The Pennsylvania State University Schreyer Honors College

THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE

DEPARTMENT OF ELECTRICAL ENGINEERING

NETWORK ANALYZER WITH STABLE OSCILLATOR FOR ICE PENETRATING RADAR

ERIC J. TIM Spring 2012

A thesis submitted in partial fulfillment of the requirements for a baccalaureate degree in Electrical Engineering with honors in Electrical Engineering

Reviewed and approved* by the following:

Sven G. Bilén Associate Professor of Engineering Design, Electrical Engineering, and Aerospace Engineering Thesis Supervisor

John D. Mitchell Professor of Electrical Engineering Honors Advisor

* Signatures are on file in the Schreyer Honors College.

ABSTRACT

This thesis explores the performance of a low-cost, portable vector network analyzer

modified for use in measuring the thickness of ice sheets. These measurements are instrumental

in determining how quickly ice is melting in regions such as the polar ice caps. The harsh

operating conditions of this application generally require temperature-controlled housings to maintain suitable operation. An alternative approach is to modify the internal oscillator to make it temperature insensitive and ultimately improve the accuracy of the measurement.

To determine the effectiveness of a network analyzer, a relationship between the frequency stability of the oscillator and the resolution is derived. Thermal testing of frequency stability is performed on the proposed network analyzer, revealing that the original oscillator is not suitable for this application. A replacement oscillator is selected, installed, and thermally tested for improvements. Ultimately, this modified network analyzer meets the requirements for ice sheet measurements using ice penetrating radar.

TABLE OF CONTENTS

LIST OF FIGURES ...... iv

LIST OF TABLES ...... vi

ACRONYMS ...... vii

ACKNOWLEDGMENTS ...... viii

Chapter 1 Introduction ...... 1

1.1 Project Scope and Requirements ...... 1 1.2 Thesis Overview ...... 3

Chapter 2 Background ...... 4

2.1 Ice Penetrating Radar ...... 4 2.2 Network Analyzer ...... 5 2.2.1 S-Parameters ...... 6 2.2.2 SDR-Kits VNA v2.6 ...... 8 2.3 Oscillators ...... 10 2.3.1 Defining Qualities ...... 10 2.3.2 Types of Oscillators ...... 13

Chapter 3 Relationship of Source XO Instability to Resolution Error ...... 16

3.1 Tolerance through an Ideal Mixer ...... 16 3.2 Resolution Error Related to Tolerance ...... 18 3.3 Conclusions ...... 19

Chapter 4 Initial Testing ...... 20

4.1 Room Temperature Testing ...... 21 4.1.1 Frequency Output of the XO ...... 22 4.1.2 Phase Noise of the XO ...... 22 4.1.3 XO Oscilloscope Data and Phase Deviation ...... 23 4.1.4 TX Phase Noise ...... 24 4.1.5 Power Supply Considerations ...... 28 4.2 Low Temperature Testing ...... 28 4.2.1 Frequency Output Instability from 0 °C to −25 °C ...... 29 4.2.2 Phase Noise of the XO ...... 30 4.2.3 Long Term XO Stability with Temperature ...... 31 4.2.4 TX Phase Noise ...... 31

Chapter 5 Replacement Oscillator Selection ...... 33

iii

Chapter 6 Replacement Oscillator Testing ...... 35

6.1 Room Temperature Testing ...... 35 6.1.1 Frequency Output of the TCXO ...... 35 6.1.2 Phase Noise of the TCXO ...... 36 6.1.3 TCXO Oscilloscope Data and Phase Deviation ...... 37 6.1.4 TX Phase Noise ...... 38 6.2 Low Temperature Testing ...... 42 6.2.1 Frequency Output Instability from 0°C to −25°C ...... 42 6.2.2 Phase Noise of the TCXO ...... 43 6.2.3 Long Term TCXO Stability with Temperature ...... 44 6.2.4 TX Phase Noise ...... 44

Chapter 7 Conclusions ...... 46

7.1 Summary ...... 46 7.2 Future Research ...... 47

References ...... 48

Appendix A SDR-Kits VNA v2.6 Schematic ...... 49

Appendix B Supporting Equations ...... 51

Academic Vita ...... 54

LIST OF FIGURES

Figure 1-1 SDR-Kits VNA v2.6 with cover removed...... 2

Figure 2-1 Radar return through a sheet of ice [1]...... 4

Figure 2-2 Phase difference of two radar reflections of a location [1]...... 5

Figure 2-3 Phase measurement with a reference signal [3]...... 6

Figure 2-4 S-Parameters defined by incident, transmitted, and reflected waves [3]...... 7

Figure 2-5 S-Parameter measurements setup for ice penetrating radar...... 8

Figure 2-6 Block diagram of SDR-Kits VNA [4]...... 9

Figure 2-7 Frequency stability and accuracy of oscillators [5]...... 10

Figure 2-8 A noisy signal with various forms of instability [5]...... 11

Figure 2-9 Causes and effects of instabilities on the frequency of an oscillator [5]...... 13

Figure 2-10 Frequency characteristics of quartz with respect to temperature [5]...... 14

Figure 4-1 Source XO phase noise across 50 kHz...... 23

Figure 4-2 Source XO phase noise from center frequency to 10 kHz...... 23

Figure 4-3 Capture of XO output (36 MHz) with OCXO reference (10 MHz)...... 24

Figure 4-4 Phase noises of a.) XO, b.)–f.) TX...... 25

Figure 4-5 Spectra of the TX signal...... 27

Figure 4-6 Phase noise of the XO with alternate power supply...... 28

Figure 4-7 Phase noises of the XO at low temperatures...... 30

Figure 4-8 Phase noises of the TX at room temperature and −25 °C...... 32

Figure 5-1 Connor Winfield TCXO on breakout board...... 34

Figure 5-2 TCXO integrated into the SDR-Kits VNA...... 34

Figure 6-1 TCXO phase noise across 50 kHz...... 37 v

Figure 6-2 TCXO phase noise from center frequency to 10 kHz...... 37

Figure 6-3 Capture of TCXO output (20 MHz) with OCXO reference (10 MHz)...... 38

Figure 6-4 Phase noises of a.) TCXO, b.)–f.) TX...... 39

Figure 6-5 Spectra of the TX signal...... 41

Figure 6-6 Phase noises of the TCXO at low temperatures...... 43

Figure 6-7 Phase noises of the TX at room temperature and −25 °C...... 45

Figure A-1 SDR-Kits VNA oscillator schematic [8]...... 49

Figure A-2 SDR-Kits VNA TCXO replacement oscillator schematic [8]...... 49

Figure A-3 SDR-Kits VNA top board layout [8]...... 50 vi

LIST OF TABLES

Table 1-1 Design Requirements for Network Analyzer...... 3

Table 4-1 Equipment used for testing the VNA...... 21

Table 4-2 Measured Frequency of the Source XO...... 22

Table 4-3 Low Temperature Frequency Output Changes of XO and TX Outputs...... 29

Table 4-4 Measured Frequency of the Source XO at −25 °C...... 31

Table 6-1 Measured Frequency of the Source TCXO...... 36

Table 6-2 Low temperature frequency output changes of TCXO...... 42

Table 6-3 Measured Frequency of the Source TCXO at −25 °C...... 44 vii

ACRONYMS

• ADC Analog-to-Digital Converter • BPF Band-Pass Filter • DDS Direct Digital Synthesizer • DSP Digital Signal Processing • DUT Device Under Test • EMI Electromagnetic Interference • IF Intermediate Frequency • GPS Global Positioning System • LC Inductor–Capacitor • LNA Low-Noise Amplifier • LO Local Oscillator • OCXO Oven Controlled Crystal Oscillator • PLL Phase-Locked Loop • RF Radio Frequency • RMS Root Mean Squared • RX Receiver • S Scattering Parameters • SNR Signal-to-Noise Ratio • SWR Standing Wave Ratio • TX Transmitter • TCXO Temperature-Compensated Crystal Oscillator • USB Universal Serial Bus • VNA Vector Network Analyzer • XO Crystal Oscillator viii

ACKNOWLEDGMENTS

I would first like to thank my honors advisor, Dr. Jack Mitchell, for all of his help throughout my honors career. With his mentorship, I was able to make the most of my undergraduate career and discover my passion for electrical engineering. I know that without him, I would never have been able to come as far as I have.

