
Thursday, 10 August 2023
The Process of Talent Management - Tips, Strategy, and Challenges

Thursday, 3 August 2023
Curious about Capacitance? Here's What You Should Know
History
The capacitor is an essential component of modern electronics, but its origins can be traced back to the 18th century. The invention of the capacitor is attributed to the Dutch scientist Pieter van Musschenbroek, who created the first capacitor, also known as the Leyden jar, in 1745.
Musschenbroek's invention was the result of his experiment with static electricity. He discovered that by placing a metal object inside a glass jar filled with water, he could store a charge of static electricity. The jar acted as a capacitor, storing the electrical charge on its metal object (Ho et al., 2010, 1). The Leyden jar was a ground-breaking invention that paved the way for the development of modern capacitors. However, it was not until the 19th century that practical capacitors began to be developed.
In 1839, an English natural philosopher named Michael Faraday discovered that a charge stored in a capacitor is directly proportional to its capacitance and the applied voltage. This discovery laid the groundwork for the development of modern capacitors, increasing its capacitance and reliability.
What Is a Capacitor?
Capacitors come in various sizes, shapes, and capacitances. Sizes can vary from as small as a grain of rice or as enormous as a building. Capacitance is measured in Farads (F), however, most commercial capacitors have values that are small in value. The most commonly used capacitors measure around microfarad (μF) to picofarad (ρF) (Nilsson & Riedel, 2015, 182).
Capacitor consists of two conductive metal plates separated by an insulating material, known as a dielectric. This means that electric charge cannot be transported through the capacitor, instead, applying a voltage to the terminals of the capacitor can displace charge within the dielectric, causing a displacement of current (Figure 1).

i = C dv / dt (1)
where i is in amperes, C in farads, and v in volts.
Figure 2 shows the passive sign convention based on Equation 1, which the current reference aligns with the voltage drop (current flows from positive sign to negative sign) across the capacitor. However, if the current reference aligns with the voltage rise (current flows from negative sign to positive sign), Equation 1 is written with a minus sign.

Figure 2
1. If the voltage across a capacitor experiences an instantaneous change, an infinite current then occurs, which is physically impossible.
2. If the voltage across the capacitor's terminals remains constant, there will be no current flow through the capacitor, since a conduction current cannot establish itself in the dielectric material; meaning, to have a displacement current, a time-varying voltage must be applied across the terminals.
Thus, a capacitor behaves like an open circuit in the presence of a constant voltage (Nilsson & Riedel, 2015, 183).
From Equation 1, we can rearrange to obtain a voltage equation:
v(t) = 1/C ∫0t idτ + v(t0) (2)
The capacitor energy equation can be expressed as,
w = 1/2 Cv2 (3)
Capacitance Connection
1. Series
When capacitors are connected in series (Figure 3), they can be simplified to a single equivalent capacitor. It can be achieved by summing the reciprocals of each individual capacitor's capacitance. The summation will equate to the reciprocal of the equivalent capacitance (Nilsson & Riedel, 2015, 188).

The equivalent capacitance equation can be expressed as:
1/Ceq =1/C1 +1/C2 +...+1/Cn (4)
If each capacitor carries an initial voltage, the equivalent capacitor's initial voltage is the sum of the individual capacitors' initial voltages. The voltage equation is obtained through:
v(t) = v1 (t) + v2 (t) + ... + vn (t) (5)
2. Parallel
When capacitors are connected parallel (Figure 4), they can be simplified into an equivalent circuit by summing the capacitance of the individual capacitors.

Figure 4
The equivalent capacitance equation can be expressed as:
Ceq = C1 + C2 + ...+ Cn (6)
When capacitors are connected in parallel, they must all have the same voltage. Hence, if an initial voltage is present across the original parallel capacitors, the equivalent capacitance Ceq will also have the same initial voltage.
v(t) = v1(t) = v2(t) = ... = vn(t) (7)
Type of Capacitor
We will now introduce the many different types of capacitors used in industry, each with their own unique characteristics and applications. The most commonly used and inexpensive capacitor found in electronics is the ceramic capacitor (Figure 5). Ceramic capacitors have a small size and high stability, making them ideal for use in high-frequency applications.

