### UPTEC F 16018

### Examensarbete 30 hp Juni 2016

## Developing of an ultra low noise bolometer biasing circuit

### Jonas Viklund

**Teknisk- naturvetenskaplig fakultet **
**UTH-enheten **

Besöksadress:

Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0

Postadress:

Box 536 751 21 Uppsala

Telefon:

018 – 471 30 03

Telefax:

018 – 471 30 00

Hemsida:

http://www.teknat.uu.se/student

### Abstract

**Developing of an ultra low noise bolometer biasing** **circuit**

*Jonas Viklund*

### Noise in electronic circuits can sometimes cause problems. It is especially problematic in for example high sensitive sensors and high end audio and video equipment. In audio and video equipment the noise will make its way into the sound and picture reducing the overall quality. Sensors that are constructed to sense extremely small changes can only pick up changes larger than the noise floor of the circuit. By lowering the noise, sensors can achieve higher accuracy.

### This thesis presents an ultra low noise solution of the biasing circuitry to the bolometer used in one of FLIR Systems high end cameras. The bolometer uses different adjustable direct current voltage sources and is extremely sensitive to noise.

### The purpose is to improve the picture quality and the thermal measurement resolution. A prototype circuit was constructed and in the end of the thesis a final circuit with successful result will be presented.

### Handledare: Anders Wistrand

### Popul¨ arvetenskaplig sammanfattning

### N¨ ar h¨ og kvalitet ¨ ar viktigt i elektroniska produkter kan brus orsaka problem. Som anv¨ andare ¨ ar detta n˚ agot som m¨ ojligtvis huvudsakligen m¨ arks i ljud- och bildprodukter. Ett brus kan till exempel h¨ oras i bakgrunden om man lyssnar p˚ a musik eller s˚ a kan bilden p˚ a en tv inte uppfattas som skarp p˚ a grund av att bakomliggande algoritmer sl¨ atar ut en vanligen brusig bild. Brus ¨ ar ¨ aven ett problem i v¨ aldigt k¨ ansliga sensorer.

### Det h¨ ar examensarbetet utf¨ ordes p˚ a FLIR Systems som tillverkar v¨ armekameror. Rapporten behandlar ett problem FLIR Systems har d¨ ar elektroniskt brus st¨ or bildsensorn i en av deras v¨ armekameror.

