Datasheet
5
LTC1046
1046fb
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Theory of Operation
To understand the theory of operation of the LTC1046, a
review of a basic switched capacitor building block is
helpful.
In Figure 2, when the switch is in the left position, capacitor
C1 will charge to voltage V1. The total charge on C1 will be
q1 = C1V1. The switch then moves to the right, discharging
C1 to voltage V2. After this discharge time, the charge on
C1 is q2 = C1V2. Note that charge has been transferred
from the source, V1, to the output, V2. The amount of
charge transferred is:
∆ q = q1 – q2 = C1(V1 – V2).
If the switch is cycled “f” times per second, the charge
transfer per unit time (i.e., current) is:
I = f • ∆q = f • C1(V1 – V2).
Examination of Figure 4 shows that the LTC1046 has the
same switching action as the basic switched capacitor
building block. With the addition of finite switch ON
resistance and output voltage ripple, the simple theory,
although not exact, provides an intuitive feel for how the
device works.
For example, if you examine power conversion efficiency
as a function of frequency (see typical curve), this simple
theory will explain how the LTC1046 behaves. The loss,
and hence the efficiency, is set by the output impedance.
As frequency is decreased, the output impedance will
eventually be dominated by the 1/fC1 term and power
efficiency will drop. The typical curves for power effi-
ciency versus frequency show this effect for various capaci-
tor values.
Note also that power efficiency decreases as frequency
goes up. This is caused by internal switching losses which
occur due to some finite charge being lost on each
switching cycle. This charge loss per unit cycle, when
multiplied by the switching frequency, becomes a current
loss. At high frequency this loss becomes significant and
the power efficiency starts to decrease.
Figure 3. Switched Capacitor Equivalent Circuit
Figure 4. LTC1046 Switched Capacitor
Voltage Converter Block Diagram
C2
R
EQUIV
=
1046 F03
V2V1
R
L
R
EQUIV
1
fC1
1046 F04
CAP
+
(2)
CAP
–
(4)
GND
(3)
V
OUT
(5)
V
+
(8)
LV
(6)
3x
(1)
OSC
(7)
OSC +2
CLOSED WHEN
V
+
> 3.0V
C1
C2
BOOST
SW1 SW2
φ
φ
+
+
Figure 2. Switched Capacitor Building Block
C1
f
C2
1046 F02
V2V1
R
L
Rewriting in terms of voltage and impedance equivalence,
I
VV
fC
VV
R
EQUIV
=
()
=
12
11
12–
/
–
.
A new variable, R
EQUIV
, has been defined such that
R
EQUIV
= 1/fC1. Thus, the equivalent circuit for the switched
capacitor network is as shown in Figure 3.