Datasheet

( )
( )
FET
DS on
2 2
RMS
P
0.50 W
R 9.8 m
2 6.13 0.674
2 I D
< = = W
´ ´
´ ´
FB FB
BIAS
OUT FB
V R
0.700 V 51.1k
R 1.53k
V V 24 V 0.700 V
´
´ W
= = = W
- -
( )
( )
OUT
OUT max
OUT min
V
24 V
R 240
I 0.1A
= = = W
( ) ( )
( ) ( )
f
f
SW
OUT
M
2 2
ISNS ISNS SW
600kHz
0.13 L
0.13 10 H
R
240
A
g 19.1
V
12m 120 12m 10 H 600kHz
R 120 R L
´ ´
´ m ´
W
= = =
W ´ ´ W + m ´
´ ´ + ´
( )
( )
( ) ( )
( )
( )
f
2
ESR OUT
OUT OUT
2 2 2
OUT OUT ESR ESR OUT
1 2 f R C
Z ( ) R
1 R 2 R R R 2 f C
+ p ´ ´ ´
= ´
+ + ´ ´ + ´ p ´ ´
( )
( )
( )
( ) ( )
( )
( )
2
f
OUT CO
2 2 2
1 2 20 kHz 60 m 39.8 F
Z 240 0.146
1 240 2 240 60m 60 m 2 20kHz 39.8 F
+ p ´ ´ W ´ m
= W ´ = W
+ W + ´ W ´ W + W ´ p ´ ´ m
( )
f
CO M OUT CO
A
K g Z 19.1 0.146 2.80
V
= ´ = ´ W =
COMP
CO
1 1
K 0.356
K 2.80
= = =
TPS40210-Q1, TPS40211-Q1
SLVS861D –AUGUST 2008–REVISED APRIL 2010 www.ti.com
(55)
A target MOSFET R
DS(on)
of 9.8 mΩ is calculated to limit the conduction losses to less than 250 mW. Reviewing
30-V and 40-V MOSFETs, an Si4386DY 9-mΩ MOSFET is selected. A gate resistor was added per Equation 30.
The maximum gate charge at Vgs = 8 V for the Si4386DY is 33.2 nC, this implies RG = 3.3 Ω.
Feedback Divider Resistors
The primary feedback divider resistor (R
FB
) from V
OUT
to FB should be selected between 10-kΩ and 100-kΩ to
maintain a balance between power dissipation and noise sensitivity. For a 24-V output a high feedback
resistance is desirable to limit power dissipation so R
FB
= 51.1 kΩ is selected.
(56)
R
BIAS
= 1.50 kΩ is selected.
Error Amplifier Compensation
While current mode control typically requires only Type II compensation, it is desirable to layout for Type III
compensation to increase flexibility during design and development.
Current mode control boost converters have higher gain with higher output impedance, so it is necessary to
calculate the control loop gain at the maximum output impedance, estimated by Equation 57.
(57)
The transconductance of the TPS40210 current mode control can be estimated by Equation 58.
(58)
The maximum output impedance Z
OUT
, can be estimated by Equation 59.
(59)
(60)
The modulator gain at the desired cross-over can be estimated by Equation 61.
(61)
The feedback compensation network needs to be designed to provide an inverse gain at the cross-over
frequency for unit loop gain. This sets the compensation mid-band gain at a value calculated in Equation 62.
(62)
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