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SC4508A

Buck or Buck-Boost (Inverting) Current Mode Controller

Semtech Corporation 

SC4508A

POWER MANAGEMENT

Application Information (Cont.)

When determining the ESR value, both the steady state

ripple-voltage and the dynamic load transient need to be

considered. To keep the steady state output ripple-voltage

< ∆Vo, the ESR should satisfy:

Resr1

<

∆Vo

δIo

To limit the dynamic output voltage overshoot/

undershoot within α (say 3%) of the steady state output

voltage) from no load to full load, the ESR value should

satisfy:

R esr 2

<

αVo

Io

Then, the required ESR value of the output capacitors

should be:

Resr = min{Resr1,Resr2 }

The voltage rating of aluminum capacitors should be at

least 1.5Vo. The RMS current ripple rating should also

be greater than:

δIo

23

Usually it is necessary to have several capacitors of the

same type in parallel to satisfy the ESR requirement.

The voltage ripple cause by the capacitor charge/

discharge should be an order of magnitude smaller than

the voltage ripple caused by the ESR. To guarantee this,

the capacitance should satisfy:

Co

>

10

2πfsResr

Buck-boost converter has higher ripple current than buck

in output. The RMS value is the most important factor to

consider. It has to be less than the output capacitor ripple

current rating.

The buck-boost output capacitor RMS current is:

IRMS _ CAP ≈ IO

VO + Vd

VIN

∆vESR = Resr ⋅ Id

the following remarks are made to clarify some practical

issues.

Remark 1: High frequency ceramic capacitors may not

carry most of the ripple current. It also depends on the

capacitor value. Only when the capacitor value is set

properly, the effect of ceramic capacitor low ESR starts

to be significant.

For example, if a 10µF, 4mΩ ceramic capacitor is

connected in parallel with 2x1500µF, 90mΩ electrolytic

capacitors, the ripple current in the ceramic capacitor is

only about 42% of the current in the electrolytic

capacitors at the ripple frequency. If a 100µF, 2mΩ

ceramic capacitor is used, the ripple current in the

ceramic capacitor will be about 4.2 times of that in the

electrolytic capacitors. When two 100µF, 2mΩ ceramic

capacitors are used, the current ratio increases to 8.3.

In this case most of the ripple current flows in the

ceramic decoupling capacitor. The ESR of the ceramic

capacitors will then determine the output ripple-voltage.

Remark 2: The total equivalent capacitance of the filter

bank is not simply the sum of all the paralleled capacitors.

The total equivalent ESR is not simply the parallel

combination of all the individual ESRs either. Instead they

should be calculated using the following formulae.

Ceq(ω) :=

(R1a + R1b )2 ω2C1a2C1b2 + (C1a + C1b )2

(R1a2C1a + R1b2C1b )ω2C1aC1b + (C1a + C1b )

Req (ω)

:=

R1aR1b (R1a

(R1a

+ R1b )ω2C1a2C1b2 + (R1bC1b2 + R1aC1a2 )

+ R1b )2 ω2C1a2C1b2 + (C1a + C1b )2

where R1a and C1a are the ESR and capacitance of

electrolytic capacitors, and R1b and C1b are the ESR and

capacitance of the ceramic capacitors respectively.

(Figure 2)

where, V and I are rectifier forward voltage and current.

d

d

In many applications, several low ESR ceramic capacitors

are added in parallel with the aluminum capacitors in

order to further reduce ESR and improve high frequency

decoupling. Because the values of capacitance and ESR

are usually different in ceramic and aluminum capacitors,

C1a

R1a

C1b

R1b

Ceq

Req

Figure 2. Equivalent RC branch.

 2007 Semtech Corp.

9

www.semtech.com

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