CS51313
Application Information: continued
The total change in output voltage as a result of a load cur-
rent transient can be verified by the following formula:
∆V
OUT
=
∆V
ESR
+
∆V
ESL
+
∆V
CAP
Step 3: Selection of the Duty Cycle,
Switching Frequency, Switch On-Time (T
ON
)
and Switch Off-Time (T
OFF
)
The duty cycle of a buck converter (including parasitic
losses) is given by the formula:
Duty Cycle = D =
V
OUT
+ (V
HFET
+ V
L
+ V
DROOP
)
,
V
IN
+ V
LFET
−
V
HFET
−
V
L
Step 4: Selection of the Output Inductor
The inductor should be selected based on its inductance,
current capability, and DC resistance. Increasing the induc-
tor value will decrease output voltage ripple, but degrade
transient response. There are many factors to consider in
selecting the inductor including cost, efficiency, EMI and
ease of manufacture. The inductor must be able to handle
the peak current at the switching frequency without satu-
rating, and the copper resistance in the winding should be
kept as low as possible to minimize resistive power loss.
There are a variety of materials and types of magnetic
cores that could be used for this application. Among them
are ferrites, molypermalloy cores (MPP), amorphous and
powdered iron cores. Powdered iron cores are very com-
monly used. Powdered iron cores are very suitable due to
their high saturation flux density and have low loss at high
frequencies, a distributed gap and exhibit very low EMI.
The inductor value can be determined by:
L=
(V
IN
−
V
OUT
)
×
t
TR
∆Ι
,
where
V
OUT
= buck regulator output voltage;
V
HFET
= high side FET voltage drop due to R
DS(ON)
;
V
L
= output inductor voltage drop due to inductor wire
DC resistance;
V
DROOP
= droop (current sense) resistor voltage drop;
V
IN
= buck regulator input voltage;
V
LFET
= low side FET voltage drop due to R
DS(ON)
.
Step3a: Calculation of Switch On-Time
The switch On-Time (time during which the switching
MOSFET in a synchronous buck topology is conducting) is
determined by:
T
ON
=
Duty Cycle
,
F
SW
where
V
IN
= input voltage;
V
OUT
= output voltage;
t
TR
= output voltage transient response time (assigned
by the designer);
∆I
= load transient.
The inductor ripple current can then be determined:
∆I
L
=
V
OUT
×
T
OFF
L
,
where F
SW
= regulator switching frequency selected by the
designer.
Higher operating frequencies allow the use of smaller
inductor and capacitor values. Nevertheless, it is common
to select lower frequency operation because a higher fre-
quency results in lower efficiency due to MOSFET gate
charge losses. Additionally, the use of smaller inductors at
higher frequencies results in higher ripple current, higher
output voltage ripple, and lower efficiency at light load
currents.
Step 3b: Calculation of Switch Off-Time
The switch Off-Time (time during which the switching
MOSFET is not conducting) can be determined by:
T
OFF
=
1
F
SW
−
T
ON
,
where
∆I
L
= inductor ripple current;
V
OUT
= output voltage;
T
OFF
= switch Off-Time;
L = inductor value.
The designer can now verify if the number of output
capacitors from step 2 will provide an acceptable output
voltage ripple (1% of output voltage is common). The for-
mula below is used:
∆I
L
=
Rearranging we have:
ESR
MAX
=
∆V
OUT
∆I
L
,
∆V
OUT
ESR
MAX
,
The C
OFF
capacitor value has to be selected in order to set
the Off-Time, T
OFF
, above:
C
OFF
=
Period
×
(1
−
D)
,
3980
where
3980 is a characteristic factor of the CS51313;
D = Duty Cycle.
where
ESR
MAX
= maximum allowable ESR;
∆V
OUT
= 1%
×
V
OUT
= maximum allowable output volt-
age ripple ( budgeted by the designer );
∆I
L
= inductor ripple current;
V
OUT
= output voltage.
The number of output capacitors is determined by:
Number of capacitors =
ESR
CAP
,
ESR
MAX
where ESR
CAP
= maximum ESR per capacitor (specified in
manufacturer’s data sheet).
12
CHERRY [ CHERRY SEMICONDUCTOR CORPORATION ]
