LM3409MY-NOPB Datasheet, PDF (11/43 Pages) Texas Instruments – PFET Buck Controller for High Power LED Drivers

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LM3409/09HV
to
PGATE
Drive
t_OFF
Control
Logic
LM3409, LM3409HV, LM3409-Q1
SNVS602J – MARCH 2009 – REVISED MAY 2013
V_O
1.24V
R_OFF
COFF
C_OFF
+
v_COFF
-
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:
t_OFF = - R_OFF x (C_OFF + 20 pF) x ln _{¨¨©§}1 - ^1.V2_O^4V_{¸¸¹·}
(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.
v_COFF(t)
V_O
dv_COFF
dt
1.24
0
t_OFF
t
R_OFF x C_OFF
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:
dv_COFF(t) ₌
V_O
e^{- ¨©§ROFtFOxFCF OFF¸¸¹·}
dt
R_OFF x C_OFF
(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:
t_OFF |
1. 24V x R_OFF x C_OFF
V_O
(6)
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