Datasheet

DocID17977 Rev 2 17/46
ST1S14 Closing the loop
6.1 G
CO
(s) control to output transfer function
The accurate control to output transfer function for a buck peak current mode converter can
be written as:
Equation 2
where R
0
represents the load resistance, R
i
the equivalent sensing resistor of the current
sense circuitry, ω
p
the single pole introduced by the LC filter, and ω
z
the zero given by the
ESR of the output capacitor.
F
H
(s) accounts for the sampling effect performed by the PWM comparator on the output of
the error amplifier that introduces a double pole at one half of the switching frequency.
Equation 3
Equation 4
where:
Equation 5
S
n
represents the ON time slope of the sensed inductor current, and S
e
the ON time slope
of the external ramp (V
PP
peak to peak amplitude) that implements the slope compensation
to avoid sub-harmonic oscillations at duty cycle over 50 %.
The sampling effect contribution F
H
(s) is:
Equation 6
where:
G
CO
s()
R
0
R
i
------ -
1
1
R
0
T
SW
⋅
L
------------------------- -
m
C
1D–()0.5–⋅[]⋅+
------------------------------------------------------------------------------------------------ -
1
s
ω
z
-----+
⎝⎠
⎛⎞
1
s
ω
p
-----+
⎝⎠
⎛⎞
-------------------- -
F
H
s()⋅⋅⋅=
ω
Z
1
ESR C
OUT
⋅
----------------------------------=
ω
n
1
R
LOAD
C
OUT
⋅
----------------------------------------
m
C
1D–()0.5–⋅
LC
OUT
f
SW
⋅⋅
------------------------------------------------+=
m
C
1
S
e
S
n
------
+=
S
e
V
pp
f
SW
⋅=
S
n
V
IN
V
OUT
–
L
----------------------------- -
R
i
⋅=
⎝
⎜
⎜
⎜
⎜
⎜
⎜
⎛
F
H
s()
1
1
s
ω
n
Q
P
⋅
-------------------- -
s
2
ω
n
2
-----++
-------------------------------------------=