IEEE Solid-States Circuits Magazine - Fall 2021 - 14

capacitor, as given in Figure 3(a),
can create a dc voltage higher than
the input voltage.
Like the buck converter, this converter
also operates in two phases.
In phase 1, when S1
is closed and S2
is open, there will be a fixed voltage
VB
across the inductor, creating
a growing magnetic flux that is the
time integral of the applied voltage.
This is similar, but perhaps less tangible,
to applying a fixed current to a
capacitor, charging up the capacitor.
Since the current of a linear inductor
is proportional to its magnetic
flux, similar to the voltage of a linear
capacitor being proportional to
its electric charge, we can say that
an inductor integrates the voltage to
produce a current with a proportionality
constant of 1/L. Again, this is
+ VL -
L
VB
S1
similar to a capacitor integrating its
input current to produce a voltage,
with a proportionality constant of
1/C. At the end of phase 1, the inductor
current reaches its maximum
level and will release this current to
the capacitor from the beginning of
the second phase (when S1
and S2
is open
is closed).
In a steady state, the inductor in
phase 2 will lose all the flux it gained
in phase 1, albeit at a different rate
(as the duration of phases 1 and 2
are not necessarily the same). If we
allocate T a time to fluxing up the
inductor, we will accumulate a total
flux of TV Ba
flux will be lost in phase 2, but over
a period of
() ,T1 ait
will produce
a voltage of V /(1Baa- ) across the
inductor, in series with V ,B
to produce
an output voltage higher than
V :B
VV () ()V11BBaa B
+- a=- For
// .
a 05= ., this circuit produces an
output voltage that is twice .VB
The
waveforms in Figure 3 correspond
with
a 025= .. As a result, the output
voltage is /.V43 B
This concludes our basic introin
phase 1. Since this
i VX
L
S2
C
(a)
v (t)
VX
t
0 αT
v (t)
VL (t)
t
2T
(c)
iL(t)
il (avg)
t
(d)
2T
FIGURE 3: (a) A simple schematic of a step-up (boost) converter. (b) The voltage waveform
at various nodes in the circuit. (c) The voltage waveform across the inductor. (d) The current
waveform through the inductor.
14
FALL 2021
IEEE SOLID-STATE CIRCUITS MAGAZINE
References
[1] H. Lee, " Fundamentals of switchedmode
power-converter design. " Accessed:
Sept. 2021. [Online]. Available: https://
resourcecenter.sscs.ieee.org/education/
short-courses.html
[2] B. Wicht, " Analog building blocks of dc-dc
converters, " IEEE Solid State Circuits Mag.,
vol. 12, no. 3, pp. 42-47, Summer 2020.
doi: 10.1109/MSSC.2020.3002141.
[3] B. Wicht, " Analog building blocks of DC-DC
converters, " SSCS Youtube Channel. [Online
Video]. https://www.youtube.com/c/
IEEESolidStateCircuitsSociety/videos
T
(b)
Vout = VB / (1 - α)
VB
Acknowledgment
This article was inspired by tutorials
given at ISSCC by Hoi Lee,
Robert Pilawa-Podgurski, Bernhart
Wicht, and Yan Lu, from 2018 to
2021, respectively.
2T
Vout = VB / (1 - α)
VB
RL
Vout
duction to buck and boost converters,
but many design considerations
and challenges remain. These include
the proper sizing of C, L, the switches
and their nonidealities, and the
feedback circuitry needed to carefully
control the duty cycle of the
switches (partly to compensate for
the drop in battery voltage through
time). For a more detailed treatment
of this topic, the reader may refer
to a 2018 International Solid-State
Circuits Conference (ISSCC) tutorial
video [1] and a written lesson
in IEEE Solid-State Circuits Magazine
[2], with a corresponding video on
the IEEE Solid-State Circuits Society
YouTube channel [3].
In summary, we can build a powerefficient
step-up and step-down
dc-dc converter by using two simple
switches, one capacitor, and one
inductor. A step-down converter
essentially finds a weighted average
between the battery voltage
and 0 V. A step-up converter creates
a positive voltage across the inductor
and puts it in series with the
original battery voltage to create a
step-up voltage.

https://resourcecenter.sscs.ieee.org/education/short-courses.html https://resourcecenter.sscs.ieee.org/education/short-courses.html https://resourcecenter.sscs.ieee.org/education/short-courses.html https://www.youtube.com/c/IEEESolidStateCircuitsSociety/videos https://www.youtube.com/c/IEEESolidStateCircuitsSociety/videos

IEEE Solid-States Circuits Magazine - Fall 2021

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