### Bruset i biaseringskretsen till bildsensorn p˚ averkar b˚ ade bild och nog-

### grannhet negativt. Rapporten g˚ ar djupare in p˚ a elektroniskt brus och

### presenterar en ny och b¨ attre l˚ agbrusig biaseringskrets som l¨ osning p˚ a

### problemet.

### Contents

### Abbreviations

### 1 Introduction 1

### 1.1 Background . . . . 1

### 1.2 Problem definition . . . . 1

### 1.2.1 Goals . . . . 1

### 1.2.2 Delimitation . . . . 2

### 2 Theory 3 2.1 Noise . . . . 3

### 2.1.1 1/f-noise (pink noise) . . . . 3

### 2.1.2 Thermal noise (Johnson-Nyquist noise) . . . . 3

### 2.1.3 Current noise (shot noise) . . . . 4

### 2.1.4 Other noise . . . . 5

### 2.2 Power spectral density . . . . 6

### 2.3 Components . . . . 6

### 2.3.1 Resistors . . . . 7

### 2.3.2 Capacitors . . . . 7

### 2.3.3 Digital to analog converter . . . . 9

### 2.3.4 Digital potentiometers . . . . 10

### 2.4 Filter topology . . . . 10

### 2.4.1 RC-filter . . . . 10

### 2.4.2 Sallen-Key . . . . 12

### 2.4.3 Multiple feedback filter . . . . 14

### 3 Method 16 3.1 Measuring equipment and software . . . . 16

### 3.1.1 Stanford research systems SR560 Low-noise preamplifier 16 3.1.2 LabVIEW . . . . 17

### 3.1.3 NI-USB 6361 . . . . 18

### 3.1.4 Aardvark I ^{2} C/SPI . . . . 18

### 3.1.5 LTspice IV . . . . 18

### 3.2 Measuring and analysis . . . . 19

### 3.3 Phase 1 - Simulating, Measuring and patching . . . . 20

### 3.4 Phase 2 - New printed circuit board . . . . 22

### 4 Results and findings 25

### 4.1 Results from measuring . . . . 25

### 4.2 Final circuit . . . . 32

### 5 Discussion 34

### 5.1 Suggested improvements . . . . 35

### 6 Conclusions 36

### 6.1 Future work . . . . 37

### 7 Appendix 40

### Abbreviations

### AC Alternating current.

### ADC Analog to digital converter.

### BOM Bill of materials.

### CAD Computer-aided design.

### DAC Digital to analog converter.

### DAQ Data acquisition device.

### DC Direct current.

### DUT Device under test.

### ESL Equivalent series inductance.

### ESR Equivalent series resistance.

### GUI Graphical user interface.

### I ^{2} C Inter-integrated circuit.

### LP-filter Low-pass filter.

### LSB Least significant bitr.

### OP-amp Operational amplifier.

### PCB Printed circuit board.

### PSD Power spectral density.

### RMS Root mean square.

### SMD Surface mounted device.

### SPI Serial peripheral interface.

### VI Virtual instrument.

### 1 Introduction

### 1.1 Background

### In an ever growing electronic world where components get smaller and smaller and the demand for devices with high quality picture and audio never seems to stop increasing, electronic noise is causing problems. The noise makes its way through the system and manifests itself in the picture and audio.

### When it comes to video applications, different signal processing techniques and algorithms can be applied to reduce the noise of the picture, an example of this is averaging over two or more frames or a median filter. The price to pay is the degradation of image quality and the increase of processing power and energy consumption. Now a day, when a lot of the new devices coming out on the market is battery powered, energy consumption plays a big role when designing new products. The possibility of both lowering the power consumption and improving the image quality by investigating and optimizing the noise of the electronic circuits is something worth exploring.

### 1.2 Problem definition

### Today FLIR Systems is using a too noisy circuit design for the biasing voltages to the bolometer in one of their products. This can be seen in the picture quality and requires them to use a lot of filtering and processing to get a nice, and to the user noise free, picture.

### Due to the fact that the existing circuit is a company secret only measure- ments will be compared in this thesis and no schematics of the original circuit will be presented.

### 1.2.1 Goals

### The main focus of this thesis is to come up with a new ultra low noise

### design for the biasing circuitry. The circuit provides multiple variable power

### supplies to the bolometer which is extremely sensitive to noise.

### theory, measurements, component specification and simulations. In the end a new prototype circuit should be produced. This should also be done with respect to a reasonable prize, size, overall producibility and with an energy consumption close to the that of the existing circuit.

### 1.2.2 Delimitation

### The thesis aim to come up with a new circuit and compare the noise perfor-

### mance from measurements done on both circuits. The new circuit will not

### be tested in an actual IR camera because this would require major rework

### of other parts which would not fit into the time schedule. This means that

### the actual difference in performance will not be known.

### 2 Theory

### 2.1 Noise

### In electronic circuits a number of different noise sources is superimposed to form the total noise. Since the noise is stochastic there is no correlation with other noise (for some noises like 1/f noise there can be a small correlation), the total noise is calculated as in equation 2.1 where V _{N} is the total noise voltage and V _{ni} is individual noise voltages.

### V N = q

### V _{n1} ^{2} + V _{n2} ^{2} ... (2.1) In a lot of applications noise is not a big problem, but when dealing with sensitive sensors, high speed circuits or audio equipment it could cause un- predictable behavior or limit the quality of the product. The sources of these noises will be presented in this section.

### 2.1.1 1/f-noise (pink noise)

### 1/f-noise is named after its inverse dependency on the frequency, the lower the frequency, the higher the noise. 1/f-noise has been observed in a lot of things, for example water level, earthquake magnitude and electronics [1].

### The origin of this noise is still a bit unclear but when it comes to electronics, some possible reasons are [2]:

### •Fluctuations in temperature, which affect the thermal equilibrium

### •Migration of impurities

### •The resistance changing over time

### 1/f noise can in some cases be calculated but in practice this requires em- pirically determined parameters [2].

### 2.1.2 Thermal noise (Johnson-Nyquist noise)

### The random movement of free charge carriers in a resistance will result in

### Equation 2.2 is the spectral noise power, where S R,th is the spectral noise power, k _{b} is the Boltzman constant and T is the temperature measured in Kelvin. To calculate the noise voltage and the noise current the spectral noise power is multiplied and divided with resistance respectively. This can be seen in equation 2.3 where R is the resistance [2].

