LM3557 Datasheet, PDF (8/11 Pages) National Semiconductor (TI) – Step-Up Converter for White LED Applications

Application Information (Continued)
FIGURE 4. Inductor Current Waveform
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CONTINUOUS AND DISCONTINUOUS MODES OF
OPERATION
Since the LM3557 is a constant frequency pulse-width-
modulated step-up regulator, care must be taken to make
sure the maximum duty cycle specification is not violated.
The duty cycle equation depends on which mode of opera-
tion the LM3557 is in. The two operational modes of the
LM3557 are continuous conduction mode (CCM) and dis-
continuous conduction mode (DCM). Continuous conduction
mode refers to the mode of operation where during the
switching cycle, the inductor’s current never goes to and
stays at zero for any significant amount of time during the
switching cycle. Discontinuous conduction mode refers to
the mode of operation where during the switching cycle, the
inductor’s current goes to and stays at zero for a significant
amount of time during the switching cycle. Figure 4 illus-
trates the threshold between CCM and DCM operation. In
Figure 4, the inductor current is right on the CCM/DCM
operational threshold. Using this as a reference, a factor can
be introduced to calculate when a particular application is in
CCM or DCM operation. R is a CCM/DCM factor we can use
to compute which mode of operation a particular application
is in. If R is ≥ 1, then the application is operating in CCM.
Conversely, if R is < 1, the application is operating in DCM.
The R factor inequalities are a result of the components that
make up the R factor. From Figure 4, the R factor is equal to
the average inductor current, I_L(avg), divided by half the
inductor ripple current, ∆i_L. Using Figure 4, the following
equation can be used to compute R factor:
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V_IN:
V_OUT:
Eff:
Input Voltage.
Output Voltage.
Efficiency of the LM3557.
Fs: Switching Frequency.
I_OUT: White LED Current/Load Current.
L:
Inductance Magnitude/Inductor Value.
D:
Duty Cycle for CCM operation.
∆i_L: Inductor Ripple Current.
I_L(avg): Average Inductor Current.
For CCM operation, the duty cycle can be computed with:
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t_ON: Internal Power FET On-Time.
T_S: Switching Period of Operation.
D: Duty Cycle for CCM Operation.
V_OUT: Output Voltage.
V_IN: Input Voltage.
For DCM operation, the duty cycle can be computed with:
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