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LMZ14201
SNVS649F – JANUARY 2010 – REVISED OCTOBER 2013
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Recommended minimum input capacitance is 10uF X7R ceramic with a voltage rating at least 25% higher than
the maximum applied input voltage for the application. It is also recommended that attention be paid to the
voltage and temperature deratings of the capacitor selected. It should be noted that ripple current rating of
ceramic capacitors may be missing from the capacitor data sheet and you may have to contact the capacitor
manufacturer for this rating.
If the system design requires a certain minimum value of input ripple voltage Δ V IN be maintained then Equation 9
may be used.
C IN ≥ I O * D * (1–D) / f SW-CCM * Δ V IN
(9)
If Δ V IN is 1% of V IN for a 24V input to 3.3V output application this equals 240 mV and f SW = 400 kHz.
C IN ≥ 1A * 3.3V/24V * (1– 3.3V/24V) / (400000 * 0.240 V)
≥ 0.9 μ F
Additional bulk capacitance with higher ESR may be required to damp any resonant effects of the input
capacitance and parasitic inductance of the incoming supply lines.
R ON RESISTOR SELECTION
Many designs will begin with a desired switching frequency in mind. For that purpose Equation 10 can be used.
f SW(CCM) ? V O / (1.3 * 10 -10 * R ON )
This can be rearranged as
R ON ? V O / (1.3 * 10 -10 * f SW(CCM) )
(10)
(11)
The selection of RON and f SW(CCM) must be confined by limitations in the on-time and off-time for the COT
Control Circuit Overview section.
The on-time of the LMZ14201 timer is determined by the resistor R ON and the input voltage V IN . It is calculated
as follows:
t ON = (1.3 * 10 -10 * R ON ) / V IN
(12)
The inverse relationship of t ON and V IN gives a nearly constant switching frequency as V IN is varied. R ON should
be selected such that the on-time at maximum V IN is greater than 150 ns. The on-timer has a limiter to ensure a
minimum of 150 ns for t ON . This limits the maximum operating frequency, which is governed by Equation 13 :
f SW(MAX) = V O / (V IN(MAX) * 150 nsec)
(13)
This equation can be used to select R ON if a certain operating frequency is desired so long as the minimum on-
time of 150 ns is observed. The limit for R ON can be calculated as follows:
R ON ≥ V IN(MAX) * 150 nsec / (1.3 * 10 -10 )
(14)
If R ON calculated in Equation 11 is less than the minimum value determined in Equation 14 a lower frequency
should be selected. Alternatively, V IN(MAX) can also be limited in order to keep the frequency unchanged.
Additionally note, the minimum off-time of 260 ns limits the maximum duty ratio. Larger R ON (lower F SW ) should
be selected in any application requiring large duty ratio.
Discontinuous Conduction and Continuous Conduction Modes
At light load the regulator will operate in discontinuous conduction mode (DCM). With load currents above the
critical conduction point, it will operate in continuous conduction mode (CCM). When operating in DCM the
switching cycle begins at zero amps inductor current; increases up to a peak value, and then recedes back to
zero before the end of the off-time. Note that during the period of time that inductor current is zero, all load
current is supplied by the output capacitor. The next on-time period starts when the voltage on the at the FB pin
falls below the internal reference. The switching frequency is lower in DCM and varies more with load current as
compared to CCM. Conversion efficiency in DCM is maintained since conduction and switching losses are
reduced with the smaller load and lower switching frequency. Operating frequency in DCM can be calculated as
follows:
f SW(DCM) ? V O *(V IN -1)*10 μ H*1.18*10 20 *I O /(V IN –V O )*R ON2
(15)
In CCM, current flows through the inductor through the entire switching cycle and never falls to zero during the
off-time. The switching frequency remains relatively constant with load current and line voltage variations. The
CCM operating frequency can be calculated using Equation 7 above.
14
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