I would also like to thank Dr. Sven Bilén for the opportunity to work on an exciting project, close to my area of interest. His willingness to work with me has given me a greater appreciation of practical engineering and allowed me to fulfill my honors requirements.

All of my colleagues in the Student Space Programs Laboratory and Systems Design Lab proved invaluable in completing my thesis and monumental to my success.

Chapter 1

Introduction

A growing concern today is rising global temperatures resulting in global climate change.

This global climate change has many consequences, but one of particular interest is the melting of polar ice caps. Measuring this melting provides a challenge since drilling cores is very costly as well as impractical for deep ice sheets. A solution to this problem is to remotely measure depth by interpreting phase differences of the return signals from ice penetrating radar to estimate the melt rate. These measurements require accurate electronic equipment including a precision vector network analyzer (VNA).

Most high end VNAs are bench-top models that are large and also generally very expensive. The size and cost presents a challenge to scientists working on vast expanses of ice sheets. These VNAs are not designed to be portable, nor are they designed to be exposed to low temperature environments. The current technique for using this equipment in harsh polar environments is to encase the VNA in a temperature-controlled case and move it on a sled. A portable, thermally stable, precision VNA would allow future researchers to track ice sheet changes without the capital investment or inconvenience of current VNA-based solutions.

1.1 Project Scope and Requirements

One portable network analyzer that is available today is the SDR-Kits Vector Network

Analyzer, developed by Prof. Dr. Thomas Baier. Figure 1-1 shows a picture of the internals of this network analyzer with the cover removed. This design uses a computer as a power source as well as for information handling via the Universal Serial Bus (USB). Moreover, this VNA is

2 much less expensive than conventional models. It costs only about $600 as compared to well

over $20,000 for basic Agilent VNAs.

Figure 1-1 SDR-Kits VNA v2.6 with cover removed.

While portability and cost are important criteria for this VNA, they are meaningless if the

device cannot produce a reasonable measurement for the thickness of the ice. Therefore, the

phase stability and resolution of the VNAs are the most important factors. To match the

application, the VNA should also be able to perform in a low-temperature environment. All other factors should be designed to be convenient for the researcher using this VNA. Table 1-1 lists the design requirements in order of importance for this application.

Table 1-1 Design Requirements for Network Analyzer. ID Name Requirement Rational The VNA shall be able to resolve the Slow rates of ice melt require thickness of a 1-km-thick sheet of ice 1 Resolution high resolution to make an with no more than 1 cm of error between accurate prediction of the rate visits This is the typical thermal Thermal The VNA shall maintain resolution over 2 environment for the locations of Stability the temperature range of 0 °C to −25 °C ice measurements This frequency range is the The VNA shall maintain resolution over a 3 Frequency expected spectrum of the ice frequency range of 200 MHz to 400 MHz penetrating radar application The VNA shall be powered by a computer One USB cable currently powers Power 4 with one USB A-to-B cable (5 V, 500 mA and transfers information, so Supply max) maintain this for simplicity All modifications of internal circuitry of The current package is minimized the VNA shall be confined within the 5 Size for convenient transport and original housing: (width 10.4 cm, depth operation 8.0 cm, height 4.6 cm) All modifications to the VNA shall be This VNA will replace expensive 6 Cost implemented with available, low cost bench-top VNAs components

1.2 Thesis Overview

This document provides an in-depth characterization of the unmodified SDR-Kits VNA system as well as an enhanced version designed for use in ice penetrating radar. Chapter 2 presents the relevant background material required to understand the application, device, and subsequent modification. Chapter 3 develops the necessary relationships for design considerations. Chapter 4 explains the rational for measurements and characterizes the unmodified system. Chapter 5 describes the selection of a replacement oscillator. Chapter 6 reports on the improvements made by replacing the crystal oscillator with a more stable source.

Chapter 7 summarizes the results with suggestions for future research with this application.

Appendix A shows the schematic and layout for the SDR-Kit VNA board. Appendix B shows further derivations in support of Chapter 3

Chapter 2

Background

2.1 Ice Penetrating Radar

The depth of a sheet of ice can be determined by transmitting a radar signal into the ice and measuring the amplitude and phase of the return signal [1]. The thickness of the ice can be

determined by observing the time it takes for a peak in the return signal to be detected as shown

in Figure 2-1. The distance traveled by a wave can be calculated by knowing the phase velocity of a wave traveling through a medium (about 168 m/µs for ice [1]) and measuring the time it takes to return to the source. The time traveled would be twice as long as the actual depth because the signal must travel through the ice to the reflection point and then travel back to the source to be detected.

Figure 2-1 Radar return through a sheet of ice [1].

5 The melt rate of the same layer of ice can be extrapolated by comparing return signal

patterns over a period of time [1]. As the ice sheet melts, the time a wave will take to travel

through it will decrease and the amplitude pattern will change. Therefore, if there is a reference

return signal pattern to compare against, the amount of ice that has melted correlates to the phase difference between the two signals. An example of phase comparison of two signals is shown by the polar plot in Figure 2-2.

Figure 2-2 Phase difference of two radar reflections of a location [1].

These polar plots of the returns can be calibrated by using the reflection peak from the ice surface as a reference [1]. The setup has antennas positioned a set distance from the ice surface.

This produces a magnitude peak from the reflection from the surface. This peak will be the same

on both plots as long as the distance between the antennas and ice remains the same between

visits. Then, by knowing the time between when two polar plots were measured, the rate of ice

melt can be determined from the phase shift in the peak amplitudes.

2.2 Network Analyzer

A VNA is required to measure the return of the radar signal. VNAs use scattering

parameters (S-parameters) to define a multiple-port device at high frequencies. They consist of a

6 source, circuitry for separating signals, a receiver to detect and down convert signals, and a processor with display or output mechanism [2]. VNAs capture information about both the

magnitude and phase of radio frequency (RF) signals. One common method for this

measurement is to down convert the RF signal to an intermediate frequency (IF) and sample it

directly with a tuned receiver [3]. The amplitude can be measured directly, but to measure the

phase information, a VNA compares the IF return signal to a reference as shown in Figure 2-3.

Figure 2-3 Phase measurement with a reference signal [3].

2.2.1 S-Parameters

S-Parameters are used to characterize RF signals because, at these high frequencies, other parameters are difficult or impossible to measure [2]. For example, impedances and admittances require shorts and opens to be connected at the ports of a device under test (DUT). Total voltage and currents are difficult to measure at high frequency because of the impedance and size of the probes. RF signals are susceptible to transmission-line effects because the wavelength of an RF signal can be short compared to the length of line. Transmission-line effects change the

impedance of shorts and opens, and could cause the circuit to oscillate or self-destruct.

Instead of measuring total voltages and currents, S-Parameters are calculated by

measuring the magnitude and phase of incident, transmitted, and reflected voltage waves.

S-Parameters are characterized by which port the signal is received on relative to which port it

came from [3]. For example, S11 would be the signal that was received on port one after being

7 sent from port one. These designations relate to the names of each S-Parameter. Signals being

introduced into port one are forward signals, and signals introduced at port two are reverse

signals. If a signal is coming from the same port to which it was introduced, it is a reflection, and

if it is from a different port, it is a transmission. This gives rise to S11, S21, S12, and S22 being

called forward reflection, forward transmission, reverse transmission, and reverse reflection,

respectfully. Figure 2-4 illustrates the S-Parameters and the signals that are used to determine

them.

Figure 2-4 S-Parameters defined by incident, transmitted, and reflected waves [3].

To determine an S-Parameter, a specific load must be placed across the opposing terminal. This load must be the characteristic impedance of the DUT, in most cases, 50 ohms.

But in applications such as ice penetrating radar, both terminals are not available. To account for this, the network analyzer must be calibrated. This is done by applying a known value to the transmission port of the network analyzer and storing the information. This is generally done with three impedances: a short, an open, and a load of 50 ohms. Calibration accounts for a total of twelve error terms that are compensated in software, six error terms in the forward direction and six error terms in the reverse direction [3].

