Calculator
Boost converter calculator
Duty cycle, inductance, currents and capacitor stress at the efficiency you give it, and the right-half-plane zero that limits how fast the loop can be.
How it works
What a boost converter does
A boost converter steps a voltage up. While the switch is on, the input charges the inductor. When it turns off, the inductor's current flows through the rectifier into the output, on top of the input voltage. The inductor sits on the input side, so its average current is the input current, not the output current.
Duty cycle and efficiency
In a lossless boost the duty cycle is one minus the ratio of input to output voltage. Losses push it higher, because part of each cycle's stored energy is spent before it reaches the output. Power balance and charge balance together give the duty below. The calculator works at the efficiency you enter, 90 % unless you change it.
Sizing the inductor
The inductance is set at the minimum input voltage, where the duty cycle and the inductor current are both largest. The ripple ratio you choose is a fraction of that average current. The ripple itself peaks higher up the range: in CCM at V_out / 2η, or at the end of the range nearest it when that voltage lies outside. The calculator searches the range for it. Targeting DCM sets the inductance at half its lossless critical value at the minimum input voltage instead, so the current returns to zero every cycle.
Currents and stress
The peak and RMS currents are read at the minimum input voltage, where each one is largest. The switch blocks the output voltage when it is off, so its rating follows V_out, not V_in. The output capacitor carries the pulsed rectifier current and supplies the whole load while the switch is on. Its ripple current is usually the largest capacitor stress in the design. The input capacitor sees only the inductor's ripple, and its worst case is searched over the range.
The right-half-plane zero
A step up in duty first shortens the time the inductor feeds the output, so the output dips before it rises. In the loop this is a zero in the right half of the s-plane. It adds gain and takes phase away, and no compensator can cancel it. The right-half-plane zero is lowest at the minimum input voltage and full load, which is where the calculator reads it.
Crossing over above a third of it cannot be recovered. The calculator suggests a fifth, or a tenth of the switching frequency if that is lower. That ceiling assumes voltage-mode control. A DCM boost has no right-half-plane zero, which is the main reason to run one discontinuous. The design tool designs the compensator for a boost and checks its margins at this corner.
What it does not model
- The compensator. The page shows the limit, and the design tool designs the loop.
- Output capacitor ESL.
- A synchronous rectifier against a diode, and the losses of either.
FAQ
What is the duty cycle formula for a boost converter?
A lossless boost runs at D = 1 − Vin / Vout. A real one runs at D = 1 − η × Vin / Vout, a little higher, because some of each cycle's energy is lost before it reaches the output. At 9 V in and 24 V out, 90 % efficiency moves the duty from 62.5 % to about 66 %.
How do you size a boost converter's inductor?
Choose the ripple current as a fraction of the inductor's average current, usually 20 to 40 %. Then L = Vin × D / (ΔIL × fsw), taken at the minimum input voltage, where the duty cycle and the inductor current are largest.
Why is a boost inductor's current higher than the output current?
The inductor sits on the input side and carries the whole input current. That is Iout / (1 − D), or Pout / (η × Vin). A 9 V to 24 V boost delivering 1 A draws about 3 A through its inductor at 90 % efficiency.
What is the right-half-plane zero in a boost converter?
When the duty cycle steps up, the inductor feeds the output for less of each cycle, so the output dips before it rises. That delayed response is a zero in the right half of the s-plane. It limits the loop's crossover to about a fifth of its frequency.
When is DCM the better choice for a boost?
A discontinuous boost has no right-half-plane zero, so its loop can cross over much higher. The price is a higher peak current, more ripple, and more stress on the capacitors. At low power that trade is often worth it.
Why is a boost switch rated to the output voltage?
When the switch turns off, its drain rises until the rectifier conducts into the output, so it blocks Vout plus the rectifier's drop. The input voltage does not set the rating. The calculator adds a 20 % margin to Vout.
Further reading
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Minimum inductance for continuous or discontinuous conduction, with the peak and RMS currents and the duty cycle that follow from it.
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A buck's or boost's MOSFET losses from datasheet values, with each junction temperature solved against its own loss, thermal runaway, and derating.
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