Datasheet

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
( ) ( )
( ) ( )
SW
OUT
M
2 2
ISNS ISNS SW
600kHz
0.13 L
0.13 10 H
R
240
A
g 19.2
V
12m 120 12m 10 H 600kHz
R 120 R L
´ ´
´ m ´
W
= = =
W ´ ´ W + m ´
´ ´ + ´
f
f
( )
( )
( ) ( )
( )
( )
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 L
2 2 2
1 2 30kHz 60m 39.8 F
Z 240 0.146
1 240 2 240 60m 60m 2 30kHz 39.8 F
+ p ´ ´ W ´ m
= W ´ = W
+ W + ´ W´ W + W ´ p ´ ´ m
( )
CO M OUT CO
A
K g Z 19.2 0.146 2.80
V
= ´ = ´ W =f
COMP
CO
1 1
K 0.357
K 2.80
= = =
COMP
CO
R7 51.1k
R4 R7 K 18.2k
K 2.80
W
= ´ = = = W
TPS40210, TPS40211
SLUS772E –MARCH 2008– REVISED OCTOBER 2011 www.ti.com
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.
(57)
R
BIAS
= 1.50 kΩ is selected.
Error Amplifier Compensation
While current mode control typically only requires 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 58.
(58)
The transconductance of the TPS40210 current mode control can be estimated by Equation 59.
(59)
The maximum output impedance Z
OUT
, can be estimated by Equation 60.
(60)
(61)
At the desired crossover frequency (f
L
) of 30 kHz, Z
OUT
becomes 0.146Ω.
The modulator gain at the desired cross-over can be estimated by Equation 62.
(62)
The feedback compensation network needs to be designed to provide an inverse gain at the cross-over
frequency for unity loop gain. This sets the compensation mid-band gain at a value calculated in Equation 63.
(63)
To set the mid-band gain of the error amplifier to K
COMP
use Equation 64.
(64)
R4 = 18.7 kΩ selected.
Place the zero at 1/10th of the desired cross-over frequency.
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