Thesis submitted for the degree of

Miniaturized E-field Experiment for CubeSats

By

Petter André Langstrand

Thesis submitted for the degree of

Master in Electrical Engineering, Informatics and Technology 60 credits

Department of Physics

Faculty of mathematics and natural sciences

UNIVERSITY OF OSLO

Miniaturized E-field Experiment for CubeSats

By

Petter Andr´e Langstrand

c

2020 By

Petter Andr´e Langstrand

Miniaturized E-field Experiment for CubeSats http://www.duo.uio.no/

Printed: Reprosentralen, University of Oslo

Nomenclature

Contents

1 Introduction 5

1.1 Motivation . . . 5

1.1.1 Spaceweather forecast . . . 5

1.1.2 Current Biased Probes . . . 6

1.1.3 Collaberation UiO & Eidel on Spaceweather instruments . . . 7

1.1.4 Goal of work . . . 7

2 Theory 8 2.1 Ionosphere . . . 8

2.2 Space Plasma . . . 9

2.2.1 Debye Shielding . . . 9

2.2.2 Electron Temperature . . . 10

2.2.3 Electric fields in the magnetosphere . . . 10

2.3 Langmuir Probe & Probe Theory . . . 12

2.3.1 Plasma-Probe coupling . . . 12

2.3.2 The I-V curve . . . 15

2.3.3 Electron Temperature from I-V curve . . . 16

2.3.4 Current-biased probes . . . 16

2.4 Double probe E-field measurements . . . 17

2.5 The CubeSat as instrument platform . . . 18

2.6 Probe interface . . . 19

2.7 Electronics Theory . . . 20

2.7.1 Voltage-to-current Conversion . . . 20

2.7.2 The dual OPAMP Current Source . . . 20

2.7.3 Instrumental Amplifier . . . 21

2.7.4 Analog filters . . . 22

2.8 Sources of Noise in measurements . . . 24

2.8.1 Thermal noise . . . 24

2.8.2 Shot noise . . . 24

2.8.3 Flick noise . . . 24

2.8.4 Noise in plasma-probe coupling . . . 25

2.8.5 Noise analysis of an inverting amplifier . . . 25

2.8.6 Analog-To-Digital Conversion . . . 26

3 System Design 28

3.1 Objective . . . 28

3.2 Requirements . . . 28

3.3 System overview . . . 29

3.3.1 Probes . . . 31

3.4 Active components . . . 32

3.4.1 AD549 . . . 33

3.4.2 AD8672 . . . 33

3.4.3 AD8426 . . . 34

3.4.4 OPA1692 . . . 34

3.4.5 Analog Filter . . . 34

3.4.6 ADC differential input . . . 34

3.5 Digital Backend . . . 35

3.5.1 AD7768 . . . 35

3.5.2 DAC104S085 . . . 37

3.5.3 TMS570 Hercules MCU . . . 37

3.5.4 The firmware . . . 38

3.6 PCB layout . . . 42

3.6.1 PCB layout . . . 43

3.6.2 Front End replacement PCB . . . 43

3.6.3 Clean Ground Plane . . . 44

3.6.4 Bypass capacitors . . . 44

4 Testing & Experiment Setup 46 4.1 Verification . . . 46

4.1.1 Power on test . . . 46

4.1.2 Signal continuity test . . . 46

4.1.3 Analog to Digital sampling test . . . 46

4.1.4 Current source test . . . 47

4.2 Calibration . . . 47

4.3 Plasma Chamber Experiment . . . 47

5 Results 49 5.1 System tests . . . 49

5.1.1 Voltage input range . . . 49

5.1.2 Frequency input range . . . 49

5.2 Output current biasing range . . . 49

5.2.1 Current sweeps . . . 50

5.3 Plasma chamber lab tests . . . 50

5.3.1 IV probe tests . . . 50

5.3.2 Probe potential current biasing . . . 51

5.3.3 Field measurements . . . 53

6 Discussion 58 6.0.1 Instrument & system design . . . 58

6.0.2 Experiment results . . . 58

6.1 Future work . . . 60

7 Conclusion 61

A Appendix 62 A.1 LTSpice Simulations . . . 62 A.2 Main PCB . . . 63

Chapter 1

Introduction

The purpose of this project has been to further the development of a current biased probe system able to fit onto a CubeSat and to produce a prototype and test its viability for E-fields measurements in a plasma chamber for near ionospheric conditions. This work is based on Huy Hoang’s Current generator design for Electric field probe, May 5th 2016. The instrument consist of a (double) pair of passive Langmuir E-field probes biased by a voltage controlled current source, and their adopted potential is measured by the instrument . The viability of sweeping the current for estimating the electron temperature was also to be investigated for this system.

1.1 Motivation

1.1.1 Spaceweather forecast

Satellites passing trough polar regions the signals may experience scintillations due to travelling trough ”plasma clouds”. This can degrade signal quality and the accuracy of satellite positioning systems such as GPS, Galileo and Glonass may be significantly reduced during periods of high ionospheric activity.

Figure 1.1: Shows the effect of space plasma in the ionosphere on GPS signals.

By employing a swarm of CubeSats in different orbits, equipped with E-field instruments one should be able to calculate the velocities of such plasma clouds by their E-field vector. Thereby providing information that could be used in space weather forecast. Possibly predicting such signal obstructions

This type of forecast may be of interest to industries like:

• The petroleum industry operating in polar regions require accurate positioning systems for their work in locating new oil or gass fields.

• Ship traffic, as the ice is melting in the polar regions so is the Nort east passage being more open for ship traffic. This opens up a new trade route between Asia and Europe.

• Artic tourism, the tourist industry have seen an increase in popularity for Artic cruises.

Lastly, continuous measurement of ionospheric E-fields may produce data that could help us understand the ionospheric processes that causes these scintillations.

1.1.2 Current Biased Probes

Current biased probes has been proposed has an alternative to voltage biased, the reason being that they allow for a better coupling to the plasma[1]. This means that they are able to measure smaller variation in local plasma potential. Such a feature is very interesting in the context of E- field instruments. A traditional challenge of such instruments are that they require several meters of boom systems in order to reliably measure differences in local plasma potential, that constitutes

an Electric field. A challenge with long boom systems however is that they need to remain rigid, as small variations in boom angles will degrade the accuracy of the entire instrument significantly.[2]

Furthermore they’re harder to deploy on miniaturised satellites like CubeSats. A consequence of the current biased probe concept is that it potentially opens the doors for E-field instruments deployed on CubeSats.

By sweeping the current and measuring the adopted potential of the probes, such a system should be able to compute the electron temperature.

