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Institutionen for systemteknikDepartment of Electrical Engineering

Examensarbete

Modelling an RFConverter in Matlab

Mattias Hjorth och Bjorn Hvittfeldt

LiTH-ISY-EX-3260-2002

13 februari 2002

Department of Electrical Engineering Linkopings tekniska hogskolaLinkoping University Institutionen for systemteknikSE-581 83 Linkoping, Sweden 581 83 Linkoping

Modelling an RFConverter in Matlab

Examensarbete utfort i datatransmissionvid Linkopings tekniska hogskola av

Mattias Hjorth och Bjorn 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 andother parameters in the RF converter of the radar warning system. Thecomponents of the RF converter have been studied, measured, and mod-elled. The modelling tool has been the Simulink toolbox for Matlab.

Extreme accuracy has been sacrificed in order to make the model easy touse for the working engineer. Instead, this model presents a rough estimateof some of the most important properties of the radar warning system withjust a few data sheet figures as input.

The simulation results are satisfactory as a whole. Simulink is the lim-iting factor in the implementation of the model. Significantly improvedresults can probably be obtained by working in another software environ-ment.

Key words: Radar warning receiver, Spurious frequencies, Model, Simu-link, Matlab, Mixer, Amplifier, Filter

Supervisor: Simon GermishuizenExaminer: Ulf Henriksson

Linkoping, February 13, 2002

Avdelning, institutionDivision, department

Data TransmissionDepartment of Electrical Engineering

DatumDate

February 13, 2002

SpråkLanguage

❑ Svenska/Swedish❑ Engelska/English❑ ______________

RapporttypReport category

❑ Licentiatavhandling❑ Examensarbete❑ C-uppsats❑ D-uppsats❑ Övrig rapport❑ _______________

URL för elektronisk versionURL for electronic version

http://www.ep.liu.se/

TitelTitle

Modellering av en radarvarningsmottagare i MatlabModelling an RF Converter in Matlab

SammanfattningAbstract

Radar warning systems are life saving equipment in modern fighter aircraft. It is therefore vital that thesystem 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 RFconverter 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 workingengineer. Instead, this model presents a rough estimate of some of the most important properties ofthe 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 implementationof the model. Significantly improved results can probably be obtained by working in another softwareenvironment.

NyckelordKey words

Radar warning receiver, Spurious frequencies, Model, Simulink, Matlab, Mixer, Amplifier, Filter

FörfattareAuthors

Mattias Hjorth and Björn Hvittfeldt

ISBN

ISRN

LiTH-ISY-EX-3260-2002

ISSN

Serietitel och serienummerTitle of series, numbering

x x


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Preface

As much as this report has meant hard work for us, it has also been anexperience far beyond what we had expected when we first decided that weshould do our final thesis together.

During our time at Linkoping University, we have discovered that wecomplete each other in the way we work and think. Mattias is the hands-onguy, who tries new ideas and never reads the user manual before springinginto action. Bjorn is the methodical type, who reads the book from coverto cover.

Our year together at LinTek in 1998–1999 made us realise that we wouldactually stand each other during the creation of a final thesis. We set ourtarget high, and decided to do our thesis together, in a country with awarm climate, and with an English speaking population.

Australia was the first country on our list, since Saab has a subsidiarythere. We had no success. After that, South Africa emerged as a possiblecandidate. Our contacts went from Saab headquarters in Linkoping, viaSaab Avionics in Jarfalla, to Avitronics in South Africa. Once the initialcontact had been made, things went fast. Before we knew it, we had landedon 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 arenow reading. But in our spare time, we have also taken the opportunityto experience South Africa. We will remember the scenery, the weather,the shopping, the crime, and the poverty. But above all, we will rememberthe people. Friendly, curious, and helpful, they helped making our stay amemory for life. Thank you!

mattias [email protected]

bjorn [email protected]

v

mailto:[email protected]

mailto:[email protected]

Acknowledgments

The authors would like to express their gratitude towards the followingpeople (in alphabetical order) for their assistance and support during ourwork on this report.

Besides these specific individuals we would like to thank all employeesat Avitronics for their hospitality.

Nico van Dalen Matlab wiz at the Signal Processing Lab.Nicklas Forsberg For helpful feedback on the report.Simon Germishuizen Our supervisor.Fredrik Gustafsson For invaluable (and quick!) help on some

Matlab issues.Bjorn Henriksson For sending us to South Africa.Ulf Henriksson Our examiner.Dave Howie For getting us started and supplying us with

the necessary papers, books, and components.Monica Kjellander Without Monica, this thesis would not have

been possible.Daniel Lindeque For being an excellent office neighbour, li-

brary, and host at a number of social events.Merenchia Louw Our main contact at Avitronics, words are not

enough to express our gratitude.Rose Mahashe For that excellent coffee.Denis Milton Always with a smile on his face and a working

knowledge in many areas.Thinus Neethling For helping us with amplifier and filter mea-

surements.Alenka Rosenqvist For that initial contact with Saab in Jarfalla.Johan Safholm For helpful feedback on the report.Anton Snyman Another guy who knows his components, and

who also provided a daily translation of thephrase of the day.

vii

Contents

Preface v

Acknowledgments vii

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Problem Identification . . . . . . . . . . . . . . . . . . . . . 11.3 The Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.3.1 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.4.1 Method Weaknesses . . . . . . . . . . . . . . . . . . 21.5 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Radar Warning Receivers 52.1 Overview of Radar Warning Receivers . . . . . . . . . . . . 52.2 Components . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2.1 The RF Converter . . . . . . . . . . . . . . . . . . . 52.2.2 The Synthesiser and LO Units . . . . . . . . . . . . 62.2.3 The DSP Unit . . . . . . . . . . . . . . . . . . . . . 62.2.4 The Controller . . . . . . . . . . . . . . . . . . . . . 7

3 Theory and Measurements of the RF Converter 93.1 RF Converter Outline . . . . . . . . . . . . . . . . . . . . . 9

3.1.1 Signals . . . . . . . . . . . . . . . . . . . . . . . . . . 93.1.2 Noise Figure . . . . . . . . . . . . . . . . . . . . . . 103.1.3 Spurious Free Dynamic Range . . . . . . . . . . . . 103.1.4 Voltage Standing Wave Ratio . . . . . . . . . . . . . 11

3.2 Mixer Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 123.2.1 Conversion Loss . . . . . . . . . . . . . . . . . . . . 133.2.2 Noise Figure . . . . . . . . . . . . . . . . . . . . . . 143.2.3 Intermodulation . . . . . . . . . . . . . . . . . . . . 143.2.4 Isolation Port-to-Port . . . . . . . . . . . . . . . . . 143.2.5 Conversion Compression Point . . . . . . . . . . . . 14

3.3 Mixer Measurements . . . . . . . . . . . . . . . . . . . . . . 153.4 Amplifier Theory . . . . . . . . . . . . . . . . . . . . . . . . 15

ix

CONTENTS

3.4.1 Saturation and Clipping . . . . . . . . . . . . . . . . 163.4.2 Linear Gain and 1 dB Compression Point . . . . . . 163.4.3 Two-Tone Third-Order Intercept Point . . . . . . . . 173.4.4 One-Tone Second-Harmonic Intercept Point . . . . . 18

3.5 Amplifier Measurements . . . . . . . . . . . . . . . . . . . . 183.6 Filter Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.6.1 Noise Figure . . . . . . . . . . . . . . . . . . . . . . 193.6.2 Cutoff Frequencies and Filter Bandwidth . . . . . . 193.6.3 Ripple . . . . . . . . . . . . . . . . . . . . . . . . . . 193.6.4 Insertion Loss . . . . . . . . . . . . . . . . . . . . . . 203.6.5 Frequency Responses . . . . . . . . . . . . . . . . . . 20

3.7 Filter Measurements . . . . . . . . . . . . . . . . . . . . . . 20

4 Implementation of the RF Converter Model 234.1 The Aim of the Model . . . . . . . . . . . . . . . . . . . . . 234.2 Earlier Work . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.2.1 Earlier Mixer Work . . . . . . . . . . . . . . . . . . 244.2.2 Earlier Amplifier Work . . . . . . . . . . . . . . . . . 244.2.3 Earlier Filter Work . . . . . . . . . . . . . . . . . . . 24

4.3 What Tool to Use . . . . . . . . . . . . . . . . . . . . . . . 254.3.1 The Simulink Block Structure . . . . . . . . . . . . . 26

4.4 Mixer Implementation . . . . . . . . . . . . . . . . . . . . . 264.4.1 Intermediate Frequency and Spurious Components . 274.4.2 Suppression . . . . . . . . . . . . . . . . . . . . . . . 284.4.3 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.5 Mixer Validation . . . . . . . . . . . . . . . . . . . . . . . . 324.6 Amplifier Implementation . . . . . . . . . . . . . . . . . . . 33

