Labsson 3: Capacitors, Diodes, and LEDs - madibabaiasl/mechatronics-course-v1 GitHub Wiki

Capacitors are fundamental components in electronics. Capacitors are ubiquitous in electronic circuits, and their importance in mechatronics cannot be overstated. As devices that store and release electrical energy, they find extensive use in filtering, timing, and energy storage applications.

At its core, a capacitor is a simple device consisting of two conductive plates separated by an insulating material known as the dielectric. When a voltage is applied across these plates, an electric field is created, allowing the capacitor to store energy in the form of an electrostatic charge. This ability to store and release charge makes capacitors invaluable in managing power supply fluctuations that can provide stability in sensitive electronic circuits and controlling the timing and frequency of electrical signals.

Capacitance is the fundamental property defining how much charge a capacitor can store. The maximum voltage the capacitor can handle without failure specifies its voltage rating.

Let's begin with a warm-up activity to get a hands-on feel of what capacitors are and how they function.

In this activity, you will construct a simple capacitor using everyday materials. This will help you understand the basic principles of how a capacitor works, including concepts of capacitance, dielectric material, and the effect of surface area and separation distance on capacitance.

Safety Notes:

• Be careful when handling the aluminum foil to avoid cuts.

What you will need:

• Aluminum foil (two sheets)
• Parchment paper (two sheets): they must be longer and wider than aluminum foils to avoid the foils touching each other
• Two electrical leads
• Multimeter capable of measuring capacitance
• ruler, scissors, tape, large-sized straw

What you should do:

• Cut two rectangular pieces of aluminum foil, each measuring about 55 cm long. These will act as the capacitor plates.
• Cut two pieces of parchment paper slightly larger than the foil. The parchment papers will act as the dielectric – the insulating layer between the two conductive plates.
• Place the parchment paper on a flat surface.
• Lay one piece of aluminum foil on top of the parchment paper.
• Place the second piece of parchment paper over the first foil sheet, ensuring it fully covers it.
• Finally, place the second foil sheet on top of this layer. Make sure the foil sheets do not touch each other; they should be separated by the parchment paper.
• Tape one electrical lead to each piece of foil. Ensure good contact between the clip and the foil.
• Utilize a single large-sized straw to carefully roll the sheets, ensuring that the leads remain accessible and extend outward. Tape the roll.
• Measure the capacitance using your multimeter set to measure capacitance. It will likely be in the range of a few nanoFarads (nF) Take a picture of your measurement (3 points).

My fancy capacitor looked something like this:

Answer these questions:

• How will changing the surface area of the plates affect the capacitance (3 points)?
• What is the role of the dielectric material (3 points)?
• How might the thickness and type of dielectric material affect the capacitance (3 points)?

Now let's see how a capacitor works.

When a capacitor is connected to a battery, the battery applies a potential difference (voltage) across the capacitor's plates. Here's what happens:

Charging Phase:

• Initially, the capacitor is uncharged, and its voltage is zero.
• Once connected to a battery, electrons start accumulating on the plate connected to the negative terminal of the battery. Simultaneously, electrons are removed from the plate connected to the positive terminal, creating a positive charge.
• This accumulation of charge on the plates creates an electric field in the dielectric, leading to energy storage within the electric field.
• The charging continues until the voltage across the capacitor equals the battery voltage.
• The equation for the voltage across the capacitor during the charging phase is

$V_c(t) = V_s (1-e^{-\frac{t}{RC}})$

Where $V_s$ is the supply voltage.

Here is an animation of what happens (note that here the dielectric material is the air):

Discharging Phase: (note the questions with points)

• The dielectric has high resistance but it is not infinite, so over time this causes the capacitor to discharge.
• When the capacitor is disconnected from the battery and connected to a circuit (like a resistor), it begins to discharge, releasing its stored energy.
• During discharging, the voltage across the capacitor decreases exponentially over time, following the equation $V(t) = V_0 e^{-\frac{t}{RC}}$, where $V_0$ is the initial voltage.