The electron temperature is another important parameter to space weather forecast which describes the kinetic energy of the electrons contained in the plasma. This parameter is a factor in magnetic field interactions. Furthermore high energy particle may penetrate spacecraft shielding and damage subsystems of satellites[3].

1.1.3 Collaberation UiO & Eidel on Spaceweather instruments

The University of Oslo and Eidel collaborates in the development of space weather instruments. It is in their interest to develop an E-field instrument which could easily be integrated together with the previously developed M-NLP(for density measurements), a floating potential probe system and a magnetometer. A CubeSat equipped with all these instruments could prove a powerful space weather station, with the capability of measuring plasma density, electron temperature, E-field, local magnetic field, floating potential.

1.1.4 Goal of work

The goal of this thesis is to design and produce a prototype of a miniaturised E-field instrument for measuring ionospheric electric fields using current biased probes. This prototype is designed in such a way that it could be mounted on a CubeSat, or future iterations of it could be. The main purpose of the prototype is to test the concept of current biased probesm proposed and schematised by Arne Pedersen [4] and Huy Hoang [5].

This instrument is to be designed on a PCB together with a floating probe potential instrument, designed by Christian Rolid Lindland. The two instruments are to both interface the same digital backbend system.

Chapter 2

Theory

In the following sections I will give a brief overview of the ionosphere, plasma physics and the current system in order to put the work presented in this thesis into context, and to give a bief overview of the forces involved. Then I will talk about langmuir probe theory and E-field measurements, the theory behind current biased probes and lastly I will go into the electronics theory involved in the instrument. For the theory concerning space and plasma physics i will refer to the books Basic Space plasma physics[6], Introduction t[7] and Introduction to Plasma Physics[8]. For the electronics theory section i will refer to [9].

2.1 Ionosphere

Figure 2.1: Shows the Electron density of the different regions of the ionosphere. Figure is The ionosphere is the upper part of the

atmosphere as shown in figure 2.1. The ionosphere span from 60km to 500km altitude and is divided into three regions, D-, E-, and the F-region. Starting at 60km altitude, here there is an abundance of atmospheric gasses to be ionized, but very little radiation penetrates as deep into the atmosphere. However as we move upwards in the D-region the drop in pressure allows electrons to free themselves from atmospheric gasses in this region. As we move further up to 250 km altitude, the degree of ionization is said to be at its maximum extent. Here the gasses are ionized by photo- ionization from solar radiation. As we move even further up the the intentsity of radiation is even higher, but the density of gasse to be ionised is much lower, causing a drop in electron density as we move upwards. It is important to note that the ionization is dominantly caused by photo-ionization from the sun, therefore the electron density varries

8

on day-side and night-side. [10]

2.2 Space Plasma

A plasma is in essence an ionized gas, that has been provided enough thermal energy to allow electrons and ions to break free from atoms or molecules, and to coexist without recombining.

Local charge separation due to the different species in the plasma will give rise to electric and magnetic fields, which forms a collective behaviour in the plasma. In contrast to neutral gasses where particle collisions forms the behaviour, in plasma motions are governed by electromagnetic forces. Despite having small momentary local charges, on large scales we consider plasma to be quasi neutral. However in smaller scales there might be irregularities of the distributions of the two species, thus we say ”quasi-neutral”. That is, neutral enough so that one can takeni =ne =n, where n is a common density called the plasma density(and ne,ni the electron and ion density correspondingly), but not so neutral that all the interesting electromagnetic forces vanish.[8]

2.2.1 Debye Shielding

Assuming frictionless plasma with no external force, the relationship with the plasma density, potential and electron temperature is described by the Boltzmann relation[11].

ne=n0exp(^φ Te

) (2.1)

Herenerepresent electron density,n0electron density at undisturbed plasma,φrepresent potential and Te electron temperature. When a local charge is introduced in a plasma, we can see from equation 2.1 that the electron density will increase proportionally to the potential of a positive local charge in order to cancel it out. Similarly the ion density will increase around a local negative charge. We call this ”Debye Shielding”[10] because it shields the electric field of the local charge from penetrating deep into the plasma. Hence the Debye lengthλ_Dis the characteristic length the potential from a local charge has been reduced toφ≈ e⁻¹. Or the length∆xto an area where the thermal motion energy is equal to the electrostatic energy.

U_th=U_E (2.2)

1

2KBTe = ^e

n∆x²

2e₀ (2.3)

Solving for∆xwith the given conditions yields the Debye length

λ_D= s

e₀·k_BTe

nee² (2.4)

where e₀ is the electrical permittivity in vacuum,kB is the Boltzman constant, Te is the electron temperature, ne is the electron density, andeis the charge of an electron. We often consider the debye length a radius of a sphere called the Debye sphere, which within collisions occur in order to restore a uniform charge distribution.

2.2.2 Electron Temperature

The Electron temperature relates to the thermal velocity of the electrons uT_e,i= ^kTe,i

me,i (2.5)

Here Te,i represents the electron and ion temperature, kthe boltzman constant, andme,i electron and ion mass. An important result to notice is that the thermal velocity of electrons will always be several magnitudes of order larger than that for ion or neutral species due to having a much smaller mass. In the context of space weather the electron temperature is an important parameter to measure, as it related to the Debye length. Another reason is that particles with high energy particles may penetrate spacecraft shielding and damage subsystems. [3]

2.2.3 Electric fields in the magnetosphere

when observing electric field in space it is important to take into account the reference system of the observer, and remember that forces are observed relative to each other. If we consider a reference system S₁ with an electric field E₁, and another reference system S₂ with a velocity v relative to S₁ and a magnetic field B. Then the electric field E₂ in S₂ can be expressed by E₂= E₁+v×B, assuming that velocityvis much smaller than the speed of light. Given that the solar wind has a velocity of approximately 400 km/s relative to earth and given the earths magnetic field an electric field will be set up in Earths magnetosphere. Due to the high conductivity along the magnetic field lines the charged solar wind particles will follow the field lines, and the electric field will be projected down into the ionosphere without any significant reduction.

Due to the coupling between the electric fields and current, it is relevant to consider the ionospheric currents. The relation between electric fields and currents are described the ohm’s law

~_J=σ~_{E (2.6)}

Where~_J is the current density, ~_E the electric field, and σ is the conductivity tensor which is dependent on electron density, collision frequency and the cyclotron frequency [12]. Furthermore, the electric field can be super positioned into two components relative to the magnetic field lines.

The paralell_E~_kandE~_⊥perpendicularly oriented electric field components. .

