DC-DC Converters & PWM Regulators

A PWM converter does not make DC by “averaging the switch voltage” in the abstract. Each switch state connects the inductor to a different voltage, so current ramps up or down; the capacitor carries the difference between converter current and load current. Periodic steady state requires zero net inductor flux change and zero net capacitor charge change over one switching period.

Derive the ideal ratios from volt-second balance #

For a buck converter in continuous conduction mode (CCM), the inductor sees $V_{in}-V_o$ for fraction $D$ and $-V_o$ for $1-D$:

$$D(V_{in}-V_o)+(1-D)(-V_o)=0,$$

so $V_o=DV_{in}$.

For a boost converter the inductor sees $V_{in}$ while charging and $V_{in}-V_o$ while delivering energy:

$$DV_{in}+(1-D)(V_{in}-V_o)=0,$$

so $V_o=V_{in}/(1-D)$.

The inverting buck-boost gives $V_o=-DV_{in}/(1-D)$. These ratios assume ideal parts, CCM, periodic steady state, and no limits. They are not controller laws for startup or overload.

Ripple is state duration made visible #

For the buck on interval,

$$\Delta I_L=\frac{(V_{in}-V_o)D}{Lf_s}.$$

Capacitor ripple has a charge component and an ESR step. Fast ceramic capacitors reduce high-frequency impedance but can create a lightly damped input network; bulk capacitance supplies lower-frequency load steps. Layout inductance adds switch-node overshoot that the ideal equations do not contain.

CCM, DCM, and boundary mode #

CCM means inductor current never reaches zero in steady state. In discontinuous conduction mode (DCM), a third interval appears with zero inductor current. The conversion ratio then depends on inductance, frequency, and load as well as duty cycle, and the small-signal plant changes. Pulse skipping or burst mode adds further states at light load.

Control consequences #

Voltage-mode control compares output error with a ramp to set duty. Peak-current-mode control terminates a cycle at commanded inductor current, making current fast but requiring slope-compensation considerations at high duty in applicable topologies. Average-current control regulates a filtered current and is common where input current shape or bidirectional power matters.

Boost-derived converters have a right-half-plane zero in CCM control-to-output response: increasing duty initially withholds energy from the output before the higher inductor current can deliver more. That inverse response limits achievable voltage-loop bandwidth. More gain cannot remove the causal delay.

Faults and limits #

Define startup into prebiased output, input undervoltage, output short, current-limit mode, inductor saturation, diode or synchronous-FET reverse current, switch-node overvoltage, loss of feedback, and shutdown discharge. A synchronous rectifier can improve efficiency but also creates a commanded reverse-current path. The regulator is complete only when every state has a bounded current path and restart policy.