4.6.1 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . 334.6.2 Amplification . . . . . . . . . . . . . . . . . . . . . . 334.6.3 Harmonics . . . . . . . . . . . . . . . . . . . . . . . . 334.6.4 Saturation . . . . . . . . . . . . . . . . . . . . . . . . 35

4.7 Amplifier Validation . . . . . . . . . . . . . . . . . . . . . . 354.8 Filter Implementation . . . . . . . . . . . . . . . . . . . . . 37

4.8.1 Frequency Response . . . . . . . . . . . . . . . . . . 374.8.2 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.9 Filter Validation . . . . . . . . . . . . . . . . . . . . . . . . 384.10 Model Implementation . . . . . . . . . . . . . . . . . . . . . 384.11 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . 40

4.11.1 Improvements . . . . . . . . . . . . . . . . . . . . . . 41

5 Conclusions and Possible Enhancements 475.1 Achievements . . . . . . . . . . . . . . . . . . . . . . . . . . 475.2 Recommended Improvements . . . . . . . . . . . . . . . . . 48

x

CONTENTS

Appendices

A Measurement data 49A.1 Mixer Measurements . . . . . . . . . . . . . . . . . . . . . . 49

References 51

Index 53

xi

Chapter 1

Introduction

1.1 Background

Avitronics is owned 51% by the Grintek group and 49% by Saab AB. Avit-ronics and Saab are both strong players on the international defence mar-ket. Avitronics markets radar warning receivers and laser warning receiverswith peripherals in the form of e.g. displays, chaff and flare dispensers, anddecoy systems.

For the new radar warning receiver, Avitronics produces the analogreceiver and Saab the digital signal processing (DSP) unit. For the analogreceiver, a design was proposed in June of 2001. Due to lack of timethe design was based on some analysis and largely practical experience.Avitronics therefore proposed that we should model the radar warningreceiver. The model would then be used to evaluate the decided designand to improve the design for future iterations.

1.2 Problem Identification

The present problems when designing a radar warning system receiver arelargely related to lack of funding and time. Specifically, we conclude thatAvitronics 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-commercialsoftware in the design process.

1.3 The Thesis

Considering the problems mentioned above and the time available for thisproject, it was decided that modelling the RF converter was most impor-

1

CHAPTER 1 · INTRODUCTION

tant. Therefore, this thesis is a study of a model of the RF converter in aradar warning receiver system. The Simulink toolbox for Matlab has beenused as a modelling tool.

1.3.1 Purpose

The main purpose of this thesis is to present an accurate model of an RFconverter. A second purpose is for the model to be easily adaptable toconfiguration 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 noiseaddition, creation of spurious frequencies, etc. These sub-blocks have thenbeen modelled one by one in the Simulink environment. Blocks that arecommon to several components have been reused.

Measurements on actual components have been compared with modeldata to validate the correctness of the model.

Naturally, simplifications and approximations have been made. Theyare mentioned throughout the report.

1.4.1 Method Weaknesses

The model is based largely on our own assumptions regarding what isimportant in the process of designing an RF converter. Also, we have haddifficulties in finding relevant literature concerning the theoretical aspectsof the components.

A more thorough approach could maybe have involved studies in thefield 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 timespent 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 ex-plains the role of the RF converter and the other components in thesystem.

Chapter 3 gives a theoretical background on the RF converter. It be-gins with a general description of the converter and its parametersand goes on to describe the converter on a component level (mixers,amplifiers, and filters).

2

1.5 · THESIS OUTLINE

Chapter 4 is the implementation chapter. The Simulink model is con-structed, block by block. Finally, the complete model is put together.

Chapter 5 presents conclusions and discusses possible enhancements ofthe present model.

Appendix A presents some measurement data too bulky to fit into thereport itself.

3

Chapter 2

Radar Warning Receivers

The purpose of this chapter is to present an overview and backgroundof radar warnings receivers. The main functionality is described and thereader with little or no knowledge of radar warnings receivers can under-stand the purpose. A reader with more experience from radar warningsreceivers can skip this and the next chapter and jump directly to Chap-ter 4.

2.1 Overview of Radar Warning Receivers

To protect themselves, military aircraft are equipped with radar warningreceivers (RWR). The RWR intercepts radar emissions from friendly as wellas hostile radar stations. These radar stations can be fixed (e.g. at air forcebases) or mobile (e.g. on board other aircraft or sea vessels).

The RWR has an RF converter that converts the incoming radio fre-quency (RF) signal to a lower intermediate frequency (IF). After receptionand conversion, the signal is fed to a digital signal processing unit. Afterprocessing the signal, the RWR system can supply the pilot with informa-tion concerning type, range, bearing, and nationality of the emitting radar.If the emission is hostile, the pilot then uses this information when decidinghow to react to the threat.

2.2 Components

Here the main parts of the RWR system are described. When reading thissection, refer to Figure 2.1 to better understand how the different parts ofthe system interact.

2.2.1 The RF Converter

The RF converter that we have focused on is of the double superheterodynetype. This type of converter combines good sensitivity (the ability to detect

5

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 thespectrum) and is the most common type on the market today. For basicand advanced theory on receivers, refer to [1] and [10], respectively.

The job of the RF converter is to convert the incoming signal to apredetermined frequency band. This band, which contains much lowerfrequencies than the incoming signal, can be more easily handled by theDSP unit. It is much easier to sample on a signal in the 1 GHz regionthan 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 theDSP unit will also be lower.

2.2.2 The Synthesiser and LO Units

To sweep the frequency spectrum, the receiver needs a reference signalgenerated by the synthesiser. The synthesiser produces sinusoidal signalsbetween 2 and 18 GHz in steps of 100 MHz. If one or more interesting sig-nals are found, the synthesiser can reduce to sweeping only the frequenciesof 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 bythe controller.

The local oscillator (LO) produces another reference signal needed bythe receiver. This reference signal is used to convert the received signal tothe 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. Heredecisions are taken on whether the received signal contains anything inter-esting. 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 asignal matching the received one is found in the library, the DSP unitknows make and model, and can even differentiate between radars ofthe same type.

Bearing The aircraft has several antennas for receiving radar signals. Bycomparing receptions of the same signal by different antennas, theDSP unit can calculate the bearing of the signal using interferometrytechniques.

Position By flying the aircraft in a circle around the radar station andconstantly calculating the bearing, the DSP unit can triangulate theposition of the station.

Mode By comparing the received signal to the match in the library, theDSP unit can decide what mode the radar station is currently work-ing in. If the station is in sweeping mode, it will be continuously

6

2.2 · COMPONENTS

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Figure 2.1: The main components of an RWR system.

monitored. If it has locked on target, the aircraft is in danger. Thepilot must take action to avoid the threat.

2.2.4 The Controller

The controller is the feedback between the DSP unit and the receiver. Ittakes its orders from the DSP unit and controls the sweep of the synthesiser.

7

Chapter 3

Theory and Measurementsof 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 thecomponents is explained from a theoretical point of view. Measurementsof 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 componentlevel.

3.1.1 Signals

In Figure 3.1, we see a basic outline of the RF converter. Our RF converterworks as mentioned like a superheterodyne receiver. The input radar signalenters the converter from the left and first passes the pre-selector and anamplifier. The radar signal is usually a pulsed sine wave with a pulserepetition interval of a few hundred microseconds. The frequency is oftenin the range 0.5–18 GHz.

The incoming RF signal is first upconverted to a higher intermediatefrequency, which passes a bandpass filter, and then downconverted again.The frequency conversion is done in the mixer, which takes two input sig-nals, the RF signal and a signal from the local oscillator. The output RFsignal has a fixed frequency predetermined by the last band pass filter inthe converter.

If we define the local oscillator signal and the synthesiser signal as in-put signals, the RF converter takes three input signals. The control unitdetermines the frequency of the synthesiser. The local oscillator, LO, hasa fixed frequency.

9

CHAPTER 3 · THEORY AND MEASUREMENTS OF THE RF CONVERTER

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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 theamount of noise power added is referred to as noise figure. Noise figure, orsingle sideband noise figure, is defined as

NF = 10 logPnoise out

Pnoise in ·G= 10 log F

where G is the gain in active devices.The cascade noise figure Gcascade is of high importance in an RF con-

verter. Since we are interested in detecting a signal with very low sig-nal 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 kTB = −87dBm at 298 K and 500 MHz bandwidth. A proposed cascade noise figureGcascade 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 signalsin the radar signal. The mixed products are referred to as harmonics. Mostof the harmonics generated are highly suppressed except for the two-tonethird order harmonics, i.e. 2f1 − f2 and 2f2 − f1. If f1 and f2 are closeto each other in the frequency domain, the third-order intermodulationproducts will be close in frequency to the wanted signal.

For design reasons the spurious free dynamic range (SFDR) are of greatinterest. It tells us in which power range we can detect a signal without

10

3.1 · RF CONVERTER OUTLINE

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Figure 3.2: System SFDR projection.

noise or harmonics disturbing the wanted signal, see Figure 3.2. The mainparameter for measuring the SFDR is the two-tone third order interceptpoint, IP3.