~_E=_E~_k+_E~_{⊥ (2.7)}

In space plasma the electric field components perpendicular to the magnetic field are usually so large in comparison to the parallel component that the parallel can be neglected, hence~_E≈_E~_⊥. In order to describe these ionospheric currents it is relevant to consider the single particle motion of these charged particles, experiencing the forces from electromagnetic fields. If we look at non stationary charged particles on a perpendicular plane to the magnetic field lines of some external magnetic field~B. The charged particles will gyrate in circular motions around the field lines. Now if we also have an electric field_E~_⊥, the field will distort the circle. Accelerating the electrons along

the field path and decelerating anti parallel to the field. The result of this is a drift of the gyrocenter of the particles in_E~_⊥×~B-direction as shown in figure 2.2, expressed by

v⊥ = _E~_⊥×~_B

B² (2.8)

Figure 2.2: Shows ExB drift for ions and electrons. Figure 2.3 from Basic Space Plasma Phycics[6]

As we can see the drift in itself is independent of the charge or mass of the particles. Hence it doesnt cause any current in itself, despite the movement of charges. In order for a current to be created by this movement a separation of charges needs to occur. Collisions with neutral does that, as it doesn’t occur indiscriminately, electrons have have a much higher collision frequency than ions due to their higher velocity. In the magnetosphere there are however few neutrals to collide with, thus no currents. But if we move down the ionosphere the density of neutral particles increases downwards as do the collision frequency. Meaning ionospheric currents will occur. Hence in the ionosphere we can have currents perpendicular to the magnetic field, in _E~_⊥ direction and _E~_⊥×

~B-direction. The corresponding conductivities to these directions are the Pederson σ_P and Hall conductivityσH[6]. Hence the total ionospheric current perpendicular to the magnetic field can be described from both these conductivities

j⊥=σ_PE~_⊥+σ_H·~_bˆ×_E~_{⊥ (2.9)} where~_bˆis the unity vector in the magnetic field direction.

As mentioned earlier the magnetic field lines have a very high conductivity σ_k leading charged particles from the solar wind along the field lines, giving rise to currents downwards and upwards the ionosphere. These currents are often referred to as the Birkeland currents which couples the magnetosphere to the ionosphere.

The total ionospheric currents can therefore be described by

~_J= ~_J⊥+~_{Jk (2.10)}

Which causes large current that may be the source of large disturbances in the ionosphere. Such currents often referred to as electrojets can be seen in figure 2.3. Where these current may be in the lower ionosphere by SuperDarn radars during a periods of heightened geomagnetic activities.

Figure 2.3: Shows a sketch of the northern hemisphere, with the ionospheric currents drawn as red circles, with arrows indicating their directions. Such a map is called a convection cell map, and may be produced for lower altitudes ionospheric current using Super Dual Auroral Network Data(SuperDarn).[13]

2.3 Langmuir Probe & Probe Theory

Any probe, wire or electrical conductor put into plasma is basically a Langmuir probe. These are widely used for scientific measurement of plasma surrounding a spacecraft, and are able to do so by me measuring either the current collected by the probe, or potential acquired by the plasma on the probe surface. [14] Langmuir probes are conductor of any geometry, often spheres or cylindrical whom have been placed in a plasma. Traditional Langmuir probes have been designed to be biased reference potential relative to the plasma potential, and measuring the collected current. A different method proposed by Arne Pedersen [4] and schematized by Huy Hoang[5] is to bias the probe with a current, and measure the potential obtained by the probe surface, by sweeping this bias a electron temperature can be estimated from the current voltage relation.

2.3.1 Plasma-Probe coupling

When a conductive material such as in our probe is placed in a plasma, the surface will build up a floating potential to cause the net current to go to zero. The dominating currents will be the current from surrounding electrons and ions in the plasma, pulled towards the probe due to electrostatics.

Electrons being smaller in mass, have a higher mobility which will cause the probes to obtain a negative potential in order to cancel out the currents. This effect will cause a sheath to form around the probe. The relation between the thickness of this plasma sheath covering the probe and probe potential is described by the relation eq.2.11.

a−r≈λ_D s

−^eV

kTe (2.11)

herercorresponds to probe radius,asheath thickness,Vprobe potential,λDthe debye length 2.4, andTethe electron temperature. Also important to note that this relation accounts for the plasma density trough the debye length.

As mention this probe potential is connected to the plasma-probe current as descrived in 2.12.

I= Ie+Ii+Iph (2.12)

For the Ie electron current in plasma, I_i ion current and I_ph photo-ionization current caused by radiation exciting electrons in the probe.

From Mott-Smith and Langmuir[15] we have that the electron and ion currents are described as Ie =−4πr²ne

s kTe

2πme

exp eV

kTe

(2.13)

Ii=πr²ne s

kTi

2πm_i

1−^a

2−r² a² exp

− ^r

2

a²−r² eV kT_i

(2.14) Whereris radius of the probe,ais radius to the outer border of the plasma sheath around the probe.

nis the electron density of the plasma andeis the electron charge,kis the Boltzman constant. me

andm_iis the electron, and ion mass, whileT_i,Tethe ion and electron temperature.

Given the assumption that the probe radius is much larger than the thickness of the plasma sheath, then the ion current can be simplified to the expression

I_i ≈4πr²ne s

kT_i

2πm_i (2.15)

Furthermore if the probe is in movement the expression can be approximated in accordance to Fahleson[16] by

I_i ≈πr²ne s8kT_i

πmi

+v² (2.16)

Due to the slowness of the ions the ion current will increase with the velocity of a moving probe.

The electrons velocity however is so large that this probe will be neglect-able in comparison.

The last component is the photo-emition current, which is described by the expression

I_ph=πr²i_ph (2.17)

Naturally the photo-emition is highly related to the radiation reaching the probe.

By inserting the equations for the electron, ions and photoemition currents respectively 2.13, 2.16 and 2.17 into the total probe current equation 2.12 and solve for the probe potential we obtain the expression.

V=−^kTe e ln

q kT_e 2πme

q _kT

i

2πm_i +₁₆^v2 +_4ne^iph −_4πr^I_2ne

(2.18) In high density plasmas the current will be dominated the electrons and ions from the surrounding plasma. Due to the higher mobility of the electrons the currents will balance out at a

negative floating potential.

An expression for the probes floating potential can be obtained by setting the probe current to zero in equation 2.3.1. Observations have revealed that the shape of the probes affect the floating potential. It is therefore essential that the probes used together have as identical geometric properties as possible.[16]

ionospheric plasma is quasineutral which means it that it has no net charge in average over time, while local charges may occur. However our probe will have a net charge due to its floating potential, and it will perturb the surroundings. The region where this perturbation occurs is called the plasma sheath which thickness is approximately one Debye lengthλS. The plasma potential is coupled to the probe potential through a sheath resistance Rs and a sheath capacitance Cs[1] as shown in figure 2.4

The sheath resistanceRsis determined by the voltage-current characteristic of the probe. WheredV is the change in adopted probe potential, anddIthe change in probe-plasma current as described in 2.12

Rs =dV/dI (2.19)

If we assume that the conductive surface of the plasma probe acts as a spherical capacitor with a conductive surface separation distance of a debye length, then the capacitance can be described by

CS=4πe0r

1+ ^r λ_D

(2.20) whereris the probe radius ande0the permittivity in vacuum.

