DC-DC converters

DC-DC converters change one DC voltage into another: stepping down 48 V to 12 V or 12 V to the 0.7 V to 1 V needed by processor cores, stepping up a battery's voltage to a DC bus, or providing isolation between circuits. They are the most numerous power converters in existence: a single AI server contains dozens, delivering hundreds of amperes to each accelerator chip. This lesson derives the three basic non-isolated converters (buck, boost and buck-boost) from the principles of inductor volt-second balance and capacitor charge balance, shows how to size their inductors and capacitors, introduces the isolated converters used when a transformer is needed, and describes how power is delivered inside a modern data center rack.

Two key principles

In steady state, the current in an inductor returns to the same value at the end of each switching period, so the average voltage across it over a period must be zero (volt-second balance):

Similarly, the voltage on a capacitor returns to the same value, so the average current into it is zero (charge balance). These two principles give the steady-state voltage ratio of any converter quickly. The inductor current ripple follows from \(v = L\, di/dt\) during each interval, and the capacitor voltage ripple from the charge that flows in and out.

The buck converter

A buck (step-down) converter has a switch from the input to a node, a diode or second switch from that node to ground, an inductor from the node to the output, and an output capacitor. With the switch on for a fraction \(D\) of each period, the node voltage is \(V_{in}\); with it off, the node is at ground (the diode or lower switch carries the inductor current). Volt-second balance on the inductor gives:

The inductor current ripple and output voltage ripple in continuous conduction are:

import numpy as np

Vin, Vo_target, R = 48.0, 12.0, 1.2
L, C, fs = 4.7e-6, 100e-6, 250e3
D = Vo_target / Vin
dt = 1 / fs / 400
steps = int(3e-3 / dt)
iL, vC = 0.0, 0.0
log_i, log_v = [], []
for k in range(steps):
    on = (k % 400) < D * 400
    vx = Vin if on else 0.0
    if not on and iL <= 0:
        vx, iL = vC, 0.0
    iL += (vx - vC) / L * dt
    vC += (iL - vC / R) / C * dt
    log_i.append(iL)
    log_v.append(vC)
n = 4 * 400
i_ss, v_ss = np.array(log_i[-n:]), np.array(log_v[-n:])
print(f"duty cycle D = {D:.2f}")
print(f"simulated: Vo = {v_ss.mean():.2f} V, ripple {1000 * np.ptp(v_ss):.0f} mV p-p; IL = {i_ss.mean():.2f} A, ripple {np.ptp(i_ss):.2f} A p-p")
dI = (Vin - Vo_target) * D / (L * fs)
dV = dI / (8 * fs * C)
print(f"formulas:  dIL = (Vin - Vo) D / (L fs) = {dI:.2f} A,  dVo = dIL / (8 fs C) = {1000 * dV:.0f} mV")
print(f"boundary of continuous conduction at load current {dI / 2:.2f} A")

duty cycle D = 0.25
simulated: Vo = 12.00 V, ripple 38 mV p-p; IL = 10.00 A, ripple 7.66 A p-p
formulas:  dIL = (Vin - Vo) D / (L fs) = 7.66 A,  dVo = dIL / (8 fs C) = 38 mV
boundary of continuous conduction at load current 3.83 A

The simulated ripple matches the formulas once the converter reaches steady state. If the load current falls below half the ripple (3.83 A in this design), the inductor current would reach zero during the off time with a diode, and the converter enters discontinuous conduction mode (DCM), where the simple voltage ratio no longer holds. Synchronous converters, which use a MOSFET instead of the diode, can keep conducting with negative current, but at the cost of circulating losses at light load, so many controllers switch to pulse skipping at light load.

The boost converter

A boost (step-up) converter places the inductor at the input, a switch from the inductor's end to ground, and a diode to the output capacitor. When the switch is on, the inductor charges from the input; when it turns off, the inductor's voltage adds to the input to push current into the output. Volt-second balance gives:

Boost converters are used in power factor correction stages (Lesson 3), solar optimizers, battery-powered devices and LED drivers. Their output capacitor receives pulsed current, so output ripple is larger than in a buck for the same capacitance, and the gain is limited in practice to about 4 to 6 by losses in the inductor and switch, which grow as \(D\) approaches 1.

Buck-boost and other non-isolated converters

A buck-boost converter can produce an output larger or smaller than the input, with inverted polarity in its basic form:

Variants such as the SEPIC and Ćuk converters give non-inverted or inverted outputs with continuous input current, and the four-switch buck-boost combines a buck and a boost stage to handle inputs above and below the output, as in USB-C chargers and battery systems. Multiphase interleaved converters place several buck stages in parallel, switching at equally spaced times, so their ripples partly cancel: processor voltage regulators commonly use 8 to over 20 phases to deliver hundreds of amperes with fast transient response.