8 Because of the ice layer, the signal must be applied to the surface. This limits the

available S-Parameters to only the S11 or S21 parameters. Figure 2-5 shows the setup for this application, where the TX and RX signals are the ports of the network analyzer with antennas attached. S11 can be measured directly since both the transmitted signal and the reflected signal are measured only at port 1. The S21 parameter can be measured by waiting for the signal injected at port one to travel to the ground and return to the receive antenna. Both parameters are used to characterize the path as completely as possible.

Figure 2-5 S-Parameter measurements setup for ice penetrating radar.

2.2.2 SDR-Kits VNA v2.6

The SDR-Kits VNA operates on the same basic principles as all VNAs. It has a source that is comprised of a crystal oscillator (XO) that drives two direct digital synthesizers (DDS).

For signal separation, the VNA uses a splitter to sample the incoming signal for reference and a balanced standing wave ratio (SWR) bridge for separation of incident and reflected waves. One

DDS is mixed with the transmitted and received signals to down convert them to an intermediate frequency (IF). The computer recognizes the VNA as a USB audio device allowing this IF signal to be transmitted to the computer soundcard. An IF is required because this soundcard acts as a low-pass filter which would block the transmitted RF signal. Multiplexing is required because a

9 sound card is normally stereo and there are three signals to be captured [4]. The low-pass nature of the sound card allows for some filtering and amplification to be done with the interface hardware. Ultimately, the computer takes the information from the sound card to do digital signal processing (DSP) and display the results with software. This layout is illustrated in the partial block diagram in Figure 2-6.

Figure 2-6 Block diagram of SDR-Kits VNA [4].

The source creates all of the signals that will be used in this VNA. This makes it one of the most important components in the device. Any error produced from the source will be carried through and affect the rest of the measurements. The source XO is a quartz crystal arranged to form a Pierce oscillator. The Pierce configuration is one of the most widely used circuits for high stability oscillators since most of the stray reactances appear across the capacitors instead of the crystal [5]. This circuit amplifies the third harmonic of the 12-MHz crystal to form an XO with an approximate output frequency of 36 MHz. This XO then drives the clocks of both DDSs. The

DDSs use a phase-locked loop (PLL) to multiply the reference XO frequency, and this multiplied

XO frequency is used as a clock to create RF signals used in the rest of the VNA.

10 2.3 Oscillators

For the SDR-Kits VNA, the source XO is used for not only creating the RF signals, but it

also provides the reference signal that is used to compare the return signals. The XO is of

significant importance for the resolution of the system because these measurements are crucial to

the accuracy of the VNA. For these reasons, some background information about oscillators is required for any improvements to the VNA’s resolution to be implemented.

2.3.1 Defining Qualities

There are many factors that can affect the precision of the VNA. The accuracy of an oscillator is determined by the average frequency of its output. If the average frequency of the output corresponds to the tuned frequency, the oscillator said to be accurate. Alternatively, an oscillator’s stability is its ability to remain at the same frequency with regard to other factors such as time, temperature, and vibration [5]. Figure 2-7 shows oscillator stability and accuracy in terms of frequency with reference to time.

Figure 2-7 Frequency accuracy and stability of oscillators [5].

Another consideration for the oscillator is reproducibility, which is the oscillator’s ability to produce the same frequency each time it is put into operation [5]. This VNA has a calibration

11 function that can compensate for any reproducibility issues from operation to operation.

Therefore, as long as the stability is maintained between calibrations, the oscillator will remain repeatable and accurate. This makes the stability of the oscillator the most important factor for high resolution in ice measurement.

Oscillator stability is further defined as short term and long term stability. Short term stability is caused by high frequency noise at the output of the oscillator. This noise can be from temperature fluctuations, active and passive components in circuitry, vibration, and stress relief due to interfacial fluctuations, but the limiting factor for XOs is Johnson or thermal noise [5].

Johnson noise is caused by thermally induced charge fluctuations due to particle movement in physical components. XOs can have noise introduced from the series resistance of the crystal as well as resistances of other components in the oscillator circuitry. Figure 2-8 shows how noise causes instability in the amplitude, frequency, and phase of the output signal.

Figure 2-8 A noisy signal with various forms of instability [5].

There are a number of different measurements of short term stability. Allan deviation

and phase noise are two more commonly specified parameters, but spectral densities of phase or

frequency deviation may also be used. Phase noise is one of the easiest of these quantities to

measure directly. Some oscilloscopes can display the phase vs. time of a signal, an RF voltmeter

can measure root-mean-squared (RMS) phase fluctuations, or a spectrum analyzer can display phase noise as a function of offset frequency from the carrier frequency [5]. The phase noise for a wide offset frequency is displayed on most oscillator datasheets, but the phase noise close to the carrier frequency is the most important for this application.

Allan variance, ( ), is the time-averaged mean of a sum of the difference between 2 푦 successive measured fre휎quencies휏 squared or

1 1 ( , ) = (y ) , 2-1 푚 2 2 2 휎푦 휏 푚 � 푘+1 − 푦푘 푚 푘=1 where is the time interval of the measurement, is the number of samples, is the fractional

frequency휏 measurement, and denotes successive푚 fractional frequencies. Allan푦 deviation or two- sample deviation is the square푘 root of Allan variance, and it is often used because it is easy and fast to compute, it has a straightforward relationship to the spectral densities, and it converges for all types of noise (as opposed to general variance) [5]. This value will decrease with increased averaging time until it reaches a noise floor. At this point, long term stability considerations must be taken into account.

Long term instability can be caused by a number of different factors. As in short term stability, noise can contribute to a change in the output frequency, but this only affects long term stability if that noise is low frequency. Crystal aging, temperature change, radiation, and other factors all contribute to a drift in frequency that ultimately describes the long term stability. Long term drift generally tapers off causing the stability of the oscillator to improve the longer it is turned on. Cycling the power to the oscillator causes the frequency output of the internal crystal

13 to begin a new trace that follows the same general pattern as before it was turned off. Figure 2-9 shows the various causes of frequency instabilities and the affect it has on the output of the oscillator.

Figure 2-9 Causes and effects of instabilities on the frequency of an oscillator [5].

2.3.2 Types of Oscillators

There are various types of oscillators available from simple inductor–capacitor (LC) tuned circuits to atomic resonators. LC circuits cost only a few dollars, but they are limited in stability due to their sensitivity to temperature as well as any reactances elsewhere in the circuit.

Similar effects exclude inverter based, ring oscillators and other simple circuits from being a high stability source. Atomic clocks monitor the emission of photons from elements such as cesium and rubidium as they change energy state. These sources are the most stable available today, but they also cost upwards of thousands of dollars. Quartz crystal oscillators bridge the gap between atomic clocks and simple timing circuits in terms of price and stability.

14 Quartz can be used to form an oscillator because of a phenomenon known as the

piezoelectric effect. Namely, when a voltage is applied across a piece of quartz, it causes strain

that deforms the crystallographic structure. When the voltage is reversed, the strain is also

reversed, giving way to resonance. This can be translated into an equivalent circuit of a

resonator. The simple equivalent circuit is a shunt capacitor in parallel with series capacitor,

inductor, and resistor. The shunt capacitor is due to the crystal plates that apply the voltage and

stray capacitances from the packaging [5]. The equivalent circuit model allows for a few

different types of quartz oscillators.

There are various arrangements for a simple quartz oscillator, but more dramatic

improvements in stability are achieved with a more complex device. Two quartz oscillators that

have higher stability are the temperature-compensated crystal oscillator (TCXO) and the oven- controlled crystal oscillator (OCXO). TCXOs typically have accuracies of 10−6, whereas OXCOs can be accurate below 10−8 [5]. This improvement over quartz oscillator accuracies of 10−4 to

10−5 is because of consideration given to the frequency of resonance for quartz at different temperatures. Figure 2-10 shows the frequency profile of quartz over a range of temperatures.

Figure 2-10 Frequency characteristics of quartz with respect to temperature [5].

TCXOs use control circuitry to adjust the frequency over the entire temperature range. A thermistor, or temperature-sensitive resistor, changes resistance based on the temperature and, therefore, controls the voltage applied to a varactor, or variable reactance component [5]. Some

TCXOs can be controlled by an external voltage. These devices have to take into account the temperature dependence of the load capacitance used for applying the voltage [6]. TCXOs are cheaper than OCXOs and use much less power.

OCXOs maintain a stable temperature inside the housing to maintain frequency accuracy.