### S _{R,th} = 4k _{b} T (2.2)

### Equation 2.3 is only applicable to ohmic resistance, for impedance the equa- tion needs to be changed, replacing R with the real component of the impedance, Re(Z).

### V _{Rn,th} ^{2} = S _{R,th} R = 4k _{b} T R (2.3) i ^{2} _{Rn,th} = S _{R,th}

### R = 4k b T R

### In theory, a capacitor would not create any thermal noise, although in re- ality capacitors have some current leakage and dielectric losses that can be modeled as a loss resistance R _{loss} in parallel with the capacity C. This is often described as a loss angle δ _{C} , this angle can be seen in equation 2.4.

### tanδ _{C} = 1

### ωCR _{loss} (2.4)

### The noise caused by this is often described as dielectric noise and is calcu- lated with equation 2.5.

### i ^{2} _{Rn,tδ} = 4K _{b} T ωC

### tanδ _{C} (2.5)

### 2.1.3 Current noise (shot noise)

### Current noise or shot noise is a noise source associated with pn-junctions or

### Schottky junctions (although some studies have shown that this can be found

### in metallic resistors as well [3]). Current noise is the result of the charge

### carriers having to overcome a potential barrier. The different probabilities

### of getting to another potential will cause a current.

### Equation 2.6 describes the current per time through a cross-sectional area, this can be seen as a random pulse train. N is the total number charge carriers q with δ as the pulse shape function. t _{n} is the time of emission for the n-th electron.

### I(t) =

### N

### X

### n=1

### qδ(t − t n ) (2.6)

### Each charge will have to get over the potential barrier and some of them will quantum tunnel through, this follows a Poisson distribution. Given that the charges can be described as white noise the current noise is calculated with the equation 2.7 [3].

### S(f ) = 2qI (2.7)

### Current noise is not as significant as other noises in electronics. Take 1A for example, it consists of 6.24 × 10 ^{18} electrons per second. This is such a big number that even if it fluctuate in the billions at any given time this will still be much less current then the 1A itself. It is however temperature and frequency independent which means than in high frequency application and/or at very low temperature, current noise could be the dominating noise source [3].

### 2.1.4 Other noise

### A lot of other factors can cause noise in electronic circuits, one is noise from the main power line getting picked up by the circuit. This is typically showing up as a large spike at and around 50 Hz and the overtones. AM and FM radio as well as air and temperature fluctuations can also induce noise into a system.

### There is also the problem of crosstalk. This is when two or more signal traces affect each other by inducing a voltage that can be seen as noise.

### This is also a problem in multichannel components such as digital to analog

### converters (DACs) where the signal from one channel will ”leak” to another.

### with a frequency in the span of human hearing, this noise could manifest itself as auditory noise. This problem goes both ways, meaning that if the PCB is bent or vibrating this would cause the capacitor to generate a small voltage. This is mostly a problem when using surface mounted device (SMD) ceramic capacitors.

### A lot of these noise sources can be reduced by a good PCB layout.

### 2.2 Power spectral density

### To analyse noise it is useful to see what frequencies these noise signals con- tain, which is done with spectrum analysing. A time varying signal can be broken down to the individual frequency components regardless of it be- ing an audio signal, radio signals, a simple sine wave or some other signal.

### This is often analyzed by computing the power spectral density (PSD), the spectral energy distribution at a given time.

### ˆ

### x T (ω) = 1

### √ T

### Z T 0

### x(t)e ^{−iωt} dt. (2.8)

### Equation 2.8 computes the Fourier transform of the signal x(t) for the finite interval [0, T ]. The PSD is then defined as equation 2.9 where E is the expected value [4].

### S(ω) = lim

### T →∞ E[|ˆ x _{T} (ω)| ^{2} ] (2.9) Depending on the type off signal and its predicted wave content, different windows can be used to improve the effectiveness of the Fourier transform.

### The window function is multiplied with the signal x(t) in equation 2.8. When measuring a broad spectrum, as in this case, a uniform window is the best choice [5].

### 2.3 Components

### The formulas for calculating noise in section 2.1 is for an ideal case. Real

### components are not ideal and behave differently depending on the type and

### manufacturing method. This section will explain some different parameters

### of components with respect to noise.

### 2.3.1 Resistors

### Resistors come in many different forms, the most common is through hole mounted and SMDs. In low noise applications SMDs are the better choice due to the fact that the legs of a through hole mounted device can pick up noise, longer legs means more noise. There are different types of SMDs such as thick film, thin film and metal foil. The different types have their pros and cons. Thin film and metal foil have been proven to have better noise characteristics than thick film [6], but is also more expensive. A comparison between the amount of noise in different resistors can be seen in figure 2.1.

