INOM
EXAMENSARBETE TEKNIK, GRUNDNIVÅ, 15 HP
STOCKHOLM SVERIGE 2020,
Levitating Magnetic Ball
KARL-EDVIN STRAND
YEMI OTELE
Levitating Magnetic Ball
Department of Applied Physics
Royal Institute of Technology
Karl-Edvin Strand
Yemi Otele
SA114X Degree Project in Engineering Physics, First cycle
Supervisor: Marcin Swillo
2020-05-16
Introduction
This project functions as a way to learn from practical applications of physics. It is intriguing for those who are knowledgeable within the field and for people not so familiar with the subject. The goal is to make a globe levitate in the air with the magnetic force created by a magnetic field. This magnetic field is created by current running through a copper coil with an iron core. The issues to be examined are therefore:
1. Can we get the globe to levitate?
2. If so, how long can we get it to levitate?
Furthermore, a control system is implemented to regulate the position of the globe. As far as industry applications are concerned an analog control system may be desirable for it’s smaller scale or the need to have full signal information. Naturally it also avoids software implementation errors.
For inquiries about the report, refer to respective person for the different parts:
• Karl-Edvin Strand: Process, Results, Error sources, Discussion
• Yemi Otele: Background, Discussion
Background
The magnetic field is generated through current running through a coil with copper wires and iron core. The coil is attached to the roof of a metal frame with three legs. An infrared diode is attached to one of the legs opposite a photo diode to detect where the globe is. The photo diode lets more current through the circuit the more light it detects. This way, when the globe is positioned higher than the operating point, it will cover the photo diode and less current will be provided to the coil thus decreasing the magnetic field strength. And reversely, if it is too low, more current will be provided. See figure below.
Figure 1: Scheme of set-up.
Electronics
This project does not require an advanced knowledge of electronics, but some rudimentary knowledge of how different components should work and how to test them saves time when troubleshooting.
Testing and replacing components that are actually broken reduces the amount of guess work one has to do. What follows is some information on the types of components used in this project.
Diode
(a) Example of LED (b) Example of TVS
Figure 2
In general an ideal diode only permits current to flow in one direction [1]. This can be interpreted as the resistance being zero in one direction and infinite in the other. If a diode is oriented such that it allows current to flow it is called forward biased. If it is oriented in the other direction it is reverse biased.
In this project we use a light emitting diode (LED), a photo diode (PD) and two transient-voltage- suppression diodes (TVS). As the name suggests an LED is designed to turn current into light. A PD works in reverse, i.e. it receives light to generate current. Unlike the previously mentioned diodes a TVS is bidirectional which means that the its orientation in a circuit can be ignored. It designed to lead current only when it reaches a specific voltage.
One can use Ohm’s law to choose a resistor for the LED. With voltage supply (VS) and LED specification for voltage (VLED) and current (ILED):
Operational Amplifier
(a) Example of operational amplifier
(b) Electronic symbol for op-amp
Figure 3
Operational amplifiers, or op-amps, are used in DC circuits to amplify voltage [2]. It does so with a feedback system. There are three terminals; the non-inverting input (+), the inverting input (−) and the output. For the amplification factor, first refer to scheme below.
Figure 4: Simple OP amp scheme.
The amplification factor, G, can be calculated as follows:
G =R1+ R2
R2 (2)
Where Vout = G ∗ Vin, in the specific case above, G = 3. For our circuit, See figure 8. In this configuration the factor by which the input voltage increases is given by the following formula:
G = 8.2kΩ + 3 3kΩ 3.3kΩ ≈ 3.5
An ideal op-amp will have infinite input resistance. This means that no current flows into the + or
− terminals. Ideally there will also be no potential between the input terminals. When using an amp in a circuit one will not see this kind of behavior, but these are important principles to recall when testing the amp with a multimeter (or something similar).
Transistor
(a) Example of transistor (b) Electronic symbol for transistor
Figure 5
A transistor is a three terminal device; base, collector, and emitter. It is designed to control current coming through a circuit (through amplification and switching)[3]. There are three states it can occupy. First there is the active region, where is operates as an amplifier, but for current. That is, the collector current is some factor larger than the base current. Secondly there is saturation. In this state the transistor is completely on and working like a switch. In the third state it also works as a switch which means that the collector current is zero.
In this project we exclusively used a type of transistor known as a Darlington transistor. It is com- posed of two transitors configured in a way such that the current can be amplified even further [4].
It can be seen as having the same three terminals as a typical bipolar transistor.
In this project direct current (DC) is used as opposed to alternating current (AC). The multimeter also had a hFE setting that measures DC gain. This was one way in which transistors were tested.
