AN1049 datasheet(19/24 Pages) STMICROELECTRONICS

19 / 24 page

obviously, DCM will take place for Pin < PinT and

CCM for Pin > PinT. This equation can be rewritten

as follows:

PinT

⋅ ZE

(A6)

by defining the "Equivalent Input Voltage" (VE) and

the "Equivalent Primary Impedance" (ZE):

Vin

;

= fSW ⋅ Lp

(A7).

VE is a function of Vin only (see fig. A2), since the

reflected voltage (VR) is fixed. The variation of VE in

its range [VEmin , VEmax ], which depends on the

mains voltage range, in turn defines the range of

PinT [PinTmin ,PinTmax].

Fig. A3 shows the diagram of (A6) while Tab. A1

presents the ranges of VE relevant to typical mains

voltage ranges, as well as the corresponding

PinTmax / PinTmin ratios.

To complete the characterization of the transition

between DCM and CCM it is convenient to define

the Transition Voltage (VET), that is the Equivalent

Input Voltage at

which the operation is on the

boundary between DCM and CCM, for a given Pin

and a given ZE:

VET

= √

⋅ ZE ⋅ Pin

(A8).

DCM will take place for VE > VET and CCM for VE <

VET.

In synchronized converters it is possible to define

also the Transition Frequency (fT), that is the switch-

ing frequency at which the operation is on the

boundary between DCM and CCM, for a given VE and a given Pin:

⋅ Lp ⋅ Pin

(A9).

DCM will take place for fsw < fT and CCM for fsw > fT.

The peak primary current at transition is then:

Ippk(T) =

√

⋅ PinT

fSW

⋅ Lp

fSW

⋅ Lp

⋅

Vin

(A9).

In case of CCM operation, equation (A4) still applies but the timing relationships (A2) change as follows:

TON

⋅ ∆Ip

Vin

; TFW

= T − TON =

⋅ ∆Ip

(A10),

where

∆Ip is the primary current ripple.

• Vout

Vinmin

Vinmax

VEmax

VEmin

Vin

Figure A2. Equivalent Input Voltage vs. DC

Input Voltage

PinT

VEmin

VEmax

VET

fsw

Figure A3. Characterization of the

transi-

tion DCM

⇐⇒ CCM

AN1049 APPLICATION NOTE

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