Choppers

Choppers are DC–DC converters that 'chop' a DC voltage with a fast switch and filter it. Learn buck, boost and buck-boost conversion ratios, inductor and capacitor sizing, continuous vs discontinuous conduction, and efficiency.

Switching a DC voltage on and off quickly and averaging it with an inductor and capacitor lets you step voltage down (buck), up (boost) or both (buck-boost) with 90–98 % efficiency — far better than a linear regulator burning the excess as heat.

Every phone, laptop, LED driver, solar charge controller and EV contains several choppers. In drive systems, a chopper also controls DC motors and braking resistors.

An analogy

A buck converter is like filling a bucket from a fire hose by opening and closing the tap quickly: the bucket's water level (average voltage) depends on what fraction of the time the tap is open (duty cycle).

Volt-second balance

In steady state the inductor's average voltage over a cycle must be zero, or its current would ramp forever. Equating the volt-seconds during on-time and off-time gives every conversion ratio directly — for a buck, (V_in − V_o)·D = V_o·(1 − D) → V_o = D·V_in.

Why switching beats linear

A linear regulator dropping 12 V to 3.3 V at 3 A wastes (12 − 3.3) × 3 = 26 W. A buck converter at 92 % efficiency wastes about 0.9 W for the same 9.9 W output.

Ripple, CCM and DCM

The inductor current is a triangle around the load current. Designers typically set ΔI_L ≈ 20–40 % of full-load current. If the load is small enough that the current reaches zero each cycle, the converter enters discontinuous conduction mode (DCM), where the conversion ratio then depends on the load.

Boost and buck-boost

A boost stores energy in L while the switch is on and releases it on top of the input when off, so V_o > V_in. Its input current is continuous (good for PFC and solar), but its output current is pulsed. Buck-boost variants (inverting, SEPIC, Ćuk, four-switch) cover inputs both above and below the output, as with a battery that discharges past the output voltage.

Control and synchronous rectification

Voltage-mode and current-mode (peak or average) control regulate the output; current mode adds inherent current limiting and easier compensation. Replacing the freewheeling diode with a MOSFET (synchronous buck) cuts loss at low voltages. The boost's right-half-plane zero limits its control bandwidth.

Formulas

• Buck: V_o = D · V_in
• Boost: V_o = V_in / (1 − D)
• Buck-boost (inverting): V_o = −V_in · D / (1 − D)
• Buck inductor: L = (V_in − V_o) · D / (ΔI_L · f_sw)
• Buck output capacitor: C ≥ ΔI_L / (8 · f_sw · ΔV_o)

Worked example: Buck inductor sizing

Given: V_in = 24 V, V_o = 5 V; I_o = 2 A, ripple 30 % (0.6 A); f_sw = 200 kHz

Find: Duty cycle and inductance.

• D = 5/24 = 0.208
• L = (24 − 5) × 0.208/(0.6 × 200e3) = 33 µH

Answer: D ≈ 0.21, L ≈ 33 µH

Worked example: Li-ion to 5 V boost

Given: V_in = 3.7 V; V_o = 5 V at 1 A; Ideal (lossless)

Find: Duty cycle and average input current.

• D = 1 − 3.7/5 = 0.26
• P = 5 W → I_in = 5/3.7 = 1.35 A

Answer: D = 0.26, I_in ≈ 1.35 A

Common mistakes

• Wrong: Choosing an inductor only by inductance. — Right: Check saturation current ≥ peak current (I_o + ΔI/2) with margin, and its DC resistance for loss.
• Wrong: Expecting boost gain to keep rising as D → 1. — Right: Parasitic resistance limits real boost gain to ~5–6×; efficiency collapses at high D.

Applications

• Point-of-load regulators: Multi-phase synchronous bucks deliver 1 V at hundreds of amps to CPUs and GPUs.
• Solar MPPT: Charge controllers use buck or boost stages whose duty cycle is adjusted to hold panels at their maximum power point.
• LED drivers: Constant-current bucks and boosts regulate LED current for lighting and backlights.

Key takeaways

• Buck V_o = DV_in, boost V_in/(1 − D), buck-boost D/(1 − D).
• Volt-second balance on the inductor gives every ratio.
• Size L for 20–40 % ripple and C for the output ripple limit.
• Switching converters reach 90–98 % efficiency vs linear regulators.

Going further

• Multiphase interleaving: Running N buck phases 360°/N apart cancels ripple current at the output capacitor and spreads heat, which is essential for 100 A+ CPU rails.
• Loop compensation: The LC filter's double pole must be compensated (Type II/III networks) so the loop crosses over at ~1/10 of f_sw with ≥ 45° phase margin.
• Soft switching: Resonant and quasi-resonant converters switch at zero voltage or zero current (ZVS/ZCS), nearly eliminating switching loss and allowing MHz operation.