Datasheet
2 x ' x R
S
x R
FB2
x A
S
x C
OUT
R
COMP
f
CROSS
=
[Hz]
R
FB2
x (C
COMP
+ C
HF
)
1
Where A
FB
(Feedback DC gain) =
,
R
COMP
x C
COMP
1
w
Z_EA
(Low frequency zero) =
,
R
COMP
x C
HF
1
w
P_EA
(High frequency pole) =
=
s
A
FB
x
Z
P_EA
V
OUT
^
V
COMP
^
-
Z
Z_EA
1 +
s
s x (1+ )
1
R
LOAD
x C
OUT
Z
P_LF
(Load pole) =
Z
Z_ESR
(ESR zero) =
1
R
ESR
x C
OUT
,
R
LOAD
R
S
x A
S
Where A
M
(Modulator DC gain) = ,
Z
Z_ESR
1 +
V
OUT
V
COMP
= A
M
x
s
1+
s
Z
P_LF
©
§
¹
·
^
^
LM25117
LM25117-Q1
www.ti.com
SNVS714E –APRIL 2011–REVISED MARCH 2013
APPLICATION INFORMATION
FEEDBACK COMPENSATION
Open loop response of the regulator is defined as the product of modulator transfer function and feedback
transfer function. When plotted on a dB scale, the open loop gain is shown as the sum of modulator gain and
feedback gain.
The modulator transfer function includes a power stage transfer function with an embedded current loop and can
be simplified as one pole and one zero system as shown in the following equations.
(15)
(16)
(17)
(18)
If the ESR of C
OUT
(R
ESR
) is very small, the modulator transfer function can be further simplified to a one pole
system and the voltage loop can be closed with only two loop compensation components, R
COMP
and C
COMP
,
leaving a single pole response at the crossover frequency. A single pole response at the crossover frequency
yields a very stable loop with 90 degrees of phase margin.
The feedback transfer function includes the feedback resistor divider and loop compensation of the error
amplifier. R
COMP
, C
COMP
and optional C
HF
configure the error amplifier gain and phase characteristics and create
a pole at origin, a low frequency zero and a high frequency pole. This is shown mathematically in the following
equations.
(19)
(20)
The pole at the origin minimizes output steady state error. The low frequency zero should be placed to cancel the
load pole of the modulator. The high frequency pole can be used to cancel the zero created by the output
capacitor ESR or to decrease noise susceptibility of the error amplifier. By placing the low frequency zero an
order of magnitude less than the crossover frequency, the maximum amount of phase boost can be achieved at
the crossover frequency. The high frequency pole should be placed well beyond the crossover frequency since
the addition of C
HF
adds a pole in the feedback transfer function.
The crossover frequency (loop bandwidth) is usually selected between one twentieth and one fifth of the f
SW
. In a
simplified formula, the crossover frequency can be defined as:
(21)
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