Some Useful math about capacitors:

• The amount of charge $Q$ on the capacitor is directly proportional to the voltage $V$ across it. Mathematically, $Q = CV$, where $C$ is the capacitance of the capacitor (usually measured in Farads (micro or nano)).
• The energy $E$ stored in a capacitor is given by $E = \frac{1}{2}CV^2$.
• The current $I$ through the capacitor during charging or discharging can be expressed as $I = C \frac{dV}{dt}$, where $\frac{dV}{dt}$ is the rate of change of voltage across the capacitor. Based on the above formula for the voltage of capacitor during discharging, find an equation for the current during discharging (7 points).
• In an RC circuit (a circuit with a resistor and a capacitor), the time constant $\tau$ is a crucial factor. It is given by $\tau = RC$, where $R$ is the resistance and $C$ is the capacitance. The time constant represents the time it takes for the voltage across the capacitor to reach approximately 63.2% of its final value during charging, or to drop to about 36.8% of its initial value during discharging. Prove this (7 points).

Frequency Response:

Capacitors respond differently to DC and AC electricity. When a capacitor is connected to a DC power source like a battery, it starts accumulating charge. The current is initially high as the voltage difference between the uncharged capacitor and the battery is maximum. As the capacitor charges, this voltage difference decreases, leading to a decrease in the charging current. When the capacitor is disconnected from the power source and connected to a load (like a resistor), it releases its stored energy. The discharging current initially is high and decreases over time as the capacitor loses its charge (as we saw above). From here, we can conclude that DC cannot pass through the capacitor as it gets blocked.

Now, after the capacitor is fully charged, we reverse the polarity of the battery. Again we get a spike of current which quickly drops to zero:

What if we do this faster like in the case of AC electricity? With AC, before the electrons drop to nothing and the current goes to zero, the polarity is reversed and this will continue the current:

Therefore, we can conclude that capacitors block DC but allow AC to pass. This property is utilized in circuits to separate AC and DC components of a signal. The faster the alternating current, the faster it passes through the capacitor. In fact, in AC circuits, capacitors exhibit reactance (Similar to resistance in DC), which varies with frequency. The capacitive reactance $X_C$ is given by $X_C = \frac{1}{2 \pi fC}$, where $f$ is the frequency of the AC signal. From this formula, we see that as the capacitance increases, the reactance decreases, and as the frequency increases, the reactance also decreases. This property is essential in filtering applications, as capacitors can block low-frequency signals while allowing higher-frequency signals to pass.

Note that the Capacitance ($C$) of a parallel plate capacitor is directly proportional to the surface area ($A$) of the plates. The formula for capacitance is given by $C = \varepsilon \frac{A}{d}$, where $\varepsilon$ is the permittivity of the dielectric material and $d$ is the distance between the plates. Increasing the plate area increases the capacitance. This is because a larger area allows more charge to be stored on the plates for a given voltage across the capacitor. A larger capacitance (due to larger plate area) means that, for the same rate of voltage change, the current will be higher.

The schematic drawing for a capacitor in circuits is:

Some capacitors can be polarized meaning that they can have positive and negative sides like one of type of the capacitor that we have in the kit:

Understanding the important ratings of capacitors is crucial for their proper selection and use in mechatronics systems. Here are the key ratings for capacitors:

1. The Capacitance Value that we talked about and is usually given in Farads (F), microfarads (µF), nanofarads (nF), or picofarads (pF). It indicates the amount of charge a capacitor can store at a given voltage.

2. Another important rating is the Voltage Rating. It specifies the maximum voltage a capacitor can handle. Remember I told you anything can conduct electricity if we apply enough voltage to it? The insulator inside the capacitor has a breakdown voltage. Therefore, if we exceed this voltage, we literally can make the capacitor a short circuit. Always choose a capacitor with a voltage rating higher than the circuit's maximum operating voltage.

3. Polarity (for polarized capacitors like electrolytic) indicates the correct orientation of the capacitor in the circuit. Incorrect polarity can lead to capacitor failure.

The above ratings are important ratings of the capacitors, but there are other ratings as well. For example, tolerance indicates how much the actual capacitance can vary from the stated value. Common tolerances are ±5%, ±10%, and ±20%. Critical applications may require capacitors with tighter tolerances. Temperature Coefficient describes how capacitance changes with temperature. This can be important in applications where the capacitor will experience temperature variations. Equivalent Series Resistance (ESR) is a measure of the internal resistance of the capacitor. This affects how quickly a capacitor can charge and discharge. Low ESR is desirable for high-frequency applications. Leakage Current is the small amount of current that flows through the capacitor when it's fully charged. This is important for applications where capacitors must hold a charge for a long time. Dielectric Type determines many of the capacitor's performance characteristics. Common types include ceramic, and electrolytic. When selecting a capacitor, it's crucial to consider all relevant ratings for your application.

