Circuit Analysis: AC, Linear Circuits and Transients

Circuit Analysis: AC, Linear Circuits and Transients: key points

Building on Ohm's law and Kirchhoff's laws from "Circuit and electromagnetism basics", this topic takes a step up to the circuit theory taught in the first and second years of university electrical and electronic engineering. Once AC voltages and currents are written as phasors (complex numbers), circuits with coils and capacitors can be solved with simultaneous linear equations just like DC circuits. Transients right after a switch closes are solved with differential equations or the Laplace transform, and the time constant and the damping ratio show how fast the response is and how it oscillates.

The calculations here cover impedance and admittance, resonance, the Q factor and bandwidth of series and parallel RLC circuits, active, reactive and apparent power and power-factor correction capacitors, maximum power by conjugate matching, and the voltages, currents and power of Y and Δ connections in three-phase AC. For linear circuits, the topic deals with nodal and mesh analysis, the superposition theorem, Thevenin's and Norton's theorems (including AC and dependent sources) and the Z parameters of two-ports. For transients, it finds initial and final values from the continuity of capacitor voltage and coil current, and covers the time constants of RC and RL circuits, overdamped, critically damped and underdamped RLC circuits, s-domain equivalent circuits with initial-condition sources, poles of transfer functions, the initial- and final-value theorems, and inverse transforms by partial fractions. Most questions come with a circuit diagram, and the explanations of the AC and transient questions show several solution methods side by side: complex numbers, phasor diagrams, differential equations, the Laplace transform and time-constant rules of thumb. It helps with the electric circuits part of the theory subject of Japan's Electrical Engineer Examination (third class) and with university circuit-theory exercises. The values in the calculation questions, including those of the wrong choices, were checked with Python. Ohm's law and electromagnetism are covered in "Circuit and electromagnetism basics", op-amp and filter circuits in "Analog and electronic circuits", block diagrams, Bode plots and stability in "Control Engineering Basics", the z-transform and digital filters in "Digital Signal Processing Basics", and rectifiers and inverters in "Power Electronics Circuits".