Page 26 – Buck Converter Detailed Derivation (CCM)
Subject: Power Electronics
Topic: Buck Converter (Step Down Chopper)
Mode: Continuous Conduction Mode (CCM)
1️⃣ Circuit Overview
Buck converter converts fixed DC into lower DC using:
- Switch (S)
- Diode (D)
- Inductor (L)
- Capacitor (C)
- Load (R)
2️⃣ ON-State Analysis (0 → DT)
When switch is ON:
VL = Vs − Vo
Using inductor equation:VL = L (di/dt)
So,di/dt = (Vs − Vo) / L
Current increases linearly.3️⃣ OFF-State Analysis (DT → T)
When switch is OFF:
VL = − Vo
Thus,di/dt = − Vo / L
Current decreases linearly.4️⃣ Volt-Second Balance Principle
In steady state:Average voltage across inductor over one cycle = 0
So,(Vs − Vo)DT + (−Vo)(1−D)T = 0
Simplifying:VsD − VoD − Vo + VoD = 0
Final result:Vo = D × Vs
5️⃣ Inductor Ripple Current
During ON time:ΔI = (Vs − Vo) D T / L
Using Vo = D Vs:ΔI = Vs D (1 − D) T / L
6️⃣ Important GATE Concepts
- Volt-second balance derivation
- Ripple current formula
- Effect of L and switching frequency
- Boundary between CCM and DCM
- Efficiency assumptions (ideal case)
Final Summary
✔ Buck converter reduces voltage
✔ Output controlled by duty cycle
✔ In CCM → Vo = D Vs
✔ Ripple depends on L and switching frequency
Prepared for GATE & PSU – Shaktimatha Learning
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