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TK65127M Datasheet(PDF) 11 Page - TOKO, Inc

Part # TK65127M
Description  STEP-UP VOLTAGE CONVERTER WITH VOLTAGE MONITOR
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Manufacturer  TOKO [TOKO, Inc]
Direct Link  http://www.toko.com
Logo TOKO - TOKO, Inc

TK65127M Datasheet(HTML) 11 Page - TOKO, Inc

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January 1999 TOKO, Inc.
Page 11
TK651xx
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


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