Figure 5
For circuits needing higher capacitance than what a ceramic capacitor is capable of, an electrolytic capacitor (Figure 6) is then required. Electrolytic capacitors have a polarized design, meaning that they have both a positive and negative terminal. While able to store more energy in its body, being polarized opens up the risks of breaking if it is installed in the incorrect orientation.
Figure 6
For higher stability and reliability, Tantalum capacitors (Figure 7) are often used, and they are also used in applications where space is limited. Some other benefits to using Tantalum capacitors over ceramic and electrolytic capacitors are that they offer higher performance and greater longevity, but at a greater expense.

Figure 7
Finally, film capacitors (Figure 8) are ideal for circuits that require high-frequency operation and high accuracy.

Figure 8
ApplicationThe popular usage of capacitors in the engineering world is to filter and smooth electrical signals. Any electronic equipment will produce electrical noise in the carrier of various frequency bands. Electronic equipment can also generate radio interference in the high frequency range. Therefore, the capacitor and other electrical passive elements can act as a filter to minimize noise and interference.
In a power supply, the output signal will never be steady. There is always a fluctuation known as ripple. The ripple produces overheating and power losses which jeopardizes the equipment efficiency. Thus, a filter circuit consisting of capacitor or a combination of electrical passive components is used to reduce the ripple at the output.
Conclusion
Each type of capacitor has its unique characteristics and applications, and choosing the right capacitor for a particular application is crucial for the performance and reliability of the circuit. By understanding the properties of different types of capacitors, designers can make informed decisions about the best capacitor to use for a particular application.
References
Ho, J., Jow, T. R., and Boggs, S. (2010). Historical introduction to capacitor technology. IEEE Electrical/Insulation Magazine, 26(1), 20-25. 10.1109/MEI.2010.5383924
Riedel, S. A., and Nilsson, J. W. (2015). Electric Circuits. Pearson.
Khoa Tran is an electrical engineer working at the Los Angeles Department of Water and Power and is currently pursuing his master's in electrical Power from the University of Southern California. He is fluent in both Vietnamese and English and is interested in outdoor activities and exploring new things.
Thursday, 27 July 2023
What is Coulomb's Law? An Introductory Guide

| Particle | Charge (C) |
| Proton (p) |
|
| Electron (e) |
-1.60218 x 10-19 |


Khoa Tran is an electrical engineer working at the Los Angeles Department of Water and Power and is currently pursuing his master's in electrical Power from the University of Southern California. He is fluent in both Vietnamese and English and is interested in outdoor activities and exploring new things.
Thursday, 20 July 2023
Demystifying Impedance: A Comprehensive Guide

