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Boost Converter Design

Power & Regulators

Will this boost deliver the current without saturating the inductor or fighting its own loop?

Inputs

The lowest input gives the highest duty and peak current.
V
V
A
The controller's minimum fsw, from its datasheet.
Hz
500 kHz
The controller datasheet's efficiency curve at this load, or an estimate. The input current scales with 1/η and sets the peak.
%
H
8.2 µH
Inductor datasheet, at your hottest operating temperature.
A
For ceramics, the value left after DC bias at Vout.
F
22 µF
Capacitor datasheet, at fsw, for the whole bank.
Ω
10 mΩ
Peak to peak.
V
50 mV
Ratings and loop
VDS of the FET or of the controller's switch pin, from its datasheet. The switch sees Vout + VF plus ringing. Blank gives no verdict.
V
Controller datasheet.
%
From your loop design or the controller datasheet. Blank shows the limit and gives no verdict.
Hz

Results

Peak inductor current Ipk
2.172A
Pass

Checked: Ipk ≤ 0.8 × Isat, design margin: 0.724 × your 3 A inductor
Show working
  1. Duty cycleD = 1 − η × V_in / V_out = 1 − 0.9 × 3.6 / 12 = 0.73
  2. Average inductor currentI_L = V_out × I_out / (η × V_in) = 12 × 0.5 / (0.9 × 3.6) = 1.852 A
  3. Inductor rippleΔI_L = V_in × D / (f_sw × L) = 3.6 × 0.73 / (500 kHz × 8.2 µH) = 641 mA
  4. Peak inductor currentI_pk = I_L + ΔI_L / 2 = 1.852 + 0.641 / 2 = 2.172 A
Duty cycle D
73.0%
Output ripple ΔVout
54.91mV
Max loop crossover fc,max
6.792kHz
All results (9)
Average inductor current IL
1.852A
Inductor ripple ΔIL
641mA
L for 35 % ripple L
8.109µH
DCM boundary Iout,crit

below this load expect DCM or pulse skipping, unless a synchronous controller runs forced PWM
86.53mA
RHP zero fRHPZ
33.96kHz
Diode ratings 

minimum ratings: IF,avg ≥ Iout, IF,pk ≥ Ipk, VR ≥ Vout
500mA avg, 2.172 A peak, 12 V reverse
Inductor RMS current IL,rms
Input power Pin
6.667W
Output power Pout
6W
iL(t)

Accuracy

Source
  • Texas Instruments SLVA372
  • Erickson and Maksimović

Texas Instruments SLVA372, Basic Calculation of a Boost Converter's Power Stage, B. Hauke the equation

Erickson and Maksimović, Fundamentals of Power Electronics the equation

Precision
Ideal continuous-mode relations with an efficiency term, exact for the assumed triangular ripple.

They leave out the inductance lost near saturation, so check the inductor curve at your peak current. The efficiency you enter sets the input current, and with it the peak.

Most of the uncertainty comes from Estimated efficiency. Tighten that first.

Verified against

2 independent cases. See the working.

This is a design aid. The engineer remains responsible for the design and for checking the standard itself.

Parameter sweep

Vary one input over a range and see the answer and verdict at each step, as a table and a curve.Pro

Worst-case corners

Put a tolerance on each input and get the worst-case band around the answer.Pro

Circuit

The principle

A boost converter stores energy in its inductor while the switch is on, and the diode passes it to the output on top of Vin, so the output sits above the input. Volt-second balance on the inductor sets the duty cycle, and from it the inductor currents, the output ripple and the right-half-plane zero that limits the loop. Check the design at the lowest input, where duty and peak current are highest.

Duty cycle with losses
D=1−η VinVoutD = 1 - \frac{\eta\, V_{in}}{V_{out}}
TI SLVA372. The efficiency term adds the on-time that makes up the losses.
Average inductor current
IL=Vout Ioutη Vin=Iout1−DI_L = \frac{V_{out}\, I_{out}}{\eta\, V_{in}} = \frac{I_{out}}{1-D}
Equal to the input current.
Inductor ripple
ΔIL=Vin Dfsw L\Delta I_L = \frac{V_{in}\, D}{f_{sw}\, L}
TI SLVA372, at the controller's minimum fsw.
Peak current
Ipk=IL+ΔIL2IL,rms=IL2+ΔIL212I_{pk} = I_L + \frac{\Delta I_L}{2} \qquad I_{L,rms} = \sqrt{I_L^{2} + \frac{\Delta I_L^{2}}{12}}
TI SLVA372. The inductor, the switch and the diode all carry Ipk.
Inductor for a ripple ratio
L=Vin Dfsw r ILL = \frac{V_{in}\, D}{f_{sw}\, r\, I_L}
The ripple equation solved for L, with r taken against IL. TI SLVA372 takes it against Iout·Vout/Vin, which leaves out η.
Output ripple
ΔVout=Iout Dfsw Cout+Ipk⋅ESR\Delta V_{out} = \frac{I_{out}\, D}{f_{sw}\, C_{out}} + I_{pk}\cdot ESR
TI SLVA372. Solved for Cout, the ESR term must stay below the target, or no capacitance meets it.
CCM / DCM boundary
Iout,crit=(1−D) Vin D2 fsw LI_{out,crit} = \frac{(1-D)\, V_{in}\, D}{2\, f_{sw}\, L}
Above this load the inductor current never reaches zero (continuous conduction mode, CCM). Below it, it reaches zero each cycle (discontinuous conduction mode, DCM) and these equations no longer apply (Erickson and Maksimović).
RHP zero
fRHPZ=(1−D)2 R2πLfc≤fRHPZ5f_{RHPZ} = \frac{(1-D)^{2}\, R}{2\pi L} \qquad f_c \leq \frac{f_{RHPZ}}{5}
Erickson and Maksimović, with the lossy D: a lower, more conservative fRHPZ than the ideal D′ = Vin/Vout gives. fc ≤ fRHPZ/5 is this page's design margin, not from the book.
  • DDduty cycle of the switch
  • η\etaestimated efficiency at this load
  • ILI_Laverage inductor current, equal to the input current
  • ΔIL\Delta I_Lpeak-to-peak inductor ripple current
  • rrripple ratio, ΔIL / IL
  • ESRESRequivalent series resistance of the whole output capacitor bank
  • RRload resistance at full load, Vout / Iout
  • fcf_cloop crossover frequency
More detail

The RHP zero

A boost delivers energy to the output only while the switch is off, so a step up in duty first lowers the output before it raises it. That is the right-half-plane zero. It adds phase lag of arctan(fc/fRHPZ): 11.3° with crossover at fRHPZ/5 and 18.4° at fRHPZ/3 (Erickson and Maksimović). The 5 and the 3 are design margins, not a standard.

Synchronous parts

With a synchronous switch in place of the diode, the TI SLVA372 equations all still apply except its diode-loss one, and the diode ratings become the second switch's. A synchronous part run in forced PWM stays in CCM at light load.

Rate the inductor's saturation current, the switch current limit and the diode for Ipk at the lowest input voltage.

SEPIC is not covered.

References: Texas Instruments SLVA372, B. Hauke, Basic Calculation of a Boost Converter's Power Stage. R. Erickson and D. Maksimović, Fundamentals of Power Electronics: the DCM boundary, DCM dynamics and the RHP zero. Related: Buck Converter Design, MOSFET Loss Budget, Decoupling & Bulk Capacitance.

Engine version ⁨1.26.4⁩