This ensures that it is actually able to amplify signals. To test that the transistor is switching between states one can remove the connection to base. The base is where the control signal enters the transistor. If the transistor is conducting between the collector and emitter one will see this as a non-zero current reading on the 60 V power supply. This means that the transistor can not go to the open switch state. In that case the transistor might be broken or it is not being operated within it’s specifications.
PD Control
In our model of the problem we want to have both proportional and derivative control. We attain proportional control by detecting light from the LED with a photo diode. The idea being that for a greater error, i.e. when the globe is too far down, we want a stronger signal (higher voltage).
The resistor parallel to the photo-diode has multiple functions. It makes sure a minimum voltage and current goes through the circuit when the photo-diode is entirely covered as no current is going through the photo-diode when that happens. It also affects the effect the photo-diode has, higher resistor gives the photo-diode more effect on the signal as a higher resistance forces the current to go through the photo-diode. However if the resistor parallel to the photo-diode is too high, it will destroy the symmetry in the response of the system from when the capacitor charges and discharges.
Recall the following equation for the current through a capacitor:
i = Cdv
dt (3)
When the photo diode is being covered dvdt will be negative for some time. This leads to an ’un- dershoot’ where the signal not only drops but goes below it’s base level. Since the current for a capacitor is depended on the time-derivative of the voltage we can use them to damp oscillations.
Process and Methods
The project started with both parties researching and reading about circuits and the different com- ponents used in the circuit such as transistors, amplifiers and diodes. Afterwards the first goal was to try and make the globe levitate by replicating the circuit and setup from the previous year. See figure 1.
Figure 6: Circuit at the project’s start.
A measurement was made to see how much current was needed to keep the globe levitating at certain distances from the coil. From the transistor’s specifications, 2 A was desired to run through the coil so the operating point was determined to match with the current. A lot of problems were prevalent during the process such as transistors being destroyed constantly, broken diodes and breadboards with gaps. A lot of time was used trying to figure out how to test the different com- ponents in the circuit. As such, a large part of the project became learning how to debug the system.
The diodes where tested using a digital multi-meter to check its polarity, this was done by turning the pointer on the multi-meter to the diode signal and connect the two sensors to the anode and cathode of the diode. If working properly, it should only show a forward voltage drop in one of the two ways you can connect the sensors.
The amplifier was tested by checking whether or not it gave the right amplification factor when the setup was correct. This was done be measuring the voltage at the non-inverting input and comparing it to the voltage at the output. If the amplifier is working then: Vout = G ∗ V+. Here G is the amplification factor explained in the Operational Amplifier sub-section.
The gap in the breadboard was discovered as some conductors would not work if connected to certain holes in the breadboard.
For the transistor the circuit was modified so that when the photo-diode was completely covered, the transistor would close hence letting no current through to the coil. And reversely, if the photo-diode was completely open, the transistor would open completely. This way, if the transistor was broken, it would still conduct current while the globe completely covered the photo-diode. The modification was made by removing the resistor parallel to the photo-diode, as this would force all the current to pass through the photo-diode. The methods described in the Transistor sub-section was also used.
In the end the transistor model were changed so new data was needed, security measurements were implemented to protect the transistor from the high voltage induced by the coil. The circuit was changed with the goal to give the globe a larger margin of were it can be put and levitate. The circuit structure used at the beginning of the project where slightly adjusted with different values on resistors and a different transistor model. Two power-sources where implemented. With the new circuit a 15V power source was used to drive the circuit while 59,1V was used to drive the transistor. The end result yielded a voltage of 1,401V-1,657V at the output (completely open or shut photo-diode). These values were attained through testing with a scale and adjustable standing.
The globe was placed on the standing that was on top of the scale. The globe was then placed so it just completely covered the photo-diode and the voltage was noted when the scale showed 0g. The same procedure was repeated for the photo-diode when it was half covered and completely covered.
The circuit was then adjusted so the output gave the interval 1,325V-1,489V depending on if the
photo-diode was blocked or open so that the globe would weight close to nothing at and around the operating point.The operating point is at were the globe covers half of the photo-diode. This allowed for levitation for a short period and the globe had to be placed carefully around the operating point with the help of an adjustable standing. This was partially solved by increasing the range of the output to 1.401V-1.657V. The globe successfully levitated in the end and could be carefully placed manually by hand in the magnetic field and stay levitated.
Results
Project start
Figure 7: A graph of current vs. position. The distance is measured from the bottom of the coil to the top of the globe.
At the project’s start, the transistor used was a BD677 Darlington transistor with a maximum voltage rating of 60V. As mentioned, this data gave us the expected current running through the coil depending on the distance.