The OCXO maintains its temperature at one of the turnover points where any temperature fluctuations produce only minimal changes in output frequency. The crystals in these applications can be manufactured with a turnover point anywhere above the highest operating temperature expected [6]. The upper turnover point is used because heating the package can be done simply with a resistor, whereas cooling the package would be much more difficult.

Ultimately, OCXOs have even better accuracy than TCXOs, but they are physically large, take longer to reach stability, and require a lot more power especially in low temperature applications.

Chapter 3

Relationship of Source XO Instability to Resolution Error

In order to determine possible modifications to the VNA, a relationship must be determined between the resolution error and the stability of the reference oscillator. The stability requirement can be described as a tolerance, where tolerance is defined as the change in frequency divided by the initial frequency or

| | = , 3-1 ∆푓 푓0 − 푓 푇 ≝ 0 0 where is the tolerance, is the initial frequency,푓 is the푓 measured frequency, and is the

0 difference푇 of the initial 푓and measured frequencies.푓 The tolerance is equal to the fractional∆푓 frequency, which is in our application, the error of the returned signal with respect to the actual

ice sheet depth, , can be expressed as the difference of the measured depth, , and the actual

depth, , over the퐸 actual depth or 푑

0 푑 | | . 3-2 푑0 − 푑 퐸 ≝ 0 For the sake of these derivations, all other conditions푑 will be ideal. This neglects any possible

error introduced from mixers, frequency multipliers, amplifiers, or any other components other

than from the source XO.

3.1 Tolerance through an Ideal Mixer

The SDR-Kits VNA has three mixers that down convert the RF signals to IF frequencies

for the computer to sample. Mixing in the frequency domain results in both the addition and

subtraction of input frequencies to be present at the output of the mixer or

17 + . 3-3 1 2 1 2 푓 푓 푓 ⊗ 푓 ≝ � 1 2 Because the DDSs are referenced with multiplied versions푓 − 푓 of the XO, the output frequency of the th DDS can be described as

푥 × , 3-3

DDS푥 DDS푥 XO where is the multiplication factor푓 and≝ �푀 is the frequency푓 � of the reference XO. Using

DDS푥 XO Equation푀 3-3, the outputs of both DDSs with푓 an ideal oscillator frequency, are given by

푓XO0 = × , 3-4

DDS10 DDS1 XO0 푓 = �푀 × 푓 � . 3-5

DDS20 DDS2 XO0 Substituting and for and푓 of Equation�푀 3-푓3 and� realizing the low pass filter inherent

DDS10 DDS20 1 2 in the computer푓 audio card푓 yields푓 푓

+ = = , 3-6 DDS10 DDS20 LPF IF0 DDS10 DDS20 푓 푓 DDS10 DDS20 푓 푓 ⊗ 푓 � DDS10 DDS20 �� 푓 − 푓 � where is the input to the computers analog푓 -to-digital− 푓 converter (ADC). Plugging in Equations

IF0 3-4 and푓 3-5 into Equation 3-6 gives the ideal IF signal into the ADC as

= × | | . 3-7

IF0 XO0 DDS1 DDS2 A frequency instability in푓 the oscillator,푓 푀 , can− be푀 considered by adding it to the ideal oscillator frequency, i.e., 훿

= + , 3-8

XO XO0 where is the actual oscillator output and푓 �푓 is the 훿ideal� output. To determine the worst-case

XO XO0 impact푓, consider this instability to appear in 푓only one of the DDS signals. This can be realized without loss of generality by replacing in Equation 3-5 yielding

푓XO0 = × + . 3-9

DDS2 DDS2 XO0 In this case, this instability would take푓 place푀 after the�푓 signal훿 has� been transmitted. Therefore, the

unstable IF signal can be described in the same manner as before yielding

= × | | + × . 3-10

IF XO0 DDS1 DDS2 DDS2 Ultimately, the worst-case tolerance푓 푓 for this푀 instability− 푀 can 훿be described푀 from Equation 3-1 as

× = . 3-11 × | DDS2 | IF 훿 푀 푇 XO0 DDS1 DDS2 Verification that this is the worst-case tolerance푓 푀 can be− found푀 in Appendix B.

3.2 Resolution Error Related to Tolerance

Now that the required tolerance is known for the mixer, the relationship between

tolerance and resolution error must be determined. To do this, the equation for the wavelength of

a signal propagating through a material is required. Wavelength, , in a medium can be defined in terms of the phase velocity of a signal through that medium, ,휆 and the frequency of the

푝 signal, , as 푣

푓 . 3-12 푣푝 휆 ≝ The phase of this signal, , can be determined using푓 Equation 3-12 and the actual depth traveled,

, as 휙

푑0 2 2 × × = × . 3-13

0 휋 0 휋 푓 푑 푑 푝 ⇒ 휙 Phase must always be converted back to 휆distance with푣 reference to another phase. This reference

phase is always the output of the reference signal, . Therefore, the calculated distance, , as

ref interpreted after this phase comparison is given by푓 푑

× . 2 × 3-14 푣푝 휙 ref ⇒ 푑 It can be seen by inspection that if there is no 휋frequency푓 deviation in the reference signal, the

software will be able to resolve the transmitted signal back to the correct depth, . Again, the only way to determine the tolerance requirement is to introduce instability into the푑0 reference

19 frequency. The worst-case scenario occurs when this instability occurs only during the TX period

of the network analyzer. Verification of this can be found in Appendix B.

Instability in the frequency of the reference, , before transmission gives wavelengths

훿 = 3-15 푣푝 휆ref 푓ref = 3-16 푝+ TX 푣 휆 ref after transmission. These translate to phases 푓 훿

2 × = × , 3-17 ref ref 0 휋 푓 휙 푑 푝 2 × (푣 + ) 3-18 = × . ref TX 0 휋 푓 훿 휙 푑 푝 Plugging Equation 3-18 into Equation 3-14 results in 푣a measured depth of

2 × ( + ) = × × = × 1 + . 3-19 ref 2 ×푝 0 휋 푓 훿 푣 0 훿 푑 �푑 푝 � ref 푑 � ref� Equation 3-19 applied to Equation 3-2푣 results in an 휋error푓 of 푓

| | × 1 + 훿 3-20 = = = . 0 0 푑0 − 푑 �푑 − �푑 � 푓ref�� 훿 퐸stable XO 푑0 푑0 푓ref

3.3 Conclusions

The result of Equation 3-20 shows that the fractional error of the depth measurement is

simply the tolerance of the reference signal. Because the reference is created by mixing the two

DDSs and the worst-case tolerance of a mixed signal was already found to be Equation 3-11, the error can be related to the tolerance of the source XO by

| | × . 3-21 × | | 푑0 − 푑 훿 푀DDS2 ≤ 푑0 푓XO0 푀DDS1 − 푀DDS2

Chapter 4

Initial Testing

With a relationship established for the depth error caused by stability issues in the oscillator, the SDR-Kits VNA can be evaluated for effectiveness in this application. The VNA must first be tested at room temperature to determine reference effectiveness. These baseline measurements can then be compared to the results tests conducted over the low temperature range described in the requirements. Long term stability with power deactivation must also be investigated because the application will likely include powering down the VNA between measurements or visits to sights.

To determine the stability of an unknown source, a more stable reference source must be used as a reference [7]. To meet the stability requirements of the reference source, a high precision, global position system (GPS)–trained OCXO was used. The GPS-trained feature ensures that this source will maintain its accuracy as long as a GPS antenna is attached and lock to the GPS constellation is maintained. This source was chosen due to availability and costs associated with higher precision oscillators. The VNA is driven only by an uncompensated XO.

The inherently more stable OCXO will not significantly contribute to any instability in the readings, thereby providing an acceptable reference.

The test equipment consists of the SDR-Kits VNA with the top cover removed, a frequency counter with the GPS-trained OCXO as a reference, an oscilloscope, a spectrum analyzer, a thermal chamber, and a computer to power and run the VNA software. Ideally, the oscilloscope would have a phase measurement setting, but due to limitations in availability, an oscilloscope with a waveform export function is used to allow for data post-processing. The oscillator output was sampled with a 10× probe to limit loading effects on the XO. Output

21 waveforms are sampled with a spectrum analyzer due to the high frequency and to determine

phase noise. The test equipment used is listed in table 4-1.