Class activity: Review several capacitors' datasheets from the link below and make sure that you understand their key ratings. Discuss how these ratings would affect the capacitor's performance in different circuit applications (7 points).

https://www.digikey.com/en/products/category/capacitors/3

Capacitor values are typically marked on their bodies, but the marking methods vary depending on the capacitor type and size.

For polarized Electrolytic Capacitors that you have in your kit and many other types of capacitors, values are directly printed in µF (microfarads). There also includes the voltage rating. In these capacitors, polarity is marked, usually with a negative (-) stripe.

For Ceramic Capacitors that you also have in your kit, they usually have some digits written on them. The first two digits indicate the capacitance value, and the third digit is the multiplier and the result is in pF (Picofarads). For example, '104' means 10 followed by 4 zeros, i.e., 100,000 pF or 100 nF. Remember that Micro is $10^{-6}$, Nano is $10^{-9}$ and Pico is $10^{-12}$.

When capacitors are connected in a circuit, they can be arranged in either series or parallel configurations.

Capacitors in Series

In a series arrangement, the capacitors are connected end-to-end, with the positive plate of one connected to the negative plate of the next. The formula for calculating the total or equivalent capacitance ($C_{eq}$) of capacitors in series is similar to the formula for resistors in parallel:

$\frac{1}{C_{eq}} = \frac{1}{C_{1}} +\frac{1}{C_{2}}+\frac{1}{C_{3}}+...$

The equivalent capacitance of a series combination is always less than the capacitance of any single capacitor in the series. In a series circuit, the total voltage across the capacitors is the sum of the voltages across each individual capacitor. The voltage is inversely proportional to the capacitance ($V = \frac{Q}{C}$), meaning a capacitor with a smaller capacitance will have a higher voltage across it. The same charge flows through each capacitor in series. The charge on each capacitor is the same and equal to the total charge.

Capacitors in Parallel

In a parallel arrangement, the positive plates of all capacitors are connected together, and all the negative plates are also connected together. The formula for calculating the total or equivalent capacitance ($C_{eq}$) of capacitors in parallel is similar to the formula for resistors in series:

$C_{eq} = C_1 + C_2 + C_3 + ...$.

This means that the equivalent capacitance is simply the sum of the individual capacitances. The equivalent capacitance of a parallel combination is always greater than the capacitance of any single capacitor in the parallel group. In a parallel circuit, the voltage across each capacitor is the same and equal to the total voltage across the parallel combination. The total charge stored in the capacitors is the sum of the charges stored in each individual capacitor. A larger capacitance in parallel will store more charge at the same voltage ($Q = CV$).

Back in the day when I was at school, electronic components were not as affordable as they are now. So, some people, especially those interested in electronics, would take apart old devices like TVs, VCRs, and microwaves to find useful parts for their projects. This might sound like a cool treasure hunt, but it was actually pretty risky!

Inside these devices, there are capacitors. By now, you know that capacitors are like energy storage tanks. Even after you unplug the device, these capacitors can still be full of electricity. Touching them could be very dangerous because they can release all that stored energy very quickly. By touching them, you can drop a huge, sudden burst of electricity through your body. At the very least, it could give you a strong shock and throw you back. But in the worst-case scenario, it could be so powerful that it stops your heart.

Diodes are the simplest type of semiconductor devices (they are semiconductors because they conduct electricity under certain circumstances). At its core, a diode is a device that allows current to flow in one direction but not the other. This unidirectional behavior makes diodes invaluable in circuits for tasks like rectification using 4 diodes (converting AC to DC), voltage regulation, and signal modulation.

In this activity, we want to measure the forward bias voltage of a silicon diode and a Light Emitting Diode (LED) using a multimeter.

• Set the multimeter to the diode check function. This setting allows the multimeter to apply a small voltage across the diode to measure the forward voltage drop.
• Connect the multimeter probes to the diode (red to anode, black to cathode).
• Observe the reading on the multimeter, which should display the forward voltage drop and record it.
• Repeat the measurement process with an LED.

