Electrical Fundamentals
Boost Converter Working Principle: Output Voltage Formula and Design
A boost converter is a DC-DC power supply that steps up an input voltage to a higher output voltage. It uses an inductor, a switch, and a diode.
This guide explains the switching cycle, the output voltage formula, component selection, a fully worked design example, and a live calculator.
Step-Up Converter
Duty Cycle Formula
Inductor Design
CCM vs DCM
Efficiency
Hello everyone, today we are going to learn about the boost converter working principle. We will understand how a boost converter steps up a DC voltage, derive the output voltage formula, and work through a complete design example step by step. By the end of this article, you will be able to calculate the duty cycle, inductor value, and peak current for any boost converter design.
A battery discharges from 4.2 V to 3.0 V as it drains. The circuit may need a stable 5 V.
A boost converter steps up the battery voltage continuously, even as it falls. This is one of its most common uses in portable electronics and industrial sensors.
How a Boost Converter Works: The 2-Phase Switching Cycle
A boost converter stores energy in an inductor during the ON phase and releases that energy at a higher voltage during the OFF phase.
ON
Switch closed duration = D x T
MOSFET conducts. Inductor current rises. Energy stores in the magnetic field.
The low-side MOSFET switches on. Current flows from Vin through the inductor and through the MOSFET to ground. The inductor current rises linearly. The diode is reverse-biased and blocks current from the output capacitor. During this phase, the output capacitor alone supplies the load.
OFF
Switch open duration = (1-D) x T
MOSFET opens. Inductor adds its voltage to Vin and pushes current through the diode.
The MOSFET switches off. The inductor opposes the change in current and reverses its voltage polarity. The inductor voltage now adds to Vin, creating a voltage higher than Vin at the diode anode. The diode conducts, charging the output capacitor and supplying the load. The inductor current falls linearly.
Did You Know? The key difference between a boost converter and a buck converter is the position of the inductor. In a buck converter, the inductor is between the switch and the output. In a boost converter, the inductor is between the input and the switch. This position change is what allows the boost converter to create a voltage higher than Vin.
The buck converter working principle explains the complementary step-down topology. Together, buck and boost cover the two fundamental DC-DC conversion directions.
The buck converter working principle explains the complementary step-down topology. Together, buck and boost cover the two fundamental DC-DC conversion directions.
Boost Converter Output Voltage Formula
Vout = Vin / (1 - D)
Output Voltage Formula for a boost converter in continuous conduction mode (CCM), ideal
Vout
Output voltage (V). Always higher than Vin in a boost converter.
Output voltage (V). Always higher than Vin in a boost converter.
Vin
Input voltage (V). The supply being stepped up.
Input voltage (V). The supply being stepped up.
D
Duty cycle (0 to 1). Fraction of each period the MOSFET is ON.
Duty cycle (0 to 1). Fraction of each period the MOSFET is ON.
1 - D
OFF-time fraction. As D approaches 1, Vout approaches infinity (in theory). In practice, losses limit the maximum achievable gain.
OFF-time fraction. As D approaches 1, Vout approaches infinity (in theory). In practice, losses limit the maximum achievable gain.
The duty cycle is rearranged to find D from a known Vin and Vout: D = 1 minus (Vin / Vout). For example, to boost 3.3 V to 12 V, the duty cycle is D = 1 minus (3.3/12) = 1 minus 0.275 = 0.725, or 72.5 percent. The MOSFET is on for 72.5 percent of each switching period.
In a real converter, MOSFET and diode losses reduce the actual output voltage slightly below the ideal formula. The controller compensates using its feedback loop. Learn how MOSFET switching characteristics affect this.
Tip: Keep duty cycle below 0.85 in any boost converter design.
As duty cycle approaches 1.0, the output gain increases but efficiency collapses because the MOSFET carries all the input current for a very long fraction of each period. Conduction losses increase as D squared. Most boost converter controllers also have a maximum duty cycle limit of 80 to 90 percent. A duty cycle above 0.85 is a signal to reconsider the input voltage range or the topology.
As duty cycle approaches 1.0, the output gain increases but efficiency collapses because the MOSFET carries all the input current for a very long fraction of each period. Conduction losses increase as D squared. Most boost converter controllers also have a maximum duty cycle limit of 80 to 90 percent. A duty cycle above 0.85 is a signal to reconsider the input voltage range or the topology.
4 Key Components in a Boost Converter
Inductor (L)
Stores energy during the ON phase and adds its voltage to Vin during the OFF phase to create Vout. The most critical component in this topology.
