek group and 49% by Saab AB. Avitronics and Saab are both strong players on the international defence market. Avitronics markets radar warning receivers and laser warning receivers with peripherals in the form of e.g. displays, chaff and flare dispensers, and decoy systems. For the new radar warning receiver, Avitronics produces the analog receiver and Saab the digital signal processing (DSP) unit. For the analog receiver, a design was proposed in June of 2001. Due to lack of time the design was based on some analysis and largely practical experience. Avitronics therefore proposed that we should model the radar warning receiver. The model would then be used to evaluate the decided design and to improve the design for future iterations.. 1.2. Problem Identification. The present problems when designing a radar warning system receiver are largely related to lack of funding and time. Specifically, we conclude that Avitronics has two major problems in system design. 1. No in-house produced software for system modelling exists. 2. Employees use unreliable sources, such as web-based non-commercial software in the design process.. 1.3. The Thesis. Considering the problems mentioned above and the time available for this project, it was decided that modelling the RF converter was most impor1.

(16) CHAPTER 1 · INTRODUCTION. tant. Therefore, this thesis is a study of a model of the RF converter in a radar warning receiver system. The Simulink toolbox for Matlab has been used as a modelling tool.. 1.3.1. Purpose. The main purpose of this thesis is to present an accurate model of an RF converter. A second purpose is for the model to be easily adaptable to configuration changes in the converter.. 1.4. Methods. We have done a theoretical study of each component of the RF converter. Each component has then been divided into smaller blocks, such as noise addition, creation of spurious frequencies, etc. These sub-blocks have then been modelled one by one in the Simulink environment. Blocks that are common to several components have been reused. Measurements on actual components have been compared with model data to validate the correctness of the model. Naturally, simplifications and approximations have been made. They are mentioned throughout the report.. 1.4.1. Method Weaknesses. The model is based largely on our own assumptions regarding what is important in the process of designing an RF converter. Also, we have had difficulties in finding relevant literature concerning the theoretical aspects of the components. A more thorough approach could maybe have involved studies in the field and interviews with engineers working with receiver design, to get a “wishlist” of features in the model. Also, the final result presents a rather rough image of the RF converter. Ideally, more time should have been invested in the model and less time spent struggling with the modelling tool.. 1.5. Thesis Outline. The thesis is structured in the following way. Chapter 2 gives a brief introduction to radar warning receivers and explains the role of the RF converter and the other components in the system. Chapter 3 gives a theoretical background on the RF converter. It begins with a general description of the converter and its parameters and goes on to describe the converter on a component level (mixers, amplifiers, and filters). 2.

(17) 1.5 · THESIS OUTLINE. Chapter 4 is the implementation chapter. The Simulink model is constructed, block by block. Finally, the complete model is put together. Chapter 5 presents conclusions and discusses possible enhancements of the present model. Appendix A presents some measurement data too bulky to fit into the report itself.. 3.

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(19) Chapter 2. Radar Warning Receivers The purpose of this chapter is to present an overview and background of radar warnings receivers. The main functionality is described and the reader with little or no knowledge of radar warnings receivers can understand the purpose. A reader with more experience from radar warnings receivers can skip this and the next chapter and jump directly to Chapter 4.. 2.1. Overview of Radar Warning Receivers. To protect themselves, military aircraft are equipped with radar warning receivers (RWR). The RWR intercepts radar emissions from friendly as well as hostile radar stations. These radar stations can be fixed (e.g. at air force bases) or mobile (e.g. on board other aircraft or sea vessels). The RWR has an RF converter that converts the incoming radio frequency (RF) signal to a lower intermediate frequency (IF). After reception and conversion, the signal is fed to a digital signal processing unit. After processing the signal, the RWR system can supply the pilot with information concerning type, range, bearing, and nationality of the emitting radar. If the emission is hostile, the pilot then uses this information when deciding how to react to the threat.. 2.2. Components. Here the main parts of the RWR system are described. When reading this section, refer to Figure 2.1 to better understand how the different parts of the system interact.. 2.2.1. The RF Converter. The RF converter that we have focused on is of the double superheterodyne type. This type of converter combines good sensitivity (the ability to detect 5.

(20) CHAPTER 2 · RADAR WARNING RECEIVERS. and amplify the signal without too much distortion) with good selectivity (the ability to select between frequencies that are close to each other in the spectrum) and is the most common type on the market today. For basic and advanced theory on receivers, refer to [1] and [10], respectively. The job of the RF converter is to convert the incoming signal to a predetermined frequency band. This band, which contains much lower frequencies than the incoming signal, can be more easily handled by the DSP unit. It is much easier to sample on a signal in the 1 GHz region than on a signal in the 18 GHz region. Also, with the lower sample rate, the amount of data created during sampling will decrease. The cost of the DSP unit will also be lower.. 2.2.2. The Synthesiser and LO Units. To sweep the frequency spectrum, the receiver needs a reference signal generated by the synthesiser. The synthesiser produces sinusoidal signals between 2 and 18 GHz in steps of 100 MHz. If one or more interesting signals are found, the synthesiser can reduce to sweeping only the frequencies of interest instead of the whole spectrum. Every once in a while though, it sweeps the entire spectrum to see if any new frequencies have appeared. What frequencies to sweep is decided by the DSP unit and controlled by the controller. The local oscillator (LO) produces another reference signal needed by the receiver. This reference signal is used to convert the received signal to the desired frequency of the DSP unit. The LO frequency is fixed.. 2.2.3. The DSP Unit. The digital signal processing unit is the heart of the RWR system. Here decisions are taken on whether the received signal contains anything interesting. If an interesting signal is found, it is analysed in several aspects. Nationality The DSP unit has a built-in library of radar signals. If a signal matching the received one is found in the library, the DSP unit knows make and model, and can even differentiate between radars of the same type. Bearing The aircraft has several antennas for receiving radar signals. By comparing receptions of the same signal by different antennas, the DSP unit can calculate the bearing of the signal using interferometry techniques. Position By flying the aircraft in a circle around the radar station and constantly calculating the bearing, the DSP unit can triangulate the position of the station. Mode By comparing the received signal to the match in the library, the DSP unit can decide what mode the radar station is currently working in. If the station is in sweeping mode, it will be continuously 6.

(21) 2.2 · COMPONENTS.

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(29) Figure 2.1: The main components of an RWR system.. monitored. If it has locked on target, the aircraft is in danger. The pilot must take action to avoid the threat.. 2.2.4. The Controller. The controller is the feedback between the DSP unit and the receiver. It takes its orders from the DSP unit and controls the sweep of the synthesiser.. 7.