Previous observations have shown that the plasma resistance for a probe in ionospheric plasma is typicallyRs ≈ 10⁵−10⁶Ω, while the debye length is around 1cm, and the sheath capacitance is typicallyCs ≈5−10pF.[17].

Figure 2.4: Shows the plasma probe coupling for spherical probes to the plasma surrounding it.

HereRsrepresents the sheath impedance,Csthe sheath capacitance, andλ_Dthe debye length, and r is the probe radius.

2.3.2 The I-V curve

A Langmuir probe has a current - voltage, I-V characteristic that can be divided into primary three regions shown in figure 4.1. A sufficiently negative biased probe will attract ions and repel electrons, this region is called the ”ion saturation region”. While applying a positive bias will cause electrons to be attracted and ions to be repelled, this would be the ”electrons saturation region”. When the the bias is so high that the electron current dominates the total current. hence I ≈ Ie. Thus the ratio between the increase in probe potential and probe current is linear. At an intermediate bias, neither the electron or ion current will dominate, this region is called the retardation region”.

Figure 2.5: Current-Voltage characteristic curve of a Langmuir probe[18])

2.3.3 Electron Temperature from I-V curve

The electron temperature can be obtained by computing the slope of the retardation region in the I-V curve as in equation 2.21. To obtain a value for the slope, the probe needs to be sweept across the bias range which may take in the order of a second to complete.

Te = ^e

kBAre f (2.21)

WhereAre f is the slope of the linear part in the I-V curve. To obtain the I-V curve the probe has to be swept from a negative to a positive potential.

A rise in negative potential relative to the plasma will cause an exponential drop in the electron current towards the probes. Assuming the ambient electrons to the probe have a Maxwellian energy distribution

Ie= Ie0exp(−V/Ve) (2.22)

Ve=kTe/e (2.23)

WhereVis the probe plasma potential,Vethe electron potential andTethe electron temperature.

2.3.4 Current-biased probes

It is possible to improve the connection between the probes and the surrounding plasma by a positive current biased probe, as demonstrated by Fahleson[16]. This current biasing would shift

the probe potential closer to the plasma potential, effectively reducing the plasma resistance, as can be seen in equation 2.19 for an increasing current. Which means less potential division between the probe and the probe-plasma coupling, and more potential obtained by the probe, thus effectively increasing the probes accuracy.

2.4 Double probe E-field measurements

The first reliable method for measuring weak electric fields in the ionosphere was developed in the 1960s. And the dominating method for measuring alternating and static fields in space plasma has become the double probe technique.

The idea behind this E-field measurement technique is to measures the potential difference between two probes in an undisturbed plasma. If we denote the plasma electric potentialV_o1and V_o2. We can describe our measurements asV_o1=V_p1+_{∆V1. whereas}V_p1is the probe potential we measures. While∆V1corresponds to a voltage drop given by the plasma-probe coupling. Given an assumption on similar plasma conditions at both probes these potentials should be similar

∆V1 ≈ _∆V2.[19] Hence the plasma potential difference around the probes are V_o1−Vo2≈V_p1−Vp2. Furthermore the potential difference can be expressed by the line integral.

V= Z _L

0

~_Eδl

whereLis the distance between the probes. The Electric field can thus be calculated by

~_E= ^Vo2−Vo1

~_L ^(2.24)

The idea of the measurement setup is as shown in figure 2.6. Here with same notations as expressed earlier, except V_d corresponding toV_∆ the potential drop between the probe and the plasma. ld represents the debyelengthλD, and the dotted line around the probe represents the outer border of the plasma sheath covering the probes. Outside this plasma sheat the plasma is considered undisturbed. In order to measure the vector components of the Electric field another pair of probes can be added.

Figure 2.6: Shows the double probe measurement setup for a CubeSat, with~_E being the electric field vector in the plane of the spin.

When determining the separation distance of the probes and between the spacecraft body it is also important to consider the size of the plasma sheath around the probes and the spacecraft body. The separation distance to the probe and any conductive surface should be much larger than the Debye length of both surfaces.

2.5 The CubeSat as instrument platform

In order to measure upper ionospheric electric fields an instrument platform is needed. A sounding rocket is one well established platform. But sounding rockets cant measure continuously, as a new rocket is needed to launch for every set of measurements. Another platform is the CubeSat, which is a type of miniaturised satellites used for space research. Such satellites have a body made up of cube units U, of the dimensions 10cm×10cmcm. Hence the volume of each instrument is an important factor, as each instrument should take up as little volume as possible. In terms of mass CubeSats are often limited by 1.33kg mass per U. Thus during the design and deployment of such satellites a mass budget is used. .[20].

In the F-region ionosphere a CubeSat will typically have an orbit velocity of 7-8 km/s, resulting in an induced electric field of 200-300 mV/m, in addition to the local electric field.[2]. The induced magnetic field provides an unwanted source of uncertainty to the measurements. If the E-field instrument is to be deployed on an CubeSat this induced electric field needs to be measured by other means, and subtracted from the measurements. As the induced field is induced by a charged spacecraft travelling in earths magnetic field we need to know the orbit velocity, thus ˜E_induced =

~u_cubeSat×~_Bearth this can be measured by an Attitude Determination system, A starcam can find the altitude of the spacecraft with much less than a degree uncertainty.[21]. Another source of uncertainty is boom system used to deploy the probes, and the the location of the probes in relation to each other and the spacecraft. The instrument requires the boom to be stiff however longer booms might bend during deployment of the CubeSat or during operation. The consequence of a small change in either the angle of the boom or as a consequence the separation distance means

that we will be unable to subtract the correct induced field. If the boom length is too short however the signal difference in probe potential between two probes may be to small to reliably measure an Electric field. A boom length of 1.0-1.5 m as proposed by Arne Pedersen[2] , could be a good compromise between having a stiff boom lined to the satellite and enough length to get a good signal between opposite probes.

Another challenge with deploying the instrument on a CubeSat is to make sure that the probes stay out of the sheath covering the surface body. Spacecraft charging is a common challenge in space instrumentation[22], and an increase in spacecraft potential will increase the sheath around it, as seen by the relation 2.11. The boom system should therefore ideally be placed on a dedicated 1U section of the CubeSat having nonconductive outwards surface. This would mean a much narrower thickness in the plasma sheath towards the probes from the spacecraft.

