Page 28 – Buck-Boost Converter Detailed Derivation (CCM)
Subject: Power Electronics
Converter Type: Buck-Boost (Step Up / Step Down)
Mode: Continuous Conduction Mode (CCM)
1️⃣ Objective of Buck-Boost Converter
A Buck-Boost converter can either increase or decrease the DC voltage.
✔ Output magnitude can be higher or lower than input
✔ Output polarity is reversed (important!)
✔ Used in DC regulated supplies
2️⃣ ON State Analysis (Switch ON)
Time Interval: 0 → DT
- Switch ON
- Diode Reverse Biased
- Inductor stores energy
VL = Vs
Using inductor equation:di/dt = Vs / L
Inductor current increases linearly.3️⃣ OFF State Analysis (Switch OFF)
Time Interval: DT → T
- Switch OFF
- Diode Conducts
- Inductor releases energy to load
VL = − Vo
So,di/dt = − Vo / L
Current decreases linearly.4️⃣ Volt-Second Balance Derivation
Steady state condition:Average inductor voltage over one cycle = 0
So,VsDT + (−Vo)(1 − D)T = 0
Simplifying:Vo = − (D / (1 − D)) Vs
⚠ Negative sign → Output polarity reversed.5️⃣ Ripple Current
During ON time:ΔI = Vs D T / L
6️⃣ Important GATE Observations
- Can step up or step down voltage
- Output polarity reversed
- Duty cycle controls magnitude
- Used in battery-powered devices
Final Formula Summary
✔ Vo = − (D / (1 − D)) Vs
✔ Inductor ripple similar to Boost converter
✔ Polarity inversion is key difference
Prepared for GATE & PSU – Shaktimatha Learning
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