Filter
Top Products
External Component Selection
2-17
Design Procedure
V
L
+
L
I
TRAN
D
t
å
L
v
V
L
I
TRAN
D
t
Where:
V
L
= the voltage applied across the output inductor,
I
TRAN
= the magnitude of the load step, and
∆t = the desired response time.
For a load step from light load to heavy load, the voltage applied across the
inductor can be assumed to be V
I
– V
O
. This also assumes that the duty cycle
is 100% as the output voltage is corrected. Alternatively, for a load step from
heavy load to light load, the voltage across the inductor can be assumed to be
V
O
. This assumes that the duty cycle is 0% as the output voltage is corrected.
For the example circuit described here, the condition which gives the smallest
inductor value is a load step from light load to heavy load for a 3.3-V output.
This is because the voltage applied to the output inductor is the lowest, i.e.,
the input voltage minus the output voltage. For this case, allowing 5 µs for the
inductor current to change, an inductance value is calculated as follows:
L
v
V
L
I
TRAN
D
t
+
5
–
3.3
6
5 10
–
6
+ 1.4 m
H
For convenience, a 1.5-µH inductor was designed for this circuit.
Figures 3–10, 3–19, 3–28, and 3–37 illustrate satisfactory transient load per-
formance for the output filter values selected in this and the previous sections.
2.2.4 Switching Frequency Analysis
After the elements of the output filter are determined, the power supply
switching frequency must be estimated. If the estimated switching frequency
is too high, the switching losses in the power MOSFETs will be high, resulting
in less than optimum efficiency. If the estimated switching frequency is too low,
the inductor value may be too high, resulting in unsatisfactory transient
response. A switching frequency outside the desired range should be
corrected by changing either the output ripple setting, the output capacitance,
or the output inductance.
To accurately predict the switching frequency of a hysteretic regulator, the
output voltage ripple must be investigated. This should be expected, since the
power supply switching instants are based upon the state of the output
voltage. A simple and accurate method of determining the switching frequency
is described below.
2.2.4.1 Output Ripple
The three elements of the capacitor that contribute to ripple are ESR, ESL, and
capacitance. Assume that all three elements are in series and there are no
other parasitic components to consider. Figure 2–6 shows the voltage
waveforms across each component of the output capacitor and the
corresponding equations.