The third-order products begin to show when the input power reachesa certain level, called IMD (short for intermodulation distortion). Theyare amplified much like the wanted signal, with the difference that the am-plification curve has a slope of three (as opposed to a slope of one for thewanted signal) in the linear region. To reach the intercept point, extrapo-late the linear regions of the fundamental curve and the third-order curve.The spurious free dynamic range is measured as SFDR = IMD −MDS.

3.1.4 Voltage Standing Wave Ratio

Our RF converter uses a 50-ohm system. If there is a mismatch in the port-to-port impedance a part of the incident wave is reflected and a standingwave is created. In the design of the RF converter the voltage standing waveratio (VSWR) is a parameter used for the mismatch. The VSWR is theratio between the peak and the valley of standing waves on a transmissionline. One can also define the VSWR through the definition of the reflectioncoefficient

ρ =ZL − ZO

ZL + ZO

where ZL is the input impedance and ZO is the feedline impedance. WhenZL = ZO the reflection coefficient is zero and there is no reflected signal.From the reflection coefficient we have

V SWR =1 + |ρ|1− |ρ|

11


and we can also calculate the return loss from LR = −20 · log(|ρ|). Returnloss is the ratio in decibels of maximum power sent down the transmissionline to the power returned toward the source. The return loss is infinite ifall the power is absorbed in the circuit.

3.2 Mixer Theory

The mixer is an RF component used for frequency conversion. A mixer hastwo input ports (RF, LO) and one output port (IF), see Figure 3.3. Thefrequency conversion is achieved by modulation of the periodic RF signalat frequency fRF with a periodic waveform LO having frequency fLO. Theoutput signal contains frequencies from the sum and difference of fLO andfRF

fIF = fRF + fLO and fIF = fRF − fLO or fIF = fLO − fRF

depending on which sums are positive. In the ideal case those are theonly two frequencies in the output signal, but in reality the mixer alsogenerates 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 andthe 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 themirror image of the signal frequency about the oscillator frequency [16].

On the market today many types of mixer circuits exist. The mostcommon type is the double balanced diode mixer. Other mixers are triplebalanced, class IV, and single ended mixers [9]. From now on we refer tothe double balanced diode mixer as “the mixer”.

In the mixer, a periodic LO signal applied at the LO port in Figure3.3 causes conduction of the alternate diode pairs. During positive LOcycles, diodes D1 and D2 are turned on while D3 and D4 are off. Fornegative LO cycles the opposite is true.

A virtual ground is therefore switched between the RF to IF transformerwindings at a rate corresponding to the LO frequency. This causes the RFsignal seen by the IF port to change phase by 180◦ every time the LOsignal changes polarity. This process is called bi-phased modulation andcan be mathematically represented [8] by multiplying the sinusoidal RFsignal voltage with the Fourier series of the square wave switching function,i.e. the diode conductance waveform

Vout = VRF sin(ωRF t)4π

∑n=1,3,5,...

1n

sin(nωLOt)

It is this equation that gives us the IM products.

12

3.2 · MIXER THEORY

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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) conver-sion loss. If we assume that no intermodulation products or losses exist,we can calculate the theoretical minimum conversion loss in a generalisedlinear mixer. The conversion loss is defined as

LC =RF input powerIF output power

For the ideal mixer we expand the Fourier series for n = 1 (no IM products),which gives us

Vout = VRF sin(ωRF t)4π

sin(ωLOt) =

VRF ·12· 4π

[cos((ωLO − ωRF ) · t)− cos((ωLO + ωRF ) · t)]

The IF voltage (the amplitude of the signal with the desired frequency) is

VIF = VRF ·12· 4π

and the RF to IF conversion loss

LC = 20 logVRF

VIF= 20 log

π

2= 3.92 dB

The conversion loss in a non-ideal diode mixer has three components: lossin 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 designedmixer.

13


3.2.2 Noise Figure

The noise figure is calculated as in Section 3.1.2. Our mixer is a passivedevice, which implies that G = 1 and that the noise figure is equal to theSSB 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 frequencycomponents generated due to intermodulation distortion are called spuriousfrequencies, or spurs. This follows because if an IM product appears in theIF output passband it may be mistaken for the real signal.

Fortunately, most of the IM products are more or less suppressed. Thesuppression increases with (m − 1) times the decrease in RF input powerPRF (dB) [15]. On some occasions one can also find an increasing sup-pression from an increase in the LO drive level, but not always. The sup-pression of IM products can be predicted by several methods. Some workbetter than others, but at the cost of a need for more background on theactual mixer. Almost all mixer manufacturers provide extensive productcharts which contain an intermodulation table for harmonics of LO and RFfor orders up to n = m = 4.

3.2.4 Isolation Port-to-Port

The isolation port-to-port (RPP ) measures the amount of leakage from oneport to another. The strongest signal in the output spectrum from a mixeris the LO signal because of the drive level, which is much higher comparedto the RF signal, and because of the poor port-to-port isolation betweenthe LO and IF ports. The isolation from the LO port to the IF port isapproximately 10 dB for an LO signal at 5 GHz. The isolation from theRF port to the IF port is better, 30 dB, and because of the weak RF signalthe leakage is of no great importance.

3.2.5 Conversion Compression Point

Normally PIF = αPRF , where PRF is the input signal level, PIF is theoutput signal level, and α is a constant. However, when the IF drive levelapproaches the LO drive level, α will no longer be constant, but will startto decrease. This is conversion compression. This will normally start toappear when the input signal level is within 10 dB of the LO drive level[13]. The conversion compression point will change with changing LO drivelevel.

The conversion compression point is specified in terms of dB of deviationfrom the nominal value of α. Therefore, one can specify the 1 dB conversioncompression point, the 3 dB conversion compression point and so on.

14

3.3 · MIXER MEASUREMENTS

Table 3.1: Values for two measurement sessions with different RF and LO fre-quencies. Frequency values in GHz and power values in dBm.

fRF fLO fIF PIF

6 10 2 −666 10 4 −226 10 6 −356 10 10 −126 10 14 −646 10 20 −52

(a)

fRF fLO fIF PIF

10 8 2 −2010 8 4 −6310 8 6 −4110 8 8 −910 8 10 −4010 8 12 −75

(b)

3.3 Mixer Measurements

To measure the output spectrum from a typical mixer a test bench involvinga double balanced mixer manufactured by Avantek was set up. The mixerwas an image rejection mixer, which means that only one of the wantedfrequencies 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 frequencyanalyser. The goal was to get a more practical experience of mixers andto get an intuitive grasp on how much the different frequency componentswhere suppressed. The measurements were made with constant LO andRF power levels PLO >> PRF . The only parameter modified was thefrequency of the RF or LO signal.

Typical values for the mixer at hand is an LO drive level of 10 dBmand an RF drive level of −10 dBm. The losses on the LO and RF cableswere measured to approximately 3 dB. Therefore, the output LO and RFlevels at the signal generators were set to 13 and −7 dBm respectively.

Table 3.1 shows values from two measurement sessions. All power valuesare in dBm, which is defined as PdBm = 10 log PmW where the m after dBstands 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 frequencyin the IF output. This is expected because of the poor isolation betweenthe LO and IF ports. We can also see that the second strongest frequencyis the wanted frequency of 4 GHz. The 16 GHz frequency has been rejectedas described at the beginning of this section. All the other frequencies areweaker than the wanted frequency, they have been attenuated according tothe intermodulation table for the mixer.

3.4 Amplifier Theory

As for the mixer, a problem of the amplifier is the generation of spuriousfrequencies. Also, when the power of the input signal reaches a certain

15


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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 amplifierhas a limitation to its output voltage. Thus input voltages over a certainlevel cannot be amplified according to the amplifier’s specifications.

A signal with an amplitude over the saturation level will experienceclipping. Particularly, a sine wave on the input will look more and morelike a square wave on the output when the input power increases. Thisclipping introduces sharp edges in the signal, and therefore generates anabundance of harmonics. Figure 3.5 shows typical clipping in the time andfrequency domains. As can be seen in Figure 3.4, the clipping is introducedgradually as the amplifier leaves the linear gain region. When the inputpower is high enough, the amplifier experiences RF burnout, and ceases tofunction.

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 pointon the gain curve where the gain has decreased 1 dB from its nominal

16

3.4 · AMPLIFIER THEORY

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Time

Am

plitu

de

(a)

0 10 20 30 40 50 60 70 80 90 1000

0.5

1

1.5

2

2.5

3

3.5

4

Frequency

Loga

rithm

ic A

mpl

itude

(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 isabbreviated 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 clippingof the signal. But these are not the only harmonics generated. As in themixer, harmonics are generated at frequencies that are multiples of theinput frequencies. The most significant harmonics in the amplifier areusually 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-orderintermodulation products will be close in frequency to the wanted signal.To avoid mix-ups, it is important to suppress the two-tone third-orderproducts.

