Application Information: continued
The CPU VCC(CORE) tolerance can be affected by any or all
∆VESR
∆IOUT
ESRMAX
=
,
of the following reasons:
1) buck regulator output voltage setpoint accuracy;
where ∆VESR = change in output voltage due to ESR
2) output voltage change due to discharging or charging of
the bulk decoupling capacitors during a load current tran-
sient;
3) output voltage change due to the ESR and ESL of the
bulk and high frequency decoupling capacitors, circuit
traces, and vias;
(assigned by the designer).
Once the maximum allowable ESR is determined, the
number of output capacitors can be found by using the for-
mula
ESRCAP
ESRMAX
4) output voltage ripple and noise.
Budgeting the tolerance is left up to the designer who must
take into account all of the above effects and provide a
Number of capacitors =
,
where
V
CC(CORE) that will meet the specified tolerance at the
ESRCAP = maximum ESR per capacitor (specified in
manufacturer’s data sheet);
ESRMAX = maximum allowable ESR.
The actual output voltage deviation due to ESR can then be
verified and compared to the value assigned by the design-
er:
CPU’s inputs.
The designer must also ensure that the regulator compo-
nent junction temperatures are kept within the manufac-
turer’s specified ratings at full load and maximum ambient
temperature. As computer motherboards become increas-
ingly complex, regulator size also becomes important, as
there is less space available for the CPU power supply.
∆VESR = ∆IOUT × ESRMAX
Step 2: Selection of the Output Capacitors
Similarly, the maximum allowable ESL is calculated from
the following formula:
These components must be selected and placed carefully to
yield optimal results. Capacitors should be chosen to pro-
vide acceptable ripple on the regulator output voltage. Key
specifications for output capacitors are their ESR
(Equivalent Series Resistance), and ESL (Equivalent Series
Inductance). For best transient response, a combination of
low value/high frequency and bulk capacitors placed close
to the load will be required.
In order to determine the number of output capacitors the
maximum voltage transient allowed during load transi-
tions has to be specified. The output capacitors must hold
the output voltage within these limits since the inductor
current can not change with the required slew rate. The
output capacitors must therefore have a very low ESL and
ESR.
∆VESL × ∆t
ESLMAX
=
,
∆I
where
∆I/∆T = load current slew rate (as high as 20A/µs);
∆VESL = change in output voltage due to ESL.
The actual maximum allowable ESL can be determined by
using the equation:
ESLCAP
ESLMAX
=
,
Number of output capacitors
The voltage change during the load current transient is:
where ESLCAP = maximum ESL per capacitor (it is estimat-
ed that a 10 × 12mm Aluminum Electrolytic capacitor has
approximately 4nH of package inductance).
The actual output voltage deviation due to the actual maxi-
mum ESL can then be verified:
tTR
COUT
ESL
∆t
∆VOUT = ∆IOUT
×
+ ESR +
,
(
)
where
∆IOUT / ∆t = load current slew rate;
∆IOUT = load transient;
ESLMAX × ∆I
∆VESL
=
.
∆t
∆t = load transient duration time;
ESL = Maximum allowable ESL including capacitors,
circuit traces, and vias;
ESR = Maximum allowable ESR including capacitors
and circuit traces;
tTR = output voltage transient response time.
The designer has to independently assign values for the
change in output voltage due to ESR, ESL, and output
capacitor discharging or charging. Empirical data indicates
that most of the output voltage change (droop or spike
depending on the load current transition) results from the
total output capacitor ESR.
The designer now must determine the change in output
voltage due to output capacitor discharge during the tran-
sient:
∆I × ∆tTR
∆VCAP
=
,
COUT
where
∆tTR = the output voltage transient response time
(assigned by the designer);
∆VCAP = output voltage deviation due to output capaci-
tor discharge;
∆I = Load step.
The maximum allowable ESR can then be determined
according to the formula
11
CHERRY [ CHERRY SEMICONDUCTOR CORPORATION ]