2.6 Probe interface

The probe-electronics interface circuit equivalent is as drawn in figure 2.7. Here the cable impedance has been neglected due to the assumption that it is sufficiently small. Here~_E·~_{Lis the} electric field,~_Eand probe separation distance~_L, and their product is the input potentialVin. Zsis the probe impedance, dominated by the plasma-probe impedance. RB is the resistance from the output resistorR_B of the biasing current source. The amplifierG = 1 is a unity gain configured amplifier, maximizing its input impedance to be infinitely high for an ideal component, but in practice at 1GΩ. In order to obtain max effect from the probe to the instrument input, the bias resistor should match the plasma impedance, R_B = Z_S. However this is quite hard to do in practice. Another approach is to make sure that the bias resistor is always larger than the plasma impedance, in order to prevent a voltage divider between them, as following.

Vout= ^RB

R_B+Z_SV_in (2.25)

AssumingRB>>_ZS, the equation becomes simply Vout≈ ^RB

RB

V_in=V_in (2.26)

Voutbeing the voltage signal out of the probe interface.

Figure 2.7: Shows the circuit equivalent of the probe - electronics interface, E being the electric field, L the distance between the probes,Rsthe probe sheath impedance, andR_Bbeing the bias resistor on the system, G=1 signifying that the output amplifier is configured unity gain.

2.7 Electronics Theory

2.7.1 Voltage-to-current Conversion

Using a bias current allows the electric field probes to approach the local plasma potential and thus reduce the sheath resistance accordingly. Furthermore an electron flux is ejected from the probes to the spacecraft body, and positive ions are injected from the spacecraft to the probes in order to reduce the negative potential of the probes. Lastly the bias current sweeps could allow estimation of the electron temperature. [5]

Positive feedbak configuration

If the amplifier is configured with unity gain as a buffer as in figure 2.8, the potential drop onRbias

can be expressed as in equation 2.27

Figure 2.8: Shows a functional diagram of the positive feedback configuration, allowing for both current biasing of the probes, and potential measurement [5]

(V_bias+Vout)−V_in=V_bias (2.27) Ideally there is no current flowing to the input of an OPAMP, the current throughR_biaswill be as in equation 2.28

i_bias=V_bias/R_bias (2.28)

While input impedance Zinapproaches infinity for unity gain as shown in equation 2.29. This is ideal for current injection to the probe as it forces the current out to the probe.

Zin=Rbias/(A−1) =∞(A→∞) (2.29)

2.7.2 The dual OPAMP Current Source

The dual OPAMP Current source is a Current Source configuration with higher complexity than others, like the Howland and Enhanced Howland Current Source configurations. Research have shown that the Howland Configuration have a more stable output when the frequency changes, though the current source configuration features a small output impedance[23]. A small output impedance makes it less suitable for interfacing a Langmuir probe with an impedance of maybe 1 MΩ. Therefore the dual OPAMP Current Source is a more desirable configuration, allowing the

designer to chose the output impedance by selectingRbias. The configuration can be seen in figure 2.9. Here the high input impedance of the buffer forces the current outwards to the probe while also absorbing all voltage. Allowing for both current biasing and voltage measurement by the same electronics interface.

Assuming ideal OpAmps a current analysis gives the following equations [23].

V₁₊≈V1− (2.30)

IL≈ ^Vo1−V2+

R₅ (2.31)

Vin−V1

R3

≈ ^V1−−Vo1

R4 (2.32)

V2−−V₁+

R2

≈ ^V1+

R1 (2.33)

V₂₊≈V2− (2.34)

(2.35) If the resistor values are chosen such that R5R2 = R3R1, then the current flowing through an external load, such as our plasma-probe coupling will be

IR_bias ≈ ^R3 R5

Vin

R_bias (2.36)

Figure 2.9: Shows the current-source probe interface design. V_biasis produced by the Digital-to- Analog converter, whileVoutis sent to the analog filters.

2.7.3 Instrumental Amplifier

An instrumental Amplifier is a differential amplifier composed of two stages, one buffer stage for each input as shown in figure 2.10. This stage eliminates need for input impedance matching of the inputs, as both inputs have a equally high impedance given by its similar buffer input. The second stage is the gain stage, which amplifies the difference of the signal output of the two buffers, by a gain given by the expression in equation 2.7.3 .

Av= ^Vout V2−V₁ =

1+ ^2R1 R_gain

R3

R2 (2.37)

Usually when using an integrated circuit instrumental amplifier, the enumerated resistors will be internal, leaving the system designer only with the choice ofRgainfor deciding the gain.

The very high input impedance of this circuit makes it ideal for measuring voltage signals, and the differential signal amplification makes it perfect for removing common mode noise, that is noise common to both inputs. This ability is quantified by its common mode rejection ratio (CMRR).

which is defined as the powers ratio of the differential gainA_dover the common mode gainAcm. CMRR=10log₁₀

A_d

|Acm|

dB (2.38)

Additional characteristics of Instrumental amplifiers are low drift, low DC offset and low noise and very high open loop gain. Instrumental Amplifiers are often used for purposes where stability and high accuracy is needed.

Figure 2.10: Shows the Instrumental amplifier circuit.

2.7.4 Analog filters

Analog filters are circuits with a focus on dampening certain frequencies or frequency ranges from the signal passing trough. A simple examples is a passive first order lowpass filter, simply constructed by a resistor connected in series and a capacitor connected to the ouput of the resistor and to ground, thus the high frequencies will propagate to ground while the rest of the signal components will pass on to the circuit output.

Sallen and Key Filter topology

The Sallen and key filter is a second order active filter topology as in figure 2.11, which can be used as building blocks cascaded together in order to construct higher order filters. The impedances Z1,Z2,Z3,Z4are decided depending on the type of filter.

Figure 2.11: Shows Sallen-Key filter topology

In order to design a lowpass filter, compontentZ1andZ2are chosen as resistors, whileZ3and Z₄are chosen to be capacitors. Thus

Z₁ = R₁, Z₂ = R₂,Z₃ = 1/sC₁ and Z₄ = 1/sC₂. Where s = jω+σ, is complex quantity of a frequency component ω and a time dependent σ, corresponding to the transients of a signals.

Assuming the signal has stabilisedσ=0

A transfer function describes the circuits frequency response, for a 2nd order active low pass filter it becomes

H(s) = ^w

20

s²+2αs+w²₀ (2.39)

where the undamped natural angular frequency ω₀, attenuation α, Q-factor Q, and dampening ratioζare expressed as following

ω0=2πf0= √ ¹

R₁R₂C₁C₂ (2.40)

2α=2ζω₀= ^ω0 Q = ¹

C1

1 R1

+ ¹ R2

(2.41) Q= ^ω0

2α =

√R1R2C1C2

C2(R₁+R2 (2.42)

The Q factor determines the sharpness of the natural frequency peak at f₀, its heigth and width.

