IEEE Solid-State Circuits Magazine - Summer 2016 - 70

The idea of reconfiguration in switchedcapacitor voltage multipliers has been expanded
into switched-capacitor dc-dc voltage down
converters as well.

I-V of ET

I-V of CP
IOUT

IS
IS MAX

RCP

RS
VS MAX

VS

VCPMAX

(a)

VOUT

(b)

Equivalent Circuit
M = N+1

RS

VCPMAX

VS

+

1:M
VS MAX

+
-

VOUT

IOUT

-

IS

(N+1)VTH
CLOAD

RLOAD

(c)

Figure 21: An equivalent circuit for the entire system.

Reduced Equivalent Circuit
RSYS = (N +1)2RS + RCP

V MAX =
(N +1)(VSMAX - VTH)

+
-

IV of Entire
System

VOUTIOUT

CLOAD

RLOAD

POUT - VOUT of Entire
System

IOUT

NOPT =

POUT
RSYS

VOUT

VOUT
V MAX

V MAX/2

V MAX

Figure 22: A reduced equivalent circuit for the entire system.

70

SU M M E R 2 0 16

IEEE SOLID-STATE CIRCUITS MAGAZINE

2VOUT
VSMAX

- VTH

-1

voltage by half but with the same
output impedance, when the same
number of stages and same size
capacitors are used.

Vibration Energy Harvesting
Figure 18(a) illustrates an energy harvester gathering vibration energy [24].
The second terminal of a capacitor is
connected with a mobile plate. The
displacement X is a sine waveform as
shown in Figure 18(b). Suppose X = 0,
CVIB = C0, and VCAP = VDD at time T0; the
charge stored in the pump capacitor
is Q 0 = C0VDD. When the displacement
is +X at T1, CVIB is increased to C0/
(1 − X). If there is no transfer transistor connected with the power supply
VDD, the capacitor voltage would be
Q 0 = C0VDD = C0/(1 − X)VCAP(T1). Thus,
VCAP(T1) would be (1 − X)VDD. With the
transfer transistor, VCAP(T1) is equalized to VDD. Thus, the charge stored
in the pump capacitor is Q1 = C0/
(1 − X)VDD. When the displacement is
−X at T2, CVIB is reduced to C0/(1 + X).
If there is no transfer transistor connected with the output terminal, the
capacitor voltage would be Q1 = C0/
(1 − X)VDD = C0/(1 + X)VCAP(T2). Thus,
VCAP(T2) would be (1 + X)/(1 − X)VDD.
Therefore, the maximum attainable
output voltage with no current load is
(1 + X)/ (1 − X)VDD. Figure 18(c) shows
the factor of (1 + X)/(1 − X) as a function of X.
Another configuration for vibration
energy harvesting is shown in Figure 19 [25]. The edge capacitor plates
N1 and N3 are unmovable whereas the
intermediate N2 is movable. As a result,
two variable capacitors Ca and Cb are
complementary. When the capacitance
of Ca becomes maximum, that of Ca
becomes minimum and vice versa.
Thus, vibration energy transfers the
charges stored in Ca to Cb, and then
those stored in Cb to the battery. Thus,
vibration energy is converted into
electrical energy.

Energy Harvesting with
Extremely Low Input Voltage
and Finite Input Impedance
Some applications use dc energy
transducers like photovoltaic and



Table of Contents for the Digital Edition of IEEE Solid-State Circuits Magazine - Summer 2016

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