Transient Response of Series RLC Circuit using MATLAB

Simscape model of a series RLC circuit showing transient response, oscillations, and damping behavior under step input.

🔹 Overview: This project demonstrates the transient response of a series RLC circuit using MATLAB Simscape. It helps in understanding oscillations, damping conditions, and second-order system behavior.

🔹 Model Description: The model consists of:

• Step input applied at t = 0.01 s
• Controlled DC voltage source
• Resistor (R)
• Inductor (L)
• Capacitor (C)
• Voltage sensors to measure responses
• Scope for waveform visualization

🔹 Key Concepts Covered:

• Second-order system behavior
• Oscillatory response
• Underdamped, critically damped, overdamped conditions
• Natural frequency and damping ratio
• Energy exchange between L and C

🔹 Output Explanation:

• Voltage/current shows oscillations
• Amplitude decreases over time (damping)
• System reaches steady state depending on R value

🔹 Mathematical Model:

Natural frequency:

ω_n = 1 / √(LC)

Damping ratio:

ζ = R / (2√(L/C))

General response:

V(t) = e^(-ζω_n t) [A cos(ω_d t) + B sin(ω_d t)]

🔹 How to Run:

1. Open the .slx file in MATLAB
2. Run the simulation
3. Observe waveform in Scope
4. Analyze oscillations and damping

🔹 Applications:

• Power systems
• Filters (band-pass, band-stop)
• Communication systems
• Resonant circuits
• EV power electronics