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(31) Chapter 3. Theory and Measurements of the RF Converter The main content of this chapter is the theory of the RF converter. First, some general aspects of the converter are presented. After that, each of the components is explained from a theoretical point of view. Measurements of each component are also presented.. 3.1. RF Converter Outline. In this section we present some general properties of the RF converter. Many of these properties will also be addressed later, on a component level.. 3.1.1. Signals. In Figure 3.1, we see a basic outline of the RF converter. Our RF converter works as mentioned like a superheterodyne receiver. The input radar signal enters the converter from the left and first passes the pre-selector and an amplifier. The radar signal is usually a pulsed sine wave with a pulse repetition interval of a few hundred microseconds. The frequency is often in the range 0.5–18 GHz. The incoming RF signal is first upconverted to a higher intermediate frequency, which passes a bandpass filter, and then downconverted again. The frequency conversion is done in the mixer, which takes two input signals, the RF signal and a signal from the local oscillator. The output RF signal has a fixed frequency predetermined by the last band pass filter in the converter. If we define the local oscillator signal and the synthesiser signal as input signals, the RF converter takes three input signals. The control unit determines the frequency of the synthesiser. The local oscillator, LO, has a fixed frequency. 9.

(32) CHAPTER 3 · THEORY AND MEASUREMENTS OF THE RF CONVERTER.

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(37) . Figure 3.1: Basic outline of the RF converter.. 3.1.2. Noise Figure. As in all designs the noise is a big parameter to care for in the RF converter. Each component adds noise to the already existing white noise and the amount of noise power added is referred to as noise figure. Noise figure, or single sideband noise figure, is defined as N F = 10 log. Pnoise out = 10 log F Pnoise in · G. where G is the gain in active devices. The cascade noise figure Gcascade is of high importance in an RF converter. Since we are interested in detecting a signal with very low signal power the noise in our converter is a main parameter in the design. The white (thermal) noise at the input has a noise power of kT B = −87 dBm at 298 K and 500 MHz bandwidth. A proposed cascade noise figure Gcascade is 10 dB which gives us a minimum detectable signal (MDS) at −87 + 10 = −77 dBm.. 3.1.3. Spurious Free Dynamic Range. The incoming radar signal is most likely a sum of more than one signal. Each RF signal of a certain frequency will mix with all the other RF signals in the radar signal. The mixed products are referred to as harmonics. Most of the harmonics generated are highly suppressed except for the two-tone third order harmonics, i.e. 2f1 − f2 and 2f2 − f1 . If f1 and f2 are close to each other in the frequency domain, the third-order intermodulation products will be close in frequency to the wanted signal. For design reasons the spurious free dynamic range (SFDR) are of great interest. It tells us in which power range we can detect a signal without 10.

(38) 3.1 · RF CONVERTER OUTLINE. . . . . . . Figure 3.2: System SFDR projection.. noise or harmonics disturbing the wanted signal, see Figure 3.2. The main parameter for measuring the SFDR is the two-tone third order intercept point, IP3 . The third-order products begin to show when the input power reaches a certain level, called IMD (short for intermodulation distortion). They are amplified much like the wanted signal, with the difference that the amplification curve has a slope of three (as opposed to a slope of one for the wanted signal) in the linear region. To reach the intercept point, extrapolate the linear regions of the fundamental curve and the third-order curve. The spurious free dynamic range is measured as SF DR = IM D − M DS.. 3.1.4. Voltage Standing Wave Ratio. Our RF converter uses a 50-ohm system. If there is a mismatch in the portto-port impedance a part of the incident wave is reflected and a standing wave is created. In the design of the RF converter the voltage standing wave ratio (VSWR) is a parameter used for the mismatch. The VSWR is the ratio between the peak and the valley of standing waves on a transmission line. One can also define the VSWR through the definition of the reflection coefficient ZL − ZO ρ= ZL + ZO where ZL is the input impedance and ZO is the feedline impedance. When ZL = ZO the reflection coefficient is zero and there is no reflected signal. From the reflection coefficient we have V SW R =. 1 + |ρ| 1 − |ρ| 11.

(39) CHAPTER 3 · THEORY AND MEASUREMENTS OF THE RF CONVERTER. and we can also calculate the return loss from LR = −20 · log(|ρ|). Return loss is the ratio in decibels of maximum power sent down the transmission line to the power returned toward the source. The return loss is infinite if all the power is absorbed in the circuit.. 3.2. Mixer Theory. The mixer is an RF component used for frequency conversion. A mixer has two input ports (RF, LO) and one output port (IF), see Figure 3.3. The frequency conversion is achieved by modulation of the periodic RF signal at frequency fRF with a periodic waveform LO having frequency fLO . The output signal contains frequencies from the sum and difference of fLO and fRF fIF = fRF + fLO and fIF = fRF − fLO or fIF = fLO − fRF depending on which sums are positive. In the ideal case those are the only two frequencies in the output signal, but in reality the mixer also generates other undesired frequencies called intermodulation products [8]. Intermodulation (IM) products are generated at frequencies fIF = ±mfRF ± nfLO where m, n are integers. The value n is called the order of modulation and the sum |m1 |+|m2 |+. . . is often referred to as the order of intermodulation. One of the IM products is known as the image because it appears as the mirror image of the signal frequency about the oscillator frequency [16]. On the market today many types of mixer circuits exist. The most common type is the double balanced diode mixer. Other mixers are triple balanced, class IV, and single ended mixers [9]. From now on we refer to the double balanced diode mixer as “the mixer”. In the mixer, a periodic LO signal applied at the LO port in Figure 3.3 causes conduction of the alternate diode pairs. During positive LO cycles, diodes D1 and D2 are turned on while D3 and D4 are off. For negative LO cycles the opposite is true. A virtual ground is therefore switched between the RF to IF transformer windings at a rate corresponding to the LO frequency. This causes the RF signal seen by the IF port to change phase by 180◦ every time the LO signal changes polarity. This process is called bi-phased modulation and can be mathematically represented [8] by multiplying the sinusoidal RF signal voltage with the Fourier series of the square wave switching function, i.e. the diode conductance waveform 4 X 1 Vout = VRF sin(ωRF t) sin(nωLO t) π n=1,3,5,... n It is this equation that gives us the IM products. 12.

(40) 3.2 · MIXER THEORY. . . Figure 3.3: Schematic diagram of a double balanced mixer.. 3.2.1. Conversion Loss. Conversion loss is normally referred to as a single sideband (SSB) conversion loss. If we assume that no intermodulation products or losses exist, we can calculate the theoretical minimum conversion loss in a generalised linear mixer. The conversion loss is defined as.

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(43) . RF input power IF output power.