The heart of a diode is the P-N junction, formed by joining P-type (lack of electrons) and N-type (excess of electrons) semiconductors. This junction creates a depletion zone (where electrons balance out meaning there is no shortage or excess of electrons). When a P-N junction is formed, electrons from the N-type region (which has extra electrons) diffuse into the P-type region (which has holes or positive charge carriers), and holes from the P-type diffuse into the N-type. This diffusion of charge carriers results in a region around the junction where the free electrons and holes have combined, leaving behind a zone depleted of mobile charge carriers. The depletion zone acts as a barrier to the flow of charge carriers due to its lack of free electrons and holes. This lack of mobile charge carriers results in high resistance in the depletion zone. This high resistance inhibits the flow of current across the junction under normal conditions (when the diode is not forward-biased).

When the diode is forward-biased, which occurs when the anode is connected to the positive terminal of a battery and the cathode to the negative terminal, the external electric field (created by the battery) supports the movement of charge carriers across the P-N junction. This results in reducing the width of the depletion zone. Electrons in the N-type region are pushed towards the P-type region, and holes in the P-type region are pushed towards the N-type region, effectively narrowing the region where they recombine. As the depletion zone narrows, its resistance decreases significantly. This lowered resistance allows charge carriers (electrons and holes) to cross the junction more easily. Once the applied voltage exceeds a certain level, known as the forward threshold voltage, significant current starts flowing through the diode. This threshold voltage (to overcome the depletion zone and to let the charge carriers flow) typically ranges from about 0.6 V to 0.7 V for silicon diodes. In forward bias, the diode conducts electricity, allowing a substantial flow of current. This current consists mainly of electrons moving from the N-type region to the P-type region and holes moving in the opposite direction.

When a diode is forward-biased (turned on), it exhibits a characteristic known as the forward voltage drop. This forward voltage drop is relatively constant for a given type of diode under normal operating conditions. For a silicon diode, this drop is typically around 0.6 to 0.7 volts, while for LEDs, it can range from about 1.8 to 3.2 volts depending on the color and type. When the diode is connected to a voltage source greater than its forward voltage drop, the diode drops its forward bias voltage and "turns on" and conducts current. This current can be high enough to burn the diode. It's crucial to use a current-limiting resistor in series with the diode, especially for LEDs, to prevent excessive current that can damage the diode. The resistor value is chosen based on the desired current and the voltage drop across the diode.

In reverse bias, it blocks current. When the cathode of a diode is connected to the positive terminal of a battery and the anode to the negative terminal, this configuration is known as reverse biasing the diode. In this scenario, the depletion zone widens because the external voltage pulls the electrons in the N-type region and the holes in the P-type region further away from the junction. This action increases the region that is depleted of free charge carriers. As the depletion zone widens, its resistance increases. This higher resistance effectively blocks the flow of current through the diode.

The current-voltage (I-V) characteristic curve of a diode is a graphical representation of the relationship between the current flowing through the diode and the voltage across it. For a typical semiconductor diode, the curve shows that the diode conducts electricity primarily in one direction. At low forward voltages, there is a small leakage current. As the forward voltage increases beyond a certain threshold (known as the forward voltage drop, typically around 0.7 V for silicon diodes and 0.3 V for germanium diodes), the current increases rapidly, indicating the diode is in its conductive state. In the reverse direction, the diode exhibits very high resistance with a tiny leakage current, until a point where the reverse breakdown voltage is reached, beyond which there is a sharp increase in reverse current.

The diode in your kit is the rectifier diode 1N4007 depicted in the figure below. Also, in this figure, you can see the schematic drawing for a diode.

Zener diodes are a type of semiconductor diode that allow current to flow not only from its anode to its cathode, like a typical diode, but also in the reverse direction when the voltage across its terminals exceeds a certain value known as the "Zener breakdown voltage." This unique feature makes Zener diodes particularly useful for voltage regulation purposes. Therefore, Zener diodes are specifically designed to work in reverse bias. They are also designed to break down at the same voltage every time.

When the voltage across a Zener diode is below the breakdown voltage, it behaves like a normal diode – it blocks reverse current. However, once the voltage exceeds this threshold, the Zener diode allows a significant reverse current to flow. This ability to maintain a relatively constant voltage across its terminals (even with changes in load current or supply voltage) makes it an invaluable component in circuits that require stable voltage supply, such as power supplies and voltage reference circuits.

