IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 54, NO. 12, DECEMBER 2019 3257
A Fast Startup CMOS Crystal Oscillator
Using Two-Step Injection
Karim M. Megawer , Student Member, IEEE, Nilanjan Pal, Student Member, IEEE,
Ahmed Elkholy , Member, IEEE, Mostafa Gamal Ahmed , Student Member, IEEE,
Amr Khashaba , Student Member, IEEE, Danielle Griffith, Member, IEEE,
and Pavan Kumar Hanumolu, Member, IEEE
Abstract—Fast startup crystal oscillators (XOs) are needed
in heavily duty-cycled communication systems for implementing
aggressive dynamic power management schemes. This article
presents the ways to improve startup time of XOs. Using a two-
step injection technique in a three-step process, the proposed
technique reduces the XO startup time to within 1.5× the theo-
retical minimum. By solving the differential equation governing
crystal resonator under injection for arbitrary injection fre-
quency, the behavior of energy build-up inside a crystal resonator
is analyzed and used to determine optimum injection time as a
function of the desired XO steady-state amplitude and injection
frequency error. Bounds on tolerable injection frequency error
to guarantee the existence of optimal timing are provided.
Fabricated in a 65-nm CMOS process, the proposed 54-MHz fast
startup XO occupies an active area of 0.075 mm
2
and achieves
a startup time of less than 20 µs across a temperature range of
− 40
◦
Cto85
◦
C while consuming a startup energy of 34.9 nJ
and operating from a 1.0-V supply.
Index Terms— Crystal oscillator (XO), digitally controlled
oscillator (DCO), injection, ring oscillator (RO), startup time.
I. INTRODUCT ION
C
RYSTAL oscillators (XOs) are at the h eart of almost
all communication systems. They are used to perform
key time keeping functions and provide precise and accurate
clocks needed in high-frequency synthesis in all wireless
systems. To reduce average power consumption, such systems
are heavily duty-cycled by turning on for a very small duration
of time and turning off for the most part [1]–[3]. In such
scenarios, long startup time of XOs (T
START
) limits the efficacy
of duty-cycling as it limits the minimum turn on duration [3].
In othe r words, while the high-quality factor of crystals is
beneficial in achieving excellent frequency stability, it becomes
a major bottleneck in reducing the average power of heavily
Manuscript received April 25, 2019; revised July 13, 2019 and
August 11, 2019; accepted August 12, 2019. Date of publication
September 10, 2019; date of current version November 22, 2019. This article
was approved by Guest Editor Youngcheol Chae. (Corresponding author:
Karim M. Megawer.)
K. M. Megawer, N. Pal, M. G. Ahmed, A. Khashaba, and P. K. Hanumolu
are with the Department of Electrical and Computer Engineering, Uni-
versity of Illinois at Urbana–Champaign, Urbana, IL 61801 USA (e-mail:
megawer2@illinois.edu).
A. Elkholy is with Broadcom, Irvine, CA 92620 USA.
D. Griffith is with Texas Instruments Incorporated, Dallas, TX 75243 USA.
Color versions of one or more of the figures in this article are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JSSC.2019.2936296
duty-cycled systems. Therefore, the focus of this article is on
reducing the startup time of XOs.
Many attempts have already been made to reduce T
START
.
Such efforts can be broadly classified into three categories that
rely on: 1) choosing crystal resonator parameters that favor
smaller T
START
; 2) increasing XO amp litude growth rate; and
3) increasing initial noise energy inside the crystal resonator
at startup. While it is possible to choose a crystal resonator
with parameters that reduce T
START
, such choices always have
a detrimental impact on steady-state XO performance. For
example, a crystal with smaller lo ad capacitance will result in
smaller T
START
but increases frequency sensitivity to environ-
mental conditions, and a crystal with lower quality factor will
have a smaller T
START
at the expense of degraded frequency
stability and phase noise. In view of these conflicting tradeoffs,
most of the recent work h as been focused on improving
T
START
by using methods that do not directly depend on crystal
resonator parameters.
For a given crystal resonator, T
START
can be reduced
by increasing XO amplitude growth rate via increasing the
negative resistance (R
N
) seen from the XO [4]–[7] by:
1) increasing the XO transconductance using multiple XO
cores connected in parallel [4]; 2 ) temporarily increasing
XO core current during startup [5]; 3) reducing startup load
capacitance using dynamically adjusted load [5]; or 4) can-
celing crystal resonator parasitic capacitance with inductive
impedance using dual-mode three-stage g
m
scheme [6] or
by adding a zero in R
N
transfer function using multistage
amplifier with feed forward path [7]. Due to the linear depen-
dence of R
N
on transconductance in [4], the existence of
parasitic capacitances in [5], settling time overhead during
switching between modes in [6], and the dependence on initial
noise seed in [7], these techniques show limited improvement
compared with techniques that employ increasing the initial
noise amplitude by injecting a surge of energy into the crystal
resonator at startup.
It has been shown that injecting energy into the crystal at
exactly the resonator frequency until the current in the res-
onator reaches its steady-state value (i
M,SS
) results in theoret-
ical m inimum startup time [4] (in some applications, oscillator
output can be used even before this time). However, matching
injection frequency to within few 100 ppm of the resonator
frequency poses a serious practical challenge in achieving
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