Select: inductance for target ΔIL, saturation current above Ipeak, low DCR
MOSFET Switch
Low-side switch that connects the inductor to ground during the ON phase. The MOSFET sees the full output voltage Vout across it when off, not Vin.
Select: voltage rating above Vout x 1.3, low RDS(on), low gate charge Qg
Rectifier Diode
Conducts during the OFF phase to transfer inductor energy to the output. A Schottky diode is preferred for its low forward voltage and fast recovery, minimising losses.
Select: fast recovery, low Vf, current rating above Iout, voltage rating above Vout x 1.3
Output Capacitor (Co)
Supplies the load during the ON phase when the diode is blocked. The output capacitor carries the full load current for D x T seconds every cycle. Low ESR is essential.
Select: low ESR, capacitance for ripple spec, voltage rating above Vout
Live Boost Converter Calculator
Worked Example: 3.3 V to 12 V at 1 A, 300 kHz
Boost converter design 3.3 V in, 12 V out, 1 A, 300 kHz
Given:
Vin = 3.3 V, Vout = 12 V, Iout = 1 A, f = 300 kHz, ripple ratio = 0.30
Step 1: Duty cycle
D = 1 minus (Vin / Vout) = 1 minus (3.3 / 12) = 1 minus 0.275 = 0.725 (72.5%)
Step 2: Average input current (inductor average current)
Iin = Iout / (1 minus D) = 1 / (1 minus 0.725) = 1 / 0.275 = 3.64 A
(Input current is much higher than output current in a the converter)
Step 3: Ripple current
ΔIL = ripple ratio x Iin = 0.30 x 3.64 = 1.09 A peak-to-peak
Step 4: Minimum inductance
L = Vin x D / (f x ΔIL) = 3.3 x 0.725 / (300000 x 1.09)
L = 2.393 / 327000 = 7.32 µH
Select standard value: 10 µH (gives lower ripple than spec)
Step 5: Peak inductor current (saturation current rating)
Ipeak = Iin + ΔIL/2 = 3.64 + 0.545 = 4.19 A
Select inductor with saturation current rating above 4.19 A (e.g. 5 A rated)
Step 6: MOSFET voltage rating
MOSFET sees Vout when off: need rating above Vout x 1.3 = 12 x 1.3 = 15.6 V
Select a 20 V rated MOSFET with low RDS(on) at 12 V gate drive
Vin = 3.3 V, Vout = 12 V, Iout = 1 A, f = 300 kHz, ripple ratio = 0.30
Step 1: Duty cycle
D = 1 minus (Vin / Vout) = 1 minus (3.3 / 12) = 1 minus 0.275 = 0.725 (72.5%)
Step 2: Average input current (inductor average current)
Iin = Iout / (1 minus D) = 1 / (1 minus 0.725) = 1 / 0.275 = 3.64 A
(Input current is much higher than output current in a the converter)
Step 3: Ripple current
ΔIL = ripple ratio x Iin = 0.30 x 3.64 = 1.09 A peak-to-peak
Step 4: Minimum inductance
L = Vin x D / (f x ΔIL) = 3.3 x 0.725 / (300000 x 1.09)
L = 2.393 / 327000 = 7.32 µH
Select standard value: 10 µH (gives lower ripple than spec)
Step 5: Peak inductor current (saturation current rating)
Ipeak = Iin + ΔIL/2 = 3.64 + 0.545 = 4.19 A
Select inductor with saturation current rating above 4.19 A (e.g. 5 A rated)
Step 6: MOSFET voltage rating
MOSFET sees Vout when off: need rating above Vout x 1.3 = 12 x 1.3 = 15.6 V
Select a 20 V rated MOSFET with low RDS(on) at 12 V gate drive
Boost Converter Design Checklist
1
Calculate duty cycle and verify it is below 0.85
Use D = 1 minus (Vin / Vout). Use the minimum expected Vin to find D max. If D max exceeds 0.85, either raise Vin or reconsider the topology.
2
Calculate average input current it is much higher than output current
Use Iin = Iout / (1 minus D). This is the average inductor current. At D = 0.725 and Iout = 1 A, Iin = 3.64 A.
The inductor and MOSFET must be rated for this current, not Iout.
3
Select inductor: saturation current above Ipeak = Iin + ΔIL/2
The inductor saturation current rating must exceed the peak current at full load. An inductor that saturates loses its inductance and the peak current spikes. See the inductor guide for selection details.
