CS5422
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12
The voltage change during the load current transient is:
DV
OUT
+ DI
OUT
ǒ
ESL
Dt
) ESR )
t
TR
C
OUT
Ǔ
where:
ΔI
OUT
/ Δt = load current slew rate;
ΔI
OUT
= load transient;
Δt = load transient duration time;
ESL = Maximum allowable ESL including capacitors,
circuit traces, and vias;
ESR = Maximum allowable ESR including capacitors
and circuit traces;
t
TR
= 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 maximum allowable ESR can then be determined
according to the formula:
ESR
MAX
+
DV
ESR
DI
OUT
where:
ΔV
ESR
= change in output voltage due to ESR (assigned
by the designer)
Once the maximum allowable ESR is determined, the
number of output capacitors can be found by using the
formula:
Number of capacitors +
ESR
CAP
ESR
MAX
where:
ESR
CAP
= maximum ESR per capacitor (specified in
manufacturer’s data sheet).
ESR
MAX
= maximum allowable ESR.
The actual output voltage deviation due to ESR can then
be verified and compared to the value assigned by the
designer:
DV
ESR
+ DI
OUT
ESR
MAX
Similarly, the maximum allowable ESL is calculated from
the following formula:
ESL
MAX
+
DV
ESL
Dt
DI
Selection of the Input Inductor
A common requirement is that the buck controller must
not disturb the input voltage. One method of achieving this
is by using an input inductor and a bypass capacitor. The
input inductor isolates the supply from the noise generated
in the switching portion of the buck regulator and also limits
the inrush current into the input capacitors upon power up.
The inductor’s limiting effect on the input current slew rate
becomes increasingly beneficial during load transients. The
worst case is when the load changes from no load to full load
(load step), a condition under which the highest voltage
change across the input capacitors is also seen by the input
inductor. The inductor successfully blocks the ripple current
while placing the transient current requirements on the input
bypass capacitor bank, which has to initially support the
sudden load change.
The minimum inductance value for the input inductor is
therefore:
L
IN
+
DV
(dIńdt)
MAX
where:
L
IN
= input inductor value;
ΔV = voltage seen by the input inductor during a full load
swing;
(dI/dt)
MAX
= maximum allowable input current slew rate.
The designer must select the LC filter pole frequency so
that at least 40 dB attenuation is obtained at the regulator
switching frequency. The LC filter is a double−pole network
with a slope of −2.0, a roll−off rate of −40 dB/dec, and a
corner frequency:
f
C
+
1
2p LC
Ǹ
where:
L = input inductor;
C = input capacitor(s).
SELECTION OF THE POWER FET
FET Basics
The use of the MOSFET as a power switch is propelled by
two reasons: 1) Its very high input impedance; and 2) Its very
fast switching times. The electrical characteristics of a
MOSFET are considered to be those of a perfect switch.
Control and drive circuitry power is therefore reduced.
Because the input impedance is so high, it is voltage driven.
The input of the MOSFET acts as if it were a small capacitor,
which the driving circuit must charge at turn on. The lower
the drive impedance, the higher the rate of rise of V
GS
, and
the faster the turn−on time. Power dissipation in the
switching MOSFET consists of 1) conduction losses, 2)
leakage losses, 3) turn−on switching losses, 4) turn−off
switching losses, and 5) gate−transitions losses. The latter
three losses are proportional to frequency.
The most important aspect of FET performance is the
Static Drain−To−Source On−Resistance (R
DS(ON)
), which
affects regulator efficiency and FET thermal management
requirements. The On−Resistance determines the amount of
current a FET can handle without excessive power
dissipation that may cause overheating and potentially
catastrophic failure. As the drain current rises, especially
above the continuous rating, the On−Resistance also
increases. Its positive temperature coefficient is between
+0.6%/°C and +0.85%/°C. The higher the On−Resistance
the larger the conduction loss is. Additionally, the FET gate
charge should be low in order to minimize switching losses
and reduce power dissipation.