BCM352x125y300A00
This is similar in form to Eq. (3), where ROUT is used to represent
the characteristic impedance of the SAC™. However, in this case a
real R on the input side of the SAC is effectively scaled by K2 with
respect to the output.
Low impedance is a key requirement for powering a high-
current, low-voltage load efficiently. A switching regulation stage
should have minimal impedance while simultaneously providing
appropriate filtering for any switched current. The use of a SAC
between the regulation stage and the point of load provides a
dual benefit of scaling down series impedance leading back to
the source and scaling up shunt capacitance or energy storage
as a function of its K factor squared. However, the benefits are
not useful if the series impedance of the SAC is too high. The
impedance of the SAC must be low, i.e. well beyond the crossover
frequency of the system.
Assuming that R = 1Ω, the effective R as seen from the secondary
side is 1.28mΩ, with K = 1/28.
A similar exercise should be performed with the additon of a
capacitor or shunt impedance at the input to the SAC. A switch in
series with VIN is added to the circuit. This is depicted in Figure 20.
A solution for keeping the impedance of the SAC low involves
switching at a high frequency. This enables small magnetic
components because magnetizing currents remain low. Small
magnetics mean small path lengths for turns. Use of low loss core
material at high frequencies also reduces core losses.
S
S
SAC™
SAC
V
Vout
+
–
K = 1/28
out
C
C
Vin
Vin
K = 1/32
The two main terms of power loss in the BCM module are:
n No load power dissipation (PNL): defined as the power
used to power up the module with an enabled powertrain
at no load.
Figure 20 — Sine Amplitude Converter™ with input capacitor
n Resistive loss (PROUT): refers to the power loss across
the BCM module modeled as pure resistive impedance.
A change in VIN with the switch closed would result in a change in
capacitor current according to the following equation:
PDISSIPATED = PNL + PROUT
(10)
(11)
Therefore,
dVIN
I (t) =
C
(7)
C
dt
POUT = PIN – PDISSIPATED = PIN – PNL – PROUT
The above relations can be combined to calculate the overall
module efficiency:
Assume that with the capacitor charged to VIN, the switch is
opened and the capacitor is discharged through the idealized SAC.
In this case,
ꢀ
POUT
PIN
PIN – PNL – PROUT
(12)
h =
=
IC = IOUT • K
(8)
PIN
substituting Eq. (1) and (8) into Eq. (7) reveals:
VIN • IIN – PNL – (IOUT)2 • ROUT
VIN • IIN
=
dVOUT
dt
C
K2
IOUT
=
(9)
•
(PNL + (IOUT)2 • ROUT
VIN • IIN
)
=
–
1
The equation in terms of the output has yielded a K2 scaling factor
for C, specified in the denominator of the equation.
A K factor less than unity results in an effectively larger
capacitance on the output when expressed in terms of the input.
With a K = 1/28 as shown in Figure 20, C = 1µF would appear as
C = 784µF when viewed from the output.
BCM® Bus Converter
Page 15 of 21
Rev 2.0
08/2016
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