Table 4-1 Equipment used for testing the VNA. Equipment Manufacturer Model Number Frequency counter Hewlett Packard 53132A

GPS-trained OCXO Hewlett Packard 58503A

Oscilloscope Agilent 54815A Spectrum analyzer Agilent E4403B Thermal chamber TestEquity 1007C

4.1 Room Temperature Testing

The room temperature testing of the VNA creates a comparison dataset that can be used to determine the absolute operating conditions of this device. The testing consists of a frequency measurement of the source XO using the GPS-trained OCXO-referenced frequency counter. The next measurement is phase noise by viewing the output of the XO on a spectrum analyzer. The

output of the source XO is viewed on an oscilloscope with the OCXO output as a reference. The

data captured by the oscilloscope is exported for interpretation. Lastly, the TX output of the

VNA is viewed on the spectrum analyzer to see any induced instability, evidenced as phase noise.

These steps are repeated after 30 minutes, 1 day, and 3 days. These times are chosen to reflect the time between subsequent sight visits in a day, the minimum amount of time between visits to a sight, and the maximum number of days between visits to a sight, respectively. The VNA is left on until the 30 minute test to simulate moving from location to location, but powered down for the 1 day and 3 day lengths as expected for subsequent visits.

22 4.1.1 Frequency Output of the XO

The initial and three delayed frequency measurements are made using the frequency counter. Any instability in the initial test represents the short term instability of the oscillator, while the delayed data shows long term instability with breaks in power. The measured frequencies from the source XO are shown in Table 4-1. The approximate short term stability is determined from the fluctuations in the frequency during measurement.

Table 4-2 Measured Frequency of the Source XO. Delay Measured Frequency (Hz) Short Term Instability (Hz) Initial 35, 910, 710. XXX ~10

30 minutes 35, 910, 698. XXX ~7 1 day 35, 910, 782. XXX ~9 3 days 35, 910, 718. XXX ~6

4.1.2 Phase Noise of the XO

The phase noise of the XO can be measured by viewing the output on a spectrum

analyzer. An improved picture of the phase noise can be seen by mixing a stable reference source

of the same frequency and 90 degrees out of phase, and then observing the noise mixed down to

baseband [7]. There are a few problems with this alternative method for this application. The

XO runs at approximately 36 MHz and the OCXO is a 10 MHz source. This is fine for a

reference, but there is no way to match the frequency without introducing more noise in the

process. Also, baseband is inherently noisy because of 60 Hz power and other applications in the

room. Therefore, phase noise measurements are determined from the output of the XO as seen in

Figures 4-1 and 4-2. No noticeable difference can be observed between delayed measurements due to low spectrum analyzer resolution.

Figure 4-1 Source XO phase noise across 50 kHz.

Figure 4-2 Source XO phase noise from center frequency to 10 kHz.

4.1.3 XO Oscilloscope Data and Phase Deviation

The XO output shape and integrity can be seen directly on an oscilloscope. Figure 4-3 shows the XO output with the GPS-trained OCXO as a reference. Notice that the shape of the

XO output is not a perfect sine wave. Some of this deformation may be due to loading effects of the 10× probe, but there is also noise from the XO. The phase can be seen by observing the XO output against the OCXO. If the XO were stable, its waveform should line up with the OCXO on approximately every thirty-sixth cycle. The sample period in Figure 4-3 is long enough to show

24 the first occurrence of this. There is some phase shift, implying that there is some short term instability in the XO.

Figure 4-3 Capture of XO output (36 MHz) with OCXO reference (10 MHz).

4.1.4 TX Phase Noise

The frequency that the VNA outputs can be measured at the TX output port. Because the signals of interest are up to 400 MHz, the best way to view them is also with the spectrum analyzer. These signals are not referenced to the other DDS, so they will only have the phase noise of the source XO with some possible multiplication or noise added. Figure 4-5 shows the

TX phase noises over the range of frequencies for the application compared to XO reference.

There is some attenuation and flattening of the spectrum, especially at the higher frequencies.

This indicates higher phase noise when the VNA is operating at higher frequencies.

a.) XO 36 MHz b.) TX (200 MHz)

c.) TX (250 MHz) d.) TX (300 MHz)

e.) TX (350 MHz) f.) TX (400 MHz) Figure 4-4 Phase noises of a.) XO, b.)–f.) TX.

26 Observing over the entire frequency range required for our application, i.e., 200 MHz to

400 MHz, is crucial for ensuring correct operation of the VNA for use in as an ice penetrating radar. Figure 4-6 shows samples of the output as the frequency is swept through the range. There is a troubling peak that shifts lower in frequency until around 350 MHz, where it crosses with the

TX signal. After this point, both peaks move off with little affect, as seen in Figure 4-6e. This is a serious concern because not only will the increased phase noise limit accuracy, but the proximity of the other high power signal could allow it to get mixed down and corrupt the data for a number of frequency readings. However, the ability to change the clock multiplier of the

DDSs in software could possibly be used to correct this TX problem.

a.) TX = 200 MHz b.) TX = 250 MHz

c.) TX= 300 MHz d.) TX= 350 MHz

e.) TX = 400 MHz Figure 4-5 Spectra of the TX signal.

28 4.1.5 Power Supply Considerations

A major source of noise for oscillators can be caused by fluctuations in the power supply [7]. Any change in the supply voltage would result in a change in the voltage applied across the oscillator crystal, and it would add some phase noise by temporarily shifting the output frequency. Figure 4-7 shows the output from the XO with a filtered external power supply. No difference in phase noise can be seen in the near frequency region of interest. The power supply circuitry built into the VNA likely cleans the power signal sufficiently for the computer supply to be as clean as an external source.

Figure 4-6 Phase noise of the XO with alternate power supply.

4.2 Low Temperature Testing

The low temperature testing of the VNA follows the same procedure as the initial, room temperature testing except it is performed over the application’s temperature range. A thermal chamber is used to ensure the correct external temperature is applied. The measurements are performed at 0 °C and then the temperature is dropped by 5 °C until the −25 °C limit is reached.

For the initial thermal testing, the same measurements as the room temperature testing are taken

29 for comparison. The greatest instabilities occur at the lowest temperatures because of internal

heating from the DDS sources. Therefore, any long term stability issues can be seen most

effectively at the lowest temperature, −25 °C.

4.2.1 Frequency Output Instability from 0 °C to −25 °C

As expected from the frequency–temperature characteristics of quartz, changing the

external temperature changes the output frequency of the oscillator. Before taking any readings,

the VNA has to be allowed to soak at the low temperature setting to ensure the internal

temperature of the circuitry is also at thermal equilibrium. In addition to the frequency output of

the XO, the calibration function allows a 10-MHz DDS output to be sampled. This can be used to

show how instability of the XO translates to the TX. Table 4-2 shows these output frequencies

over the temperature range with the changes between measurements. The increasing change of

output frequency with the same increase in temperature shows that the slope of the thermal

characteristic is increasing. This proves the worst instabilities will occur at the −25 °C temperature. Also, there is an amplification of the phase noise through the DDS, shown by the change in TX frequency. The instability of the XO over this temperature range is approximately

20 parts per million (ppm) overall.

Table 4-3 Low Temperature Frequency Output Changes of XO and TX Outputs. Temperature XO Frequency (Hz) ΔXO (Hz) TX Frequency (Hz) ΔTX (Hz) 0 °C 35, 910, 327. XXX — 9, 999, 860. 9XX, X —

−5 °C 35, 910, 222. XXX −105 9, 999, 830. 1XX, X −30.8

−10 °C 35, 910, 117. XXX −105 9, 999, 801. 3XX, X −28.8 −15 °C 35, 909, 995. XXX −122 9, 999, 762. 8XX, X −38.5

−20 °C 35, 909, 845. XXX −150 9, 999, 725. 1XX, X −37.7 −25 °C 35, 909, 688. XXX −157 9, 999, 677. 7XX, X −47.4

30 4.2.2 Phase Noise of the XO

The phase noise of the XO at lower temperature should also indicate poorer stability performance. As seen in Figure 4-8, the amplitude of the XO output power actually increases at lower temperatures. This could be due to changes in the supporting circuitry, applying more power to the oscillator. There are slight increases in the widths of the peaks at lower temperatures. These indicate higher close phase noise, and therefore lower short term stability.

a.) 0 °C b.) -5 °C

c.) -10 °C d.) -15 °C

e.) -20 °C f.) -25 °C

Figure 4-7 Phase noises of the XO at low temperatures.

