A Problem-Solving Approach to Electric Circuits

Inhaltsverzeichnis

1. Frontmatter

2. Chapter 1. Frequency Response and Circuit Analysis in the s-Domain

   Farzin Asadi

   Abstract

   s-domain circuit analysis is a powerful technique used to analyze linear, time-invariant (LTI) circuits containing resistors, inductors, and capacitors by transforming time-domain signals and circuit elements into the complex frequency domain (s-domain). This transformation, achieved through the Laplace transform, converts differential equations describing the circuit’s behavior into algebraic equations in terms of the complex frequency variable s.

3. Chapter 2. Fourier Series and Transform

   Farzin Asadi

   Abstract

   In our study of electric circuits so far, we have primarily focused on circuits driven by sinusoidal sources. However, many real-world signals encountered in electrical engineering are non-sinusoidal, yet often exhibit periodic behavior. This chapter introduces the powerful tool of Fourier Series, which allows us to represent such periodic signals as a sum of sinusoids of different frequencies. Building upon this foundation, we will then explore the Fourier Transform, a technique that extends this concept to analyze non-periodic signals in the frequency domain. Understanding these concepts is crucial for analyzing the behavior of circuits subjected to complex waveforms and for designing systems that operate across a spectrum of frequencies.

4. Chapter 3. Natural Frequencies

   Farzin Asadi

   Abstract

   The natural frequencies of a circuit are the values of complex frequency s that characterize the circuit’s zero-input response. Specifically, if a voltage or current in the circuit has a zero-input response of the form \( {k}_1{e}^{s_1t}+{k}_2{e}^{s_2t}+{k}_3{e}^{s_3t}+\dots \) where k_i are non-zero constant determined by the initial conditions, then that values of s_i are the natural frequencies of the circuit.

5. Backmatter