SM74203 Datasheet, PDF (13/24 Pages) Texas Instruments – SM74203 60V Low Side Controller for Boost and SEPIC

Inductance for Maximum Input Voltage
D_VIN(MAX) = (40 - 16 + 0.5) / (40 + 0.5) = 60%
I_L-VIN(MIAX) = 0.5 / (1 – 0.6) = 1.25A
Δi_L = 0.4 x 1.25A = 0.5A
selected based on their capacitance, C_O, their equivalent se-
ries resistance (ESR) and their RMS or AC current rating.
The magnitude of ΔV_O is comprised of three parts, and in
steady state the ripple voltage during the on-time is equal to
the ripple voltage during the off-time. For simplicity the anal-
ysis will be performed for the MOSFET turning off (off-time)
only. The first part of the ripple voltage is the surge created
as the output diode D1 turns on. At this point inductor/diode
current is at the peak value, and the ripple voltage increase
can be calculated as:
ΔV_O1 = I_PK x ESR
The second portion of the ripple voltage is the increase due
to the charging of C_O through the output diode. This portion
can be approximated as:
Maximum average inductor current occurs at V_IN(MIN), and the
corresponding inductor ripple current is 0.92A_P-P. Selecting
an inductance that exceeds the ripple current requirement at
V_IN(MIN) and the requirement to stay in CCM for V_IN(MAX) pro-
vides a tradeoff that allows smaller magnetics at the cost of
higher ripple current at maximum input voltage. For this ex-
ample, a 33 µH inductor will satisfy these requirements.
The second criterion for selecting an inductor is the peak cur-
rent carrying capability. This is the level above which the
inductor will saturate. In saturation the inductance can drop
off severely, resulting in higher peak current that may over-
heat the inductor or push the converter into current limit. In a
boost converter, peak current, I_PK, is equal to the maximum
average inductor current plus one half of the ripple current.
First, the current ripple must be determined under the condi-
tions that give maximum average inductor current:
Maximum average inductor current occurs at V_IN(MIN). Using
the selected inductance of 33 µH yields the following:
Δi_L = (9 x 0.78) / (0.5 x 33) = 425 mA_P-P
The highest peak inductor current over all operating condi-
tions is therefore:
ΔV_O2 = (I_O / C_O) x (D / f_SW)
The final portion of the ripple voltage is a decrease due to the
flow of the diode/inductor current through the output
capacitor’s ESR. This decrease can be calculated as:
ΔV_O3 = Δi_L x ESR
The total change in output voltage is then:
ΔV_O = ΔV_O1 + ΔV_O2 - ΔV_O3
The combination of two positive terms and one negative term
may yield an output voltage ripple with a net rise or a net fall
during the converter off-time. The ESR of the output capacitor
(s) has a strong influence on the slope and direction of ΔV_O.
Capacitors with high ESR such as tantalum and aluminum
electrolytic create an output voltage ripple that is dominated
by ΔV_O1 and ΔV_O3, with a shape shown in Figure 5. Ceramic
capacitors, in contrast, have very low ESR and lower capac-
itance. The shape of the output ripple voltage is dominated by
ΔV_O2, with a shape shown in Figure 6.
I_PK = I_L + 0.5 x Δi_L = 2.3 + 0.213 = 2.51A
Hence an inductor must be selected that has a peak current
rating greater than 2.5A and an average current rating greater
than 2.3A. One possibility is an off-the-shelf 33 µH ±20% in-
ductor that can handle a peak current of 3.2A and an average
current of 3.4A. Finally, the inductor current ripple is recalcu-
lated at the maximum input voltage:
Δi_L-VIN(MAX) = (16 x 0.6) / (0.5 x 33) = 0.58A_P-P
OUTPUT CAPACITOR
The output capacitor in a boost regulator supplies current to
the load during the MOSFET on-time and also filters the AC
portion of the load current during the off-time. This capacitor
determines the steady state output voltage ripple, ΔV_O, a crit-
ical parameter for all voltage regulators. Output capacitors are
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FIGURE 5. ΔV_O Using High ESR Capacitors