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TK65127M Datasheet(PDF) 11 Page - TOKO, Inc |
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TK65127M Datasheet(HTML) 11 Page - TOKO, Inc |
11 / 20 page 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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