(44). For the ideal mixer we expand the Fourier series for n = 1 (no IM products),

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(47) . 4 sin(ωLO t) = π 1 4

(48) · · [cos((ωLO − ωRF ) · t) − cos((ωLO + ωRF ) · t)] 2 π. Vout = VRF sin(ωRF t) VRF. The IF voltage (the amplitude of the signal with the desired frequency) is VIF = VRF ·. 1 4 · 2 π. and the RF to IF conversion loss LC = 20 log. VRF π = 20 log = 3.92 dB VIF 2. The conversion loss in a non-ideal diode mixer has three components: loss in the diode resistance, loss in the diode junction due to IM products etc., and RF and IF mismatch loss. The total loss is 5 to 8 dB in a well designed mixer. 13.

(49) CHAPTER 3 · THEORY AND MEASUREMENTS OF THE RF CONVERTER. 3.2.2. Noise Figure. The noise figure is calculated as in Section 3.1.2. Our mixer is a passive device, which implies that G = 1 and that the noise figure is equal to the SSB conversion loss. This is not strictly true, but works as a rule of thumb.. 3.2.3. Intermodulation. Intermodulation distortion is the main problem with mixers. The frequency components generated due to intermodulation distortion are called spurious frequencies, or spurs. This follows because if an IM product appears in the IF output passband it may be mistaken for the real signal. Fortunately, most of the IM products are more or less suppressed. The suppression increases with (m − 1) times the decrease in RF input power PRF (dB) [15]. On some occasions one can also find an increasing suppression from an increase in the LO drive level, but not always. The suppression of IM products can be predicted by several methods. Some work better than others, but at the cost of a need for more background on the actual mixer. Almost all mixer manufacturers provide extensive product charts which contain an intermodulation table for harmonics of LO and RF for orders up to n = m = 4.. 3.2.4. Isolation Port-to-Port. The isolation port-to-port (RP P ) measures the amount of leakage from one port to another. The strongest signal in the output spectrum from a mixer is the LO signal because of the drive level, which is much higher compared to the RF signal, and because of the poor port-to-port isolation between the LO and IF ports. The isolation from the LO port to the IF port is approximately 10 dB for an LO signal at 5 GHz. The isolation from the RF port to the IF port is better, 30 dB, and because of the weak RF signal the leakage is of no great importance.. 3.2.5. Conversion Compression Point. Normally PIF = αPRF , where PRF is the input signal level, PIF is the output signal level, and α is a constant. However, when the IF drive level approaches the LO drive level, α will no longer be constant, but will start to decrease. This is conversion compression. This will normally start to appear when the input signal level is within 10 dB of the LO drive level [13]. The conversion compression point will change with changing LO drive level. The conversion compression point is specified in terms of dB of deviation from the nominal value of α. Therefore, one can specify the 1 dB conversion compression point, the 3 dB conversion compression point and so on. 14.

(50) 3.3 · MIXER MEASUREMENTS. Table 3.1: Values for two measurement sessions with different RF and LO frequencies. Frequency values in GHz and power values in dBm.. fRF 6 6 6 6 6 6. fLO 10 10 10 10 10 10. fIF 2 4 6 10 14 20. PIF −66 −22 −35 −12 −64 −52. fRF 10 10 10 10 10 10. (a). 3.3. fLO 8 8 8 8 8 8. fIF 2 4 6 8 10 12. PIF −20 −63 −41 −9 −40 −75. (b). Mixer Measurements. To measure the output spectrum from a typical mixer a test bench involving a double balanced mixer manufactured by Avantek was set up. The mixer was an image rejection mixer, which means that only one of the wanted frequencies will pass through. The tools used were two signal generators, one for the RF signal and one for the LO signal, and of course a frequency analyser. The goal was to get a more practical experience of mixers and to get an intuitive grasp on how much the different frequency components where suppressed. The measurements were made with constant LO and RF power levels PLO >> PRF . The only parameter modified was the frequency of the RF or LO signal. Typical values for the mixer at hand is an LO drive level of 10 dBm and an RF drive level of −10 dBm. The losses on the LO and RF cables were measured to approximately 3 dB. Therefore, the output LO and RF levels at the signal generators were set to 13 and −7 dBm respectively. Table 3.1 shows values from two measurement sessions. All power values are in dBm, which is defined as PdBm = 10 log PmW where the m after dB stands for milli. The rest of the data is in Appendix A. We can see in Table 3.1, that the LO signal is the strongest frequency in the IF output. This is expected because of the poor isolation between the LO and IF ports. We can also see that the second strongest frequency is the wanted frequency of 4 GHz. The 16 GHz frequency has been rejected as described at the beginning of this section. All the other frequencies are weaker than the wanted frequency, they have been attenuated according to the intermodulation table for the mixer.. 3.4. Amplifier Theory. As for the mixer, a problem of the amplifier is the generation of spurious frequencies. Also, when the power of the input signal reaches a certain 15.

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(63) $"%& Figure 3.4: Fundamental parameters of the amplifier.. level, the amplifier saturates and starts clipping the output signal. In Figure 3.4 (from [4]), the fundamental parameters of the amplifier are pointed out. They will be explained in the following.. 3.4.1. Saturation and Clipping. Depending on the supply voltage (and physical limitations), the amplifier has a limitation to its output voltage. Thus input voltages over a certain level cannot be amplified according to the amplifier’s specifications. A signal with an amplitude over the saturation level will experience clipping. Particularly, a sine wave on the input will look more and more like a square wave on the output when the input power increases. This clipping introduces sharp edges in the signal, and therefore generates an abundance of harmonics. Figure 3.5 shows typical clipping in the time and frequency domains. As can be seen in Figure 3.4, the clipping is introduced gradually as the amplifier leaves the linear gain region. When the input power is high enough, the amplifier experiences RF burnout, and ceases to function.. 3.4.2. Linear Gain and 1 dB Compression Point. In the linear region, the gain of the amplifier conforms to its specifications. But when the amplifier starts saturating, the gain will decrease. The point on the gain curve where the gain has decreased 1 dB from its nominal 16.