The schematic drawing of a zener diode is like as follows:

Light Emiting Diodes (LEDs) are a type of semiconductor device that emits light when an electric current passes through them. They are a special class of diodes, which harness the movement of electrons in a semiconductor material to create light. Like other diodes, LEDs are made from a semiconductor material, typically formed from a P-N junction. When forward-biased, electrons cross from the N-type material and recombine with holes in the P-type material, releasing energy in the form of photons, which is visible light.

Different semiconductor materials produce different colors of light. For example, gallium arsenide (GaAs) emits infrared light, indium gallium nitride (InGaN) can produce blue light, and a combination of materials can produce white light. LEDs have a characteristic forward voltage drop that varies based on the color (wavelength) of the LED. For example, red LEDs may have a forward voltage of about 1.8 volts, while blue LEDs might be around 3.0 to 3.5 volts. LEDs require a certain range of current to operate effectively. Too little current and the LED will be dim; too much current can damage the LED. This current is typically in the range of 10 to 20 milliamperes for standard indicator LEDs.

A resistor is often used in series with an LED to limit the current to a safe value. The resistor value is calculated based on the supply voltage, the LED's forward voltage, and the desired current.

Choosing the correct current-limiting resistor for an LED is crucial to ensure it operates safely and efficiently. Here are the steps to choose a current-limiting resistor for an LED:

• Identify the LED's forward voltage ($V_f$) by measuring it using the diode test of the multimeter or alternatively read it from its information sheet.
• Determine the LED's forward current ($I_f$) which is the recommended operating current ($I_f$) from the LED's datasheet. Standard small LEDs usually operate around 10 to 20 mA. This is the absolute maximum current. You should avoid the max current but also the current should be high enough to make the LED bright.
• Now use Ohm’s Law to calculate the resistance. The voltage drop across the resistor ($V_r$) is the supply voltage minus the LED's forward voltage: $V_r = V_s - V_f$.
• The current through the resistor will be the same as the current through the LED ($I_f$).
• Use the Ohm's law to calculate the resistor needed: $R = \frac{V_r}{I_f}$.
• Now choose a resistor with an appropriate power rating. Calculate the power dissipated by the resistor using $P = RI^2 \text{ or } P = VI$. Select a resistor with a power rating greater than the calculated value for safety. Commonly, a 1/4 watt resistor is sufficient for most small LED applications. Note that you might not find a resistor with the exact calculated value. Choose the nearest higher standard value.

Class Activity: Designing a current-limiting resistor for an LED (make sure to follow steps above and provide pictures to get the full points)

Suppose the following circuit:

You have an LED and you want to design an appropriate resistor to protect it. Suppose that the supply voltage is 5 V.

• Design a resistor that you can safely turn on the LED using the 5 V power source. You may get different amounts for the resistor using different colors for the LED (15 points).

• Implement the circuit on your breadboard, and measure the voltage across the LED. Is it the same as the forward bias voltage of the LED that you measured using the diode test (15 points)?

• Measure the current and verify that it is less than the LED's forward current. Make sure that you choose the right range for current on your multimeter. You should plug the red probe into the correct port based on the current range or else you will burn the fuse (15 points).

Passive components, like resistors and capacitors, have fixed values. For example, a 10k resistor will consistently present 10k resistance, irrespective of the applied voltage.

In contrast, a diode, an active component, exhibits dynamic behavior. Its resistance changes significantly with the applied voltage. When reverse-biased, its resistance is effectively infinite, blocking current flow. This is depicted in the following diagram.

Upon forward-biasing, the diode initially shows infinite resistance, which drastically drops to almost zero ohms once the forward voltage is sufficient to 'turn on' the diode. These transitions from high to low resistance demonstrate the diode's active response to voltage changes, as shown in the diagram below.

Hence, a diode's resistance varies dynamically with the applied voltage, categorizing it as an active component that actively modulates its resistance based on external conditions.

• The grading criteria are as follows:

  • each activity and question according to respective points mentioned throughout the text (total = 90 points)
  • a conclusion paragraph that talks about what challenges you had and how you solved those (5 points)
  • references (disclose the use of AI) (5 points)

• Some useful notes:

  • Keep it concise and to the point.
  • You can use any text editing software that you are comfortable with, like Google Docs or Latex.
  • make sure to provide photos of the activities done when needed
  • include the labsson title and your name in the report

Good luck