The third-order products begin to show when the input power reachesa certain level, called IMD (short for intermodulation distortion). Theyare amplified much like the wanted signal, with the difference that theamplification curve has a slope of three (as opposed to a slope of one forthe wanted signal) in the linear region. To reach the intercept point IP3,extrapolate the linear regions of the fundamental curve and the third-ordercurve. As a rule of thumb, one can assume that the intercept point is 10dB above the 1 dB compression point [4].

It is important to realise that the two-tone third-order intercept pointis only a measure of the impact of the third-order harmonics. The interceptpoint can never be reached in real life since it is above the amplificationcurve.

17


Table 3.2: The measured output frequencies and power levels of the Miteq AFD4-020060-45 amplifier.

Input power (dBm) Output power (dBm) at frequencyf = 2.8 GHz 2.8 GHz 5.6 GHz 8.4 GHz 11.2 GHz

−25 5.5 −46 — —−20 9.5 −29 — —−15 14.3 −22 −40.5 —−10 15 −9.7 −23 —−5 19.3 4 −2 −190 25.7 8.9 2.1 −13.45 26.9 7.9 −0.6 −13.810 27.2 5.1 0.7 −11.811 27.3 4.2 1.8 −10.312 27.5 4.7 2.3 −8.315 27.5 5.5 2.3 −5.7

3.4.4 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 simplypositioned at double the input frequencies in the frequency spectrum. Aswith the two-tone third-order harmonics, the effect of the one-tone secondharmonics is measured with an intercept point.

The one-tone second harmonics amplification curve has a slope of twoand the intercept point HP2 can be found by extrapolating the curves inexactly 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 wasset up. Unfortunately, no data sheet was available for this component, butcolleagues guessed that the saturation power level was probably at about15 dBm. The input frequency f was set to 2.8 GHz, and the input powerwas 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 thatthe saturation power level was higher than 15 dBm. But since the amplifieris a rather expensive component (≈ USD1000), we were not allowed to testthis by pushing the input power level up even further.

18

3.6 · FILTER THEORY

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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 thesignal. How the noise figure is calculated is described in Section 3.1.2. Thefilter 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 frequen-cies where the frequency response has dropped 3 dB from its peak value.A bandpass filter thus has a bandwidth measured between the cutoff fre-quencies.

Lowpass and highpass filters only have one cutoff frequency and there-fore no bandwidth is defined.

To measure between the cutoff frequencies is only one definition of band-width, others exist. This one will be used throughout the thesis.

3.6.3 Ripple

Characteristic wave-like behaviour in the frequency response. Ripple canoccur in the stopband, in the passband, or both.

19


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, andelliptic filters.

Butterworth filters offer a maximally flat passband at the cost of a rela-tively wide transition band.

Chebyshev filters have a steeper incline in the transition band, but alsoa ripple in the passband.

Elliptic filters are a compromise between the Butterworth and Chebyshevfilters. They have ripple in both the passband and the stopband.

For each of these filters, a filter order is defined. The order determines thecomplexity of the describing transfer function. A higher filter order meansa 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 spu-rious frequencies and clipping. The filter has no such drawbacks. Asthis measurement will show, properly designed filters generate impulse re-sponses that closely match the ideal curve.

A bandpass filter manufactured by Avitronics was chosen for the mea-surements. The cutoff frequencies of the filter were 9 and 12 GHz (thesewere the only data available for the filter). Firstly, different frequenciesat different power levels were input to the filter, to make sure that noharmonics or other phenomena were created. No unexpected results wereobserved.

Finally, the filter was connected to a Hewlett-Packard network analyser.The network analyser measures the frequency response of the filter andoutputs the data to a file. The data was imported to and plotted in Matlaband the result can be seen in Figure 3.7.

20

3.7 · FILTER MEASUREMENTS

0.6 0.8 1 1.2 1.4 1.6

x 1010

−50

−45

−40

−35

−30

−25

−20

−15

−10

−5

0

Frequency (Hz)

Mag

nitu

de (d

B)

Figure 3.7: Measured frequency response of the 9–12 GHz bandpass filter.

21

Chapter 4

Implementation of the RFConverter Model

In this chapter the decisions leading up to the RF converter model arepresented and justified. Earlier work in the field is researched. A choice ofsoftware is made. Finally, the complete RF converter model is presentedin 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 topresent an accurate model of an RF converter. A second purpose is for themodel to be easily adaptable to changes in the converter design.

From the company’s point of view, it is important that the model is easyto 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 contra-dictory, and they are preferably combined in the model. How well thiscombination 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. Manyproposed models for microwave components exist, from the very advancedto the simpler ones. However, none seem to exist with the same focus asthe model proposed in this thesis.

Below, we present some examples of previous work. While this shortpresentation is in no way complete, it should give the reader a startingpoint for further studies.

23

CHAPTER 4 · IMPLEMENTATION OF THE RF CONVERTER MODEL

4.2.1 Earlier Mixer Work

Maas [12] describes a technique for calculating intermodulation levels andmaximising dynamic range. Maas claims unprecedented accuracy at thetime of writing (1987). The drawback of the method is the complexity. Cal-culations involve both large-signal and small-signal analysis of the mixer,and this in turn requires in-depth knowledge of the actual mixer. AlthoughMaas gives hints on how to start, the designer will have to write his ownsoftware to perform the calculations.

Another paper presenting a numerical method for mixer analysis isFaber and Gwarek [5].

Regev [15] has presented a simplified model that does not require the useof special computer programs. In the model, the mixer diode currents arerepresented using analytical expressions, which are then Taylor expanded.The cost of having a simpler model is of course that the results are notas accurate as those of e.g. Maas or Faber and Gwarek. However, Regevpresents expressions and conclusions that should be of use to the workingengineer.

An even simpler model has been presented by Henderson [7]. Hender-sons article is targeted almost exclusively towards the working engineerand presents an equation for calculating the IM suppression based on theRF and LO power levels only. If one measures certain parameters of themixer, these can be input into the equation for higher accuracy. The resultspresented by Henderson have later been implemented as a Java applet byRoetter and Belliveau [17]. With this applet, one can easily get a roughoutline of the spurious frequencies and their respective power levels in amixer.

4.2.2 Earlier Amplifier Work

A common property of the available amplifier models seems to be theircomplexity. 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 amplifiermodels. We therefore again emphasise that the models mentioned here areonly a starting point for further studies.

Intermodulation characteristics of IMPATT amplifiers are investigatedin Kuno and English [11]. They also give an example of how to model anamplifier analytically.

Numerical methods for modelling nonlinearities in MESFET and HFETamplifiers 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 ratherstraightforward. In our view, not much work is done or has been done

24

4.3 · WHAT TOOL TO USE

(lately, anyway) in the field of filter modelling. This view is based on thefact that there is virtually no documentation to be found concerning filtermodels. As an example, no documents at all where found in the IEEE Mi-crowave Library, partly available online at http://www.ieeexplore.ieee.org/,a library covering tens of thousands of texts in the microwave field pub-lished between the 1950s and today.

General principles of filter design can be found in any undergraduatecourse textbook of filter theory (e.g. [6, 18]). Some of these principles havebeen mentioned in the previous chapter and we will return to them lateron.

4.3 What Tool to Use

In order to make the model as adaptable as possible, a modular design ispreferred. Recall now Figure 3.1. It is easy to divide the converter intothree basic building blocks, namely mixers, amplifiers, and bandpass filters.Naturally, the best approach is to make each block flexible enough to workin any part of the receiver, i.e. to make one mixer block, one amplifierblock, and one filter block.

The aim throughout the modelling process has been to model eachcomponent of the converter as a separate block. Care has also been takento ensure that each block gives a correct description of that component, sothat not only the model as a whole is correct, but also so that each blockcan be reused in other models. By choosing this approach, it is easy toadapt 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 onMatlab, powerful mathematical functions are available to the designer. Itwas also an explicit wish from Avitronics that the model be implementedin Simulink. Thus, it was chosen as the tool for the model.

Of course, Simulink has its disadvantages as well. It is a real timesystem, and performs calculations on discreet samples of the signal. Oper-ations on parts of the signal, or all of it, pose problems. Also, the built-infunctions 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 ex-amples are ADS (Advanced Design System), and Microwave Office. Unfor-tunately, these programs tend to focus on design of individual componentsrather than complete systems. They also require extensive knowledge ofthe components involved, contradictory to the aim of our model. The Mat-lab/Simulink environment also scores points on being readily available atAvitronics, since the price is much more affordable than that for specialisedmicrowave modelling software.