31 4.2.3 Long Term XO Stability with Temperature

The long term stability at low temperatures is even more important than at room

temperature. This stability will be affected the crystal being powered down as well as the short

term instability during each testing. Because the crystal and the biasing circuitry are thermally

dependant, any heating of the low temperature environment will make repeating the same

frequency at the same temperature dependant on the dynamic heating of the surrounding circuitry.

Table 4-3 shows the long term stability of the XO over the four day period at −25 °C.

Table 4-4 Measured Frequency of the Source XO at −25 °C. Delay Measured Frequency (Hz) Δ Frequency (Hz) Initial 35, 909, 688. XXX — 30 minutes 35, 909, 706. XXX +18

1 day 35, 909, 640. XXX −66 3 days 35, 909, 607. XXX −33

4.2.4 TX Phase Noise

The TX output shows how much extra phase noise is added because of the lower

temperature. Figure 4-9 shows the room temperature phase noise characteristics as compared to

those at −25 °C. There is a significant drop in power with the decrease in temperature. No noticeable differences can be seen from one low temperature measurement to the next. It is possible that the thermal chamber could contribute to some added noise in this setup. The thermal chamber has pumps and a switching power supply, both of which can introduce noise through vibration or electromagnetic interference (EMI), respectively. The anomalous secondary peak is still present at low temperatures.

a.) Room Temperature (200 Mz) b.) -25 °C (200 MHz)

c.) Room Temperature (300 Mz) d.) −25 °C (300 MHz)

e.) Room Temperature (400 MHz) f.) −25 °C (400 MHz)

Figure 4-8 Phase noises of the TX at room temperature and −25 °C.

Chapter 5

Replacement Oscillator Selection

Using the resolution requirements of 1 km thick ice and 1 cm accuracy and

Equation 3-21, the stability required for the TX signal is 10 ppm. This means the source XO must be approximately twenty times more stable, or 0.5 ppm. The current XO is obviously unacceptable to meet this requirement, and it must be replaced with a new oscillator. Because of the size, output, and power requirements, OCXOs are not applicable. This limits the possibilities to only a few TCXOs that are commercially available.

These oscillators can further be limited by the supply voltages available. There are 1.8 V,

3.3 V, and 5 V rails available on the VNA, so only these supplies can drive the oscillator. The output of the oscillator should also be a sine wave because of the setup of the VNA. The temperature range must be below −25 °C because of the application’s temperature range. The only remaining functional option to choose is frequency. The original configuration overclocks the DDSs adding heat to the system. A 20-MHz TCXO can avoid overclocking and possibly the extra power spikes in the spectrum of interest. This VNA has previously been modified with a

38.4-MHz TCXO but with little documentation on how this is achieved.

The least expensive oscillator that meets these requirements is a Connor Winfield TCXO model D53G. Figure 5-1 shows this TCXO on a breakout board with headers for initial functionality testing. This TCXO has a temperature stability of ±0.5 ppm and −80 dB of phase noise from the center frequency. It produces a clipped sine wave, which is the closest output to a pure sine wave in high precision oscillators. In addition, unlike comparable OCXOs, this TCXO only requires 5 ms to reach a stability of 0.5 ppm. These parameters should allow it to be perfect for a VNA for ice penetrating radar.

Figure 5-1 Connor Winfield TCXO on breakout board.

Integrating this TCXO into the VNA requires disabling the original XO and integrating the TCXO in its place. A breakout board is required because of the small chip size of this TCXO.

The breakout board allows the chip to be soldered to contacts and gives leads for further connections to be made. Power, ground, and output are connected with short wire leads directly to the inputs of the two DDSs. To allow for proper operation, the biasing network must be left operational. This is done by simply removing the crystal in the original XO setup. Appendix A shows the modifications to the original circuitry. Figure 5-2 shows the integration with the VNA with non-conductive tape used for insulation.

Figure 5-2 TCXO integrated into the SDR-Kits VNA.

Chapter 6

Replacement Oscillator Testing

The modified VNA must also be tested for performance to determine if the improved oscillator meets the requirements for the ice penetrating radar application. As in the original round of testing, a baseline at room temperature is required. Following this, thermal testing over the temperature range determines how the VNA will perform in the field. Unlike the unmodified testing, the DDS calibration cannot be measured on the frequency counter because of the change of oscillator frequency. The results of these tests can be compared to the unmodified VNA to see what improvements have been made.

6.1 Room Temperature Testing

The room temperature testing is performed after confirming that the VNA operates as it did before the modification. Testing consists of measuring the output of the TCXO with a frequency counter, determining the phase noise of the TCXO and the TX output with a spectrum analyzer, and observing the waveform on an oscilloscope. These measurements are repeated as in the initial testing after 30 minutes, 1 day, and 3 days. This gives an idea of the short term stability as well as the longer term stability required for this application.

6.1.1 Frequency Output of the TCXO

The key to determining if this replacement oscillator is an improvement over the

unmodified crystal oscillator is the frequency of the TCXO output. This can be used for a rough

36 estimate of the short term stability, but it is much more reliable as an indication of the typical

long term stability during operation. Table 6-1 shows the output of the TCXO over the three day

observation period. Short term stability to a tenth of a hertz implies that this oscillator is at least

ten times more stable than the original XO.

Table 6-1 Measured Frequency of the Source TCXO. Delay Measured Frequency (Hz) Short Term Instability (Hz) Initial 19, 999, 973. 6X ~0.1 30 minutes 19, 999, 973. 4X ~0.2

1 day 19, 999, 972. 3X ~0.4

3 days 19, 999, 971. 8X ~0.2

6.1.2 Phase Noise of the TCXO

The phase noise around the peak of the replacement oscillator output can be seen on a

spectrum analyzer. Figure 6-1 shows the output of the oscillator with the phase noise around the center frequency. Although the amplitude of the peak is lower than that of the XO, the TCXO has considerably less phase noise, shown by the sharp fall off. Figure 6-2 shows the high

sideband with the 3-dB noise level. Overall, the phase noise looks very similar to the XO, but it

seems slightly improved in the TCXO.

Figure 6-1 TCXO phase noise across 50 kHz.

Figure 6-2 TCXO phase noise from center frequency to 10 kHz.

6.1.3 TCXO Oscilloscope Data and Phase Deviation

The output waveform of the TCXO should be observed on an oscilloscope to ensure the signal integrity. Figure 4-3 shows the clipped sine wave output from the TCXO. The output does not look like an ideal sine wave, but it does look very similar to the output of the original XO.

This indicates that normal operation of the VNA should be maintained because the reference signal is the same general shape. Any phase deviation can be easily seen for the TCXO because

38 the output frequency is twice that of the OCXO. Therefore, every intersection of the waveforms shows any phase deviation between them. Since the OCXO is assumed to be more stable, any deviation would be caused by the TCXO. As seen in the top output of Figure 6-3, the phase deviation of the TCXO is excellent.

Figure 6-3 Capture of TCXO output (20 MHz) with OCXO reference (10 MHz).

6.1.4 TX Phase Noise

The output of the TX is still the main concern in this application. Without a clear signal to transmit, the depth of the ice cannot be measured accurately. The more stable source should provide a more accurate TX output with less phase noise. The output of the TX over the frequency range with the TCXO output can be seen in Figure 6-4. There is still a considerable amount of phase noise added by the DDS, but the modified version looks better than the original

XO source.

a.) TCXO 20 MHz b.) TX (200 MHz)

c.) TX (250 MHz) d.) TX (300 MHz)

e.) TX (350 MHz) f.) TX (400 MHz) Figure 6-4 Phase noises of a.) TCXO, b.)–f.) TX.

