tpeak =

'IOUT(MAX) x L

VOUT-DMINVIN

- COUTRESR

'Vq =

COUT

'IOUT(MAX)

t -

2 X L X COUT

t

2 (V)

VOUT - DMINVIN

RESR(MAX) =

VOS(MAX)

'IOUT(MAX):

'Vr = RESR('IOUT(MAX) -

L

VOUT - DMINVIN

t) (V)

'V

c2

Time

Upper Voltage

Limit

VOS (MAX)

'V

c1

0

ESR too large

capacitance too small

LM3477

SNVS141K – OCTOBER 2000 – REVISED MARCH 2013

www.ti.com

Figure 29. Output Voltage Overshoot Violation

The ESR and the capacitance of the output capacitor must be carefully chosen so that the output voltage

overshoot is within the design's specification VOS(MAX). If the total combined ESR of the output capacitors is not

low enough, the initial output voltage excursion will violate the specification, see

ΔVC1. If the ESR is low enough,

but there is not enough output capacitance, the output voltage will travel outside the specification window due to

the extra charge being dumped into the capacitor, see

ΔVC2. The LM3477/A has output over voltage protection

(OVP) which could trigger if the transient overshoot is high enough. If this happens, the controller will operate in

hysteretic mode (see OVER VOLTAGE PROTECTION) for a few cycles before the output voltage settles to its

steady state. If this behavior is not desired, substitute VOVP (referred to the output) for VOS(MAX) (VOVP is found in

the Electrical Characteristics) to find the minimum capacitance and maximum ESR of the output capacitor.

CALCULATIONS FOR THE OUTPUT CAPACITOR

During a loading transient, the delta output voltage

ΔVc has two changing components. One is the voltage

difference across the ESR (

ΔVr), the other is the voltage difference caused by the gained charge (ΔVq). This

gives:

ΔVc = ΔVr + ΔVq

(24)

The design objective is to keep

ΔVc lower than some maximum overshoot (VOS(MAX)). VOS(MAX) is chosen based

on the output load requirements.

Both voltages

ΔVr and ΔVqwill change with time. For ΔVr the equation is:

(25)

where,

RESR = the output capacitor ESR

ΔIOUT = the difference between the load current change IOUT(MAX) − IOUT(MIN)

DMIN = Minimum duty cycle of device (0.165 typical)

Evaluating this equation at t = 0 gives

ΔVr(max). Substituting VOS(MAX) for ΔVr(MAX) and solving for RESR gives:

(26)

The expression for

ΔVq is:

(27)

From Figure 30 it can be told that

ΔVC will reach its peak value at some point in time and then decrease. The

larger the output capacitance is, the earlier the peak will occur. To find the peak position, let the derivative of

ΔVC

go to zero, and the result is:

(28)

20

Submit Documentation Feedback

Copyright © 2000–2013, Texas Instruments Incorporated

Product Folder Links: LM3477