LM3409 Datasheet, PDF (10/30 Pages) National Semiconductor (TI) – PFET Buck Controller for High Power LED Drives

There are three different methods to set the current sense
threshold (V_CST) using the multi-function IADJ pin:
1. IADJ pin left open: 5µA internal current source biases the
Zener diode and clamps the IADJ pin voltage (V_ADJ) at
1.24V causing the maximum threshold voltage:
2. External voltage (V_ADJ) of 0V to 1.24V: Apply to the IADJ
pin to adjust V_CST from 0V to 248mV. If the V_ADJ voltage
is adjustable, analog dimming can be achieved.
3. External resistor (R_EXT) placed from IADJ pin to ground:
5µA current source sets the V_ADJ voltage and
corresponding threshold voltage:
Controlled Off-Time
Once Q1 is turned off, it remains off for a constant time
(t_OFF) which is preset by an external resistor (R_OFF), an ex-
ternal capacitor (C_OFF), and the output voltage (V_O) as shown
in Figure 3. Since I_LED is tightly regulated, V_O will remain
nearly constant over widely varying input voltage and tem-
perature yielding a nearly constant t_OFF.
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FIGURE 4. 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 ca-
pacitance at the COFF pin, v_COFF(t) is plotted in Figure 4. The
time derivative of v_COFF(t) can be calculated to find a linear
approximation to the t_OFF equation:
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:
FIGURE 3. Off-Time Control Circuit
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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 con-
stant 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 termi-
nated and v_COFF(t) is reset to zero. t_OFF is calculated as
follows:
Using the actual t_OFF equation, the inductor current ripple
(Δi_L-PP) of a buck current regulator operating in CCM is:
Using the t_OFF approximation, the equation is reduced to:
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 cir-
cuit. 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 oc-
cur.
Δi_L-PP is independent of both V_IN and V_O when in CCM!
The Δi_L-PP approximation only depends on R_OFF, C_OFF, and
L1, therefore the ripple is essentially constant over the oper-
ating range as long as V_O >> 1.24V (when the t_OFF approxi-
mation is valid). An exception to the t_OFF approximation
occurs if the IADJ pin is used to analog dim. As the LED/in-
ductor current decreases, the converter will eventually enter
DCM and the ripple will decrease with the peak current thresh-
old. The approximation shows how the LM3409/09HV
achieves constant ripple over a wide operating range, how-
ever t_OFF should be calculated using the actual equation first
presented.
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