25

http://www.ieeexplore.ieee.org/


1Display out

LO

Synth

RF

IF

RF Converter 2

RF

Synth

LO

IF

RF Converter 1

IF1 in

IF2 in

Control out

Display out

DSP Unit

DSP in

LO

Synth

Controller

2CH2 in

1CH1 in

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 notso interested user will be able to use a Simulink model without any deeperunderstanding of the model. A more interested user can easily probe intothe structure to make his own refinements or just quench his thirst forknowledge of the inner workings of the model.

A very appealing feature of Simulink is the ability to drag and dropthe components to form more complex models. In Figure 4.1 we see thecomplete RWR system as described in Chapter 2. As we can see, thisfigure 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 themodel. 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 lookexactly as Figure 3.1.

Of course, the final model will consist of a number of layers, each morerefined than the one preceding it. The layers of the individual componentsin 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 themodel. To each modelling block, modelling parameters can be added. Thedesigner can save default values for the parameters or leave them blank.The user can then change parameter values by simply double-clicking onthe block and entering the desired values in a graphical user interface.

4.4 Mixer Implementation

After studying mixer theory and performing measurements we are nowready to implement a non-ideal mixer in Matlab/Simulink. Simulink workswith time steps and is ideal for simulating real time systems. If the true

26

4.4 · MIXER IMPLEMENTATION

1IF

rf x lo

rf x 2lo

2rf x lo2

2rf

2

2lo

2LO

1RF

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, theimplementation would be fairly easy. Now, considering that we want togenerate other undesired frequencies with correct suppression, one under-stands that some careful planning is necessary.

The user will have to input some data to the mixer to make it workproperly. Of course the mixer block we are about to create in Simulink willhave default values of all the necessary parameters. The input variableswill be NF , LC , RPP , and an intermodulation table I of order four. Ina future updated version of the mixer block, a choice between inputtingthe intermodulation table by hand or letting Simulink predict one for you,using one or two different methods, is a possible option. Another option isto implement third-order two-tone intercept point so that the model workscorrectly for frequencies close to each other.

4.4.1 Intermediate Frequency and Spurious Components

Multiplying two sinusoidal signals with each other generates the wantedfrequency components [14]

VRF sin(ωRF t) · VLO sin(ωLOt) =VRF · VLO

2[cos((ωRF − ωLO)t)− cos((ωRF + ωLO)t)]

With an intermodulation table of order four we need to generate all the IMproducts up to that order. It follows from the equation above that we mustdownsample our RF and LO signals two, three, and four times each to beable to generate the correct IM products. By doing this we can implementthe IF calculation part of the mixer rather easy. The components used formodelling the first part of this block were an ideal mixer, a downsampleblock, and a sum block, se Figure 4.2.

The next step in the implementation of the model is to set the correctamplitude of all the different signals in the IF output.

27


4.4.2 Suppression

Since the wanted signal is generated by the product of RF and LO it hasthe amplitude Vout = 1

2 · VRF · VLO The correct amplitude VIF is

VIF =VRF

D

where D is the algebraic conversion loss factor calculated from

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 amplitudeof the IF signal. Since the SNR is high for the LO signal the LO voltageshould be quite easy to detect. For that purpose a Matlab function fordetecting the true signal and calculating the inverse LO voltage 1/VLO waswritten.

Other IM products, say 2fRF + fLO, are suppressed relative to thewanted signal amplitude VIF according to the intermodulation table (I)given in dBc where the c stands for carrier. The algebraic suppressionfactor is for each IM product in I

C(i, j) =√

10I(i,j)/10 for all{

i = 1, . . . ,mj = 1, . . . , n

where m, n are the variables mentioned in Section 3.2. Since the suppres-sion for i = j = 1 is 0 dB (the wanted product), it follows that we cancalculate 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 Figure4.3.

4.4.3 Noise

If we want our mixer model to be close to the real component, the noisefigure NF needs to be implemented. In this implementation we are lookingfor a method that just adds the correct amount of noise to the originalsignal. Since the noise figure for a passive component is

NF = 10 logPnoise out

Pnoise in= 10 log F

it follows thatPnoise out = Pnoise in · F

28


1 IF

rf x

lo

rf x

4lo

rf x

3lo

rf x

2lo

-K-

Gai

n9

-K-

Gai

n8

-K-

Gai

n7

-K-

Gai

n6

-K-

Gai

n5

-K-

Gai

n4

-K-

Gai

n32

-K-

Gai

n31

-K-

Gai

n30

-K-

Gai

n3

-K-

Gai

n29

-K-

Gai

n28

-K-

Gai

n27

-K-

Gai

n26

-K-

Gai

n25

-K-

Gai

n24

-K-

Gai

n23

-K-

Gai

n22

-K-

Gai

n21

-K-

Gai

n20

-K-

Gai

n2

-K-

Gai

n19

-K-

Gai

n18

-K-

Gai

n17

-K-

Gai

n16

-K-

Gai

n15

-K-

Gai

n14

-K-

Gai

n13

-K-

Gai

n12

-K-

Gai

n11

-K-

Gai

n10

-K-

Gai

n1

-K-

Gai

n

4rf

x lo

4rf

x 4l

o

4rf

x 3l

o

4rf

x 2l

o

4

4rf 4

4lo

3rf

x lo

3rf

x 4l

o

3rf

x 3l

o

3rf

x 2l

o

3

3rf 3

3lo

2rf

x lo

2rf

x 4l

o

2rf

x 3l

o

2rf

x 2l

o

2

2rf 2

2lo

3

1/V

_lo

2 LO1 RF

Figure 4.3: Realisation of the complete mixer IF calculation unit.

29


Now take the difference in noise power between the output and the inputsignals as ∆P = Pnoise out − Pnoise in and we have

∆P = Pnoise in · F − Pnoise in = Pnoise in · (F − 1)

With F = 10NF/10 the equation above transforms to

∆P = Pnoise in · (10NF/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 rootimplementation of the least-square method [6].

In an AR model, time is discreet. Generally, the assumption of themodel is

y(t) = a1y(t− 1) + · · ·+ an(t− n) = e(t)

where e(t) is a gaussian stochastic process with zero mean. If we nowintroduce

ϕ(t) = (−y(t− 1) − y(t− 2) · · · − y(t− n))T

θ = (a1 a2 · · · an)T

we can writey(t) = ϕ(t)T

θ + e(t)

which is the usual expression used for estimation of AR models. This worksfine for small n, but we will be working with models of order n ≥ 50. Wewant 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 sampleas

y(1) = ϕ(1)Tθ + e(1)

y(2) = ϕ(2)Tθ + e(2)

...y(N) = ϕ(N)T

θ + e(N)

and with the expressions

YN =

y(1)y(2)

...y(N)

ΦN =

ϕT (1)ϕT (2)

...ϕT (N)

EN =

e(1)e(2)

...e(N)

we can write

YN = ΦNθ

The error vector EN is stochastic and cannot be used when solving theequations. That is why the solution is just an estimation of the true ARmodel.

30


1Out

MATLABFunction

Noise EstimationBuffer

AWGN

Reshape

sqrt(u*(10^(NF/10)-1))

1In

Figure 4.4: Realisation of the serial noise calculation block.

We now continue by doing a QR factorisation of the matrix ΦN , i.e. writ-ing it on the form

ΦN = Q

(R0

)where Q is orthonormal, i.e. QT Q = I. By observing that QT = Q−1, wecan write

ΦNθ = YN ⇐⇒(

R0

)θ = QT YN

4=

(LM

)Now we are getting close. The solution θN is found by solving the

system Rθ = L. The residual vector is

QT (YN − ΦN θN ) =(

LM

)−

(L0

)=

(0M

)and the loss function

VN (θ) =N∑

t=1

(y(t)− ϕT (t)θN )2

= (YN − ΦN θN )T QQT (YN − ΦN θN )

= 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 shouldadd 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 σ2 = 1, multiplied with

√∆P , and

added the noise with a sum block to the existing RF signal. Figure 4.4shows the noise figure block as it is implemented in the mixer.

We can now present an overall view of the mixer implementation withthe noise calculation block in serial with the IF calculation block. SeeFigure 4.5. In the same figure we can also see the block for calculation of1/VLO as mentioned in Section 4.4.2.

31


Buffer

Buffer

1IF

Unbuffer

LO 1/V_LO

Pre Process Unit

In Out

Noise Figure

RF

1/V_LO

LO

IF

IF Calculation

2LO

1RF

Figure 4.5: Realisation of the mixer in Simulink.

Table 4.1: Intermodulation table for mixer validation. Values in dBc for harmon-ics up to order four.

1fLO 2fLO 3fLO 4fLO

1fRF 0 25 18 402fRF 50 55 50 583fRF 65 70 55 704fRF 70 70 70 70

4.5 Mixer Validation

To validate the mixer an input signal was created in Matlab. The signalconsisted of two frequencies, fRF = 6 GHz at −20 dBm and fLO = 8GHz at −20 dBm. The noise power was −60 dBm. The mixer blockinput parameters were set to those of the mixer measured in Section 3.3.These parameters were taken from the mixer data sheet. The numberswere NF = 6.5 dB, LC = 6.5 dB, and the intermodulation table I as inTable 4.1. The table values are in dBc which means decibel carrier, i.e. theattenuation is measured against a carrier wave. In this case the carrier waveis the wanted frequency, and that frequency of course has the attenuation0 dBc. The isolation port-to-port, RPP , was 30 dB between the RF andIF ports and 15 dB between the LO and IF ports.