New circuit and problems
Scheme of new circuit.
completely covered by the globe, it would close the transistor hence a large change in current and magnetic flux occurred. Because of Faraday’s law
Emf = −NdΦB
dt , N = Number of windings on the coil, ΦB = Magnetic flux (4) the induced voltage (emf) reached high numbers, (theoretically infinite depending on how fast the magnetic flux would change or how fast the globe would oscillate in front of the photo diode), which lasted for approximately 30 ms before discharging. This was measured by an oscilloscope by our supervisor. This meant the voltage over the transistor, if the photo diode was covered and uncovered at a high pace, was equal to the voltage from the power source running the transistor plus the induced voltage from the coil. This was high enough to instantly kill any transistor used.
Security measurements for transistor
After many tests with different transistors, the transistor used in the end is a BDX53C transistor with a maximum voltage rating of 100V. In addition to a higher maximum voltage rating, two bi- polar diodes (TVS in the scheme) with 83V forward voltage were used to stop the induced voltage from the coil. This proved to be effective but not ideal as the voltage could potentially still kill the transistor if the oscillation had high enough frequency. Another problem was that the bi-polar diodes could easily be killed if overheated. This happened while soldering one of the bi-polar transistors to the circuit.
Final result
With the new circuit the globe could be carefully placed by hand around the operating point with larger margins for the position and managed to levitate for 4 minutes and 47 seconds (longest measured time). During this time, the voltage at the output went from 1,465V - 1,654V and the current through the coil went from 2A - 2,17A. This specific measurement was done when the coil was already heated up. As such, it’s properties such as inner resistance was different from if the measurement was made when the coil was cool.
The transistor had a fan attached to the heat sink which kept the transistor at a constant tem- perature during the levitation period. Hence earlier problems of transistors overheating is not a problem with the current set-up as the globe falls down before the transistor overheats.
Error sources
Material errors
• The globe used in the project was very buckled and not perfectly symmetrical. Certain points on the globe had a stronger attraction force than others which meant that the globe would spin and rotate so that theses points where pointing upwards towards the coil. This meant the operating point would change depending on the position oh the globe which made it harder to get accurate numbers for the voltage output and levitating distance.
• The specifications of the bi-polar diodes stated that it had a forward voltage of 68V,but when tested, actually had a forward voltage of 83V.
• The photo-diode was not placed in the center of it’s holder. This problem was not resolved.
Human errors
• The levitating distance was measured by hand and naked eye measurement.
• The alignment of the diode and photo-diode was also measured with naked eye measurement.
• The levitating time was measured by a manually controlled timer.
Discussion
Due to the unfortunate situation in the world as of this report with COVID-19 the project came to a halt which slowed down the process. However, time could have been saved if we knew that com- ponents were broken and didn’t enter the project with the mindset that all the components worked as they should. This would have made debugging a higher priority as a lot of time was spent on thinking we did something wrong and we didn’t even consider or didn’t dare to think that perhaps the components were broken. After the first time the transistor model was changed, the operating point was adjusted by had to get the desired output values from the amplifier.
Generally in this project, it was easier to manually using different resistors and circuit setups to try and make the globe levitate. The theoretical calculations and specifications given where used more like a guide line to, for example, determine what resistance should be used at certain points. For future work, methods to cool down the coil is needed as with the current circuit scheme, the heating of the coil is what prevents the globe from levitating longer as it’s inner resistance increases with higher temperature, requiring more current to hold the globe at position. With an average collector current and collector-emitter voltage of around 2 A and 2 V respectively we have 4 W generated in the transistor alone. The collector current is also going through the coil, adding to the power being dissipated. Note: There are methods to alleviate this problem for industrial applications, but they are outside the scope of this project. (Water-cooled cables or superconducting power cables cooled by liquid nitrogen.)
A fan was also attached to the heat sink of the transistor but this method can probably be improved upon. Other improvements also include moving the circuit to one breadboard instead of the current use of two. Using one power source instead of two, this would most likely require a change to the circuit structure.
A tip to future workers on this project is to sort out resistors and structure up the working environ- ment as it gets messy pretty quick when testing with different resistors and working with different components. Also be careful when testing to not overheat the coil too much as it gives misleading data and results (since the properties of the coil changes with temperature) and it could melt the roof it is attached to. It is also suspected that the circuit at the project’s start that was attempted to be replicated doesn’t work as the transistor was already burned out and that the circuit used a 50V power source but the amplifier had a maximum voltage rating of 22V.
References
[1] What is a diode? https://www.fluke.com/en/learn/best-practices/measurement- basics/electricity/what-is-a-diode.
[2] Operational amplifier basics. https://www.electronics-tutorials.ws/opamp/opamp_1.
html?utm_referrer=https%3A%2F%2Fwww.google.com%2F.
[3] Transistors – basics, types baising modes. https://www.elprocus.com/transistors-basics- types-baising-modes/.
[4] Darlington Transistors. https://www.electronics-tutorials.ws/transistor/darlington- transistor.html.
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