Page 62 – Buck-Boost Converter in DCM (Complete Derivation)
Subject: Power Electronics
Level: GATE / PSU Conceptual + Numerical
🔹 1️⃣ What is DCM?
DCM occurs when inductor current falls to zero before next switching cycle.
✔ Happens at light load
✔ Smaller inductance
✔ High switching frequency
🔹 2️⃣ DCM Operation (Three Intervals)
- Interval 1 (0 → DT): Switch ON, inductor charges
- Interval 2 (DT → (D+δ)T): Diode conducts, inductor discharges
- Interval 3: Inductor current = 0
🔹 3️⃣ Inductor Current Peak
ΔIL = (Vin × D) / (L × fs)
Since current starts from zero:Ipeak = (Vin × D) / (L × fs)
🔹 4️⃣ Average Output Current
Output current equals average diode current.Io = (1/2) × Ipeak × Î´
Where δ = diode conduction fraction.🔹 5️⃣ Final DCM Voltage Gain (Important Result)
After solving energy balance:Vo / Vin = − (D² × R) / (2Lfs)
🔥 VERY IMPORTANT: In DCM, voltage gain depends on: ✔ Duty cycle ✔ Load resistance ✔ Inductance ✔ Switching frequency Unlike CCM, gain is NOT only function of D.🔹 6️⃣ Numerical Example
Vin = 20 V D = 0.4 L = 100 μH fs = 50 kHz R = 10 Ω Find output voltage (DCM).
Vo/Vin = − (D² R) / (2Lfs) = − (0.16 × 10) / (2 × 100×10⁻⁶ × 50000) = − (1.6) / (10) = −0.16
Vo = −0.16 × 20 = −3.2 V
Final Answer: −3.2 V
🔹 7️⃣ Critical Condition (Boundary CCM/DCM)
Boundary inductance:Lcritical = R(1−D)² / (2fs)
If L < Lcritical → DCM If L > Lcritical → CCMCCM vs DCM Comparison
| Feature | CCM | DCM |
|---|---|---|
| Inductor Current | Never zero | Falls to zero |
| Voltage Gain | −D/(1−D) | Depends on R, L, fs |
| Control | Simpler | More complex |
GATE Strategy Tip
If question gives L, R, fs → Think DCM possibility.
If only D given → Usually CCM.
Advanced DC-DC Control Series – Shaktimatha Learning
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