Inductors in Chipsun | Inductors and capacitors for boost circuits

Dear readers, it’s been a while since we last discussed topics related to inductors. Today, we bring you the latest installment of the Chipsun Inductor Series, where we’ll explore the formulas for calculating inductors and capacitors in boost circuits. Without further ado, let’s dive in.

 

A bootstrap circuit, also known as a boost circuit, uses components like bootstrap diodes and capacitors to superimpose the capacitor discharge voltage with the power supply voltage, thereby increasing the voltage. In some circuits, the boosted voltage can reach several times the input voltage. So, how do we calculate the inductor and capacitor values in a boost circuit? Here’s how:

Given Parameters:

• Input voltage: 12V — Vi

• Output voltage: 18V — Vo

• Output current: 1A — Io

• Output ripple: 36mV — Vpp

• Operating frequency: 100KHz — f

1. Duty Cycle (don)

Under steady-state conditions, the increase in inductor current during the switch’s ON period equals the decrease during the OFF period.

This can be expressed as:

Vi × don / (f × L) = (Vo + Vd – Vi) × (1 – don) / (f × L)

Simplifying, we get:

don = (Vo + Vd – Vi) / (Vo + Vd)

Substituting the given values: don = 0.572

2. Inductance (L)

First, calculate the inductance value (Lx) where the initial inductor current equals the output current in each switching cycle:

Lx = Vi × (1 – don) / (f × 2 × Io)

Substituting the values: Lx = 38.5 µH

The current ripple (deltaI) is given by:

deltaI = Vi × don / (L × f)

Substituting the values: deltaI = 1.1 A

When the inductance is less than Lx, the output ripple decreases noticeably as inductance increases.

Beyond Lx, further increases in inductance have minimal effect on ripple reduction.

To minimize hysteresis losses and account for input fluctuations, we select L = 60 µH.

Recalculating deltaI:

deltaI = Vi × don / (L × f) = 0.72 A

The initial and peak inductor currents are:

I1 = Io / (1 – don) – (1/2) × deltaI
I2 = Io / (1 – don) + (1/2) × deltaI

Substituting the values: I1 = 1.2 A, I2 = 1.92 A

 

3. Output Capacitor (C)

In this example, ceramic capacitors are used, so ESR can be ignored.

C = Io × don / (f × Vpp)

Substituting the values: C = 99.5 µF

Three 33 µF/25V ceramic capacitors are connected in parallel.

 

4. Core and Wire Gauge

Select a core from the datasheet that does not saturate at the peak current (I2 = 1.92 A).

The RMS current (Irms) is calculated as:

Irms² = (1/3) × (I1² + I2² – I1 × I2)

Substituting the values: Irms = 1.6 A

Choose the wire gauge based on this RMS current and operating frequency.

Other Parameters:

• Inductance: L

• Duty cycle: don

• Initial current: I1

• Peak current: I2

• Coil current: Irms

• Output capacitor: C

• Current ripple: deltaI

• Diode forward voltage drop: Vd