Datasheet

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75
125
275
325
175
25
225
250 400 700550 1000850
gm − Sense Amplifier Transconductance − µS
R
GM
− Gain Setting Resistance − kΩ
Control to Output Gain of the Converter
K
CO
(s) +
V
IN
K
PWM
K
FILT
(s)
1 ) Y(s) K
CS
K
PWM
V
IN
(dimensionless)
(24)
R
LOAD
R
LDC
) R
LOAD
R
ESR
C
OUT
s ) 1
L C
OUT
)R
LOAD
R
LDC
)R
LOAD
s
2
)
L)C
OUT
ǒ
R
LOAD
R
ESR
)R
LDC
R
LOAD
)R
LDC
R
ESR
Ǔ
R
LOAD
s ) 1
K
FILT
(s) +
R
ESR
C
OUT
s ) 1
L C
OUT
s
2
)
ƪ
L)R
LOAD
C
OUT
ǒ
R
ESR
)R
LDC
Ǔ
R
LOAD
ƫ
s ) 1
(26)
TPS40100
SLUS601–MAY 2005
APPLICATION INFORMATION (continued)
CURRENT SENSE AMPLIFIER GAIN SETTING RESISTANCE
vs
CURRENT SENSE AMPLIFIER GAIN
Figure 5.
A model that gives a good first order approximation to the control to output gain of a converter based on the
TPS40100 controller is shown in Figure 6. This model can be used in conjunction with a simulator to generate ac
and transient response plots. The block labeled “X2” is a simple gain of 2. The amplifier gm can be a simple
voltage controlled current source with a gain equal to the selected gm for the current sense amplifier (CSA).
Analytically, the control to output gain of this model ( Figure 6 ) can be expressed as follows:
K
FILT
(s) is the output filter transfer function:
K
FILT
(s) =
(25)
(dimensionless)
Usually, R
LDC
<< R
LOAD
and the following approximation holds:
Y(s) is the current signal transfer function and assumes that the inductor intrinsic time constant is matched to the
current sense filter network time constant.
15