### Figure 2.1: Shows a comparison of noise in different types of resistors, lower value means lower noise. Picture taken from reference [6]

### 2.3.2 Capacitors

### Figure 2.2 shows the ideal capacitor and the representation of a real capac-

### itor.

### (a) (b)

### Figure 2.2: (a) Show the representation of a ideal capacitor. (b) Shows the representation of a real capacitor.

### The real capacitor can be modeled as having a resistor in parallel with the capacitor, this represents the leakage current. It has also got a resistance and a inductance in series with the capacitor. These are called equivalent series resistance (ESR) and equivalent series inductance (ESL). The main difference between different types of capacitors is what the dielectric is made from [7]. Ceramic (multilayered), film and electrolytic is the most commonly used types.

### Ceramic capacitors are very common these day because of the low prize, relatively high capacitance to size factor and low ESR/ESL. The capacitance depend on the type of capacitor and what kind of ceramic dielectric that is being used. A ceramic capacitor can have a capacitance ranging from some pF up to a hundred µF . The main problem with the ceramic capacitor is the piezoelectric effect which can translate mechanical vibrations into system noise. Ceramic capacitors which contain a large amount of barium titanate also exhibits a ”pyroelectric” effect (changing due to temperature fluctuations).

### Tantalum capacitor is polarized with the anode made of tantalum and

### a cathode made from a solid or liquid electrolyte. The dielectric is made

### from a very thin oxide and combined with high permittivity this gives the

### tantalum capacitor one of the highest capacitance to size of all capacitors.

### Solid electrolyte tantalum have a low ESR and have a stable behavior over a large temperature range. A Tantalum capacitor have no piezoelectric like effect but have a higher direct current (DC) leakage current than ceramic and film capacitors. Because of the polarization, the capacitor always have to be connected with the cathode to the the higher potential and the an- ode to the lower potential. Reverse polarization can cause the capacitor to explode violently, which is important to consider when designing a circuit with tantalum capacitors.

### Film capacitors have some sort of plastic film as the dielectric, this could for example be polypropylene (PP), polyethylene terephthalate (PET) or polyphenylene sulfide (PPS). They often feature electrodes of aluminum or zinc created by applying the material to the surface of the plastic dielectric.

### Film capacitors are constructed like many capacitors in parallel, this gives the film capacitor a very low ESR and ESL, they are also stable and with good temperature characteristics. For a given capacitance a film capacitor is much larger in size than a ceramic or a tantalum capacitor. SMD film capacitors only have a range from pF to some µF . Unlike the ceramic capacitors, film capacitors do not have a piezoelectric effect.

### 2.3.3 Digital to analog converter

### A DAC is a components that converts digital signals to analog signals. They are frequently used in audio equipment as a way of translating digital music into analog music signals. They can also be used to accurately control voltage in a circuit. Some typical parameters of a DAC can be seen in table 2.1.

### Table 2.1: Some typical parameters of a DAC.

### Parameter Typical Unit

### Resolution 8-16 bits

### Channels 1-8

### Output noise (1-10 Hz) 1-20 µV _{p−p}

### Output noise spectral density 20-150 nV/ √ Hz

### Differential nonlinearity (DNL) 0.2-1 Least significant bit (LSB)

### Temperature drift 1-25 ppm/ ^{◦} C

### 2.3.4 Digital potentiometers

### A digital potentiometer is a component in which the resistance can be digi- tally controlled via some sort of communication protocol, for example serial peripheral interface (SPI) or inter-integrated circuit (I ^{2} C). Some typical pa- rameters of a digital potentiometer can be seen in table 2.2.

### Table 2.2: Some typical parameters of a digital potentiometer.

### Parameter Typical Unit

### Resistance accuracy 10-20 %

### Resolution 4-8 bits

### Channels 1-2

### Output noise (1-10 Hz) Resistor noise µV _{p−p} Output noise spectral density Resistor noise nV/ √

### Hz

### Differential nonlinearity (DNL) 0.2-1 Least significant bit (LSB)

### Temperature drift 15-50 ppm/ ^{◦} C

### 2.4 Filter topology

### Since this thesis primarily focuses on DC voltages, meaning the goal is to filter out as much alternating current (AC) voltages as possible, this section will present some different low-pass filter (LP-filter) designs with their pros and cons.