(64) 3.4 · AMPLIFIER THEORY. 1. 4. 0.8. 3.5. 0.6 3. Logarithmic Amplitude. 0.4. Amplitude. 0.2. 0. −0.2. 2.5. 2. 1.5. −0.4 1 −0.6 0.5. −0.8. −1. 0. 0.2. 0.4. 0.6. 0.8. 1 Time. (a). 1.2. 1.4. 1.6. 1.8. 2. 0. 0. 10. 20. 30. 40. 50 Frequency. 60. 70. 80. 90. 100. (b). Figure 3.5: Figure (a) shows a clipped sine wave in the time domain. Figure (b) shows the same signal in the frequency domain.. value is called the 1 dB compression point. The 1 dB compression point is abbreviated P1 dB and is usually measured in dBm.. 3.4.3. Two-Tone Third-Order Intercept Point. As was mentioned above, the amplifier generates harmonics due to clipping of the signal. But these are not the only harmonics generated. As in the mixer, harmonics are generated at frequencies that are multiples of the input frequencies. The most significant harmonics in the amplifier are usually the two-tone third order ones, i.e. 2f1 − f2 and 2f2 − f1 . If f1 and f2 are close to each other in the frequency domain, the third-order intermodulation products will be close in frequency to the wanted signal. To avoid mix-ups, it is important to suppress the two-tone third-order products. The third-order products begin to show when the input power reaches a certain level, called IM D (short for intermodulation distortion). They are amplified much like the wanted signal, with the difference that the amplification curve has a slope of three (as opposed to a slope of one for the wanted signal) in the linear region. To reach the intercept point IP3 , extrapolate the linear regions of the fundamental curve and the third-order curve. As a rule of thumb, one can assume that the intercept point is 10 dB above the 1 dB compression point [4]. It is important to realise that the two-tone third-order intercept point is only a measure of the impact of the third-order harmonics. The intercept point can never be reached in real life since it is above the amplification curve. 17.

(65) CHAPTER 3 · THEORY AND MEASUREMENTS OF THE RF CONVERTER. Table 3.2: The measured output frequencies and power levels of the Miteq AFD4020060-45 amplifier.. Input power (dBm) f = 2.8 GHz −25 −20 −15 −10 −5 0 5 10 11 12 15. 3.4.4. Output power (dBm) at frequency 2.8 GHz 5.6 GHz 8.4 GHz 11.2 GHz 5.5 −46 — — 9.5 −29 — — 14.3 −22 −40.5 — 15 −9.7 −23 — 19.3 4 −2 −19 25.7 8.9 2.1 −13.4 26.9 7.9 −0.6 −13.8 27.2 5.1 0.7 −11.8 27.3 4.2 1.8 −10.3 27.5 4.7 2.3 −8.3 27.5 5.5 2.3 −5.7. One-Tone Second-Harmonic Intercept Point. The second-most important harmonics (after the two-tone third order ones) are the one-tone second harmonics. The frequencies generated are simply positioned at double the input frequencies in the frequency spectrum. As with the two-tone third-order harmonics, the effect of the one-tone second harmonics is measured with an intercept point. The one-tone second harmonics amplification curve has a slope of two and the intercept point HP2 can be found by extrapolating the curves in exactly the same way as for the third-order products.. 3.5. Amplifier Measurements. A test bench for measurements on a Miteq AFD4-020060-45 amplifier was set up. Unfortunately, no data sheet was available for this component, but colleagues guessed that the saturation power level was probably at about 15 dBm. The input frequency f was set to 2.8 GHz, and the input power was varied between −25 and 15 dBm. As can be seen in Table 3.2, no harmonics due to saturation occurred, only multiples of the input frequency showed on the spectrum analyser. Unfortunately, this could not be explained. One possible explanation is that the saturation power level was higher than 15 dBm. But since the amplifier is a rather expensive component (≈ USD1000), we were not allowed to test this by pushing the input power level up even further. 18.

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(72) % " Figure 3.6: Fundamental parameters of the filter.. 3.6. Filter Theory. When reading the following sections, refer to Figure 3.6.. 3.6.1. Noise Figure. No matter how easy the filter is to model, it will still add noise to the signal. How the noise figure is calculated is described in Section 3.1.2. The filter is a passive device which implies that G = 1.. 3.6.2. Cutoff Frequencies and Filter Bandwidth. The cutoff frequencies for a bandpass filter are defined as the two frequencies where the frequency response has dropped 3 dB from its peak value. A bandpass filter thus has a bandwidth measured between the cutoff frequencies. Lowpass and highpass filters only have one cutoff frequency and therefore no bandwidth is defined. To measure between the cutoff frequencies is only one definition of bandwidth, others exist. This one will be used throughout the thesis.. 3.6.3. Ripple. Characteristic wave-like behaviour in the frequency response. Ripple can occur in the stopband, in the passband, or both. 19.

(73) CHAPTER 3 · THEORY AND MEASUREMENTS OF THE RF CONVERTER. 3.6.4. Insertion Loss. Insertion loss is the difference in dB between a perfect transmission (where |H(ω)| ≡ 1) and the value of |H(ω)| at the centre frequency of the filter.. 3.6.5. Frequency Responses. Filters are produced with various responses to meet different demands [4, 6, 18]. The most important types are Butterworth, Chebyshev, and elliptic filters. Butterworth filters offer a maximally flat passband at the cost of a relatively wide transition band. Chebyshev filters have a steeper incline in the transition band, but also a ripple in the passband. Elliptic filters are a compromise between the Butterworth and Chebyshev filters. They have ripple in both the passband and the stopband. For each of these filters, a filter order is defined. The order determines the complexity of the describing transfer function. A higher filter order means a transfer function that more closely resembles the ideal one.. 3.7. Filter Measurements. As we have seen, the mixer and the amplifier cause such problems as spurious frequencies and clipping. The filter has no such drawbacks. As this measurement will show, properly designed filters generate impulse responses that closely match the ideal curve. A bandpass filter manufactured by Avitronics was chosen for the measurements. The cutoff frequencies of the filter were 9 and 12 GHz (these were the only data available for the filter). Firstly, different frequencies at different power levels were input to the filter, to make sure that no harmonics or other phenomena were created. No unexpected results were observed. Finally, the filter was connected to a Hewlett-Packard network analyser. The network analyser measures the frequency response of the filter and outputs the data to a file. The data was imported to and plotted in Matlab and the result can be seen in Figure 3.7.. 20.

(74) 3.7 · FILTER MEASUREMENTS. 0 −5 −10. Magnitude (dB). −15 −20 −25 −30 −35 −40 −45 −50. 0.6. 0.8. 1. 1.2 Frequency (Hz). 1.4. 1.6 10. x 10. Figure 3.7: Measured frequency response of the 9–12 GHz bandpass filter.. 21.

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(76) Chapter 4. Implementation of the RF Converter Model In this chapter the decisions leading up to the RF converter model are presented and justified. Earlier work in the field is researched. A choice of software is made. Finally, the complete RF converter model is presented in detail, both in writing and graphically.. 4.1. The Aim of the Model. As described earlier in Chapter 1, the main purpose of this thesis is to present an accurate model of an RF converter. A second purpose is for the model to be easily adaptable to changes in the converter design. From the company’s point of view, it is important that the model is easy to use, and requires a minimum of knowledge of the components involved. This is the aim of the model. The purpose of the thesis and the aim of the model are not contradictory, and they are preferably combined in the model. How well this combination is performed depends largely on the tool used for the model.. 4.2. Earlier Work. Searching for earlier work in this field generates a plethora of results. Many proposed models for microwave components exist, from the very advanced to the simpler ones. However, none seem to exist with the same focus as the model proposed in this thesis. Below, we present some examples of previous work. While this short presentation is in no way complete, it should give the reader a starting point for further studies. 23.

