LTC7813 datasheet(22/36 Pages) LINER

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LTC7821

Rev A

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APPLICATIONS INFORMATION

current, but also carries the balancing current that flows

between CFLY and CMID due to an imbalance of voltage

between the two capacitors at the end of phase 1. There-

fore M4 has an increase in conduction losses compared

to its counterpart in a traditional buck converter. The

current flowing through M2 is dependent on the voltage

differential between the capacitors, their ESR, RDSON of

M2 and M4, and inductance of the MOSFETs, capacitors,

and board traces (see Figure 13b).

When the controller is operating in continuous mode the

duty cycles for M1, M3, M2 and M4 are given by:

M1, M3 Switch Duty Cycle =

2 • VOUT

VIN

M2, M4 Switch Duty Cycle =

VIN – 2 • VOUT

VIN

The power dissipation of M1 and M3 is given by:

PM1=

IMAX • CFLY

CFLY + CMID

⎛

⎝⎜

⎞

⎠⎟

2 2 • VOUT

VIN

⎛

⎝⎜

⎞

⎠⎟

1+ d

(

)RDS(ON)

PM3 =

IMAX • CMID

CFLY + CMID

⎛

⎝⎜

⎞

⎠⎟

2 2 • VOUT

VIN

⎛

⎝⎜

⎞

⎠⎟

1+ d

(

)RDS(ON)+

VIN

⎛

⎝⎜

⎞

⎠⎟

IMAX • CMID

2 • CFLY + CMID

(

)

⎛

⎝

⎜

⎞

⎠

⎟ RDR

(

) CMILLER

(

)•

VINTVCC – VTH(MIN)

VTH(MIN)

⎡

⎣

⎢

⎤

⎦

⎥ • f

where d is the temperature dependency of RDS(ON), RDR

is the effective top driver resistance (approximately 2Ω

at VGS = VMILLER), and VIN is the input supply. VTH(MIN)

is the data sheet specified typical gate threshold voltage

specified in the power MOSFET data sheet at the specified

drain current. CMILLER is the calculated capacitance using

the gate charge curve from the MOSFET data sheet and

the technique described above.

If the switching loss contribution of PM3 is relatively small

compared to its conduction loss, then the overall power

dissipation(PM1+PM3)willbethelowestwhenCFLY=CMID.

The power dissipation of M2 and M4 is harder to calcu-

late, because the current flowing through these MOSFETs

exhibits a 2nd order system response due to the presence

of parasitic package inductance of the MOSFETs and ca-

pacitors, ESR of the capacitors, RDS(ON) of the MOSFETs

and the capacitance of CMID and CFLY. Complicating the

matter is that the current could exhibit overdamped, criti-

cally damped or underdamped characteristics, depending

on the RLC values mentioned above; this would impact

the RMS current significantly. Use ADI/LTC power tool to

help select M2 and M4.

With the RMS current flowing through M2 and M4 deter-

mined, the power dissipation is given by:

PM2 = I2rms2 • 1+ d

(

)RDS(ON)

PM4 = I2rms4 • 1+ d

(

)RDS(ON)

CFLY and CMID Selection

Inthishybridtopology,capacitorsCFLYandCMIDarepartof

theenergytransferelements.Thereforeceramiccapacitors

are attractive since they have the lowest ESR. However,

care should be taken when choosing this type of capacitor.

During operation the DC voltage across the CFLY and CMID

is approximately half the VIN supply, therefore the voltage

rating of the capacitors should be greater than that. As

a general rule, select the voltage rating of the capacitor

to be twice the operating voltage of the capacitor. For the

same voltage rating and capacitance, a larger case size

will have a lower failure rate.

In addition, the operating temperature of the capacitors

needs to be considered. For operating temperature above

85°C, capacitors with the X7R dielectric need to be used

while X5R dielectric is adequate for operation below 85°C.

For long term reliability of the capacitor, keep the tem-

perature rise of the capacitor to be below 20°C, preferably

10°C. The temperature rise of the capacitor is dependent

on the amount of RMS current through the capacitor and

the operating frequency. Consult the manufacturer’s data

sheet for this data.

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