It is easy to calculate the frequencies and levels that, according to thedata sheet, will appear at the mixer output. The LO signal will be at-tenuated by the isolation port-to-port only which gives us fLO out at −35dBm. The wanted frequency will be attenuated LC = 6.5 dB and thespurious frequencies will be attenuated from that level according to theintermodulation 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 levelis not correctly shown. As we can see, all the signals that are supposed toappear 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

4.6 · AMPLIFIER IMPLEMENTATION

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 1010

−100

−90

−80

−70

−60

−50

−40

−30

−20

IF Frequency [Hz]

IF P

ower

(dB

m)

Figure 4.6: Validation output signal from the mixer in the frequency domain.

varies over time. The noise levels have been calculated with similar methodsto those described in Section 4.4.3.

4.6 Amplifier Implementation

The user of the system will have to supply the noise figure (NF ), the gain(G), the one-tone second harmonic intercept point (HP2), and the 1 dBcompression point (P1 dB) of the amplifier. From those four parametersthe 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 inthe mixer, i.e. a noise calculation block in series with the other amplifiercomponents, adding noise according to the noise figure. See Section 4.4.3for the theoretical background.

4.6.2 Amplification

The gain of the amplifier is implemented simply with an ideal Simulinkgain 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


0 10 20 30 40 50 60 70 80 90 100−62

−60

−58

−56

−54

−52

−50

−48

−46

Number of buffers, each with 512 samples

Noi

se P

ower

(dB

m)

P noise outP noise in

Figure 4.7: Validation noise power in to and out from the mixer.

1RF+Harmonics

Unbuffer

MATLABFunction

Suppression HP2

2

DownsampleBuffer

1RF

Figure 4.8: The harmonics addition block in the amplifier implementation.

version, it will hopefully be possible to add the two-tone third-order har-monics 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 afactor 2. We then need the correct suppression, which varies with theinput power Pin and HP2. These calculations are straightforward andbased on the fact that the slope of the fundamental curve in Figure 3.4 isthree and the slope of the curve corresponding to the second harmonic istwo [4]. After a few minor calculations we conclude that the suppressionSHP2 equals

SHP2 = HP2 − Pin (dB)

The suppression is implemented using a simple Matlab function in theSimulink model. We also need to buffer the signal in order to get thesame time scale on the original and downsampled signals. The harmonicsare then added to the signal and finally the signal is unbuffered. Theharmonics addition block is depicted in Figure 4.8.

34

4.7 · AMPLIFIER VALIDATION

1Out

in out

Saturation

in out

Noise Figure

in out

Harmonics

in out

Amplification

1in

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 introducedgradually, as the gain leaves the linear region. In the model, the softcurvature of the gain curve is disregarded. Instead, the linear region ofthe gain curve is prolonged up to the saturated output level, and fromthere the amplifier is considered to have reached saturation. The saturatedoutput level is set 3 dB above the 1 dB compression point. This is a typicalvalue [4].

The saturated output level is then converted into a threshold amplitudeand the amplified signal (remember that the amplification block comes be-fore the saturation block) is compared to the threshold. If it is above, it isclipped. Otherwise, it passes straight through. The Simulink implementa-tion is straightforward as a Matlab function.

The implementation of the amplifier is now complete, and can be seenin Figure 4.9.

4.7 Amplifier Validation

To validate the amplifier, the same input signal as in the mixer validationwas chosen, see Section 4.5. In the output signal, we can expect to seethe noise and the wanted signal amplified, and also harmonics due to theone-tone second harmonic intercept point and saturation.

The parameters of the amplifier were chosen to be those of one havingroughly the same specifications as an amplifier in a future prototype of theRF converter. Specifically, the Simulink amplifier block parameters wereset to G = 11 dB, NF = 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 typicalclipping pattern is not visible since the input power is the same as for themixer validation (too low for the clipping to show). However, the one-tonesecond harmonic is showing. Figure 4.11 shows the noise power in the inputand output signals. It is clear that the noise power in the output signal isapproximately 20 dB higher than the input signal which makes sense sinceNF = 10 dB and G = 11 dB.

From Section 4.6.3, we know that the suppression of the one-tone second

35


0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 1010

−70

−60

−50

−40

−30

−20

−10

0

IF Frequency [Hz]

IF P

ower

(dB

m)

Figure 4.10: The amplifier validation output in the frequency domain.

0 5 10 15 20 25 30 35−65

−60

−55

−50

−45

−40

−35


Noi

se P

ower

(dB

m)


Figure 4.11: Validation noise power in to and out from the amplifier.

36

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 weexpect to find the one-tone second harmonic at −9 − 56 = −65 dBm. Aclose 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 implementationof the amplifier we see that the harmonics addition block comes after theamplification block, and if we interpret Pin as the input power to the har-monics block we get Pin is −20 + 11 = −9 dB and the correct suppressionshould be 36− (−9) = 45 dB. With that suppression we expect to find theone-tone second harmonic at −54 dBm which is close to the measured −57dBm.

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 howto model them using only a few data sheet parameters. The filter is quitedifferent. As we have seen, the behaviour of the filter is very similar to thetheoretical 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 graphicalinterface. The filter is implemented using two Simulink blocks, one for theactual 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 anatural conclusion that the bandpass filters of the RF converter are bestmodelled as Butterworth filters.

For a given filter order n, a Butterworth filter is rather easy to imple-ment. In Matlab, the Signal Processing Toolbox offers algorithms for filtercomputations. The filters in our model are implemented in Simulink usingSimulink’s discrete transfer function block. The numerator and denomina-tor for the transfer function are calculated in a Matlab function that callsthe Signal Processing Toolbox function butter.

4.8.2 Noise

Some of the bandpass filters in the model are narrowband with a 500 MHzbandwidth. Our model is working in discrete time with a global samplingfrequency of a few hundred gigahertz.

The very narrow filter bandwidth relative to the sampling frequencywill result in the filter filtering out most of the noise if the noise additionis done in serial. We need to find another solution.

37


Bandpass filter, f1 - f2 GHz

1CH out

In Out

Noise Figure

numerator(f1,f2,Ts,n)(z)

denominator(f1,f2,Ts,n)(z)1

CH in

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 differencebetween the noise power of the incoming signal and the predicted noisepower of the output signal. The prediction is made from the noise figurethat is provided by the user of the model. Our filter is a passive componentwithout losses in the passband. We are be able to measure the incomingnoise power and add the predicted difference to the filtered signal, i.e. tohave a parallel noise figure block. The filter model works well for noisefigures separated from zero because if NF = 0 no noise is added and theincoming noise is filtered out.

The complete filter with a parallel noise calculation block is depicted inFigure 4.12.

4.9 Filter Validation

As when validating the amplifier, the filter parameters were chosen to beroughly those of a filter in a future prototype of the RF converter. Specifi-cally, the Simulink filter block input parameters were NF = 5 dB, f1 = 5.75GHz, f2 = 6.25 GHz.

We also need to decide the filter order. With a user requirement of a55 dB attenuation in the stopband (f ≥ 7 GHz) a calculated filter order isn = 4 [18].

The input signal was chosen to be almost the same as for the mixervalidation, see Section 4.5. The only difference is that we added anotherRF frequency fRF = 12 GHz, also at −20 dBm. Figure 4.13 shows thevalidation output signal from the filter. As we can see, the 12 GHz signalhas been filtered out completely, which is the desired result. As for thenoise, see Figure 4.14, the added amount is close to the noise figure NF = 5dB, which is acceptable.

4.10 Model Implementation

When all three components had been modelled in Simulink, the work withthe model for the complete RF converter took place. Simulink works intime steps and since the mixer model incorporates a Matlab function that

38

4.10 · MODEL IMPLEMENTATION

0 0.5 1 1.5 2 2.5

x 1010

−90

−80

−70

−60

−50

−40

−30

−20

−10

IF Frequency [Hz]

IF P

ower

(dB

m)

Figure 4.13: Validation output signal from the filter in the frequency domain.

0 10 20 30 40 50 60 70 80 90 100−60.5

−60

−59.5

−59

−58.5

−58

−57.5

−57

−56.5

−56

−55.5

−55


Noi

se P

ower

(dB

m)


Figure 4.14: Validation noise power in to and out from the filter.