(77) CHAPTER 4 · IMPLEMENTATION OF THE RF CONVERTER MODEL. 4.2.1. Earlier Mixer Work. Maas [12] describes a technique for calculating intermodulation levels and maximising dynamic range. Maas claims unprecedented accuracy at the time of writing (1987). The drawback of the method is the complexity. Calculations involve both large-signal and small-signal analysis of the mixer, and this in turn requires in-depth knowledge of the actual mixer. Although Maas gives hints on how to start, the designer will have to write his own software to perform the calculations. Another paper presenting a numerical method for mixer analysis is Faber and Gwarek [5]. Regev [15] has presented a simplified model that does not require the use of special computer programs. In the model, the mixer diode currents are represented using analytical expressions, which are then Taylor expanded. The cost of having a simpler model is of course that the results are not as accurate as those of e.g. Maas or Faber and Gwarek. However, Regev presents expressions and conclusions that should be of use to the working engineer. An even simpler model has been presented by Henderson [7]. Hendersons article is targeted almost exclusively towards the working engineer and presents an equation for calculating the IM suppression based on the RF and LO power levels only. If one measures certain parameters of the mixer, these can be input into the equation for higher accuracy. The results presented by Henderson have later been implemented as a Java applet by Roetter and Belliveau [17]. With this applet, one can easily get a rough outline of the spurious frequencies and their respective power levels in a mixer.. 4.2.2. Earlier Amplifier Work. A common property of the available amplifier models seems to be their complexity. They also model just one type (or a few types) of amplifier, e.g. HFET, MESFET or IMPATT amplifiers. It is impossible to give a complete summary of the existing amplifier models. We therefore again emphasise that the models mentioned here are only a starting point for further studies. Intermodulation characteristics of IMPATT amplifiers are investigated in Kuno and English [11]. They also give an example of how to model an amplifier analytically. Numerical methods for modelling nonlinearities in MESFET and HFET amplifiers are presented in Crosmun and Maas [3] and Yhland et al. [19]. Crosmun and Maas also give many examples of earlier work.. 4.2.3. Earlier Filter Work. As we will see later in this chapter, the implementation of the filter is rather straightforward. In our view, not much work is done or has been done 24.

(78) 4.3 · WHAT TOOL TO USE. (lately, anyway) in the field of filter modelling. This view is based on the fact that there is virtually no documentation to be found concerning filter models. As an example, no documents at all where found in the IEEE Microwave Library, partly available online at http://www.ieeexplore.ieee.org/, a library covering tens of thousands of texts in the microwave field published between the 1950s and today. General principles of filter design can be found in any undergraduate course textbook of filter theory (e.g. [6, 18]). Some of these principles have been mentioned in the previous chapter and we will return to them later on.. 4.3. What Tool to Use. In order to make the model as adaptable as possible, a modular design is preferred. Recall now Figure 3.1. It is easy to divide the converter into three basic building blocks, namely mixers, amplifiers, and bandpass filters. Naturally, the best approach is to make each block flexible enough to work in any part of the receiver, i.e. to make one mixer block, one amplifier block, and one filter block. The aim throughout the modelling process has been to model each component of the converter as a separate block. Care has also been taken to ensure that each block gives a correct description of that component, so that not only the model as a whole is correct, but also so that each block can be reused in other models. By choosing this approach, it is easy to adapt the model to different converters. The Matlab toolbox Simulink offers the modularity we are looking for. It also offers a user friendly graphical interface. Since Simulink is based on Matlab, powerful mathematical functions are available to the designer. It was also an explicit wish from Avitronics that the model be implemented in Simulink. Thus, it was chosen as the tool for the model. Of course, Simulink has its disadvantages as well. It is a real time system, and performs calculations on discreet samples of the signal. Operations on parts of the signal, or all of it, pose problems. Also, the built-in functions are somewhat limited, and building new ones is not a trivial task. These disadvantages introduce limitations on the converter model. Other tools are available for modelling microwave components. Two examples are ADS (Advanced Design System), and Microwave Office. Unfortunately, these programs tend to focus on design of individual components rather than complete systems. They also require extensive knowledge of the components involved, contradictory to the aim of our model. The Matlab/Simulink environment also scores points on being readily available at Avitronics, since the price is much more affordable than that for specialised microwave modelling software. 25.

(79) CHAPTER 4 · IMPLEMENTATION OF THE RF CONVERTER MODEL. 1 CH1 in. RF Synth. IF. LO. RF Converter 1. LO DSP in. Control out. IF1 in. Display out. IF2 in. Synth. Controller. DSP Unit. LO Synth. 2 CH2 in. IF. RF. RF Converter 2. 1 Display out. Figure 4.1: An example of the Simulink block structure. 4.3.1. The Simulink Block Structure. The block structure of Simulink allows a high level of abstraction. The not so interested user will be able to use a Simulink model without any deeper understanding of the model. A more interested user can easily probe into the structure to make his own refinements or just quench his thirst for knowledge of the inner workings of the model. A very appealing feature of Simulink is the ability to drag and drop the components to form more complex models. In Figure 4.1 we see the complete RWR system as described in Chapter 2. As we can see, this figure closely resembles Figure 2.1. With the aid of a simple product chart, a model of the RWR system has been created. This is the top layer of the model. If we want to see the second layer, we just select a component and “open” it. If we open one of the RF converters of Figure 4.1, it will look exactly as Figure 3.1. Of course, the final model will consist of a number of layers, each more refined than the one preceding it. The layers of the individual components in the RF converter are explained in Sections 4.4, 4.6, and 4.8. Simulink offers simple ways for the designer to add user control to the model. To each modelling block, modelling parameters can be added. The designer can save default values for the parameters or leave them blank. The user can then change parameter values by simply double-clicking on the block and entering the desired values in a graphical user interface.. 4.4. Mixer Implementation. After studying mixer theory and performing measurements we are now ready to implement a non-ideal mixer in Matlab/Simulink. Simulink works with time steps and is ideal for simulating real time systems. If the true 26.

