wP1 +
1
C
R
O
(10)
wP2 +
1
C
O
RL
(11)
wP3 +
1
C
C2
R
C
(12)
wZ1 +
1
C
R
C
(13)
wZ2 +
1
C
O
ESR
(14)
f
0 +
1
2p
R1
R1 ) R2
gm
C
O
R
C
R
S
+
1
2p
0.75
V
OUT
gm
C
O
R
C
R
S
(15)
L +
1
I
IND(ripple)
f
V
IN(max) * VOUT
V
OUT
V
IN(max)
+
2
I
OUT(max)
f
V
IN(max) * VOUT
V
OUT
V
IN(max)
(16)
I
IND(peak) +
V
TRIP
R
DS(on)
)
1
L
f
V
IN(max) * VOUT
V
OUT
V
IN(max)
(17)
R
C v 2p
f
0
V
OUT
0.75
C
O
gm
R
S
(18)
R
C + 2.8
V
OUT
C
O [mF]
R
S [mW]
(19)
www.ti.com................................................................................................................................................................ SLUS609H – MAY 2004 – REVISED JULY 2009
Usually, each frequency of those poles and zeros is lower than the 0 dB frequency, f0. However, the f0 should be
kept under 1/3 of the switching frequency to avoid effect of switching circuit delay. The f0 is given by Equation 15. Based on small signal analysis above, the external components can be selected by following manner.
1. Choose the inductor. The inductance value should be determined to give the ripple current of
approximately 1/4 to 1/2 of maximum output current.
The inductor also needs to have low DCR to achieve good efficiency, as well as enough room above peak
inductor current before saturation. The peak inductor current can be estimated as shown in
Equation 17.2. Choose rectifying (bottom) MOSFET. When RDS(on) sensing scheme is selected, the rectifying MOSFET’s
on-resistance is used as this RS so that lower RDS(on) does not always promise better performance. In order
to clearly detect inductor current, minimum RS recommended is to give 15 mV or larger ripple voltage with
the inductor ripple current. This promises smooth transition from CCM to DCM or vice versa. Upper side of
the RDS(on) is of course restricted by the efficiency requirement, and usually this resistance affects efficiency
more at high-load conditions. When using external resistor current sensing, there is no restriction for low
RDS(on). However, the current sensing resistance RS itself affects the efficiency
3. Choose output capacitor(s). In cases of organic semiconductor capacitors (OS-CON) or specialty polymer
capacitors (SP-CAP), ESR to achieve required ripple value at stable state or transient load conditions
determines the amount of capacitor(s) need, and capacitance is then enough to satisfy stable operation. The
peak-to-peak ripple value can be estimated by ESR times the inductor ripple current for stable state, or ESR
times the load current step for a fast transient load response. In case of ceramic capacitor(s), usually ESR is
small enough to meet ripple requirement. On the other hand, transient undershoot and overshoot driven by
output capacitance becomes the key factor to determine the capacitor(s).
4. Determine f0 and calculate RC using Equation 18. Note that higher RC shows faster transient response in cost of unstableness. If the transient response is not enough even with high RC value, try increasing the out
put capacitance. Recommended f0 is fOSC/4. Then RC can be derived by Equation 19. 5. Calculate CC2. Purpose of this capacitance is to cancel zero caused by ESR of the output capacitor. In case
Copyright 2004–2009, Texas Instruments Incorporated
19