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If you're studying electrical engineering, circuit theory is the most fundamental and essential course. Without a solid understanding of it, you'll struggle to grasp more advanced topics like electric motors, power system analysis, or high-voltage systems. To truly master this subject, the key lies in never stopping your thinking process. This is the most crucial point I want to emphasize. Let me use Jiang Jiguang’s "Circuit Principles" as an example (a highly recommended textbook) to explain why continuous thinking is so important.
Circuit theory is one of the first subjects that helps shape an engineer's way of thinking. Unlike mathematics or physics, where many concepts can be derived theoretically, circuit analysis relies more on logical reasoning and accumulated experience. In Jiang’s book, the first four chapters cover the basics of resistive circuits—reference directions, substitution theorem, branch method, node voltage, mesh current, Thevenin’s theorem, Tellegen’s theorem, and the Reciprocity Theorem. These foundational concepts must be thoroughly understood to excel in later chapters.
How do you get used to this? I always remind myself to stay curious and keep questioning. The exercises at the end of each chapter are not just practice problems—they are a treasure trove for sharpening your mind. Each question is designed to target specific knowledge points and isn’t overly complicated. Solving them consistently builds your confidence and deepens your understanding.
A good engineer should spend more time thinking about the most efficient way to solve a problem rather than getting lost in lengthy calculations. Circuit analysis often involves complex equations, such as a quaternary equation from a node voltage method. These are best left to calculators, allowing you to focus on the logic behind the solution. I recommend investing in a Casio 991 calculator to save time on tedious computations, so you can concentrate on the core concepts.
The first four chapters form the bedrock of your circuit knowledge. Don’t just memorize formulas—understand their origins. Try proving theorems yourself. For instance, Thevenin’s theorem is based on superposition, which only applies to linear circuits. And the superposition principle itself is derived from Tellegen’s theorem. Building this foundation step by step will make the rest of the course much easier.
At first, everything might seem confusing, but trust the process. Over time, you’ll start to see the beauty in circuit theory and even grow to love it. When you finally solve a problem in just a few lines of paper, you’ll feel a sense of accomplishment that makes all the effort worthwhile.
The second half of the course introduces non-linear circuits, which are less demanding in terms of difficulty and exams. They’re also more interesting to study. Then comes the dynamic circuits—first-order and second-order. If you have a good grasp of differential equations, these topics become manageable. The core idea is solving differential equations, and with the right mindset, even second-order circuits can be approached similarly to first-order ones.
One of the most powerful tools in circuit analysis is the three-element method for first-order circuits. Once you understand the initial value, final value, and time constant, you can solve problems without writing out full differential equations. This method simplifies things significantly, and with a bit of creativity, you can apply similar logic to second-order circuits too.
Another fascinating concept is convolution. Many students are intimidated by its name, thinking it's overly complex. But once you understand its essence, it becomes a powerful tool that enhances your circuit thinking. Convolution helps you analyze how signals interact over time, and there are plenty of online resources to help you grasp it better.
Don’t overlook convolution just because your teacher doesn’t emphasize it. It’s a critical concept that can greatly improve your analytical skills. I remember when I first encountered Duhamel’s integral (a type of convolution), it felt like discovering a hidden gem. Even though it was briefly mentioned in the textbook, it had a lasting impact on my understanding of circuit behavior.
Next up is sinusoidal steady-state analysis. This is where circuits transition from the time domain to the frequency domain. It’s a major conceptual shift that allows engineers to simplify complex AC problems using phasors. By representing inductors and capacitors as complex impedances (jωL and 1/jωC), you can solve circuits more efficiently. But to truly master this, you need to trace back to the fundamentals—like Euler’s formula, which transforms sine waves into complex exponentials.
Drawing vector diagrams is essential for visualizing phasor relationships. A well-drawn diagram can reveal hidden information and guide you toward the correct solution. Don’t rush through this step; take the time to understand how each component interacts. Mistakes in the diagram can lead to incorrect results, so precision is key.
Mutual inductance is another tricky topic that many students find confusing. Understanding the “same-polarity†convention is crucial. When currents enter the same polarity ends, the magnetic fields add up, affecting the equations accordingly. Don’t get bogged down by direction assumptions—your reference directions can be arbitrary, and the final result remains valid.
Resonance is a fascinating and practical concept. It plays a vital role in filtering, amplification, and energy transfer. Whether in power systems, communication, or high-voltage applications, resonance is a powerful tool. The basic idea is simple: when the imaginary part of impedance or admittance is zero, resonance occurs. This concept bridges the gap between energy storage and dissipation in circuits.
Three-phase circuits often intimidate students, but they’re actually simpler than they look. Think of them as a normal circuit with three power sources. Once you understand the relationship between line and phase quantities, the complexity fades away. Line voltages are just three times the square root of the phase voltage, and the same goes for currents. Don’t get stuck on terminology—treat them as regular circuits and apply standard methods like node voltage or mesh current analysis.
Laplace transforms mark another significant leap in circuit theory. They allow us to convert time-domain differential equations into algebraic expressions, making complex systems easier to analyze. This transformation is especially useful when dealing with transient responses or non-sinusoidal inputs. Fourier transforms, on the other hand, extend this idea further by analyzing signals in the frequency domain.
To truly master circuit theory, you need both deep thinking and strong calculation skills. It’s not enough to just understand the concepts—you must be able to apply them effectively. Learning circuits takes time, patience, and consistent practice. When you see a professor solve a problem effortlessly, it might seem easy, but that’s the result of years of dedicated study.
During my postgraduate studies, I spent about 100 days immersed in circuit theory. My textbooks were worn out, and I solved over 1,500 problems without repetition. There were moments when time seemed to stop, and I was completely absorbed in the work. The joy of finally solving a difficult problem after hours of thinking was unmatched—it was the best reward I could ask for.
So, if you want to learn circuit theory, you must approach it with passion and dedication. Only then will you truly appreciate its beauty and complexity.