(80) 4.4 · MIXER IMPLEMENTATION. 1 RF 2 LO. rf x lo. 1 IF. 2 2rf. 2rf x lo. 2 2lo. rf x 2lo. Figure 4.2: A part of the realisation of the IF calculation block.. frequency components of the IF output were the only ones of interest, the implementation would be fairly easy. Now, considering that we want to generate other undesired frequencies with correct suppression, one understands that some careful planning is necessary. The user will have to input some data to the mixer to make it work properly. Of course the mixer block we are about to create in Simulink will have default values of all the necessary parameters. The input variables will be N F , LC , RP P , and an intermodulation table I of order four. In a future updated version of the mixer block, a choice between inputting the intermodulation table by hand or letting Simulink predict one for you, using one or two different methods, is a possible option. Another option is to implement third-order two-tone intercept point so that the model works correctly for frequencies close to each other.. 4.4.1. Intermediate Frequency and Spurious Components. Multiplying two sinusoidal signals with each other generates the wanted frequency components [14] VRF sin(ωRF t) · VLO sin(ωLO t) = VRF · VLO [cos((ωRF − ωLO )t) − cos((ωRF + ωLO )t)] 2 With an intermodulation table of order four we need to generate all the IM products up to that order. It follows from the equation above that we must downsample our RF and LO signals two, three, and four times each to be able to generate the correct IM products. By doing this we can implement the IF calculation part of the mixer rather easy. The components used for modelling the first part of this block were an ideal mixer, a downsample block, and a sum block, se Figure 4.2. The next step in the implementation of the model is to set the correct amplitude of all the different signals in the IF output. 27.

(81) CHAPTER 4 · IMPLEMENTATION OF THE RF CONVERTER MODEL. 4.4.2. Suppression. Since the wanted signal is generated by the product of RF and LO it has the amplitude Vout = 12 · VRF · VLO The correct amplitude VIF is VIF =. VRF D. where D is the algebraic conversion loss factor calculated from p D = 10LC /10 We can now calculate the wanted amplitude as VIF = Vout ·. 2 VLO · D. We can directly see that we need the LO voltage VLO for correct amplitude of the IF signal. Since the SNR is high for the LO signal the LO voltage should be quite easy to detect. For that purpose a Matlab function for detecting the true signal and calculating the inverse LO voltage 1/VLO was written. Other IM products, say 2fRF + fLO , are suppressed relative to the wanted signal amplitude VIF according to the intermodulation table (I) given in dBc where the c stands for carrier. The algebraic suppression factor is for each IM product in I p i = 1, . . . , m C(i, j) = 10I(i,j)/10 for all j = 1, . . . , n where m, n are the variables mentioned in Section 3.2. Since the suppression for i = j = 1 is 0 dB (the wanted product), it follows that we can calculate all the amplitudes in the IF output (except leakage) from VIF (i, j) =. 2 · Vout VLO · D · C(i, j). We can now implement the complete mixer IF calculation unit as in Figure 4.3.. 4.4.3. Noise. If we want our mixer model to be close to the real component, the noise figure N F needs to be implemented. In this implementation we are looking for a method that just adds the correct amount of noise to the original signal. Since the noise figure for a passive component is N F = 10 log. Pnoise out = 10 log F Pnoise in. it follows that Pnoise 28. out. = Pnoise. in. ·F.

(82) LO. 2. 1 RF. 3 1/V_lo. 4. 4lo. 4. 4rf. 3lo. 3. 3rf. 3. 2lo. 2. 2rf. 2. rf x 4lo. rf x 3lo. rf x 2lo. rf x lo. 2rf x 4lo. 2rf x 3lo. 2rf x 2lo. 2rf x lo. 3rf x 4lo. 3rf x 3lo. 3rf x 2lo. 3rf x lo. 4rf x 4lo. 4rf x 3lo. 4rf x 2lo. 4rf x lo. Gain3. -K-. -K-. Gain6. -K-. -K-. -K-. -K-. -K-. -K-. -K-. -K-. -K-. -K-. -KGain29. -KGain14. Gain28. -K-. Gain27. -K-. Gain26. Gain13. Gain12. Gain32. -KGain31. -K-. Gain17. -K-. Gain11. Gain16. -KGain30. -KGain15. Gain10. Gain2. Gain25. Gain9 -K-. -KGain24. -K-. Gain23. Gain22. Gain8. -K-. Gain7. -K-. -KGain21. Gain20. Gain19. Gain5. -K-. Gain4. -K-. Gain18. -K-. -K-. Gain1. -K-. Gain. -K-. 1 IF. 4.4 · MIXER IMPLEMENTATION. Figure 4.3: Realisation of the complete mixer IF calculation unit.. 29.

(83) CHAPTER 4 · IMPLEMENTATION OF THE RF CONVERTER MODEL. Now take the difference in noise power between the output and the input signals as ∆P = Pnoise out − Pnoise in and we have ∆P = Pnoise. in. · F − Pnoise. in. = Pnoise. in. · (F − 1). With F = 10N F/10 the equation above transforms to ∆P = Pnoise. in. · (10N F/10 − 1). To use this formula we need the noise power of the incoming RF signal, and for that end we will use an autoregressive model of order n, AR(n). We will estimate the noise power with the loss function of the square root implementation of the least-square method [6]. In an AR model, time is discreet. Generally, the assumption of the model is y(t) = a1 y(t − 1) + · · · + an (t − n) = e(t) where e(t) is a gaussian stochastic process with zero mean. If we now introduce T. ϕ(t) = (−y(t − 1) − y(t − 2) · · · − y(t − n)) T. θ = (a1 a2 · · · an ) we can write. T. y(t) = ϕ(t) θ + e(t) which is the usual expression used for estimation of AR models. This works fine for small n, but we will be working with models of order n ≥ 50. We want to use the square root method so we continue a little bit more. For an N sample signal, we can write the expressions for each sample as T y(1) = ϕ(1) θ + e(1) T y(2) = ϕ(2) θ + e(2) .. . T. y(N ) = ϕ(N ) θ + e(N ) and with the expressions   y(1)  y(2)    YN =  .   ..  y(N ).    ΦN =  . ϕT (1) ϕT (2) .. . ϕT (N ). . .    .   EN =  . e(1) e(2) .. ..     . e(N ). we can write YN = ΦN θ The error vector EN is stochastic and cannot be used when solving the equations. That is why the solution is just an estimation of the true AR model. 30.

