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TK65127

STEP-UP VOLTAGE CONVERTER WITH VOLTAGE MONITOR

Toko America Inc  

TK651xx

SINGLE-CELL APPLICATION (CONT.)

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:

and:

IOUT = [IPK x t(off)] x f / 2

and:

IPK = (VIN / L) x t(on) = VIN D / f L

where “VIN” 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, “VOUT” 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:

VIN ≤ (VOUT + VF)(1 - D)

(2)

The implication from Equation 2 is that the inductor will

operate in discontinuous mode.

t(off) = IPK / [(VOUT + VF - VIN) / L]

=(VIN D / f L) / [(VOUT + VF - VIN) / L

= VIN D / f (VOUT + VF - VIN)

therefore:

IOUT = (VIN)2 (D)2 / 2 f L (VOUT + 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:

IOUT =

(VIN)2 (D)2

(1)

2 f L (VOUT + VF - VIN)

Using worst-case conditions, the inductor value can be

determined by simply transforming the above equation in

terms of “L”:

L(MIN) =

VIN(MIN)2 D(MIN)2

2 f(MAX) IOUT(MAX) [VOUT(MIN) + VF(MAX) - VIN(MIN)]

(3)

where “VF(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:

VIN D

IPK = f L

(4)

Some reiteration is implied because “L” is a function of “VF”

which is a function of “IPK” which, in turn, is a function of “L”.

The best way into this loop is to first approximate “VF”,

determine “L”, determine “IPK”, and then determine a new

“VF”. 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 “VIN” 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

January 1999 TOKO, Inc.

Page 11

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