4
Select MOSFET with voltage rating above Vout x 1.3
The MOSFET in a boost converter sees the full output voltage Vout when it switches off, not Vin. Switching transients add ringing on top of Vout.
Use a MOSFET with a VDS rating at least 30 percent above Vout to provide safe margin.
5
Select output capacitor for low ESR and sufficient capacitance
The output capacitor supplies the load for D x T every cycle. The output ripple voltage is ΔVout = Iout x D / (f x Co).
For 50 mV ripple at 1 A, 0.725 duty cycle, 300 kHz: Co = 1 x 0.725 / (300000 x 0.050) = 48.3 µF. Select 100 µF for margin.
Tip: Right-half-plane zero makes the converter control loops harder to stabilise than buck converters.
A the converter has a right-half-plane (RHP) zero in its control-to-output transfer function. This means that increasing the duty cycle initially decreases the output current before increasing it, causing a phase shift that limits how fast the feedback loop can respond. the converter control loops are generally designed with a lower bandwidth than equivalent buck converter loops. Use your controller IC's reference design and compensation guidelines for the feedback loop component values.
A the converter has a right-half-plane (RHP) zero in its control-to-output transfer function. This means that increasing the duty cycle initially decreases the output current before increasing it, causing a phase shift that limits how fast the feedback loop can respond. the converter control loops are generally designed with a lower bandwidth than equivalent buck converter loops. Use your controller IC's reference design and compensation guidelines for the feedback loop component values.
Boost vs Buck vs Buck-Boost Converters
| Parameter | Boost Converter | Buck Converter | Buck-Boost Converter |
|---|---|---|---|
| Output vs Input | Vout always greater than Vin | Vout always less than Vin | Vout can be above or below Vin |
| Voltage formula | Vout = Vin / (1 minus D) | Vout = Vin x D | Vout = Vin x D / (1 minus D) (inverting) |
| Inductor position | Between Vin and switch (series with input) | Between switch and output (series with output) | Both input and output sides |
| Input current | Pulsating. Much higher than output current at high duty cycle. | Continuous (ripple only). Equal to output current on average. | Pulsating at both input and output |
| Control difficulty | Harder. RHP zero in control transfer function limits loop bandwidth. | Easier. No RHP zero. Wider control bandwidth achievable. | Hardest. RHP zero plus more complex topology. |
| Typical applications | Battery-to-rail boost, LED drivers, USB power delivery | DC bus regulation, MCU power, point-of-load regulation | Battery-operated systems with wide input voltage range |
Watch: Boost Converter Working Principle Explained
Boost Converter Questions Engineers Ask
What is the output voltage formula for a boost converter?
The output voltage formula is Vout = Vin / (1 minus D). For Vin = 3.3 V and D = 0.725, Vout = 12 V. Vout is always higher than Vin in a boost converter.
How is a boost converter different from a buck converter?
A boost converter steps up the input voltage. A buck converter steps it down. The inductor is in series with the input in a boost, and with the output in a buck converter.
Why is the input current of a boost converter higher than the output current?
By conservation of energy, since Vout is higher than Vin, Iin must be higher than Iout. The relationship is Iin = Iout / (1 minus D) in an ideal converter.
What is the right-half-plane zero in a boost converter?
The RHP zero causes phase lag without attenuation. It limits the feedback loop bandwidth of a boost converter, making the control loop harder to stabilise than a buck converter.
What is the maximum duty cycle for a boost converter?
Most designs target a maximum duty cycle of 0.80 to 0.85. Above this, efficiency drops sharply as MOSFET conduction losses increase with duty cycle squared. Most controller ICs impose a hardware limit.
Related Articles on This Site
- Buck Converter Working Principle: Duty Cycle Formula and Design Guide
- What Is a MOSFET? Working Principle Explained
- Inductor Working Principle
- How Decoupling Capacitors Work
- Active, Reactive and Apparent Power Explained
External References
- Basic Calculation of a the converter's Power Stage | Texas Instruments SLVA372C
- Boost Regulator Design Guide | Analog Devices
What We Learn Today
- A boost converter steps up DC voltage using an inductor and a switch. The output voltage formula is Vout = Vin / (1 minus D). To boost 3.3 V to 12 V, the duty cycle is 72.5 percent.
- The input current in a the converter is always higher than the output current by the factor 1/(1 minus D). This is critical for inductor and MOSFET selection, where peak current Ipeak = Iin + ΔIL/2 must be used, not Iout.
- Keep duty cycle below 0.85 in any the converter design. The right-half-plane zero in the control transfer function limits feedback loop bandwidth and requires careful compensation design.
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