Circuits and Systems (EE44 Caltech)

EE 44 explores the deterministic analysis of systems and circuits, focusing on the mathematical abstraction of physical systems with a primary emphasis on electrical systems. Students will delve into various deterministic methods for system analysis, including matrix representations, time-domain analysis utilizing impulse and step responses, signal superposition and convolution, Heaviside operator solutions for linear differential equations, and the application of transfer functions, Laplace, and Fourier transforms.

The course places a significant emphasis on electrical circuits, covering a range of examples such as energy and data converters, wired and wireless communication channels, instrumentation, and sensing. Additionally, students will gain exposure to a variety of other applications where deterministic analysis tools can be effectively applied, including public opinion dynamics, acoustic cancellation systems, financial market modeling, traffic analysis, drug delivery systems, mechanical systems dynamics, news cycle prediction, and heat exchange processes.

Through a combination of theoretical study and practical examples, students will develop a strong understanding of deterministic analysis techniques and their real-world applications in diverse fields. EE 44 equips students with the skills necessary to analyze and design systems and circuits with precision and efficacy.

Course: EE44 Circuits & Systems

Objective: Establishing the link between fundamental mathematical concepts and their application in electrical engineering to understand the relationship with the physical world.

Course Overview:

1. Fundamentals:
   • Introduction to mathematical concepts.
   • Relationship with physical phenomena.
2. Circuit Theory:
   • Circuit elements overview.
   • Linear vs. non-linear circuits.
   • Network diagrams.
   • Node and mesh analysis.
   • Time domain analysis.
3. System Theory:
   • Understanding systems with inputs and outputs.
   • Modeling system behavior.
   • Impulse, step, and sinusoidal responses.
   • Operator theory and analysis.
4. Frequency Domain Analysis:
   • Transition from time to frequency domain.
   • Complex frequency domain.
   • Transfer functions, poles, and zeros.
   • Laplace and Fourier transforms and their applications.
5. Time and Transform Constants:
   • Introduction if time permits.

Course Focus:

• Emphasizing the mathematical model of the physical world.
• Practical applications of mathematical concepts in electrical engineering.
• Meeting experimental results in physics

Instructor: Hajimiri.