(84) 4.4 · MIXER IMPLEMENTATION. MATLAB Function. 1 In. Reshape. sqrt(u*(10^(NF/10)-1)). 1 Out. Noise Estimation. Buffer. AWGN. Figure 4.4: Realisation of the serial noise calculation block.. We now continue by doing a QR factorisation of the matrix ΦN , i.e. writing it on the form R ΦN = Q 0 where Q is orthonormal, i.e. QT Q = I. By observing that QT = Q−1 , we can write 4 R L ΦN θ = YN ⇐⇒ θ = QT YN = 0 M Now we are getting close. The solution system Rθ = L. The residual vector is L T ˆ Q (YN − ΦN θN ) = − M. θˆN is found by solving the. L 0. . =. 0 M. . and the loss function ˆ = VN (θ). N X. 2 (y(t) − ϕT (t)θˆN ). t=1. = (YN − ΦN θˆN )T QQT (YN − ΦN θˆN ) = MT M The variance of the incoming noise (i.e., the noise power) is given as Pnoise. in. =. MT M N. Now we know everything we need to calculate how much noise we should add to the existing RF signal. Since we are working in Matlab and Simulink, additive white gaussian noise (AWGN) is easy to create. For implementa√ tion we created AWGN with variance σ 2 = 1, multiplied with ∆P , and added the noise with a sum block to the existing RF signal. Figure 4.4 shows the noise figure block as it is implemented in the mixer. We can now present an overall view of the mixer implementation with the noise calculation block in serial with the IF calculation block. See Figure 4.5. In the same figure we can also see the block for calculation of 1/VLO as mentioned in Section 4.4.2. 31.

(85) CHAPTER 4 · IMPLEMENTATION OF THE RF CONVERTER MODEL. 1 RF. In. Out. Noise Figure. Buffer RF. LO. 1/V_LO. 1/V_LO. IF. 1 IF. LO. Pre Process Unit. IF Calculation. Unbuffer. 2 LO Buffer. Figure 4.5: Realisation of the mixer in Simulink.. Table 4.1: Intermodulation table for mixer validation. Values in dBc for harmonics up to order four.. 1fRF 2fRF 3fRF 4fRF. 4.5. 1fLO 0 50 65 70. 2fLO 25 55 70 70. 3fLO 18 50 55 70. 4fLO 40 58 70 70. Mixer Validation. To validate the mixer an input signal was created in Matlab. The signal consisted of two frequencies, fRF = 6 GHz at −20 dBm and fLO = 8 GHz at −20 dBm. The noise power was −60 dBm. The mixer block input parameters were set to those of the mixer measured in Section 3.3. These parameters were taken from the mixer data sheet. The numbers were N F = 6.5 dB, LC = 6.5 dB, and the intermodulation table I as in Table 4.1. The table values are in dBc which means decibel carrier, i.e. the attenuation is measured against a carrier wave. In this case the carrier wave is the wanted frequency, and that frequency of course has the attenuation 0 dBc. The isolation port-to-port, RP P , was 30 dB between the RF and IF ports and 15 dB between the LO and IF ports. It is easy to calculate the frequencies and levels that, according to the data sheet, will appear at the mixer output. The LO signal will be attenuated by the isolation port-to-port only which gives us fLO out at −35 dBm. The wanted frequency will be attenuated LC = 6.5 dB and the spurious frequencies will be attenuated from that level according to the intermodulation table I. Figure 4.6 shows a plot of the output signal from the mixer. In this plot, the levels of the sinusoidal signals are correct in dBm, but the noise level is not correctly shown. As we can see, all the signals that are supposed to appear in the plot are there, and they have the correct power levels. Figure 4.7 shows the noise of the input and output signals and how it 32.

(86) 4.6 · AMPLIFIER IMPLEMENTATION. −20. −30. −40. IF Power (dBm). −50. −60. −70. −80. −90. −100. 0. 0.5. 1. 1.5. 2. 2.5 3 IF Frequency [Hz]. 3.5. 4. 4.5. 5 10. x 10. Figure 4.6: Validation output signal from the mixer in the frequency domain.. varies over time. The noise levels have been calculated with similar methods to those described in Section 4.4.3.. 4.6. Amplifier Implementation. The user of the system will have to supply the noise figure (N F ), the gain (G), the one-tone second harmonic intercept point (HP2 ), and the 1 dB compression point (P1 dB ) of the amplifier. From those four parameters the amplifier is modelled in Simulink using four sub-blocks.. 4.6.1. Noise. Noise calculations in the amplifier are done in exactly the same way as in the mixer, i.e. a noise calculation block in series with the other amplifier components, adding noise according to the noise figure. See Section 4.4.3 for the theoretical background.. 4.6.2. Amplification. The gain of the amplifier is implemented simply with an ideal Simulink gain block. Nothing fancy at all.. 4.6.3. Harmonics. In this implementation of the amplifier, only the one-tone second harmonic, i.e. double the input frequency, is added to the output signal. In a future 33.

(87) CHAPTER 4 · IMPLEMENTATION OF THE RF CONVERTER MODEL. P noise out P noise in. −46. −48. Noise Power (dBm). −50. −52. −54. −56. −58. −60. −62. 0. 10. 20. 30 40 50 60 70 Number of buffers, each with 512 samples. 80. 90. 100. Figure 4.7: Validation noise power in to and out from the mixer.. 1 RF. 2 Buffer. Downsample. MATLAB Function. 1 RF+Harmonics Unbuffer. Suppression HP2. Figure 4.8: The harmonics addition block in the amplifier implementation.. version, it will hopefully be possible to add the two-tone third-order harmonics as well, since these harmonics are more important to model. Then, of course, the user needs to know the two-tone third-order intercept point. To obtain the double frequency, the signal is first downsampled by a factor 2. We then need the correct suppression, which varies with the input power Pin and HP2 . These calculations are straightforward and based on the fact that the slope of the fundamental curve in Figure 3.4 is three and the slope of the curve corresponding to the second harmonic is two [4]. After a few minor calculations we conclude that the suppression SHP2 equals SHP2 = HP2 − Pin (dB) The suppression is implemented using a simple Matlab function in the Simulink model. We also need to buffer the signal in order to get the same time scale on the original and downsampled signals. The harmonics are then added to the signal and finally the signal is unbuffered. The harmonics addition block is depicted in Figure 4.8. 34.

