L1 = VOUT1 x (VIN - VOUT1)
IOR x Fs x VIN
LM5009
SNVS402H –FEBRUARY 2006–REVISED OCTOBER 2015
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8.2.2 Detailed Design Procedure
8.2.2.1 Output Resistor Divider Selection
R1 and R2: From the Functional Block Diagram section, VOUT1 can be determined to be equal to VFB × (R1 +
R2) / R2, and because VFB = 2.5 V, the ratio of R1 to R2 calculates as 3:1. Standard values of 3.01 kΩ(R1) and
1.00 kΩ(R2) are chosen. Other values can be used as long as the 3:1 ratio is maintained. The selected values,
however, provide a small amount of output loading (2.5 mA) in the event that the main load is disconnected and
allows the circuit to maintain regulation until the main load is reconnected.
8.2.2.2 Frequency Selection
Fsand RON:Unless the application requires a specific frequency, the choice of frequency is generally a
compromise because the size of L1 and C2, and the switching losses are affected. The maximum-allowed
frequency, based on a minimum on-time of 250 ns, is calculated by Equation 6:
FMAX = VOUT / (VINMAX × 250 ns) (6)
For this exercise, FMAX = 444 kHz. From Equation 2, RON calculates to 180 kΩ. A standard-value, 237-kΩresistor
is used to allow for tolerances in Equation 2, resulting in a nominal frequency of 337 kHz.
8.2.2.3 Inductor Selection
L1: The main parameter affected by the inductor is the output current ripple amplitude. The choice of inductor
value therefore depends on both the minimum and maximum load currents, keeping in mind that the maximum
ripple current occurs at maximum VIN.
a. Minimum load current: To maintain continuous conduction at minimum IO(100 mA), the ripple amplitude
(IOR) must be less than 200 mA peak-to-peak so the lower peak of the waveform does not reach zero. L1 is
calculated using Equation 7:
(7)
At VIN = 90 V, L1 (min) calculates to 132 µH. The next larger standard value (150 µH) is chosen and, with
this value, IOR calculates to 176 mA peak-to-peak at VIN = 90 V and 33 mA peak-to-peak at VIN = 12 V.
b. Maximum load current: At a load current of 150 mA, the peak of the ripple waveform must not reach the
minimum value of the LM5009 current limit threshold (250 mA). Therefore, the ripple amplitude must be less
than 200 mA peak-to-peak, which is already satisfied in Equation 7. With L1 = 150 µH, at maximum VIN and
IO, the peak of the ripple is 238 mA. Although L1 must carry this peak current without saturating or exceeding
its temperature rating, L1 must also be capable of carrying the maximum value of the LM5009 current limit
threshold (370 mA) without saturating because the current limit is reached during startup.
8.2.2.4 VCC and Bootstrap Capacitor
C3: The capacitor on the VCC output provides not only noise filtering and stability, but also prevents false
triggering of the VCC UVLO at the buck switch on and off transitions. For this reason, C3 must be no smaller than
0.1 µF.
C4: The recommended value is 0.022 µF for C4 because this value is appropriate in the majority of applications.
A high-quality ceramic capacitor, with low ESR is recommended because C4 supplies the surge current to
charge the buck switch gate at turn-on. A low ESR also ensures a quick recharge during each off-time. At
minimum VIN when the on-time is at maximum, C4 can possibly not fully recharge at start-up during each 300-ns
off-time. This failure to recharge results from the circuit being unable to complete the start-up and achieve output
regulation. This condition can occur when the frequency is intended to be low (for example, RON = 500 kΩ). In
this case, increase C4 to maintain sufficient voltage across the buck switch driver during each on-time.
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