Transient Analysis in Circuits

Introduction

• Topic covers transient analysis in circuits over 3-4 videos.
• Key points:
  • Definition of transient analysis
  • Importance of transient analysis
  • Behavior of basic circuit components during transients.

Definition of Transient

• Transient occurs when a circuit is connected to a voltage source for the first time.
• The circuit takes time to reach steady-state values of voltage and current.
• Transition time is known as transient and ranges from microseconds to milliseconds.

Importance of Transient Analysis

• Behavior during abrupt changes:
  • Necessary to analyze how circuits respond to voltage spikes or surges.
  • Helps to ensure components do not fail during sudden changes.
• Design considerations:
  • Important in switching applications.
  • Understanding how components like transistors switch states is crucial for design.

Behavior of Basic Components During Transients

Resistor

• At time t=0 (when the switch is closed):
  • Current through resistor: I = V/R (immediate change).
  • Resistor reacts instantaneously to changes in voltage/current.

Inductor

• Before t=0: No current flows through the inductor.
• At t=0 (switch closed):
  • Voltage across inductor: VL = L*(di/dt).
  • Inductor opposes instantaneous changes in current.
  • Current just before (t=0-) and just after (t=0+) switch closure is the same.
  • At t=0+: If no previous current (0), it acts as an open circuit.
  • If previous current I0 exists, at t=0+, it acts as a current source (I0).
• After sufficient time (t=∞): Inductor acts as a short circuit.

Capacitor

• Before t=0: No voltage across the capacitor.
• At t=0 (switch closed): Voltage across capacitor is V0.
  • Current through capacitor: i = C*(dV/dt).
  • Capacitor opposes instantaneous changes in voltage.
  • Voltage just before (t=0-) and just after (t=0+) switch closure is the same.
• After a long time (t=∞): Capacitor acts as an open circuit (no change in voltage).

Summary of Components' Behavior

• Inductor:
  • Opposes instantaneous change of current.
  • Acts as open circuit if no current before switch closure.
  • Acts as current source immediately after closure.
  • Acts as short circuit after a long time.
• Capacitor:
  • Opposes instantaneous change of voltage.
  • Acts as short circuit if no voltage before switch closure.
  • Acts as voltage source immediately after closure.
  • Acts as open circuit after a long time.

Initial and Final Conditions

• Conditions at time t=0+ are initial conditions.
• Conditions at time t=∞ are final conditions.

KVL and KCL in Circuits with Inductors and Capacitors

• Writing KVL/KCL equations will involve derivative terms.
• General form of KVL equation during transient: di/dt + P*i = Q.
  • P: constant
  • Q: forced excitation (AC, DC, etc.).
• Solutions to differential equations:
  • Complementary function: Response without source (source-free response).
  • Particular integral: Response with forced excitation (steady-state response).
  • Complementary function represents transient response.

Future Videos

• Next video will cover transient response of R-L and R-C circuits:
  • Source-free behavior
  • With DC excitation
• Graphical and mathematical solutions will be provided.