Isolated converters

Many applications require galvanic isolation (for safety, to separate grounds, or to allow large voltage ratios) and use a high-frequency transformer. Because transformer size falls with frequency, a transformer operating at 100 kHz is far smaller than a 60 Hz transformer of the same power.

• Flyback: a buck-boost with a coupled inductor; energy is stored in the core while the switch is on and released to the output when it turns off. Simple and cheap, used up to about 100 W to 150 W in chargers, adapters and auxiliary supplies.
• Forward: a buck with a transformer; energy is transferred while the switch is on, needing a way to reset the core. Used from tens to hundreds of watts.
• Half-bridge and full-bridge (phase-shifted) converters: for hundreds of watts to tens of kilowatts.
• LLC resonant converters: a resonant tank of inductors and a capacitor allows switches to turn on at zero voltage (soft switching), greatly reducing switching loss and allowing high frequencies and efficiencies near 98%. Widely used in server power supplies after the PFC stage.
• Dual active bridge (DAB): two full bridges linked by a transformer, controlling power flow in either direction by the phase shift between them; used in solid-state transformers, EV chargers and battery systems.

Control

DC-DC converters regulate their output with feedback. In voltage-mode control, an error amplifier compares the output with a reference and adjusts the duty cycle through a pulse-width modulator. Peak current-mode control adds an inner loop that turns the switch off when the inductor current reaches a level set by the voltage loop, giving inherent current limiting and simpler compensation. Designers check stability with loop gain and phase margin (ELE-390). Digital controllers implement these loops in microcontrollers or dedicated chips, report telemetry such as voltage, current and temperature over the PMBus interface, and allow voltages to be adjusted dynamically, which processors use to save energy.

Efficiency and losses

Converter losses come from three groups with different dependence on load: fixed losses (gate drive, control circuits, core losses, switching losses at constant voltage) that are present even at no load; losses proportional to current (diode and IGBT drops); and losses proportional to current squared (resistance in switches, windings and traces). Efficiency is therefore low at light load, peaks at an intermediate load where fixed losses equal the \(I^2R\) losses, and falls slightly at full load.

P_rated = 3000.0
fixed, prop, quad = 18.0, 0.012, 1.4e-5
titanium = {10: 90, 20: 94, 50: 96, 100: 91}
print("load   output W   losses W   efficiency   Titanium minimum")
for pct in [5, 10, 20, 50, 75, 100]:
    P = P_rated * pct / 100
    loss = fixed + prop * P + quad * P ** 2
    eff = 100 * P / (P + loss)
    req = titanium.get(pct)
    note = f"{req}% {chr(10003) if req and eff >= req else (chr(10007) if req else chr(32))}" if req else ""
    print(f"{pct:>3}%   {P:8.0f}   {loss:8.1f}   {eff:9.2f}%   {note}")
best = max(range(1, 101), key=lambda p: (P_rated * p / 100) / (P_rated * p / 100 + fixed + prop * P_rated * p / 100 + quad * (P_rated * p / 100) ** 2))
print(f"peak efficiency near {best}% load, where fixed losses equal load-squared losses")

load   output W   losses W   efficiency   Titanium minimum
  5%        150       20.1       88.18%
 10%        300       22.9       92.92%   90% ✓
 20%        600       30.2       95.20%   94% ✓
 50%       1500       67.5       95.69%   96% ✗
 75%       2250      115.9       95.10%
100%       3000      180.0       94.34%   91% ✓
peak efficiency near 38% load, where fixed losses equal load-squared losses

This matters in data centers, where redundant power supplies often share load and therefore operate at 20% to 40% of rating. Efficiency certifications such as 80 PLUS Titanium specify minimum efficiency at 10%, 20%, 50% and 100% load. In the model, the supply misses the 50% requirement, so the designer would reduce resistance (larger conductors, lower on-resistance devices) or core losses.

Power delivery in a data center rack

The power path inside a modern AI or cloud rack shows how many converters work in series:

1. AC (often 415/240 V or 480/277 V three-phase in North America) enters rack power shelves.

2. Power supply units with PFC and LLC stages convert it to a DC bus, increasingly about 48 V to 54 V (the Open Compute Project standard) instead of 12 V, which cuts bus current and distribution losses by a factor of 16 for the same power.

3. On each board, intermediate bus converters (often fixed-ratio, highly efficient) step 48 V down to 12 V or lower.

4. Multiphase voltage regulators step down to about 0.7 V to 1 V at hundreds to over a thousand amperes for each processor or accelerator, often mounted directly beneath the chip (vertical power delivery) to minimize resistance.

Because rack power has grown from about 10 kW to over 100 kW for AI clusters, the industry has begun developing higher-voltage DC distribution (for example ±400 V or 800 V DC to the rack) to reduce copper and conversion stages. Each conversion stage costs 1% to 5%, so the end-to-end efficiency from the utility to the chip is the product of many efficiencies.

Lesson 6 develops the averaged models and compensator design behind the control methods outlined here, and Lesson 12 applies these converters in a complete power supply design.