
January 2001 TOKO, Inc.
Page 11
TK651xxM
where “V
IN” is the input voltage, “D” is the on-time duty ratio
of the switch, “
f ” is the switching (oscillator) frequency, “L”
is the inductor value, “V
OUT” is the output voltage, and “VF”
is the diode forward voltage. It is important to note that
Equation 1 makes the assumption stated in Equation 2:
V
IN " (VOUT + VF)(1 - D)
(2)
The implication from Equation 2 is that the inductor will
operate in discontinuous mode.
Using worst-case conditions, the inductor value can be
determined by simply transforming the above equation in
terms of “L”:
(3)
where “V
F(MAX)” is best approximated by the diode forward
voltage at about two-thirds of the peak diode current value.
The peak diode current is the same as the peak input
current, the peak switch current, and the peak inductor
current. The formula is:
(4)
Some reiteration is implied because “L” is a function of “V
F”
which is a function of “I
PK” which, in turn, is a function of “L”.
The best way into this loop is to first approximate “V
F”,
determine “L”, determine “I
PK”, and then determine a new
“V
F”. Then, if necessary, reiterate.
When selecting the actual inductor, it is necessary to make
sure that peak current rating of the inductor (i.e., the current
which causes the core to saturate) is greater than the
maximum peak current the inductor will encounter. To
determine the maximum peak current, use Equation 4
again, but use maximum values for “V
IN” and “D”, and
minimum values for “
f ” and “L”.
It may also be necessary when selecting the inductor to
check the rms current rating of the inductor. Whereas peak
current rating is determined by core saturation, rms current
The output current of the boost converter comes from the
second half of the input current triangle waveform (averaged
over the period or multiplied by the frequency) given by the
equation:
I
OUT = [IPK x t(off)] x f / 2
and:
I
PK = (VIN / L) x t(on) = VIN D / f L
and:
t(off) = I
PK / [(VOUT + VF - VIN) / L]
=(V
IN D / f L) / [(VOUT + VF - VIN) / L
= V
IN D / f (VOUT + VF - VIN)
therefore:
I
OUT = (VIN)
2 (D)2 / 2 f L (V
OUT + VF - VIN)
which derives Equation 1 of the next section.
INDUCTOR SELECTION
It is under the condition of lowest input voltage that the
boost converter output current capability is the lowest for a
given inductance value. Three other significant parameters
with worst-case values for calculating the inductor value
are: highest switching frequency, lowest duty ratio (of the
switch on-time to the total switching period), and highest
diode forward voltage. Other parameters which can affect
the required inductor value, but for simplicity will not be
considered in this first analysis are: the series resistance
of the DC input source (i.e., the battery), the series resistance
of the internal switch, the series resistance of the inductor
itself, ESR of the output capacitor, input and output filter
losses, and snubber power loss.
The converter reaches maximum output current capability
when the switch runs at the oscillator frequency, without
pulses being skipped. The output current of the boost
converter is then given by the equation:
(1)
SINGLE-CELL APPLICATION (CONT.)
2
f L (V
OUT + VF - VIN)
I
OUT =
(V
IN)
2 (D)2
2
f
(MAX) IOUT(MAX) [VOUT(MIN) + VF(MAX) - VIN(MIN)]
L
(MIN) =
V
IN(MIN)
2 D
(MIN)
2
f L
I
PK =
V
IN D