Texas Instruments TPS40090EVM-002 - Manual (Page 10)

SLUU195 − June 2004
10 TPS40090 Multi-Phase Buck Converter and TPS2834 Drivers Steps-Down from 12-V to 1.5-V at 100 A
where
•
D is the duty cycle for a single phase
•
N
PH
is the number of active phases
•
K (N
PH
) is the intermediate function for calculation
In this case, N
PH
=4 and D
min
=0.107 which yields k=0.573.
The actual output ripple is calculated in equation (7)
I
RIPPLE
+
V
OUT
L f
K
ǒ
N
PH
, D
Ǔ
+
1.5 V
0.6
m
H 420 kHz
0.573
+
3.41 A
0
0.2
0.6
0.4
0.8
1.0
0 10 20 30 40 50 60 70 80 90 100
Duty Cycle − %
I RMS_Cout(nom)
− Normalized RMS Input − A
NPH = 1
NPH = 2
NPH = 3
NPH = 6
NPH = 4
Figure 5. Output Ripple Current Cancellation
Selection of the output capacitor is based on many application variables, including function, cost,
size, and availability. There are three ways to calculate the output capacitance.
1. The minimum allowable output capacitance is determined by the amount of inductor ripple
current and the allowable output ripple, as given in equation (8).
C
OUT(min)
+
I
RIPPLE
8 f V
RIPPLE
+
3.41 A
8 420 kHz 10 mV
+
101
m
F
In this design, C
OUT(min)
is 101-
µ
F with V
RIPPLE
=10 mV. However, this affects only the
capacitive component of the ripple voltage, and the final value of capacitance is generally
influenced by ESR and transient considerations.
2. ESR limitation. (To limit the ripple voltage to 10 mV, the capacitor ESR should be less than
the value calculated in equation (9)).
R
C
t+
V
RIPPLE
I
RIPPLE
+
10 mV
3.41 A
+
2.93 m
W
(7)
(8)
(9)