40 One of the considerations for the 20-MHz frequency of the replacement oscillator is to try to eliminate the moving peak at around 350 MHz. To see the affect the TCXO has on the TX output spectrum, the entire frequency range must be observed. Figure 6-6 shows this TX output over the frequency range of interest. The software for the VNA allows the multiplication of the

DDS clock signals to be changed. In the original setup, the multiplication factor of the PLL creating the clock would change depending on the output frequency. This is simply done with a table of multiplications for ranges of output frequencies, presented to the user when the DDS multiplication is set to automatic. For the highest accuracy, the multiplication should be as high as possible. To eliminate filters, the two DDSs should have different clock frequencies; in this case, different multiplication factors [4]. Static multiplications of 19 and 20 were used for DDS1 and DDS2, respectively, for the TCXO. This creates a stationary peak at the clock frequency of

DDS1 in the TX output, approximately 380 MHz as seen in Figure 6-5.

a.) TX = 200 MHz b.) TX = 250 MHz

c.) TX= 300 MHz d.) TX= 350 MHz

e.) TX = 400 MHz Figure 6-5 Spectra of the TX signal.

42 6.2 Low Temperature Testing

The thermal testing of the VNA with the TCXO replacement oscillator follows the same

procedure as the initial thermal testing. Initially, the temperature is decremented from 0 °C to

−25 °C in steps of 5 °C. At each of these six temperatures, the frequency and phase noise are

measured. Long term stability is repeated at the harshest temperature, −25 °C, for continuity

from the previous oscillator testing and to account for internal heating considerations.

6.2.1 Frequency Output Instability from 0°C to −25°C

As expected, the TCXO is much more stable over this frequency range than just a simple crystal oscillator circuit. The compensation methods are not perfect, but there is much less deviation with temperature change. Little deviation from the temperature frequency is observed with the DDSs producing TX frequencies. This also shows that the TCXO is much more stable in the short term due to internal heating interference. Table 6-2 shows the results of the frequency over the temperature range. The instability of the TCXO over this temperature range is approximately 0.3 ppm maximum.

Table 6-2 Low temperature frequency output changes of TCXO. Temperature XO Frequency (Hz) ΔXO (Hz) 0 °C 19, 999, 965. 7X — −5 °C 19, 999, 967. 0X +1.3

−10 °C 19, 999, 969. 5X +2.5 −15 °C 19, 999, 971. 6X +2.1

−20 °C 19, 999, 970. 5X 1.1 −25 °C 19, 999, 967. 4X 3.1

43 6.2.2 Phase Noise of the TCXO

The improved short term stability should be reflected by decreased phase noise in the output of the oscillator across the temperature range. Figure 6-6 shows the phase noise of the

TCXO as the temperature changes. There is very little change over the range of temperatures.

This means the TCXO is performing almost equally well at any low temperature.

a.) 0 °C b.) −5 °C

c.) −10 °C d.) −15 °C

e.) −20 °C f.) −25 °C

Figure 6-6 Phase noises of the TCXO at low temperatures.

44 6.2.3 Long Term TCXO Stability with Temperature

The long term drift of the TCXO can be affected by a number of different factors. This

test assumes the VNA will be shut down between subsequent visits. This is the worst-case

scenario because the long term stability of the internal crystal is reset when power is disrupted. If the VNA were left on for this length of time, the drift would likely be much less considerable.

Table 6-3 shows the long term stability at −25 °C. The long term stability is approximately

0.1 ppm. This too should show the worst-case scenario in that any thermal fluctuations causing short term stability would appear in this measurement. Internal heating would be an uncontrollable factor. Warm-up time could be controlled if necessary to make the aging of the oscillator more uniform from visit to visit, but the long term stability seems acceptable for this application.

Table 6-3 Measured Frequency of the Source TCXO at −25 °C. Delay Measured Frequency (Hz) Δ Frequency (Hz) Initial 19, 999, 967. 5X — 30 minutes 19, 999, 967. 4X −0.1 1 day 19, 999, 969. 4X +2.0

3 days 19, 999, 968. 3X −1.1

6.2.4 TX Phase Noise

The increased stability of the TCXO as a source should also improve the TX output from

the DDS with respect to temperature dependence. Figure 6-7 shows the output at room

temperature compared to the same output at −25 °C to show the greatest difference. There is some minor flattening associated with the drop in temperature. This flattening is even less evident if the reference signal is at 0 °C. This would represent the full temperature range for the

45 application, but this would not show the difference as well as the room temperature reference

phase noise plot.

a.) Room Temperature (200 MHz) b.) −25 °C (200 MHz)

c.) Room Temperature (300 MHz) d.) −25 °C (300 MHz)

e.) Room Temperature (400 MHz) f.) −25 °C (400 MHz)

Figure 6-7 Phase noises of the TX at room temperature and −25 °C.

Chapter 7

Conclusions

The replacement TCXO for the SDR-Kits VNA is a significant improvement over the

original source XO. The TCXO has improved short and long term stabilities, with less

temperature sensitivity and similar phase noise at the TX output. Similar bandwidth limitations

are observed with extraneous peaks limiting the TX output range. The frequency of the TCXO

improves on the XO bandwidth, with greater improvements possible through software

manipulation of the PLL multiplication.

7.1 Summary

The new TCXO should provide an adequate source for an ice penetrating radar network

analyzer. The requirement of 1 cm resolution of 1 km thick ice theoretically requires a maximum stability of approximately 0.5 ppm over the temperature range. The total short term, long term, and thermal stabilities of the replacement TCXO are approximately 0.05 ppm, 0.1 ppm, and 0.3 ppm, respectively. Therefore, the TCXO’s total combined instabilities are within the maximum allowed requirement. Even if greater stability is required beyond the theoretical indications, there is some margin for error.

The other requirements for this application are mostly met. The TCXO is stable across the 0 °C to −25 °C temperature range. It fits within the original housing. It is powered by the internal biasing circuitry. And it is reasonably priced, with the entire assembly still costing a fraction of a benchtop VNA. The only parameter not fully met is the frequency range of 200

MHZ to 400 MHz. The output peak at 380 MHz seems to limit the output bandwidth of the

47 system to slightly below this frequency. Changing the DDS multipliers can extend this output range somewhat, but it is not necessarily as reliable beyond this point. This may be overcome with software modification, but most ice penetrating radar applications do not require this high of a frequency. Therefore, the current operation may be acceptable even though it does not meet the full design specification.

7.2 Future Research

While this thesis focused on the theoretical requirements of a source oscillator for an ice penetrating radar network analyzer, the application may elucidate unexpected behavior. To fully test this system, a comparison between the unmodified VNA, the TCXO source VNA, and a benchtop network analyzer would prove if this improvement is truly as accurate as required. All three devices could be taken to a known thickness of ice of approximately 1 km. The devices could use the same antennas and amplifiers and the returns could be compared for accuracy. The benchtop network analyzer would likely still yield the best results, but it would be beneficial to prove the TCXO-modified SDR-Kits VNA is accurate enough for the application.

Other research could include designing and building the supporting circuitry required for ice penetrating radar. The output of the network analyzer requires amplification to travel through the ice, and these signals need to be transmitted and received. The devices required for these processes would be a power amplifier and two antennas. A low-noise amplifier might also be required on the receive side to detect the return signal. These components could also be designed for this application to provide convenience and portability to the researchers investigating ice melt rates.

References

[1] Corr, Hugh F J, Adrian Jenkins, Keith W Nicholls, and C S M Doake. 2002. “Precise Measurement of Changes in Ice-shelf Thickness by Phase-sensitive Radar to Determine Basal Melt Rates.” Geophysical Research Letters, 29(8), pp. 1–4. http://nora.nerc.ac.uk/13237/.

[2] Agilent. 2004. Agilent Network Analyzer Basics. Application Note 5965-7917E. http://cp.literature.agilent.com/litweb/pdf/5965-7917E.pdf.