Bessel & linear phase filter

A linear phase filter is a filter where the phase is a linear function of the frequency. Thus the frequency components of the input signal wil be timeshifted with a constant delay refered to as group delay, corresponding to the slope of the linear function. Hence there is no phase distortion due to frequencies being shifted relative to each other.

A bessel filter is an analog linear filter type with a maximally flat linear phase in order to preserve the shape of the filtered signal in the passband. The filter gets its name from the bessel polynomial which is implemented in the transfer function of the filter trough the resistance and capacitance values chosen.

2.8 Sources of Noise in measurements

An important part of system design becomes limiting the effects of these noise components. Noise cant be removed in its entirety but it can be made manageable. In the probes we have two kinds of noise, thermic noise also refereed to as Nquist noise, generated by the sheat resistance and shot noise generated by charged particles colliding with the surface of the probes. [24]

2.8.1 Thermal noise

Thermal noise also called Nyquist noise is generated by movement of charges in a conductor. The electrons adopts a random movement and velocity proportional to its temperature. Thus at absolut zero temperature there will be no thermal noise. Furthermore thermal is considered a white noise, or a noise with a constant manifistation at all frequencies across the spectrum. For frequencies less than 100 MHz thermal noise can be estimated by the Nyquist relation as in equation 2.8.1 or 2.8.1[25].

E_th=^p4kTR∆f (2.43)

I_th=

r4kT∆f

R (2.44)

Where E_th is the thermal noise in rms voltage, I_th is the thermal noise in rms current.k is the boltzmann constant,Tabsolut temperature,Ris the resistance, and∆f is the noise bandwidth.

2.8.2 Shot noise

Shot noise is the result of current fluctuations. When the electrons encounter a potential barrier they have to build up enough potential energy to overcome this potential barrier. Thus the each individual electron will pass this barrier at a random time. When this occurs the released energy will be contribute to shot noise. The shot noise will be inversely proportional to the current in the conductor. This shot noise current can be described by equation 2.8.2.[25]

I_sh =^q_∆f(2eI_dc+4eI₀) _(2.45)

Whereeis the electron charge,I_dcis the average dc current, I0the saturation current and∆f the bandwidth.

2.8.3 Flick noise

Flick noise is inversely proportional to the frequency of the signal causing it, hence also refered to as 1/F-noise. This noise occurs in all both passive and active compontents in a circuit. It is proportional to the dc current and can therefore be considered absorbed by the thermal noise.

Given that the dc current is kept low enough. The flick noise current can be estimated by equation

??.(Carter and Mancini 2002)

In=K_i s

lnfmax

f_min (2.46)

WhereK_iis a proportionality constant representingInat 1 Hz. And fmax,f_minis the maximum and minimum frequency in signal.

2.8.4 Noise in plasma-probe coupling

Since shot noise is caused by charged partic collisions it is heavily dependent on the collison rate between the charged particles and the probe, and thus the size of the probe surface. It is desirable to make the probes as big as possible as they will reduce the impedance. Which is beneficial due to the fact the the sensors impedance needs to be smaller than the electronics front impedance, in order to prevent signal loss in the sheat impedance. However with increasage in size larger ratio of shot noise is introduced.

Considering a spherical probe as in this instrument. In the coupling between the probe surface and ambient plasma or the sheath, there are two types of noise. That is thermal noise and shot noise. Thermal noise is caused by the sheath impedance, and shot noise is caused by charged particles hitting the probe surface [26]. Shot noise increases with radius as the surface of the probe increases, a smaller surface is theretofore helpful in limiting this type of noise. However from eq.

2.11 we can see that the impedance(trough its capacitance) is inversely proportional to probe size.

2.8.5 Noise analysis of an inverting amplifier

Here a noise analysis of the operational amplifier AD8610 is preformed, with a noise circuit equivalent as shown in figure 2.12.

Figure 2.12: Shows the noise circuit equivalent for an inverting amplifier

Here e1 and ef corresponds to the thermal noise generated at the resistors R1 and Rf. ei

corresponds to the product of the operational amplifiers current noise and the feedback resistance.

evcorresponds to the operational amplifiers voltage noise. Given the assumption of uncorrelated noise sources the total noise can be calculated by the exression in equation??.

etot =^qe²_i +e²_f +e (2.47)

The operational amplifier AD8610 is an high precision JFEt-amplifier with a current densityJnof 5 fA /√

Hz and a voltage noise densityvnof 6 nV /√ Hz.

e1= ^Rf R1

p4kT∆FR1 (2.48)

e_F=^q_4kT∆FRf (2.49)

ev=vn

√∆F (2.50)

e_i= Jn

√∆FRf (2.51)

(2.52) Which gives us a total noise of

etot =8.5µV (2.53)

The signal to noise ratio (SNR) for an inverting amplifier is given by the relation in equation 2.8.5

SNR=

R_f R_IV_in

etot (2.54)

2.8.6 Analog-To-Digital Conversion

An analog to digital converter transforms the analog signal of voltage variations to a discrete bineary representation. This conversion occurs at discrete time intervals. In order to not lose any information of the sampled signal it is important for the sampling frequency fs to be higher than or at least twice the frequency of the highest frequency compontent fmax of the sampled signal.

The minimum sampling frequency that satisfies this Nyquist criteria is called the Nyqvist frequency and is expressed as in equation 2.8.6. When the sampling frequency is lower than twice of the sampled signal the reconstruction process will produce an incorrect signal with a lower frequency than the original. This is called aliasing. However aliasing can be easily avoided by either choosing a higher sampling frequency or employing anti-aliasing filters to reduce the effects of unwanted frequency components.

fs ≥2fmax (2.55)

Figure 2.13: Shows the produced signal from sampling below the nyqvist criteria.

Where N is the number of bits in the converter above the noise floor, which is the smallest change in voltage that the ADC is able to detect.

Smallest Detectable Voltage Change= Voltage Range

2^N (2.56)

Noise with an amplitude below this value will be undetected by the ADC. Here the Signal-To-Noise Ratio (SNR) becomes important. It describes the relation between the signal RMS and noise RMS value. The signal to noise ratio to an analog to digital converter can be calculated as shown in equation 2.8.6 (Baker 2007)

SNR=6.02N+1.76dB (2.57)

For a 24bit ADC like AD7768 the SNR becomes ≈ 146dB. That is signals above the Nyquist frequency must be dampened by 146 dB in order to prevent aliasing.

