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## Background and theory

In the following chapter, the thesis goes through a short background at section 2.1 and a longer theory part from 2.2.

**Background**

Safety is paramount in railway systems, this safety is done by interlocking. Interlock-ing is that valid actions are only permitted in the railway system, it checks that the action is safe. One of the functions is to monitor the optical signalling system. The optical system is monitored by checking if a threshold current is being drawn from the unit [2]. If the current being drawn from the optical unit is lower than a given setpoint then the interlocking system knowns that the optical unit is faulty. Since these systems have been in use for an extended time, they are configured to detect older types of optical units, incandescent bulbs. The incandescent bulb is a very in-efficient light source, which draws a lot of power for little illumination [4]. This means that older interlocking systems are configured to detect a large current being drawn when the optical unit is being used.

**The 48 Optical Unit**

The design description and schematics for the 48 OU were provided by Alstom [5]. The OU was placed on printed circuit board with the dimensions of 80 ∗ 88 . To remove overcurrents, overvoltages and electrostatic discharges from the alternating current (AC) voltage input, a fuse, a transient voltage suppression (TVS) and a choke were used. The AC input voltage of the microcontroller has a software notch filter to eliminate signals from passing trains, 16.67 , and voltage ripples.

The AC voltage is sensed by a microcontroller, that decides what operation mode is active on the OU. The operation modes are:

– Off-mode, where no light is to be emitted from the OU.

– Day-mode, with nominal 48 AC input. The OU emits 830 .

– Night-mode with nominal 33 AC input. The OU emits 310 .

For the two active operation modes, the OU is to efficiently emit light for sufficient visibility at a distance of 200 but a minimum of 100 [1]. The rectified direct cur-rent (DC) voltage feeds a linear regulator, which in turn supplies the microcontroller with 5 [5]. The rectified DC voltage is also connected to 4 LEDs in series. The DC voltage and current is sensed by the microcontroller, which in turn regulates the LED current with pulse width modulation (PWM) on a transistor in series with the LEDs. The PWM is regulated with a closed loop, with parameters set by software. Also fea-tured in the OU is a continuity test circuit, a phototransistor for LED lighting diag-nostics and a serial port for external programming interfacing.

**Theory**

Initially, some theory on AC and capacitance is covered. In the middle of the section some interdisciplinary theory of LEDs is covered. In the final part of the theory sec-tion some engineering principles for LED power supplies are covered.

**Alternating Current**

AC consists of a voltage and a current which alternates with a sinusoidal waveform [6]. The periodicity of the waveform, in European grid, is 50 . A load draws appar-ent power ( ) which consists of a voltage and a current, see formula (3). Apparent power can be broken down into two different components. The components are re-ferred to active power ( ) and reactive power ( ), see formula (4). AC has another important property called the phase angle (∅) which comes from the sinusoidal be-haviour. The phase angle in a circuit at a specific node is the difference between volt-age and current in time, voltage is the reference and either current leads or lags the voltage in time, see formula (1,2). This phase is angle usually described together with, ∅ , where ∅ is the power factor.

The relationship is usually described in a triangle. Apparent power, denoted , is the hypotenuse, while active power ( ) is on the bottom and reactive power ( ) is the right side. The angle relationship is between S and P. By making modifications in an AC-circuit, by using either inductors (L) or capacitors (C) or resistors (R), the angle will change.

To simplify calculations complex numbers were introduced. Where resistors (R) has only real components, inductors (L) have imaginary components which are positive and capacitors (C) have negative imaginary components [6]. The imaginary compo-nents are called reactance, − . These reactances form an impedance which will have a phase angle in the complex plane. And if the impedance is not present in a formula its phase angle contribution is appended to the current e.g., 15°. This phase angle also denotes how much active power or reactive power is produced. Hav-ing a current magnitude of 1 with a phase angle of 0° would mean 0 and 1 . Having a current magnitude of 1 with a phase angle of 90° would mean 1 and 0 . Both these could be said having 1 . The magnitude of the current is not changed even though the phase angle changes.

where is the voltage, is the current, is the impedance, is the inductive reac-tance, is the capacitive reactance, is the angular velocity of an alternating cur-rent and its respective frequency.

**Thermal energy in an AC-circuit**

Thermal energy is called Joule heating or Ohmic heating in electrical circuits [6]. In an AC-circuit the thermal energy is given by resistive loads. In AC-circuits a load can be calculated by using formula (9). Usually, the circuit is not purely resistive, which means that the formula (9) needs to be modified if average power is of interest. The formula then is modified into formula (10). The heating power only has a resistive component which is the real part of the impedance. This means that imaginary parts or reactive power has no joule heating. If reactive loads are being used that shouldn’t increase the thermal energy in the AC-circuits.