(88) 4.7 · AMPLIFIER VALIDATION. 1 in. in. out. Noise Figure. in. out. Amplification. in. out. Harmonics. in. out. 1 Out. Saturation. Figure 4.9: Realisation of the amplifier in Simulink.. 4.6.4. Saturation. As was mentioned in Section 3.4.1, saturation in the amplifier is introduced gradually, as the gain leaves the linear region. In the model, the soft curvature of the gain curve is disregarded. Instead, the linear region of the gain curve is prolonged up to the saturated output level, and from there the amplifier is considered to have reached saturation. The saturated output level is set 3 dB above the 1 dB compression point. This is a typical value [4]. The saturated output level is then converted into a threshold amplitude and the amplified signal (remember that the amplification block comes before the saturation block) is compared to the threshold. If it is above, it is clipped. Otherwise, it passes straight through. The Simulink implementation is straightforward as a Matlab function. The implementation of the amplifier is now complete, and can be seen in Figure 4.9.. 4.7. Amplifier Validation. To validate the amplifier, the same input signal as in the mixer validation was chosen, see Section 4.5. In the output signal, we can expect to see the noise and the wanted signal amplified, and also harmonics due to the one-tone second harmonic intercept point and saturation. The parameters of the amplifier were chosen to be those of one having roughly the same specifications as an amplifier in a future prototype of the RF converter. Specifically, the Simulink amplifier block parameters were set to G = 11 dB, N F = 10 dB, HP2 = 36 dBm, and P1 dB = 13 dBm. The complete data sheet of the Avantek PPA-18232 mixer can be found in [2]. Figure 4.10 shows the output in the frequency domain. The typical clipping pattern is not visible since the input power is the same as for the mixer validation (too low for the clipping to show). However, the one-tone second harmonic is showing. Figure 4.11 shows the noise power in the input and output signals. It is clear that the noise power in the output signal is approximately 20 dB higher than the input signal which makes sense since N F = 10 dB and G = 11 dB. From Section 4.6.3, we know that the suppression of the one-tone second 35.

(89) CHAPTER 4 · IMPLEMENTATION OF THE RF CONVERTER MODEL. 0. −10. −20. IF Power (dBm). −30. −40. −50. −60. −70. 0. 0.2. 0.4. 0.6. 0.8 1 1.2 IF Frequency [Hz]. 1.4. 1.6. 1.8. 2 10. x 10. Figure 4.10: The amplifier validation output in the frequency domain.. −35 P noise out P noise in. −40. Noise Power (dBm). −45. −50. −55. −60. −65. 0. 5. 10 15 20 25 Number of buffers, each with 512 samples. 30. 35. Figure 4.11: Validation noise power in to and out from the amplifier.. 36.

(90) 4.8 · FILTER IMPLEMENTATION. harmonics is SHP2 = HP2 − Pin = 36 − (−20) = 56 dB and since the power of the wanted signal is −9 dBm after amplification we expect to find the one-tone second harmonic at −9 − 56 = −65 dBm. A close look in the plot gives us −57 dBm for the one-tone second harmonic, an 8 dB difference from the expected value. If we check the implementation of the amplifier we see that the harmonics addition block comes after the amplification block, and if we interpret Pin as the input power to the harmonics block we get Pin is −20 + 11 = −9 dB and the correct suppression should be 36 − (−9) = 45 dB. With that suppression we expect to find the one-tone second harmonic at −54 dBm which is close to the measured −57 dBm.. 4.8. Filter Implementation. As we have seen, the traps when modelling mixers and amplifiers are many. The most serious problems are caused by the spurious frequencies and how to model them using only a few data sheet parameters. The filter is quite different. As we have seen, the behaviour of the filter is very similar to the theoretical predictions. This makes modelling the filter straightforward. In our model the user can choose the start and stop frequencies f1 and f2 , the filter order n, and the sampling time Ts from the graphical interface. The filter is implemented using two Simulink blocks, one for the actual filtering of the signal, and one for noise addition.. 4.8.1. Frequency Response. Figure 3.7 shows a frequency response with a flat passband. Thus, it is a natural conclusion that the bandpass filters of the RF converter are best modelled as Butterworth filters. For a given filter order n, a Butterworth filter is rather easy to implement. In Matlab, the Signal Processing Toolbox offers algorithms for filter computations. The filters in our model are implemented in Simulink using Simulink’s discrete transfer function block. The numerator and denominator for the transfer function are calculated in a Matlab function that calls the Signal Processing Toolbox function butter.. 4.8.2. Noise. Some of the bandpass filters in the model are narrowband with a 500 MHz bandwidth. Our model is working in discrete time with a global sampling frequency of a few hundred gigahertz. The very narrow filter bandwidth relative to the sampling frequency will result in the filter filtering out most of the noise if the noise addition is done in serial. We need to find another solution. 37.

(91) CHAPTER 4 · IMPLEMENTATION OF THE RF CONVERTER MODEL. 1 CH in. numerator(f1,f2,Ts,n)(z) denominator(f1,f2,Ts,n)(z). 1 CH out. Bandpass filter, f1 - f2 GHz. In. Out. Noise Figure. Figure 4.12: Realisation of the filter with a parallel noise calculation block.. The noise in the amplifier and the mixer is added as the difference between the noise power of the incoming signal and the predicted noise power of the output signal. The prediction is made from the noise figure that is provided by the user of the model. Our filter is a passive component without losses in the passband. We are be able to measure the incoming noise power and add the predicted difference to the filtered signal, i.e. to have a parallel noise figure block. The filter model works well for noise figures separated from zero because if N F = 0 no noise is added and the incoming noise is filtered out. The complete filter with a parallel noise calculation block is depicted in Figure 4.12.. 4.9. Filter Validation. As when validating the amplifier, the filter parameters were chosen to be roughly those of a filter in a future prototype of the RF converter. Specifically, the Simulink filter block input parameters were N F = 5 dB, f1 = 5.75 GHz, f2 = 6.25 GHz. We also need to decide the filter order. With a user requirement of a 55 dB attenuation in the stopband (f ≥ 7 GHz) a calculated filter order is n = 4 [18]. The input signal was chosen to be almost the same as for the mixer validation, see Section 4.5. The only difference is that we added another RF frequency fRF = 12 GHz, also at −20 dBm. Figure 4.13 shows the validation output signal from the filter. As we can see, the 12 GHz signal has been filtered out completely, which is the desired result. As for the noise, see Figure 4.14, the added amount is close to the noise figure N F = 5 dB, which is acceptable.. 4.10. Model Implementation. When all three components had been modelled in Simulink, the work with the model for the complete RF converter took place. Simulink works in time steps and since the mixer model incorporates a Matlab function that 38.

(92) 4.10 · MODEL IMPLEMENTATION. −10. −20. −30. IF Power (dBm). −40. −50. −60. −70. −80. −90. 0. 0.5. 1. 1.5 IF Frequency [Hz]. 2. 2.5 10. x 10. Figure 4.13: Validation output signal from the filter in the frequency domain.. −55 P noise out P noise in. −55.5 −56. Noise Power (dBm). −56.5 −57 −57.5 −58 −58.5 −59 −59.5 −60 −60.5. 0. 10. 20. 30 40 50 60 70 Number of buffers, each with 512 samples. 80. 90. 100. Figure 4.14: Validation noise power in to and out from the filter.. 39.

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