Chapter 3

System Design

3.1 Objective

The objective of this work is to create a prototype of a miniaturized E-field instrument for measuring ionospheric electric fields. This prototype is to be designed in such a way that it could or future iterations could be mounted on a CubeSat. For this purpose it a current biasing probe system is to be implemented in order to improve the probe plasma coupling, allowing higher accuracy on the field measurements. Finally the system should be able to conduct current sweeps to produce an I-V curve, in order to compute the electron temperature.

3.2 Requirements

For the instrument to work as intended a set of functional, performance and design requirements have been identified. In order for the instrument to measure E-field it needs to be able to meassure either singular or differential probe potential, while to be able to generate I-V curves to estimate an electron temperature, singular probe potential measurements are needed. Current biased probes has been chosen in order to improve the accuracy of local plasma potential measurements of each probe. this is order to measure weak field signals in the local plasma, which will allow a shorter probe separation distance / boom length. The instrument shall be operated as a subsystem by an OnBoard Computer controlling several instruments and subsystems. Hence the following functional requirements

Table 3.1: Functional requirements for miniaturised E-field experiment system

# Description

F.1 The system shall measure singular and diffrential probe potential F.2 The system shall be able to bias the probes with a current

F.3 The system shall be able to conduct current sweeps while measuring the probe potential

F.4 The measurements shall be sampled and transmitted by a microcontroller to a onBoard computer.

Table 3.2: Preformance requirements for miniaturised E-field experiment system

# Description

P.1 The system shall measure plasma potential down to 10 mV.

P.2 The system shall measure alternating electric field up to several kilohertz P.3 The current injected to the probes may range from 10nA to 2µA

The instrument shall fit onto a Cubesat and therefore needs to have a certain dimension. The probes have been chosen to have 2 cm diameter in order to limit the sheath size and thus its influence and chance of being influenced by the sheath of the spacecraft.

Table 3.3: Design requirements for miniaturised E-field experiment system

# Description

D.1 The system shall have the dimensions∼96 x 90 mm D.3 The probes should have a diameter of 2 cm.

D.4 The probes shall each have a separation distance of 1 m each

D.5 The probes should each be connected to the system trough a coax cable

3.3 System overview

An overview of the instrument and its main components are shown in figure 3.6, the arrow indicates the direction of the signals. Due to design errors however section of the instrument was disconnected and a replacement front end PCB was produced, replacing the design errors. The old PCB was kept as a data acquisition PCB and Current Source PCB while the new one had the probe interface and amplifying stage and analog filtering section. A block diagram of the whole system is as shown in figure 3.2

Figure 3.1: Shows the initial overview of the system

Figure 3.2: Shows the distribution of system function across the two PCBs after spiting the system In short the functions of the different system components are as follows:

• Digital-to-Analog Converter: recieves a digital voltage signal from the MCU, which is converted into an analog voltage signal passed on to the Current Source.

• Current Source:is controlled by its input voltage, which it converts to an output current, that is used to bias the probe(s).

• Probes: coupled to the local plasma and obtains the local plasma potential. The coupling towards the local plasma is improved by its bias current

• Instrumental Amplifiers: Amplifies the signal and removes common mode noise for each probe, and also amplfies the difference between the probes.

• Low pass filter: removes noise from frequencies above 10kHz. used to prevent aliasing in sampling, while designed for maximum linear phase

• Diffential amplifier Converts the singular voltage signal with respect to ground, into a differential signal in order to interface the ADCs differential signal input

• Analog-to-digital Converter:samples the analog signal recieved from the filter output.

• MicroController: Configured as slave and waits for commands from the master computer.

At command outputs a digital voltage signal to the DAC, and passes on the sampled signal from the ADC to the master computer.

3.3.1 Probes

This instrument is designed to have four spherical probes with a diameter of 20 mm each. The probes are to be used in a dual probe setup, deployed on booms with a length of 1 m each.

The motivation for choosing small probes is too minimize the sheath around them, and possible interference from other spacecraft sheaths. As we saw im eq. 2.11 the probe radii is related to the sheath thickness. However as we can see in eq. 2.13 and 2.16, the choice in probe radii also affects the plasma-probe currents. A consequence of choosing smaller probes is therefore an increase in the plasma-probe impedance which is related trough eq. 2.19. Which decreases the accuracy of local plasma potential measurements, that constitutes a E-field measurement. Furthermore this high plasma-probe impedance puts high requirements on the input impedance of the system, in order to prevent a resistance division between the instrument and plasma-probe coupling.

Current Biased probes

A current source is used force a current out trough the plasma-probe coupling and by doing so reducing the plasma-probe impedance. We saw the effect of increased current on the plasma-probe impedance in eq. 2.19. In order to do this a Dual OpAmp current source is to be used. This current source configuration allows for both biasing a current and measuring the potential adopted by a connected probe.

Passive and active probes

In order to realise the requirements on the probes, they where decided to be passive, or not containing any preamplifier inside. The benefits of this decision is that it reduces the complexity of the system and reduces the chance of local signal disturbances in the plasma due to signal from the cables. However a preamplifier placed inside the probe could have amplified the measured signal improving the signal to noise ratio early on in the system. Furthermore the main benefit lost in this trade-off decision is that a preamplifier would reduce the output impedance of the probe, easing the input impedance requirement of the system.

bootstrapping

The main purpose of the buffer is its contribution to the Current source, having a high input impedance forcing the current trough the probe while simultaneously allowing for voltage measurements and positive feedback. The buffer is also utilized in a bootstrapping configuration by connecting the outer layer of the coax cable to the output of the buffer interfacing the probe. By this implementation the capacitance of the cable is reduced. Thereby decreasing the signal distortions caused the cable capacitance and the plasma-probe impedance on on the frequencies measured.

Figure 3.3: Shows the implementation of Bootstrapping, Probes for proof of concept

For proof of concept the instrument designed will utilise two out of four probe interface. The probes available from the instrumentation lab at the University of Oslo had a diameter of 20 and 30 mm.

As we saw in eq. 2.11, the size of the probe does effect the plasma potential measurements, it is therefore expected that difference in probe diameter will noticeable in the measurements. A proof of concept should however still be possible.

3.4 Active components

The Analog front end active components and passive component values was chosen after being simulated in LTSpice[27] as the circuit show in figure 3.4. Here we can see the a pair dual opAmps current source configurations followed by connections to instrumentation amplifiers. The current source outputs are here connected to a resistance and a capacitance simulating the plasma sheath resistance and capacitance.

Figure 3.4: Shows the circuit used in simulations done in Ltspice[27] for determining suitable active components in analog front end, and fitting values of the passive components.

3.4.1 AD549

The AD549 amplifier is configured as the voltage controlled current source output amplifier. Its chosen for its rail-to-rail voltage of±18V. Though an even higher rail-to-rail would be satisfactory.

