Boost converter calculator

A 5 V to 12 V boost at 1 A needs a duty cycle of 0.65. That is TI's SLVA372 at 85 % efficiency and 500 kHz, evaluated at the minimum input. The inductor averages 2.82 A and the switch peaks at 3.22 A. For 30 % ripple the inductor is 8.10 µH. The currents scale with load, but at light load the inductor current reaches zero and these equations fail.

The power stage of a step-up converter, in the order TI's application note works it: duty cycle at the minimum input with the efficiency folded in, the inductor and its ripple, the peak current the switch, inductor and diode must carry, whether the chosen IC's current limit can deliver the load, and the rectifier and output capacitor.

Fig 1 — inductor current over one period at 3.00 V in, D = 0.79: 2.35 A average for 500 mA out, 419 mA of ripple, peaking at 2.56 A against a 3.00 A switch limit.

Input voltage, minimum (V)

Input voltage, typical (V)

Output voltage (V)

Output current, maximum (A)

Switching frequency, minimum (kHz)

Efficiency estimate (%)

Ripple estimate (% of input current)

Inductance fitted (0 to use the estimate) (µH)

Switch current limit (0 to skip) (A)

Diode forward voltage (0 for synchronous) (V)

Output ripple target (0 to skip) (mV)

Output capacitor ESR (0 to skip) (mΩ)

Duty cycle at 3.00 V in, 85 % efficient: 0.788 · 0.750 ideal
Inductor estimate from the ripple rule: 3.66 µH for 545 mA of ripple at 3.30 V
Ripple with 4.70 µH fitted, at 3.00 V: 419 mA peak-to-peak
Average inductor and input current: 2.35 A · 4.71 × the output current
Peak switch current: 2.56 A · the rating the inductor, switch and diode need
Output the IC can deliver with a 3.00 A limit: 593 mA · covers the 500 mA load
Rectifier average current: 500 mA · 225 mW at 450 mV
Output capacitance for 50.0 mV of ripple: 6.56 µF · plus 25.6 mV from 10.0 mΩ of ESR
Input power · loss at this efficiency: 7.06 W · 1.06 W

How this is calculated

Standard: TI SLVA372 — Basic Calculation of a Boost Converter's Power Stage (Rev D); TI SNVA559 — Switching Regulator Fundamentals

$D = 1 - \frac{V_{in(min)}\,\eta}{V_{out}}$: SLVA372 Eq 14. Evaluated at the minimum input, where the duty cycle and the switch current are largest, with the efficiency included because "the converter has to deliver also the energy dissipated". The note suggests 80 % to 85 % as a worst-case estimate.
$\Delta I_L = \frac{V_{in(min)}\, D}{f_s\, L}, \qquad L \approx \frac{V_{in}\,(V_{out} - V_{in})}{\Delta I_L\, f_s\, V_{out}}$: Eq 15 gives the ripple with the fitted inductor. Eq 18 estimates the inductor when the datasheet gives no range, from a ripple taken as 20 % to 40 % of I_out·V_out/V_in (Eq 19), at the typical input.
$I_{sw(max)} = \frac{\Delta I_L}{2} + \frac{I_{out}}{1 - D}, \qquad I_{maxout} = \left(I_{lim(min)} - \frac{\Delta I_L}{2}\right)(1 - D)$: Eq 17 is the peak "the inductor, the integrated switch(es) and the external diode has to withstand"; Eq 16 runs it backwards from the IC's minimum switch limit to the output it can deliver.
$I_F = I_{out}, \qquad P_D = I_F\, V_F$: Eq 20 and 21: the rectifier carries the output current on average; a Schottky is recommended, and its peak rating comfortably exceeds the average.
$C_{out(min)} = \frac{I_{out}\, D}{f_s\, \Delta V_{out}}, \qquad \Delta V_{ESR} = ESR \left(\frac{I_{out}}{1 - D} + \frac{\Delta I_L}{2}\right)$: Eq 25 and 26: the capacitor alone feeds the load for the whole on-time, and the ESR sees the full peak current at every edge. Both are for externally compensated converters; an internally compensated one wants its datasheet values.