In this blog, we will go over a fundamental concept in electrical engineering, specifically a core component in modeling alternating current (AC) circuits. Impedance refers to a component's natural opposition to the flow of alternating current in an electrical circuit.
What Is Phasor?
Before discussing what impedance is, I would like to address what a phasor is. Understanding phasor will help break down the complex concept of impedance.
A phasor is a type of complex number that contains information about both the amplitude and phase angle of a sinusoidal function. A phase angle is the angular difference between two sinusoidal signals of the same frequency. You can refer to Figure 1 for an illustration of the phase angle between two sinusoidal waves.
The mathematical concept is based on Euler's identity, which shows how the exponential and trigonometric functions are related (Nilsson & Riedel, 2015, 310):
From Equation 1, we can see cosine represented as the real part and sine represented as the imaginary part of the exponential function. The R denotes "the real part" and I denotes "the imaginary part".
In this example, the cosine function is represented as a voltage function to analyze the phasor representation:
Equation 2 represents the voltage function in the frequency domain, where ω is the angular frequency,
From Equation 1, there is another abbreviation form of the exponential function ejθ or phasor form.
What Is Impedance?
Impedance is a complex quantity that combines both resistance and reactance. Resistance is classified as the opposition of flow in direct current (DC), while reactance is the opposition of flow in AC; this is due to capacitance and inductance. Impedance is also measured in ohms (Ω), where the real part of the complex function is resistance, and the imaginary part denotes reactance. The mathematical representation of impedance is given by the following equation:
where Z, R, and X are impedance, resistance, and reactance, respectively (Nilsson & Riedel, 2015, 318).
In AC circuits, impedance plays a critical role in determining the behavior of the circuit, as it affects the voltage drop and the current flow. Impedance of an AC circuit is calculated using Ohm's law, which relates current to voltage and to impedance. The equation for Ohm's law is
where V is the voltage, I is the current, and Z is the impedance.
From here, we will evaluate the impedance of the resistor, inductor, and capacitor.
Impedance of Resistor
The equation of current in terms of cosine is given as i = I1cos(ωt + θ) and when combined with Ohm's Law (Nilsson & Riedel, 2015, 315), the resulting voltage equation of the resistor is
where I1 is the maximum amplitude, and φ is the phase angle (degree) of the current.
Voltage can then be rewritten as
From Equation 1, I1 < θ is the phasor form so we can write the voltage equation:
Impedance of Inductor
Given the equation of current in terms of cosine, i = I1 cos(ωt + θ) and the expression of inductor voltage, L di/dt (Nilsson & Riedel, 2015, 316),
we are able to rewrite Equation 10 as a cosine function:
The inductor voltage can be illustrated in the phasor form:
From Equation 1, we can simplify e-j90°
This allows Equation 12 to be further simplified to
Therefore, the impedance of inductor can be represented as
The equation of voltage in terms of cosine is v = V1 cos(ωt + θ), and the expression of capacitor current is C dv/dt (Nilsson & Riedel, 2015, 317).
We can rewrite Equation 16 as a cosine function:
The capacitor current can be illustrated in the phasor form:
Using Equation 13 and combining with Equation 18, we then are able to simplify the current further to
The voltage of capacitor can be expressed as
Therefore, the impedance of capacitor can be represented as
Application of Impedance
Impedance has numerous real-world applications in electrical engineering, including filter design, power electronics, antenna design, and audio systems. In filter design, impedance is used to control the flow of current, allowing only specific frequencies to pass through a given system. In power electronics, impedance is used to regulate the flow of current, ensuring efficient operation of the circuit. Antenna design requires impedance matching to ensure maximum power transfer of a signal or signals. Finally, in audio systems, impedance is used to match amplifiers to speakers for optimal sound quality.
1. Impedance in Transmission Line
Impedance matching is a critical factor in the design of transmission lines used to transmit electrical signals over long distances. The impedance of the transmission line needs to match the impedance of the load to ensure maximum power transfer, otherwise, any mismatch in impedance will result in a partial reflection of the energy and signal loss.
The equation for the impedance of a transmission line is
where Z0 is the characteristic impedance of the transmission line, L is the inductance per unit length, and C is the capacitance per unit length.
2. Impedance Measurement and Testing
Impedance measurement and testing are essential in many fields of electrical engineering, including telecommunications, audio systems, and power electronics. Impedance meters and testers are used to measure impedance, and the techniques used depend on the application.
Conclusion
Impedance is an essential function in modeling AC circuits; it can be easily derived as the inherent resistance of electrical components. Understanding impedance allows for real-world applications and problem-solving of systems in the frequency domain. These applications can range from small signal designs of antennas in cell phones to long-distance power transfer of transmission lines.
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References
Riedel, S. A., & Nilsson, J. W. (2015). Electric Circuits. Pearson
Khoa Tran is an electrical engineer working at the Los Angeles Department of Water and Power and is currently pursuing his master's in electrical Power from the University of Southern California. He is fluent in both Vietnamese and English and is interested in outdoor activities and exploring new things.
Thursday, 13 July 2023
Mastering Employee Onboarding: Key Strategies for Success

Anna Taylor is a freelance writer and avid researcher- a jack of all trades, but a master of none. She graduated from the University of Hawai'i with an Associate Degree in Liberal Arts because she had no idea what she wanted to be when she grew up. She has since found her love of Extended Reality and the possibilities it brings to the world, as well as gardening, cooking, and writing. Anna lives in Interior Alaska with her family.
Thursday, 6 July 2023
How to Deal with FE Exam Test Anxiety

How to Overcome Anxiety
Khoa Tran is an electrical engineer working at the Los Angeles Department of Water and Power and is currently pursuing his master's in electrical Power from the University of Southern California. He is fluent in both Vietnamese and English and is interested in outdoor activities and exploring new things.
Instructor Spotlight: Madison Rose Florian, PMP, PMI-ACP

