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3433EFE

High Voltage Step-Up/Step-Down DC/DC Converter

Linear Technology 

LT3433

APPLICATIO S I FOR ATIO

RL = Inductor series resistance

∆BST = Boosted switch drive currents IVBST/ISW (in A/A)

∆OUT = Grounded switch drive currents IVOUT/ISW

(in A/A)

VF1 = Switch node catch diode forward voltage

VF2 = Pass diode forward voltage

IVIN = VIN quiescent input current

IIN = VIN switched current

IBIAS = VBIAS quiescent input current

RCESR = Output capacitor ESR

Operational duty cycle is a function of voltage imposed

across the switched inductance and switch on/off times.

Using the relation for change in current in an inductor:

δI = V • δt/L

and putting the application variables into the above rela-

tion yields:

δION(BRIDGED) = (DC/fO • L)[VIN – ISW • (RSWH + RSWL

+ RL)]

δION(BUCK) = (DC/fO • L)[VIN – VOUT – VF2 – ISW

• (RSWH + RL + RESR)]

δIOFF = [(1 – DC)/fO • L][VOUT + VF1 + VF2 – ISW

• (RL + RESR)]

Current conservation in an inductor dictates δION = δIOFF,

so plugging in the above relations and solving for DC yields:

DC(BRIDGED) = [VOUT + VF1 + VF2 – ISW • (RL + RESR)]/

[VIN – ISW • (RSWH + RSWL + 2RL + RESR) + VOUT +

VF1 + VF2 ]

DC(BUCK) = [VOUT + VF1 + VF2 – ISW • (RL + RESR)]/

[VIN – ISW • (RSWH + 2RL + 2RESR) + VF1]

In order to solve the above equations, inductor ripple

current (∆I) must be determined so ISW can be calculated.

∆I follows the relation:

∆I = (VOUT + VF1 + VF2 – ISW • RL)(1 – DC)/(L • fO)

As ∆I is a function of DC and vice-versa, the solution is

iterative. Seed ∆I and solve for DC. Using the resulting

value for DC, solve for ∆I. Use the resulting ∆I as the new

seed value and repeat. The calculated value for DC can be

used once the resulting ∆I is close (<1%) to the seed value.

Once DC is determined, maximum output current can be

determined using current conservation on the converter

output:

Bridged Operation: IOUT(MAX) = ISW • [1 – DC •

(1 + ∆BST + ∆OUT)] – IBIAS

Buck Operation: IOUT(MAX) = ISW • (1 – DC • ∆BST)

– IBIAS

PIN = POUT + PLOSS, where PLOSS = PSWON + PSWOFF + PIC,

corresponding to the power loss in the converter. PIC is the

quiescent power dissipated by the LT3433. PSWON is the

loss associated with the power path during the switch on

interval, and PSWOFF is the PowerPathTM loss associated

with the switch off interval.

PLOSS equals the sum of the power loss terms:

PVIN = VIN • IVIN

PBIAS = VOUT • IBIAS

PSWON(BRIDGED) = DC • [ISW 2 • (RSWH + RSWL+ RL)

+ ISW • VOUT • (∆BST + ∆OUT) + RCESR • IOUT2]

PSWON(BUCK) = DC • [ISW 2 • (RSWH + RL) + ISW •

VOUT • ∆BST + RCESR • (ISW • (1 – ∆BST) – IBIAS –

IOUT)2]

PSWOFF = (1 – DC) • [ISW • (VF1 + VF2) + ISW2 • RL +

RCESR • (ISW – IBIAS – IOUT)2]

Efficiency (E) is described as POUT/PIN, so:

Efficiency = {1 + (PVIN + PBIAS + PSWON + PSWOFF)/POUT}–1

Empirical determination of converter capabilities is ac-

complished by monitoring inductor currents with a cur-

rent probe under various input voltages and load currents.

Decreasing input voltage or increasing load current re-

sults in an inductor current increase. When peak inductor

currents reach the switch current limit value, maximum

output current is achieved. Limiting the inductor currents

to the LT3433 specified W/C current limit of 0.5V (cold)

will allow margin for operating limit variations. These

limitations should be evaluated at the operating tempera-

ture extremes required by the application to assure robust

performance.

PowerPath is a trademark of Linear Technology Corporation

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