Circuit Analysis: Kirchhoff's Laws & Theorems

Circuit Analysis

• ** Kirchhoff's Laws: **
  • KVL (Kirchhoff's Voltage Law): Sum of voltage changes around a closed loop is zero.
  • KCL (Kirchhoff's Current Law): Sum of currents entering a node is equal to sum of currents leaving a node.
• Thevenin's and Norton's Theorems:
  • Thevenin's Theorem: Represents a complex circuit as a single voltage source and series resistance.
  • Norton's Theorem: Represents a complex circuit as a single current source and parallel resistance.
• AC Analysis:
  • Impedance (Z): Total opposition to current flow in an AC circuit.
  • Phasors: Represent AC signals as rotating vectors in the complex plane.

Microcontrollers

• Microcontroller Types:
  • 8-bit (e.g., AVR, PIC)
  • 16-bit (e.g., MSP430)
  • 32-bit (e.g., ARM Cortex-M)
• Microcontroller Components:
  • CPU (Central Processing Unit)
  • Memory (Flash, RAM, EEPROM)
  • Input/Output (GPIO, UART, SPI, I2C)
  • Timers and Counters
• Programming Languages:
  • Assembly Language
  • C and C-derived languages (e.g., C++, Arduino)

Signal Processing

• Types of Signals:
  • Continuous-time signals (analog)
  • Discrete-time signals (digital)
• Signal Operations:
  • Filtering (Low-pass, High-pass, Band-pass, Notch)
  • Amplification
  • Modulation (Amplitude, Frequency, Pulse-width)
• Fourier Analysis:
  • Fourier Series: Representation of periodic signals as a sum of sinusoids.
  • Fourier Transform: Representation of non-periodic signals as a continuous spectrum.

Electronic Circuits

• ** Passive Components: **
  • Resistors (R)
  • Capacitors (C)
  • Inductors (L)
• Active Components:
  • Diodes (Rectifier, Zener, LEDs)
  • Transistors (BJT, FET)
  • Operational Amplifiers (Op-amps)
• Circuit Configurations:
  • Series and Parallel Connections
  • Voltage Dividers
  • Current Mirrors

Robotics

• Robot Types:
  • Autonomous (Self-driving cars, drones)
  • Remote-controlled (RC cars, robotic arms)
  • Hybrid (Combination of autonomous and remote-controlled)
• Robot Components:
  • Sensors (Sonar, Camera, GPS, IMU)
  • Actuators (Motors, Servos, Pneumatic cylinders)
  • Control Systems (Microcontrollers, Computers)
• Robotics Algorithms:
  • Motion Planning
  • Obstacle Avoidance
  • Localization and Mapping

Circuit Analysis

• Kirchhoff's Voltage Law (KVL) states that the sum of voltage changes around a closed loop is zero.
• Kirchhoff's Current Law (KCL) states that the sum of currents entering a node is equal to the sum of currents leaving a node.
• Thevenin's Theorem represents a complex circuit as a single voltage source and series resistance.
• Norton's Theorem represents a complex circuit as a single current source and parallel resistance.

Microcontrollers

Microcontroller Types

• 8-bit microcontrollers are used in applications such as AVR and PIC.
• 16-bit microcontrollers are used in applications such as MSP430.
• 32-bit microcontrollers are used in applications such as ARM Cortex-M.

Microcontroller Components

• CPU (Central Processing Unit) executes instructions in a microcontroller.
• Memory in a microcontroller includes Flash, RAM, and EEPROM.
• Input/Output components in a microcontroller include GPIO, UART, SPI, and I2C.
• Timers and Counters are used to keep track of time and count events in a microcontroller.

Programming Languages

• Assembly Language is a low-level programming language used in microcontrollers.
• C and C-derived languages such as C++ and Arduino are used to program microcontrollers.

Signal Processing

Types of Signals

• Continuous-time signals are analog and vary continuously with time.
• Discrete-time signals are digital and vary at discrete time intervals.

Signal Operations

• Filtering includes Low-pass, High-pass, Band-pass, and Notch filters.
• Amplification increases the amplitude of a signal.
• Modulation includes Amplitude, Frequency, and Pulse-width modulation.

Fourier Analysis

• Fourier Series represents periodic signals as a sum of sinusoids.
• Fourier Transform represents non-periodic signals as a continuous spectrum.

Electronic Circuits

Passive Components

• Resistors (R) oppose the flow of current in a circuit.
• Capacitors (C) store energy in a circuit.
• Inductors (L) store energy in a magnetic field.

Active Components

• Diodes are used for Rectification, Zener diodes, and LEDs.
• Transistors are used as BJT (Bipolar Junction Transistors) and FET (Field-Effect Transistors).
• Operational Amplifiers (Op-amps) are used to amplify weak signals.

Circuit Configurations

• Series connections connect components one after the other.
• Parallel connections connect components between the same two points.
• Voltage Dividers divide voltage between two points.
• Current Mirrors mirror the current in one branch of a circuit to another.

Robotics

Robot Types

• Autonomous robots operate independently without human intervention.
• Remote-controlled robots are controlled by humans using a remote.
• Hybrid robots combine autonomous and remote-controlled capabilities.

Robot Components

• Sensors include Sonar, Camera, GPS, and IMU (Inertial Measurement Unit).
• Actuators include Motors, Servos, and Pneumatic cylinders.
• Control Systems include Microcontrollers and Computers.

Robotics Algorithms

• Motion Planning algorithms plan the motion of a robot.
• Obstacle Avoidance algorithms enable robots to avoid obstacles.
• Localization and Mapping algorithms enable robots to determine their position and create a map of their environment.