39


1IF

in out

Pre Selector

in out

Pre Amp

X

RF

LO

IF

Mixer 3

XRF

LOIF

Mixer 2

XRF

LOIF

Mixer 1

inou

t

LO Filter

inou

t

LO Amp

in out

IF Filter 2

in out

IF Filter 1

in out

IF Amp

3LO

2Synth

1RF

Figure 4.15: The RF converter model in Simulink.

uses FFT to detect the inverse LO voltage, the RF converter model mustwork in discrete time mode. The RF converter model takes an alreadysampled RF signal as input from the Matlab workspace and outputs an IFsignal to the workspace for further analysis. We have already mentionedthat a sampling time is needed for the implementation of the filter. Thus,when we create the complete model, all blocks must use the same samplingtime. So, the user of the model must set the global sampling time Ts equalto the sampling time of the sampled RF signal from the Matlab workspace.

The single channel RF converter model takes three signals as input,the above-mentioned RF signal, the continuous wave (CW) signal from thesynthesiser and the CW signal from the local oscillator. The signals fromthe synthesiser and the LO are sampled with the global sampling timeTs. The model was created according to Figure 3.1. All components haddefault settings from Avitronics requirements and the synthesiser and LOsignals used default frequencies and power levels.

4.11 Model Validation

When we tried our Simulink model, see Figure 4.15, with an RF signal at6 GHz the result was miles away from what we expected. The output IFsignal looked like pure white noise with a power of +300 dBm! Somethingwas very wrong. After some trial and error testing we discovered that thelast bandpass filter was not working as it should do. The error in the filterwas caused by the high sampling rate. A sampling rate of a few hundredgigahertz together with a low start frequency for the bandpass filter causednumerical problems in the discrete Butterworth filter. A test with a lowersampling rate worked out well but instead aliasing was more visible in theoutput spectrum.

When we examined the output signal in Matlab we could see some otherdrawbacks with our model. The power of the noise in the output signalwas too high and there were transient effects, see Figure 4.16, and glitchesin the time domain, see Figure 4.17. The transients and glitches are not a

40

4.11 · MODEL VALIDATION

1.8 2 2.2 2.4 2.6 2.8 3

x 104

−4

−3

−2

−1

0

1

2

3

4

5

Sample

Vol

tage

(V

)

Figure 4.16: Transients in the time domain.

big issue if the simulation time is long enough, but the high noise powermakes sensitive analysis difficult.

4.11.1 Improvements

The model was now scrutinised component by component to find out whythe extra noise was added to the signal. It was easy to establish that themixer generated the extra noise if one or both of the input signals containedmore than one frequency component. In our converter almost all signalscontain more than one frequency.

To battle the high noise power we had the choice of either redesigningthe mixer or to try a noise reduction component of some sort. At this latestage of the project, redesigning the mixer did not seem like fun. There-fore a noise reducer was constructed, using methods similar to the noisepower estimation in Section 4.4.3. The noise reducer worked fine for signalswith a small number of frequency components, but did not work at all onthe signals in the RF converter. Instead of decreasing the power our newnoise reduction component increased the noise power. We could not clearlyestablish why the noise reducer worked for some signals, but not for others.

Now redesign of the mixer had to be tried. After several attempts toimplement the mixer differently we could only conclude that limitations inSimulink prevented us from doing what we wanted to do.

Our last resort was to filter out the noise of the mixer. This is anunwanted solution since it reduces the adaptability of the model. Eachmixer will have its own specially configured filter for the frequencies thatare coming out of that mixer. This means that the user will have to have

41


1 2 3 4 5 6 7 8 9 10

x 104

0.025

0.03

0.035

0.04

0.045

Sample

Vol

tage

(V

)

Figure 4.17: Glitches in the time domain.

1IF

in out

Noise Figure

XRF

LOIF

Mixer

in out

Bandpass Filter2LO

1RF

Figure 4.18: The mixer with a filter to reduce noise.

knowledge of the frequencies of every mixer in the model. This is nota big problem for the advanced user since he or she knows exactly whatfrequencies to expect in the output spectrum.

We notice in Figure 4.15 that all the mixers of the RF converter modelare followed by bandpass filters. We will use these filters to remove theunwanted noise added in the mixers. We first remove the noise figurecalculation components from the mixer and the filter and instead calculatethe noise figure over the mixer and filter simultaneously. This is to preventthe noise added in the noise figure component from being filtered out aswell. The solution can be seen in Figure 4.18. The user will simply have toadd the NF of the mixer and the filter together, and input the combinedNF to the noise figure calculation component connected in parallel withthe mixer and the filter. The combined mixer and bandpass filter can nowbe seen as a new Simulink block and the new look of the complete model

42


1

IF

In Out

Pre Selector

in Out

Pre Amp

RF

LO

IF

Mixer + LO filter

RF

LOIF

Mixer + IF filter 2

RF

LOIF

Mixer + IF filter 1

inO

ut

LO Amp

in Out

IF Amp

3

LO

2

Synth

1

RF

Figure 4.19: The RF converter model with the combined mixer and bandpassfilter block.

can be seen in Figure 4.19. This solution works out well and the model isnow more useful for sensitivity analysis.

Now, the RF converter model was closer to completion. Still, as men-tioned earlier, our last bandpass filter was creating errors (totally destroyingthe signal) at high sampling rates. Since aliasing effects are unwanted andsome signals in our model reach 40 GHz we had to think of a solution. Weconcluded that two possible solutions existed. We could try with anotherdigital filter design, FIR etc., and still use a bandpass filter. Or we coulduse a lowpass Butterworth filter in series with a highpass Butterworth fil-ter. The decision was in favour for use of the already existing filter design.So we tried a lowpass Butterworth filter from DC to a cutoff frequency f2

and a highpass filter from cutoff frequency f1. The solution worked outwell and our problem was solved.

Once again we have created an ad hoc solution that reduces the adapt-ability of the model. Not as serious as the solution with the mixer but in away that makes the complete model in Figure 4.19 look static and not atall as flexible as we would like it to be.

Still, we wondered if our improved model would work adequately. Asimulation with the complete RF converter with almost the same signal asused for validation of the mixer and amplifier gave us the wanted feedback.The RF signal was a CW signal at 6 GHz with a signal power of −40 dBm.The noise power in the RF signal was −87 dBm. The RF converter hada cascade gain Gcascade of 58 dB and the cascade attenuation for the RFsignal Lcascade was 13 dB. The cascade noise figure NFcascade was 10 dB.In Figure 4.20 we can see that the output noise level is −42 dBm.

The expected value should be

Pnoise out = Pnoise in + Gcascade − Lcascade + NFcascade

and with values inserted

Pnoise out = −87 + 58− 13 + 10 = −32 dBm

43


0 5 10 15 20 25 30 35 40−90

−80

−70

−60

−50

−40

−30

−20


Noi

se P

ower

(dB

m)


Figure 4.20: Validation noise power in to and out from the RF converter.

We have a difference in noise power of a few dB. This is the best result everfor our complete RF converter.

In Figure 4.21 we see that our wanted 1 GHz signal has a power of 5dBm. The expected value is

Pout = Pin + Gcascade − Lcascade = −40 + 58− 13 = 5 dBm

and so we have a perfect match between simulated and expected value.Also, the signal is very clear and it should be no problem for the DSP unitto make decisions based on a sampled version of the signal.

44


0 1 2 3 4 5 6 7 8 9 10

x 109

−80

−70

−60

−50

−40

−30

−20

−10

0

10

IF Frequency [Hz]

IF P

ower

(dB

m)

Figure 4.21: Validation output signal from the RF converter in the frequencydomain.

45

Chapter 5

Conclusions and PossibleEnhancements

The analog nature of the RF converter makes it a superb source of non-linearities in the radar warning system. Control over these phenomena isessential to the designer.

Most of the non-linearities are introduced by the mixer. This is re-flected in the number of existing mixer models, but also in the time spentmodelling the mixer compared to the time spent on the other componentswhile working on this thesis.

The model presented in this thesis will give the designer a rough outlineof the spurious frequencies and the total noise figure of the design. Thismay be sufficient during a preliminary phase of the design, but will notsuffice when constructing such a critical system as a complete radar warningsystem. Knowledge obtained from the model must be complemented witheither simulations from more advanced (= more expensive) software and/oryears of design experience.

It is the view of the authors that Simulink is the main limiting factorin the model. Simulink is a real time system and prevents us from doingcalculations on the complete signal. This is desirable when working in thefrequency domain.

Simulink was originally constructed to simulate systems on a higherlevel. It is therefore not very well suited to model electrical components onthe level needed in this application. To correctly model e.g. the mixer (if itis at all possible) would require time, knowledge, and money not availablefor this project.

5.1 Achievements

In Chapter 1, the purposes of this thesis were defined to be

1. to present an accurate model of an RF converter

47

CHAPTER 5 · CONCLUSIONS AND POSSIBLE ENHANCEMENTS

2. to allow for the model to be easily adaptable to configuration changesin the converter.

