# Boost Converter ```升壓式轉換器
Boost Converter
Instructor: Po-Yu Kuo (郭柏佑)

Boost Converter

A boost converter is shown below. It is called a boost
converter because the output voltage is higher than the
input

When the switch is ON, inductor current increases.
When the switch is OFF, inductor current decreases
and charges up the capacitor. In that time, voltage at
node A must be greater than Vs for decreasing the
inductor current. Assume voltage across the diode is
zero, Vo &gt; Vs
2
3

If the switch is open and D is zero, the output is the same as the input.
As D increases, the denominator becomes smaller and the output
becomes larger than the input. i.e. the boost converter can only produce
an output voltage higher than or equal to the input voltage

As D approaches to 1, the output voltage goes to infinity according to
the equation. However, it is not the case for non-ideal components and
this will be discussed later

An alternative derivation using volt-second balance
equation(conservation of flux in inductor): average inductor voltage is
zero for periodic operation. i.e.
4
Boost Converter: Inductor Value(1)

Now the inductor current IL is not the same as the load
current. In fact, IL is the source current Is. Since the input
power equals to the output power, Ps = VsIs = VsIL and Po =
Vo2/R, the inductor current can be computed as

The maximum &amp; minimum inductor current can be
computed as
5
Boost Converter: Inductor Value(2)

Since the inductor current is always positive (CCM). To
satisfy ILmin must be greater than 0

The minimum inductance value required for CCM operation
is
6
Boost Converter: Output Voltage Ripple


Similar to the buck converter, the output voltage cannot be kept perfectly
constant with a finite capacitor value. The ripple voltage vr can be computed
as follow
When the switch is closed, the capacitor is discharged by the load current:
The change in capacitor charge can be
calculated from


The ripple voltage is given as

It should be noted that fs &gt;&gt; 1/RC where RC is the time constant of the
output
7
Boost Converter: Waveforms(1)
8
Boost Converter: Waveforms(2)
9
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