In an ideal situation the capacitors and inductors wouldn’t produce any thermal en-ergy. The real capacitors and inductors have a resistive component to them and in-ductive or capacitive component, known as equivalent series resistance (ESR), equivalent series inductance (ESL) and self-capacitance. This resistive component is a small part of the total impedance of the component. Capacitors and inductors will then contribute to overall thermal energy in a circuit [7].

### Capacitors

Capacitors are built up by having parallel conducting surfaces facing each other and collecting positive charges on one side and negative charges on the other one [7]. Between these surfaces a dielectric is required, it can be made of many different ma-terials, including air. This means that even two wires lying next to each other is a capacitor, although with a very small capacitance. The dielectric material is what gives the capacitor its name: film capacitors, ceramic capacitors, mica capacitors, electrolytic capacitors and vacuum capacitors.

In a capacitor a charge between the two conducting areas will create an electrical field [7]. The electrical field will increase in strength if voltage potential is rising and decrease in strength when the distance between the plates increases, see formula (15). An electrical field also loses its strength if the opposing plates are orthogonal. They should be parallel for optimal strength.

Where is the electrical field strength, is the force of the field, is the electrical charge and is the distance between the dielectric surfaces.

Capacitance is the ability of a capacitor to store energy and the unit is called Farad, see formula (16) [6, 7]. One farad is when one coulomb per plate with one volt being the potential over the capacitor, one plate has a positive charge and the other one has a negative charge. A capacitor is charged up over time, see formula (17). What can be seen about the capacitance is that if permittivity or area increases then the capaci-tance increases and if distance increases then capacitance decreases, see formula (18).

When a capacitor is empty and connected to a DC power supply then a current will be created that charges the capacitor [7]. Initially the capacitor behaves as a short circuit, due to the rush of charges into the unsaturated surface materials. Already after one time constant (denoted , see formula (19)) the capacitor has reached 63% charge. The current will taper off after 5 when it is approximately 99% charged and behave as an open circuit. When discharging the opposite happens, 63% of the charge is lost after 1 . When finding out how much energy, denoted , that is stored in a capacitor one can use the kinetic energy formula with some modifications, see formula (22).

The capacitor current is a function of the time derivate of the voltage [7]. If the volt-age is steady, DC, there is no current flow. In the case of steady sinusoidal AC voltage across the capacitor then a simplified mathematical solution can be used with the frequency. This is the reason why capacitors ‘block’ DC and ‘pass’ AC.

**The dielectric**

The dielectric is the material that gives the capacitor its properties and is expressed as permittivity [7]. The dielectric constant is the relative permittivity, , which is used to calculate the capacitance of a capacitor. Vacuum has the dielectric constant of one.

Dielectric breakdown strength is an important characteristic for a dielectric [7]. This is the measure of the material to withstand high voltage potential differences. It is measured in 10 AC per mm or 50 DC per mm. If a voltage potential difference is greater than the dielectric breakdown strength, then a current will start to flow across the conductors. This called a dielectric breakdown. When this happens, the dielectric can either be damaged or recover when the voltage potential difference is reduced. In power transmission a gas called sulfurhexaflourid ( ) is used as a die-lectric and it recovers as soon as the voltage potential difference is lower. Many die-lectric gases have this ability. Many dielectrics don’t survive a break down such as electrolytical capacitors, film capacitors and other solids. The dielectric strength is influenced by temperature, frequency and the electrodes.

The dissipation factor is the third factor in dielectrics [7]. This factor is the ratio of equivalent series resistance (ESR) and reactance ( ). It is also the inverse of quality factor of a capacitor. ESR is more than just the dielectric resistance and is composed of insulation resistance (dielectric) and series resistance e.g., solder, wire resistance and end connections. As seen in the formula (14, 8) the dissipation factor increases with frequency. In the same formula (14) it can be seen that the loss is the ratio of real power and apparent power. Dissipation factor is called many things: tangent of loss (tan ), loss angle and power factor of capacitors.

There is also dielectric absorption. Dielectric absorption happens when a capacitor is discharged [7]. The capacitor reaches zero charge but then the dielectric reorients into original state and an increase of charge happens and a small voltage across the capacitor can be seen. This small charge will disappear over time and the voltage potential will be zero. Electrolytic and electrochemical capacitors have the biggest influence of dielectric absorption. This process can be quickened by using a short-circuit.