[3] Anritsu. 2009. Vector Network Analyzer Primer. Application Note No. 11410-00387, Rev. B. http://www.anritsu.com/en-US/Downloads/Application-Notes/Application- Note/DWL2600.aspx

[4] Baier, Thomas. 2009. A Small, Simple, USB-Powered Vector Network Analyzer Covering 1 kHz to 1.3 GHz. SDR-Kits. http://sdr-kits.net/DG8SAQ/VNWA/Baier_VNWA2_QEX.pdf

[5] Vig, John R. 2004. “Quartz Crystal Resonators and Oscillators for Frequency Control and Timing Applications—A Tutorial. 2004 IEEE International Frequency Control Symposium Tutorials, January 2004. http://www.ieee-uffc.org/frequency_control/teaching/vig/vig3.htm

[6] Kenny, Dave. 2008. TCXO Application vs. OCXO Application. Application Note 803, Rev 1. http://www.pletronics.com/getfile.php?id=231

[7] Esterline, John. 2008. Oscillator Phase Noise: Theory vs. Practicality. Greenray Industries, Inc. http://www.greenrayindustries.com/library/PhaseNoise08.pdf

[8] Baier, Thomas. 2009. DG8SAQ Vector Network Analyzer – VNWA 2.6 Kit Assembly Manual. SDR-Kits. http://sdr-kits.net/VNWA/VNWA2.6a%20Kit%20Manual.pdf

Appendix A

SDR-Kits VNA v2.6 Schematic

Figure A-1 SDR-Kits VNA oscillator schematic [8].

Figure A-2 SDR-Kits VNA TCXO replacement oscillator schematic [8].

Figure A-3 SDR-Kits VNA top board layout [8].

Appendix B

Supporting Equations

TX Signal:

= ×

TX0 DDS1 XO0 푓 = (�푀 × 푓 ), � = +

TX DDS1 XO XO XO0 푓 푀= ( 푓 × ) 푓 �푓 훿�

DDS1 DDS1 XO ∴ 푓 푀 푓 × × + × = = = TX0 TX DDS1 XO0 DDS1× XO 0 DDS1 푓 �푓 − 푓 � �푀 푓 − �푀 푓 푀 훿 �� 훿 푇 TX0 DDS1 XO0 XO0 DSP푓 Mixed Signal: 푀 푓 푓

1 2 1 2 푓 ⊗ 푓 ≝ 푓 푓× , = multiplication factor of DDS

푓DDS푥 ≝ �푀DDS푥 푓XO0 � 푀DDS푥 푥 = = ± , < LPF DSP0 DDS10 DDS20 DDS10 DDS20 DDS10 DDS20 DDS20 DDS10 푓 =푓 ⊗×푓 푓 푓 �� 푓 − 푓 푓 푓

DDS10 DDS1 XO0 푓 = �푀 × 푓 �,

푓DDS20 �푀DDS2 푓XO0� 푀DDS2 ≠ 푀DDS1 = × ( )

∴ 푓DSP0 푓XO0 푀DDS1 − 푀DDS2 = = ± , < LPF DSP DDS1 DDS2 DDS1 DDS2 DDS1 DDS2 DDS2 DDS1 푓 =푓( ⊗×푓 ) 푓 푓 �� 푓 − 푓 푓 푓

DDS1 DDS1 XO 푓 = (푀 × 푓 ),

DDS2 DDS2 XO DDS2 DDS1 푓 = 푀 + 푓 푀 ≠ 푀

푓XO �푓XO0 훿� = × ( ) + × ( )

∴ 푓DSP 푓XO0 푀DDS1 − 푀DDS2 훿 푀DDS1 − 푀DDS2 = DSP0 DSP DSP �푓 − 푓 � 푇 DSP0 푓× ( ) × ( ) + × ( ) = = × ( ) �푓XO0 푀DDS1 − 푀DDS2 − �푓XO0 푀DDS1 − 푀DDS2 훿 푀DDS1 − 푀DDS2 �� 훿 푓XO0 푀DDS1 − 푀DDS2 푓XO0

Depth to Phase (clock stable after TX):

푣푝 휆 ≝ 푓 2 2 × × = × 휋 휋 푓 휙 ⇐ 푑 푑 휆 푣푝 × = × , = 2 ×푝 2 ×푝 푣 푣 ref XO0 푑 ⇐ 휙 ref 휙 XO0 푓 푓 ∀ 휙 휋 푓 휋 푓

= 푣푝 휆XO 푓XO0 = = 푝 푝+ TX 푣 푣 휆 XO XO0 푓 2푓 × 훿 = × XO0 XO 0 휋 푓 휙 푑 푝 2 ×푣 ( + ) = × XO0 TX 0 휋 푓 훿 휙 푑 푝 푣 2 × = × = × × = 2 ×푝 XO0 2 ×푝 XO XO 푣 0 휋 푓 푣 0 푑 휙 XO0 푑 푝 XO0 푑 휋 푓 2 푣× ( +휋 ) 푓 + = × = × × = × = × 1 + 2 ×푝 XO0 2 ×푝 XO0 TX TX 푣 0 휋 푓 훿 푣 0 푓 훿 0 훿 푑 휙 XO0 �푑 푝 � XO0 푑 � XO0 � 푑 � XO0 � 휋 푓 푣 휋 푓 푓 푓

| | × 1 + = = 훿 = 0 0 XO TX �푑 − �푑 � 푓XO0�� stable XO 푑 − 푑 훿 퐸 XO 0 XO0 푑 푑 푓

Depth to Phase (clock unstable after TX):

푣푝 휆 ≝ 푓 2 2 × × = × 휋 휋 푓 휙 ⇐ 푑 푑 휆 푣푝 × = × , = ( + ) 2 ×푝 2 × ( 푝 + ) 푣 푣 ref XO0 푑 ⇐ 휙 ref 휙 XO0 푓 푓 훿 ∀ 휙 휋 푓 휋 푓 훿

= + 푣푝 휆XO 푓XO0 훿 = = 푝 푝 TX 푣 푣 휆 XO XO0 푓 2푓 × ( + ) = × XO0 XO 0 휋 푓 훿 휙 푑 푝 2 × 푣 = × XO0 TX 0 휋 푓 휙 푑 푝 푣 2 × ( + ) = × = × × = 2 × ( 푝 + ) XO0 2 × ( 푝 + ) XO XO 푣 0 휋 푓 훿 푣 0 푑 휙 XO0 푑 푝 XO0 푑 휋 푓 훿 2 × 푣 휋 푓 훿 = × = × × = × = 2 × ( + ) 2 × ( + ) + 푣푝 휋 푓XO0 푣푝 푓XO0 1 +푑0 TX TX 0 0 훿 푑 휙 XO0 �푑 푝 � XO0 푑 � XO0 � 휋 푓 훿 푣 휋 푓 훿 푓 훿 푓XO0

× 1 + | | −1 1 훿 훿 = = = 1 = < 0 0 XO �푑 − 푑 � 푓 0� � 푓XO0 푑XO − 푑TX 1 + 1 + 훿 unstable XO 훿 훿 퐸 XO 0 − XO0 푑 푑 푓XO0 푓XO0 푓

Academic Vita of Campus Address: Permanent Address: 600 E. Pollock Rd. ERIC J. TIM 2186 Hill Road Nittany Apt. 5103D [email protected] Perkiomenville, PA 18074

State College, PA 16801

Education: The Pennsylvania State University, University Park: • College of Engineering – Electrical Engineering • Expected Graduation Date: May 2012 • Schreyer’s Honors College – Electrical Engineering Thesis Title: Network Analyzer with Stable Oscillator for Ice Penetrating Radar Relevant Coursework: Analog device design and construction: • Designed and constructed current feedback operational amplifier using discrete transistors • Device met or exceeded design constrains including: 50 MHz bandwidth, 50 V/µs slew rate, Rail-to-rail operation, <1W power consumption Digital design (transistor level) RF design, construction, and analysis: • Use of RF equipment including: Spectrum Analyzer, Network Analyzer • Use of Agilent Technologies Advanced Design System • Construction and testing of microstrip amplifiers

Work Experience: Electrical Integration Engineer Intern - GE Transportation, Erie (Summer 2011) • Created electrical equipment list from subsystems design specs and verified that this specified equipment agrees with electrical point-to-point diagrams. • Worked with subsystems design engineers to resolve inconsistencies in the subsystem design documentation. • Identified and selected the appropriate wire size and configuration for locomotive wiring circuitry. • Grouped wires into harnesses according to locomotive area and wire/signal class. • Determined functional connectivity for device termination points and harness interface points. • Researched and wrote specifications for assigned, new components for use in locomotive electrical systems.

Honors: Dean’s List, Fall 2008–Spring 2010 and Spring 2011–Fall 2012 Phi Eta Sigma National Honor Society member Golden Key International Honor Society member National Society of Collegiate Scholars member William J. and Ethel Harer Madden Memorial Honors Scholarship Eta Kappa Nu, Treasurer 2011–2012