Electronic Circuits

Introduction

Electronic circuits play a central role in system modeling, providing the foundation for analyzing and designing dynamic systems. By combining basic components such as resistors, capacitors, inductors, and operational amplifiers (op-amps), engineers can represent electrical behavior mathematically and translate it into models applicable to control theory, signal processing, and system dynamics.

Resistor

At the most fundamental level, resistors, capacitors, and inductors describe how circuits respond to voltages and currents. A resistor follows Ohm’s law:

(opposing current and dissipating energy as heat.)

Capacitor

A capacitor stores electrical energy in an electric field, with current proportional to the rate of change of voltage:

Inductor

An inductor, in contrast, stores energy in a magnetic field, where voltage depends on the rate of change of current:

Each of these elements introduces distinct time-dependent behaviors that form the basis of dynamic system responses.

Op-Amp

An operational amplifier is an active circuit element used for amplification and signal processing. Under ideal assumptions (infinite gain, infinite input resistance, and zero output resistance), op-amps can perform operations such as addition, subtraction, integration, and differentiation.

KCL

Kirchhoff’s Current Law states that the algebraic sum of currents entering a node in a circuit is zero:

(This expresses the conservation of electric charge.)

KVL

Kirchhoff’s Voltage Law states that the algebraic sum of voltages around any closed loop in a circuit is zero:

(This expresses the conservation of energy in electrical circuits.)

Summary

Ultimately, electronic system modeling demonstrates how simple building blocks—resistors, capacitors, inductors, and op-amps—combine to form complex behaviors. Through this framework, engineers and scientists can design, predict, and optimize circuits and systems that power modern technologies, from communication networks to robotics and automation.