Datasheet

OFF
t |
O
OFFOFF
V
CRV24.1 xx
e
¸
¸
¹
·
¨
¨
©
§
-
x
OFFOFF
OFF
CR
t
O
V
x
OFFOFF
CR
=
dt
COFF
dv (t)
v
COFF
(t)
t
V
O
0
R
OFF
x C
OFF
dv
COFF
dt
1.24
t
OFF
-1
1.24V
O
V
x-
=
OFFOFF
(C
OFF
+ 20 pF)Rt x ln
¸
¸
¹
·
¨
¨
©
§
V
O
R
OFF
C
OFF
+
-
COFF
1.24V
t
OFF
Control
Logic
to
PGATE
Drive
-
+
v
COFF
LM3409/09HV
LM3409, LM3409HV, LM3409-Q1
www.ti.com SNVS602J –MARCH 2009–REVISED MAY 2013
Figure 23. Off-Time Control Circuit
At the start of t
OFF
, the voltage across C
OFF
(v
COFF
(t)) is zero and the capacitor begins charging according to the
time constant provided by R
OFF
and C
OFF
. When v
COFF
(t) reaches the off-time threshold (V
OFT
= 1.24V), then the
off-time is terminated and v
COFF
(t) is reset to zero. t
OFF
is calculated as follows:
(4)
In reality, there is typically 20 pF parasitic capacitance at the off-timer pin in parallel with C
OFF
, which is
accounted for in the calculation of t
OFF
. Also, it should be noted that the t
OFF
equation has a preceding negative
sign because the result of the logarithm should be negative for a properly designed circuit. The resulting t
OFF
is a
positive value as long as V
O
> 1.24V. If V
O
< 1.24V, the off-timer cannot reach V
OFT
and an internally limited
maximum off-time (typically 300µs) will occur.
Figure 24. Exponential Charging Function v
COFF
(t)
Although the t
OFF
equation is non-linear, t
OFF
is actually very linear in most applications. Ignoring the 20pF
parasitic capacitance at the COFF pin, v
COFF
(t) is plotted in Figure 24. The time derivative of v
COFF
(t) can be
calculated to find a linear approximation to the t
OFF
equation:
(5)
When t
OFF
<< R
OFF
x C
OFF
(equivalent to when V
O
>> 1.24V), the slope of the function is essentially linear and
t
OFF
can be approximated as a current source charging C
OFF
:
(6)
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