Assumptions

Continuous conduction mode throughout, as SLVA372 states in its scope. The calculator reports the load below which the inductor current reaches zero.
The efficiency is an estimate entered by hand. It sets the duty cycle and everything computed from it; the datasheet's typical characteristics are the better source once the IC is chosen.
The inductor estimate uses the typical input, as the note does; the ripple, peak and switch check use the minimum input, where they are worst.
Capacitance is the value at the DC operating point. SLVA372 asks for X5R or better and warns of the loss to DC bias; derate before comparing.
The control loop is out of scope, as it is for the note. Compensation, the feedback divider and the input capacitor follow the converter's datasheet.

What sets a boost converter's power stage

A boost stores energy in its inductor while the switch is on and delivers it to the output through the diode while the switch is off. SNVA559 describes the two intervals: with the switch closed the input voltage is forced across the inductor and its current ramps up; with the switch open the falling current swings the switch end of the inductor positive, the diode conducts, and the capacitor charges to a voltage above the input. During that off-time the inductor feeds both the capacitor and the load; during the on-time the capacitor alone feeds the load. Everything that makes a boost harder to design than a buck follows from that last sentence.

SLVA372 lays out the calculation in the order the calculator follows. First the duty cycle, evaluated at the minimum input voltage because that is where it is largest, and with the efficiency folded in: D = 1 − V_in(min)·η / V_out. The note is explicit about why the efficiency belongs there: "the converter has to deliver also the energy dissipated", so a duty cycle computed from the ideal ratio is optimistic, and it suggests 80 % to 85 % as a worst-case figure when the datasheet curve is not to hand.

Then the inductor ripple, ΔI_L = V_in(min)·D / (f_s·L), with the inductor the datasheet recommends or the one the note's own estimate gives. The estimate takes the ripple as 20 % to 40 % of the average input current, I_out·V_out/V_in, and turns it into L = V_in(V_out − V_in) / (ΔI_L·f_s·V_out) at the typical input.

The number that matters most comes next. The average inductor current is not the output current; it is the input current, I_out/(1 − D), and for a 3.3 V to 12 V converter that is nearly four times the load. The peak switch current is that average plus half the ripple, I_sw(max) = ΔI_L/2 + I_out/(1 − D), and SLVA372 states what it rates: "the peak current, the inductor, the integrated switch(es) and the external diode has to withstand". The same relation run backwards from the IC's minimum switch current limit gives the largest output the IC can deliver, (I_lim(min) − ΔI_L/2)(1 − D), which is the check that decides whether the chosen converter is the right one at all.

The diode carries the output current on average and the peak in pulses; the note asks for a Schottky, sized by I_F = I_outand P_D = I_F·V_F. The output capacitor has to hold the output up for the whole on-time on its own, so its minimum value is I_out·D / (f_s·ΔV_out), and its ESR adds ripple of its own, ESR × (I_out/(1 − D) + ΔI_L/2), the full peak current stepping through the resistance at every switching edge.

Boost converter chart: switch current and inductor for common step-ups

The step-ups a board actually needs, at 1 A out, 85 % efficiency and 500 kHz, computed by the calculator above. The two currents scale directly with the output current, so double them for 2 A; the inductor halves with it, and halves again for every doubling of the switching frequency. The duty cycle does not depend on the load at all.

Conversion	Duty at V_in(min)	Input current	Peak switch current	Inductor, 30 % ripple
2.5 V → 3.3 V	0.36	1.55 A	1.84 A	3.06 µH
3 V → 5 V	0.49	1.96 A	2.27 A	4.80 µH
3.3 V → 5 V	0.44	1.78 A	2.08 A	4.94 µH
3.3 V → 12 V	0.77	4.28 A	4.85 A	4.39 µH
5 V → 12 V	0.65	2.82 A	3.22 A	8.10 µH
5 V → 24 V	0.82	5.65 A	6.40 A	5.50 µH
12 V → 24 V	0.57	2.35 A	2.70 A	20.0 µH
12 V → 48 V	0.79	4.71 A	5.34 A	15.0 µH

Read the input current column against the output current it was computed for. A 3.3 V to 12 V boost delivering one amp draws over four from its source, and its switch carries nearly five at the peak; the same output from a 5 V input costs a third less. That column is the argument for boosting from the highest input available, and the reason a single-cell boost to 12 V is a different class of part from a 5 V one.

Worked example: 3.3 V to 12 V at 500 mA and 1.2 MHz

The defaults: a single Li-ion cell at 3.0 V minimum and 3.3 V typical, boosted to 12 V at 500 mA by a 1.2 MHz converter with a 3 A switch, assumed 85 % efficient, with a 4.7 µH inductor, a 0.45 V Schottky, a 50 mV ripple target and a 10 mΩ ceramic on the output. Each line is one of SLVA372's numbered equations.

