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39DC-DC Converter Design and Magnetics
Note also, that for any topology, a high duty cycle corresponds to a low input voltage,
and a lo
w duty cycle is equivalent to a high input. So increasing D amounts to decreasing
the input voltage (its magnitude) in all cases. Therefore, in a boost or buck-boost, if the
difference between the input and output voltages is large, we get the highest DC inductor
current.
Finally, with the DC and AC components known, we can calculate the peak current using
III
I
I
PK AC DC L

2
(3-9)
3.5 Defi ning the Worst-case Input Voltage
So far, we have been implicitly assuming a xed input voltage. In reality, in most practical
applications, the input voltage is a certain range , say from V
INMIN
to V
INMAX
.
We therefore also need to know how the AC, DC, and peak current components change
as we vary the input voltage . Most importantly, we need to know at what specifi c voltage
within this range we get the maximum peak current. As mentioned, the peak is critical
from the standpoint of ensuring there is no inductor saturation . Therefore, defi ning the
worst-case voltage (for inductor design) as the point of the input voltage range where
the peak current is at its maximum, we need to design/select our inductor at this particular
point always. This is in fact the underlying basis of the general inductor design procedure
that we will be presenting soon.
We will now try to understand where and why we get the highest peak currents for
each topology. In Figure 3.3 , we have drawn various inductor current waveforms to
help us better visualize what really happens as the input is varied. We have chosen two
topologies here, the buck and the buck-boost, for which we display two waveforms each,
corresponding to two different input voltages. Finally, in Figure 3.4 we have plotted
out the AC, DC, and peak values. Note that these plots are based on the actual design
equations, which are also presented within the same fi gure. While interpreting the plots,
we should again keep in mind that for all topologies, a high D corresponds to a low input.
The following analysis will also explain certain cells of the previously provided Table 3.2 ,
where the variations of I and I
DC
, with respect to D , were summarized.
a ) For the buck , the situation can be analyzed as follows:
As the input increases , the duty cycle decreases in an effort to maintain
regulation. But the slope of the down-ramp I/t
OFF
cannot change , because
it is equal to V
OFF
/ L , that is, V
O
/ L , and we are assuming V
O
is fi xed. But now,
since t
OFF
has increased, but the slope I / t
OFF
has not changed, the only
possibility is that I must have increased (proportionally). So we conclude

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