DC-DC Converters (Choppers)
Step-down (buck), step-up (boost) and buck-boost converters, duty ratio, continuous conduction, inductor ripple current, capacitor ripple voltage, chopper quadrants and control strategies.
A DC–DC converter (chopper) switches a DC source on and off quickly and filters the result, giving a different DC voltage with high efficiency.
Duty ratio and control
D = T_on/T, with switching frequency f = 1/T. The output is controlled by PWM (fixed f, vary T_on) or frequency modulation.
Basic converters (ideal, continuous conduction)
| Converter | V_o/V_in | Notes |
|---|---|---|
| Buck (step-down) | D | Output ≤ input |
| Boost (step-up) | 1/(1 − D) | Output ≥ input |
| Buck–boost | −D/(1 − D) | Inverted polarity, either higher or lower |
| Ćuk | −D/(1 − D) | Capacitive energy transfer, smooth input and output currents |
Input–output power balance (lossless): V_in I_in = V_o I_o.
Ripple
Buck converter:
- Inductor ripple current ΔI_L = V_in D(1 − D)/(L f) = V_o(1 − D)/(L f); maximum at D = 0.5.
- Output ripple voltage ΔV_o = ΔI_L/(8 C f).
- Boundary of continuous conduction: the minimum inductance L_c = (1 − D)R/(2f).
Boost converter: ΔI_L = V_in D/(L f); ΔV_o = I_o D/(C f).
Chopper quadrants (for DC motors)
| Class | Quadrant | Operation |
|---|---|---|
| A | I | Forward motoring |
| B | II | Regenerative braking |
| C | I and II | Two-quadrant (current reversal) |
| D | I and IV | Two-quadrant (voltage reversal) |
| E | All four | Full bridge |
Worked example
A buck converter: V_in = 24 V, D = 0.5, L = 100 µH, f = 20 kHz.
- V_o = 12 V; ΔI_L = 24 × 0.5 × 0.5/(100 × 10⁻⁶ × 20 × 10³) = 3 A peak-to-peak.
Practice
A boost converter has V_in = 12 V and D = 0.75. What is the output voltage in V?
Show answer and explanation
Answer: 48V_o = V_in/(1 − D) = 12/0.25 = 48 V.
A buck–boost converter has V_in = 12 V and D = 0.6. What is the magnitude of the output voltage in V?
Show answer and explanation
Answer: 18The magnitude is D/(1 − D) × V_in = 1.5 × 12 = 18 V (with reversed polarity).
A buck converter steps 48 V down to 12 V while delivering 2 A. What is the average input current in A (lossless)?
Show answer and explanation
Answer: 0.5V_in I_in = V_o I_o, so I_in = 24/48 = 0.5 A.
For a buck converter with fixed V_in, L and f, the inductor ripple current is maximum at a duty ratio of:
Show answer and explanation
Answer: AΔI_L ∝ D(1 − D), which is largest at D = 0.5.