The voltage range will be needed to prevent saturation if the plasma impedance becomes similar or larger than the CS output impedance given by the resistorR_bias. Furthermore the low input voltage noise 4µVp−pis important to accurately being able to control the current output. Lastly the slew rate of 3 V/µs, with a settling time of 5µs for a 10 V input step to 0.01% should be sufficient for the current sweeps. Though the downside of this amplifier is that it requires a lot of space as it has a diameter of 9.40 mm, and is only found in single package, meaning the design will need four of these packages. in adition they are trough holes components.

3.4.2 AD8672

The AD8672 amplifier is configured as a buffer in the dual opAmp CS, it prevents the current from flowing backwards in the system while the voltage signal does. The AD8672 is chosen for its rail-to-rail voltage of±18V, quite usefully for the first stage in the electronics-probe interface, the

AD8672 have integrated ESD diodes to provide overvoltage protection with a safty range of±40V.

Furthermore it has a high common mode rejection ratio of 86 dB minimum up to 10Khz, which should supress time-constant common-mode noise. The slew rate of this amplifier is 1.1 V/µs

3.4.3 AD8426

The AD8426 Instrumental amplifier is used for improving the signal-to-noise ratio of the signal, by amplifying the signal and dampening the common mode noise. It has a wide rail-to-rail voltage of

±18V, and a common mode rejection ratio of 80/90 dB minimum at G=1/10 correspondingly. The gain of the amplifier is given by the formula

G=1+^49.4kΩ

R_G (3.1)

whereRGis an external resistor, freely chosen to achieve the desired gain.

3.4.4 OPA1692

The OPA1692 is used in the 4th order linear phase low pass filter. Its chosen for its low noise and distortion. Which is very important paramaters for an amplifier in filter applications, especially filters with a focus on linear phase. Furthermore its rail-to-rail range is±18 V, which allows for the entire front-end electronics rail-to-rail range to be raised to up to±18 V if desired.

3.4.5 Analog Filter

Behind the instrumental amplifiers the signal has to pass trough a Low Pass filter each. Here the Sallen and Key 3rd Order Bessel filter was chosen for its maximum linear phase, with zero decibel gain and a cut-off frequency of 10kHz. It does however have no effect on the tests to be preformed for proof of concept, as the proof of concept does not depend on the frequencies measured. Though the error does reduce the capability of sampling high frequency potential from a potential 10-50kHz range. The Filter Design was done using the Texas Instruments Filter Design Tool[28], which recommended the components used, specifically the OPA1692. The ADC does however also contain an integrated Anti-Aliasing which reduces the requirement of the LP filter employed.

3.4.6 ADC differential input

A consequence of the choice of ADC, that is the AD7768 is that we need to convert the input signal to a differential signal. As the AD7768 only supports differential signal inputs, with a maximum of 5V on each channel. In order to do this conversion we use the differential amplifier AD8476, for its low power and its ability to drive sigma-delta ADC and its heritage use by the electronics group at the university of Oslo, on similar instruments. The amplifier takes±10 V on its input and convert it to differential voltage signal in the range ±0−5 V. The differential mode voltage signal can be calculated as

V_out,dif=VOUT+−VOUT− (3.2)

Another benefit of using the AD8476 is that it can take 18 V above supply voltage without being damaged thus it acts as protection for the ADC as well.

3.5 Digital Backend

The focus of this thesis has been the development of the analog electronics of this instrument. In order to limit the scope of this thesis the digital section was not designed by me, instead i have been relying on heritage solutions of previous work by the Electronics group at the University of Oslo. These design solutions was taken from the m-NLP daughters on the ICI-5 sounding rocket.

Specifically this includes the choice in Analog-To-Digital Converter, the Microcontroller, Digital- To-Analog Converter, power circuits. The firmware has been developed by the electronics group and by Kosaka for his master theisis??. Other modifications were done in order to integrate this instrument together with the Floating potential probe instrument by Lindland together on a single PCB.

3.5.1 AD7768

In order to have enough channel inputs for both this instrument and the Floating Probe Potential by Lindland the 8-channel AD7768 was used, its block diagram is as shown in figure 3.5.

Figure 3.5: Shows the block diagram of AD7768 as drawn in its datasheet.

This type of ADC is called a sigma-delta ADC, which characteristically provides a high resolution and a wide range of sampling rates. A method often employed by these kind of ADCs is that they rely on oversampling followed by downsampling in order to reduce the power of the noise. This method rely on sampling at a frequency called the oversampling frequency f_mod that is much higher than the double Nyquist frequency. Only a small part of the noise will be in this bandwidth and which is removed digitally by a low-pass filter.

Once beyond the filtering, our signal is downsampled to a output data rate that is desirable.

ODR≥2fN (3.3)

This technique is implemented in the AD7768, with the additional advantage of being implemented as an anti-aliasing filter as well. Thus relaxing the requirements on analog low pass filter in front of the ADC.

The master clock in this system operates at 8MHz. Thus the oversampling frequency is given by

f_mod =8MHz/8=1MHz (3.4)

Furthermore the ODR can be calculated by dividing the oversampling frequency with a decimation ratiodr, expressed in order of 2^N

ODR= ^fmod

dr (3.5)

The E-field instrument as implemented should be able to measure frequencies up to 10kHz (ideally even higher), thus requiring a ODR of at least 10kHz. Therefore a decimation ratio of 64 was chosen, resulting in ODR = 15.625kHz. However because of limitations in the relation between sampling time and sample rate an ODR of 3.906 kHz was chosen. This limits the instruments capabilities to only measure electric field up to 1.953 kHz according to Nyquist’s theorem. Thus in order to measure higher frequency signals a different ADC should be chosen.

Furthermore it is important to note that even though the AD7768 is a 24 bit ADC, the data is sampled as 16 bit integers. Hence having a range of 2¹⁶bit values. The voltage range of the input is given by the differential amplifier of±5V or rather 10V range. This gives us a Least Significant Bit corresponding to

LSB= ^10V

2¹⁶bits =0.153mV

bit (3.6)

0.153 mV will thus be the smallest voltage change sampled by the ADC. However due to implementing gains in the instrumental amplifiers the smallest voltage change detected by the system need to take these gains into account also. Correcting for the gain by the instrumental Amplifiers the LSB becomes

LSBGain= ^LSB Av

=_0.153^mV

bit ·2.36V

V =_0.36108^mV

bit (3.7)

The system is thus capable of measuring voltage signals down to well beyond the 10mV resolution required.

The low pass filter of the ADC does however add a group delay of τg= ³⁴

ODR ≈8.7ms (3.8)

which is a dominating time delay in our system, however if taken into account it does not affect our results as our system does not require hard time deterministic behaviour. Though it might be of interest for future work to choose a different type of ADC with less group delay if the intention is to initiate some response in real time based on the measurement results.