One realises that the term “accurate” is very relative. The model is notaccurate enough to support the complete RF converter design. However,spurious frequencies and overall noise figure can be roughly predicted. Rep-resentatives of Avitronics have expressed their satisfaction with the model.Bear in mind though, that from the company’s point of view not only themodel results are important, but also its ease of use. That is the advantageof Simulink.

Unfortunately, the adaptability of the model must be seriously ques-tioned. The best results of the model are achieved using a number of adhoc solutions. This is not a prominent feature when trying to construct ascalable, adaptable, and easy-to-use model.

To summarise, one can say that it is not impossible to model the RFconverter of a radar warning system. However, a lot more research is neededto complete the task.

5.2 Recommended Improvements

When modelling the individual components of the RF converter, manytools are available that are more specialised than the Matlab/Simulinkenvironment. But when it comes to availability and adaptability, Matlabis well known in the industry and has proven itself time and time again.

The real time feature of Simulink which is so appealing when workingwith e.g. a control system is its Achilles’ heel in this project. Matlab ispreferable when dealing with signals in the frequency domain. The graph-ical user interface of Simulink can be implemented in Matlab as well, sinceMatlab from version 6 offers powerful GUI tools.

Therefore, a possible way to improve the present model could be asfollows.

• Re-implement the model in a pure Matlab environment.

• Perform model simulations in Matlab.

• Use the Matlab GUI tools to increase ease of use.

48

Appendix A

Measurement data

A.1 Mixer Measurements

These are the measurements not presented in Section 3.3. They are pre-sented without comments.

Table A.1: Mixer measurement data for various fRF and fLO.

fRF fLO fIF PIF fRF fLO fIF PIF

11 10 1 −19 12 10 2 −2111 10 2 −71 12 10 4 −7311 10 3 −74 12 10 6 −6011 10 8 −64 12 10 8 −4711 10 9 −50 12 10 10 −1111 10 10 −12 12 10 12 −5211 10 11 −50 12 10 20 −5311 10 20 −5211 10 21 −659 10 1 −19 8 10 2 −209 10 2 −73 8 10 6 −539 10 3 −78 8 10 8 −359 10 8 −59 8 10 10 −119 10 9 −38 8 10 12 −719 10 10 −12 8 10 20 −539 10 11 −649 10 19 −589 10 20 −529 10 21 −60

14 10 2 −69 13 10 3 −2014 10 4 −21 13 10 4 −6514 10 6 −43 13 10 6 −6714 10 10 −12 13 10 7 −4814 10 14 −58 13 10 10 −11

49

APPENDIX A · MEASUREMENT DATA

Table A.1: (continued)

fRF fLO fIF PIF fRF fLO fIF PIF

14 10 16 −70 13 10 13 −5314 10 18 −71 13 10 20 −5014 10 20 −5110 6 4 −2210 6 6 210 6 8 −4510 6 10 −4910 6 12 −5110 6 16 −6510 6 18 −5110 6 20 −62

50

References

[1] Lars Ahlin and Jens Zander. Principles of Wireless Communications.Studentlitteratur, Lund, Sweden, second edition, 1998.

[2] Avantek, Inc., Milpitas, CA, USA. Modular and Oscillator Compon-tents, Data Book, second edition, 1990.

[3] Andrea M. Crosmun and Stephen A. Maas. Minimization of intermod-ulation distortion in GaAs MESFET small-signal amplifiers. IEEETransactions on Microwave Theory and Techniques, 37(9):1411–1417,September 1989.

[4] Elisra Electronic Systems, Ltd., Bene Beraq, Israel. Microwave Com-ponents Catalog. Catalog reference No. 0514152.

[5] Marek T. Faber and Wojciech K. Gwarek. Nonlinear-linear analysis ofmicrowave mixer with any number of diodes. IEEE Transactions onMicrowave Theory and Techniques, MTT-28(11):1174–1181, Novem-ber 1980.

[6] Fredrik Gustafsson, Lennart Ljung, and Mille Millnert. Signalbehan-dling. Studentlitteratur, Lund, Sweden, 2000.

[7] Bert C. Henderson. Reliably predict mixer IM suppression. Mi-crowaves & RF, 22(12), November 1983.

[8] Bert C. Henderson. Mixers in microwave systems (part 1). WJ Tech-Note, 17(1), January/February 1990. Revised and reprinted in 2001.

[9] Bert C. Henderson. Mixers in microwave systems (part 2). WJ Tech-Note, 17(2), March/April 1990. Revised and reprinted in 2001.

[10] Herbert L. Krauss, Charles W. Bostian, and Frederick H. Raab. SolidState Radio Engineering. John Wiley & Sons, Inc., second edition,1980.

[11] H. J. Kuno and D. L. English. Nonlinear and intermodulation char-acteristics of millimeter-wave IMPATT amplifiers. IEEE Transactionson Microwave Theory and Techniques, MTT-24(11):744–751, Decem-ber 1976.

51

REFERENCES

[12] Stephen A. Maas. Two-tone intermodulation in diode mixers. IEEETransactions on Microwave Theory and Techniques, MTT-35(3):307–314, March 1987.

[13] Mini-Circuits, New York, NY, USA. Modern Mixer Terms Defined,August 1999. Published as an Application Note at http://www.minicircuits.com.

[14] Lennart Rade and Bertil Westergren. Mathematics Handbook. Stu-dentlitteratur, Lund, Sweden, fourth edition, 1998.

[15] Dror Regev. Characterization of spurious-response suppression indouble-balanced mixers. IEEE Transactions on Microwave Theoryand Techniques, 38(2):123–128, February 1990.

[16] Dennis Roddy. Microwave Technology. Prentice Hall, EnglewoodCliffs, NJ, USA, second edition, 1986.

[17] Alex Roetter and Dave Belliveau. Single-tone IMD analysis via theweb: A spur chart calculator written in Java. Microwave Journal,40(11), November 1997.

[18] Sune Soderkvist. Tidskontinuerliga Signaler & System. Sune Soder-kvist, Linkoping, Sweden, second edition, 1993.

[19] Klas Yhland, Niklas Rorsman, Mikael Garcia, and Harald F. Merkel. Asymmetrical nonlinear HFET/MESFET model suitable for intermod-ulation analysis of amplifiers and resistive mixers. IEEE Transactionson Microwave Theory and Techniques, 48(1):15–22, January 2000.

52

http://www.minicircuits.com

http://www.minicircuits.com

Index

Symbols1 dB compression point, 17

aadaptability, 41, 43, 48adaptable, 2Advanced Design System, 25amplification curve, 17amplifier, 15antenna, 6AR model, 30Australia, vAvantek, 15Avitronics, 1, 20

bbandwidth, 10, 19bearing, 6bi-phased modulation, 12block structure, 26burnout, 16butter, 37Butterworth filter, 20

ccentre frequency, 20Chebyshev filter, 20clipping, 16controller, 7conversion

compression point, 14loss, 13

cutoff frequency, 19

ddBc, 28, 32dBm, 15desired frequency, 13

digital signal processing, 6diode, 12drag and drop, 26

eelliptic filter, 20examiner, iexperience, 1, 47

ffeedback, 7filter, 19filter order, 20frequency

conversion, 12response, 20

gglitches, 40global sampling time, 40graphical user interface, 25, 48Grintek, 1

hharmonics, 10, 16HP2, 18

iimage rejection mixer, 15IMD, 11insertion loss, 20intermediate frequency, 9intermodulation

distortion, 11, 17products, 12table, 14

IP3, 11, 17isolation port-to-port, 14

53

INDEX

jJava, 24

kkTB, 10

lLC , 13leakage, 14library, 6linear gain, 16local oscillator, 6

mMatlab, 25MDS, 11Microwave Office, 25minimum detectable signal, 10mismatch, 11Miteq, 18mixer, 12mode, 6model, 1

aim, 23layer, 26

nnationality, 6network analyser, 20NF , 10noise

figure, 10reducer, 41

oone-tone second-harmonic intercept

point, 18order of

intermodulation, 12modulation, 12

pP1 dB , 17position, 6purpose, 2, 23, 47

rradar

frequency, 9warning receiver, 5

real time, 25, 47reflection coefficient, 11return loss, 12RF converter, 5ripple, 19RPP , 14

sSaab, 1saturation, 16SFDR, 11SHP2 , 34Signal Processing Toolbox, 37Simulink, 25, 47software, 1, 47South Africa , vspurious free dynamic range, 10spurious frequency, 14standing wave, 11superheterodyne, 5, 9supervisor, isuppression, 14sweep, 6synthesiser, 6

tthreat, 5threshold amplitude, 35transients, 40Ts, 40two-tone third order

harmonics, 10intercept point, 11

two-tone third-order intercept point,17

vvalidation signal, 32variance, 31virtual ground, 12voltage standing wave ratio, 11V SWR, 11

wwhite noise, 10, 31

54

modelling an rf converter in matlab - diva-portal.org17004/fulltext01.pdf · modelling an rf...

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