**Different types of capacitors**

Capacitors are usually divided into three main categories: electrostatic capacitors, electrolytic capacitors and electrochemical capacitors [7].

Electrostatic capacitors are non-polar. Non-polar capacitors can be placed with ei-ther lead on the positive side. The capacitors can tolerate AC because of being non-polar. There are several different ones: ceramic, mica, vacuum, plastic and- paper film or foil.

#### Electrostatic capacitors

Film capacitors use a plastic compound as a dielectric [7]. There are a few different dominating plastics: polyester, polypropylene, polyethylene naphtalate (PEN), poly-phenylene sulphide (PPS) and polycarbonate. Film capacitors are normally the go to capacitor for AC. Polyester type has high dielectric constant, low cost, high dielectric strength and high maximum operating temperature but varying dissipation factor with temperature, then the losses tend to be non-linear for polyester capacitors. The dissipation factor makes it hard to use the polyester type for high frequency applica-tions. Polypropylene has low dissipation factor, low dielectric absorption and good stability for higher frequencies but low dielectric constant and maximum tempera-ture is 105° . PPS has excellent properties, very low temperature change in capaci-tance, very low change in capacitance over time and a low dissipation factor. The big shortcoming of PPS is the low dielectric constant. This makes them large compared to other capacitors with the same capacitance.

Film capacitors also come with metal infused in the dielectric and is becoming more dominant [7]. The metals that are being used is aluminium and zinc, either by them-selves or a combination. Silver can also be used in combination with the other metals. Zinc makes the capacitor more stable but is very sensitive to oxidation, which will degrade the capacitor. Metal improves the film capacitors in many ways but have disadvantages as well. One of the advantages are self-healing if there is a dielectric breakdown. When the break down happens, the metal will react and isolate the weak spot, this will give a little lower capacitance but greatly improve lifetime of the ca-pacitor. Other advantages of metallized capacitors are smaller size for equal capaci-tance. Also, if the capacitor stops working despite self-healing, the capacitor will be an open circuit while regular film capacitors will likely be a short circuit. A short circuit will likely damage other components because of thermal runaway. Disad-vantages are that the capacitors are sensitive to humidity, when being manufactured air voids can be present which decrease capacitance, very low tolerance for overvolt-age.

Mica is a good dielectric [7]. It has excellent working voltage, up to 70 and Mica-paper capacitors can exceed 150 and withstand 100 in surge current. Mica is very resistant to heat, chemicals and radiation. Mica has very low dissipation factor, 0.0001 to 0.0004. The dissipation factor is also very stable over time. This makes the capacitor very linear with increasing frequency. Mica has very low loss of capacitance over time and it is linear, 0.1% per year in stable environment. When being manu-factured the capacitors have very low tolerances, +/− 1%. Mica capacitors are ex-pensive and have a low dielectric constant, from 5 to 7 , which makes them larger relative to their capacitance.

Glass is the best dielectric when it comes to performance [7]. Glass capacitors have very low dissipation factor even at high frequency, 1 ℎ . They can also have lifetime up to 50 years without degradation. The capacitance is small, the capacitors are very expensive and only used when extreme precision is needed.

**Table of contents :**

**1 Introduction **

Problem

Aim

Used methods

Delimitation

Acronyms and abbreviations

**2 Background and theory **

Background

The 48𝑉𝐴𝐶 Optical Unit

Theory

Alternating Current

Thermal energy in an AC-circuit

Capacitors

Permittivity

The dielectric

Different types of capacitors

Lighting measurement

LED

Breakdown issues with LED

Thermal failures in LED

Prototype LEDs

Power supply designs for LED applications

Passive Control

Linear voltage regulator with shorted load protection

Buck Converter

Boost converter

**3 Methods and results **

Method summary

Basic circuit analysis

Choosing components for reactive power

Reactive compensation and rectification

DC power supply

LED-array

Results

Results – basic circuit analysis

Results – reactive components

Results – reactive compensation and rectification

Results – DC power supply

Results – LED array

**4 Analysis and discussion **

Analysis – Basic circuit analysis

Analysis – Reactive components

Analysis – Reactive compensation and rectification

Analysis – DC power supply

Analysis – LED array

Analysis – Impact on social, ethical, the environmental and cost-benefits

**5 Conclusions **

Concluding remarks

Suggestions for further studies

**References **

Appendix A

Appendix B

Appendix C

Appendix D: List of figures

Appendix E: List of tables