(14) D           = 1 − 3.0 × 0.85 / 12                   = 0.788    (0.750 without efficiency)
(19) ΔI estimate = 0.3 × 0.5 A × 12 / 3.3                 = 545 mA
(18) L estimate  = 3.3 × (12 − 3.3) / (0.545 × 1.2 MHz × 12) = 3.66 µH   →  4.7 µH fitted
(15) ΔI_L        = 3.0 × 0.788 / (1.2 MHz × 4.7 µH)        = 419 mA
     I_L average = 0.5 / (1 − 0.788)                       = 2.35 A    (4.7 × the output)
(17) I_sw(max)   = 0.419 / 2 + 2.35                        = 2.56 A
(16) I_maxout    = (3 − 0.209) × (1 − 0.788)               = 593 mA   ≥ 500 mA, the IC will do
(20,21) diode    = 500 mA average; 0.5 × 0.45              = 225 mW
(25) C_out(min)  = 0.5 × 0.788 / (1.2 MHz × 50 mV)         = 6.56 µF
(26) ΔV from ESR = 10 mΩ × (2.35 + 0.209)                  = 25.6 mV
     input power = 6 W / 0.85                              = 7.06 W    (1.06 W lost)

Two things stand out. The IC passes, but only by 93 mA: a converter with a 2.4 A limit would not, and SLVA372's remedy for a small shortfall is a larger inductor within the recommended range, which reduces the ripple and hands back some of the limit. And the ESR adds half as much ripple again as the capacitance was sized for, because the whole 2.56 A peak steps through it at every edge; on a boost, unlike a buck, the output capacitor sees the full switch current.

Where the boost equations stop being valid

Continuous conduction only. SLVA372 says so in its first sentence, and SNVA559 defines the mode: the inductor current never reaches zero. Below a load where I_out/(1 − D) falls under ΔI_L/2 it does, the duty cycle drops away from these equations and the ripple changes shape. The calculator reports the condition; a battery product spends most of its life below it.

The efficiency is an estimate. The duty cycle, the input current and the peak all carry it. An 85 % guess on a converter that achieves 92 % overstates the peak by a few per cent, which is the safe direction; on one that only reaches 75 % at the minimum input, the error is the other way. SLVA372 points at the datasheet's typical characteristics, and that is where the number should come from once the part is chosen.

Large ratios. A step-up past four or five to one puts the duty cycle above 0.8 and leaves the diode a fifth of the period to deliver all of the output charge. Peak currents climb, the switch's minimum off-time starts to matter, and the efficiency falls in a way the estimate cannot predict. The calculator flags a duty cycle past 0.8; the fix is usually a different topology or two stages.

No control loop. The note is explicit that it covers the power stage and not compensation, and so does this page. An internally compensated converter wants the inductor and capacitor its datasheet names, or the L × C ratio it specifies; an externally compensated one accepts any capacitance above the minimum if the loop is redone for it.

Capacitance at the operating point. SLVA372 asks for X5R or better and warns that a ceramic can lose much of its value to DC bias. The minimum capacitance computed here is the value the capacitor must still have at V_out, not the value printed on it.

Common boost converter mistakes

Sizing the inductor and switch for the output current. The inductor carries the input current, I_out/(1 − D), and the switch carries that plus half the ripple. At a 4:1 step-up that is four to five times the output current, and a part rated for the output current saturates on the first cycle.
Evaluating at the typical input. The duty cycle, the input current and the peak are all largest at the minimum input, and an empty battery is exactly when the converter is asked to work hardest.
Reading the IC's current limit as an output rating. The limit is on the switch; the output it allows is (I_lim − ΔI_L/2)(1 − D), a fraction of it, and the fraction shrinks as the step-up grows.
Forgetting that a boost cannot turn off. With the switch idle the diode connects input to output, so the output can never be below the input and a short on the output is a short on the source. Protection needs a separate element, or a converter with true disconnect.
Sizing the output capacitor from the capacitance formula alone. The ESR term carries the full peak current and on a boost it is often the larger of the two; a low-ESR ceramic, derated for bias, is the note's recommendation for that reason.
Leaving the efficiency at 100 %. The ideal duty cycle understates the real one, and everything downstream of it, by the loss the converter has to make up.