### A LP-filter is a filter that from a certain cut-off frequency will reduce the amplitude of a signal. The filter order is referring to the rate at which the filter reduces the amplitude. In a first order filter the amplitude is reduced by a factor of 2 every time the frequency is doubled and in a second order the factor is 4. This is generalized as f actor = order × 2.

### 2.4.1 RC-filter

### The RC-Filter is a passive first order LP-filter. Figure 2.3 shows a general

### representation of a RC-filter.

### Figure 2.3: Shows a first order passive RC LP-filter

### A capacitor can be seen as a complex impedance that decreases as the fre- quency increases, this can be expressed in equation 2.10 [8]

### Z _{C}

_{1}

### = 1

### iωC _{1} (2.10)

### The equation for the voltage V _{out} is the voltage divider equation. Equation 2.11 shows the transfer function from V in to V out , this has a pole in _{R} ^{1}

1

### C

1### . H _{C}

_{1}

### (iω) = V out

### V _{in} = 1

### 1 + iωC _{1} R _{1} (2.11)

### The cut-off frequency can be calculated from equation 2.12.

### f c = 1

### 2πRC (2.12)

### The pros and cons of the RC topology in respect to low frequency:

### + Simple design

### + Low component count + Cheap

### − Requires relatively large capacitors to get a low cut-off

### − No signal amplification

### 2.4.2 Sallen-Key

### Sallen-Key is an active second order filter design which can be used both with a unity and non unity gain configured operational amplifier (OP-amp).

### Figure 2.4 shows a unity gain Sallen-Key LP-filter.

### Figure 2.4: Shows a second order unity gain Sallen-Key filter

### In equation 2.13 the transfer function for figure 2.4 is shown [9]. This can be rewritten as equation 2.14 where ω 0 is the cut-off frequency in radians and is given by 2.15.

### H(s) = 1

### s ^{2} (R1R2C1C2) + s(R1C1 + R2C1) + 1 (2.13)

### H(s) = ω ^{2} _{0}

### s ^{2} + 2αs + ω _{0} ^{2} (2.14)

### ω _{0} = 2πf _{0} = 1

### √ R _{1} R _{2} C _{1} C _{2} (2.15)

### α is the attenuation coefficient and is given by equation 2.16 where ζ is the

### damping factor, or as it is also called, the quality factor Q. The quality factor

### describes at which rate the energy of a system is lost. Low quality factor

### means big suppression of oscillations and vice versa, this can be calculated from equation 2.17.

### 2α = 2ω _{0} ζf _{0} = ω _{0} Q = 1

### C1

### R _{1} + R _{2} R 1 R 2

### (2.16)

### Q = ω 0

### 2α =

### √ R 1 R 2 C 1 C 2

### C2(R _{1} + R _{2} ) (2.17)

### As can be seen from equation 2.18 the transfer function has two complex poles and no finite zeros. If these poles have a negative real component the transfer function will be decaying, non-oscillating and stable.

### s = −α ± i q

### α ^{2} − ω _{0} ^{2} (2.18)

### When designing a Sallen-Key filter one will choose the values of the com- ponents based on the wanted damping factor and cut-off frequency. This means that one often chooses the components as in equation 2.19,

### R _{1} = mR R _{2} = R C 1 = nC C 2 = C

### (2.19)

### and equation 2.15 and 2.17 can be rewritten as equation 2.20.

### Q =

### √ mn

### m + 1 (2.20)

### ω 0 = 1

### RC √ mn

### The pros and cons of the Sallen-Key topology in respect to low frequency:

### + Low output impedance

### − Requires more components than RC-filter

### − Active design, needs a power supply

### 2.4.3 Multiple feedback filter

### Like the Sallen-Key filter, the multiple feedback filter is an active second order filter. Multiple feedback filters is often used when a filter with high gain, high quality factor and/or high frequency functionality is required [10].

### A general second order representation can be seen in figure 2.5.

### Figure 2.5: Shows a second order general representation of a multiple feed- back filter.

### The transfer function is given as equation 2.21 [11], with the variables Q, K and ω 0 expressed in equation 2.22.

### H(s) = Kω _{0} ^{2}

### s ^{2} + ^{ω} _{Q}

^{0}