Page 27 – Boost Converter Detailed Derivation (CCM)
Subject: Power Electronics
Converter Type: Step-Up Chopper
Mode: Continuous Conductio
n Mode (CCM)
1️⃣ Objective of Boost Converter
A Boost Converter increases DC voltage.
✔ Output Voltage > Input Voltage
✔ Used in SMPS, Solar Systems, EVs
2️⃣ ON State Analysis (Switch ON)
Time Interval: 0 → DT
- Switch ON
- Diode Reverse Biased
- Inductor stores energy
VL = Vs
Using:V = L (di/dt)
So:di/dt = Vs / L
Inductor current increases linearly.3️⃣ OFF State Analysis (Switch OFF)
Time Interval: DT → T
- Switch OFF
- Diode Conducts
- Inductor releases stored energy
VL = Vs − Vo
Since Vo > Vs, inductor voltage is negative.di/dt = (Vs − Vo) / L
Current decreases linearly.4️⃣ Volt-Second Balance Derivation
Steady state condition:Average inductor voltage over one cycle = 0
So,VsDT + (Vs − Vo)(1 − D)T = 0
Simplifying:Vo = Vs / (1 − D)
5️⃣ Ripple Current
During ON time:ΔI = Vs D T / L
Ripple depends on:- Switching frequency
- Inductance
- Duty cycle
6️⃣ Important GATE Observations
- As D → 1, output voltage increases sharply
- Efficiency reduces for very high duty cycle
- Inductor stores energy during ON time
- Used in renewable & DC bus applications
Final Formula Summary
✔ Vo = Vs / (1 − D)
✔ ΔI = Vs D T / L
Prepared for GATE & PSU – Shaktimatha Learning
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