IEEE Solid-State Circuits Magazine - Spring 2017 - 7

A C irCu it for All SeA SonS

Behzad Razavi

The Crystal Oscillator

15
12

13
14
20

19 16

4
1

17
2

5
21

18
6

Crystal Model

22
Figure 1: Cady's crystal oscillator.

Brief History
In 1880, Pierre and Jacques Curie discovered "piezoelectricity" [1], namely,
the ability of a device to generate a
voltage if subjected to mechanical
force. In 1881, Lippman predicted
that a converse effect must also exist,
which was confirmed by the Curies
shortly thereafter [1].
The use of a piezoelectric device-
a "crystal"-to define the oscillation
frequency of a circuit can be traced
to Cady's 1922 paper [2]. Cady proposes the oscillator shown in Figure 1, which applies feedback around
a three-stage amplifier through two
coupled piezoelectric resonators.
Crystal oscillators continued to
advance in the ensuing decades, naturally migrating to bipolar and, eventually, MOS technologies. The interest
in such oscillators was rekindled with
the conception of the electronic watch
in the 1960s and 1970s. In Figure 2, (a)
shows a MOS realization reported by
Luscher as prior art in a patent filed
in 1969 [3], and (b) depicts a more
familiar structure that dates back to
a patent filed by Walton in 1970 [4].
The need for an extremely low-power,

oscillators have found new importance for their low phase noise in
addition to their long-term frequency
stability. The low temperature coefficient of crystals also proves critical
in most applications.

high-precision time-base circuit motivated extensive studies on crystal
oscillators in that time frame [5], [7].
In addition to a precise resonance
frequency, piezoelectric devices exhibit extremely high quality factors
(Qs), a property that has proved
essential in communication transceivers. While resonance frequency
drifts can be eventually compensated
as the received signal is processed,
the phase noise of the crystal oscillator cannot. In other words, crystal

For circuit design purposes, we need
an electrical model of the electromechanical crystal. The mechanical resonance is fundamentally represented
by a series RLC branch, with a resistor
modeling the loss [Figure 3(a)]. These
components are called the "motional"
resistance, inductance, and capacitance of the crystal, respectively. With
this series branch, the crystal can act
as a short circuit at resonance. In addition, since the crystal is formed by
two parallel plates, a parallel capacitance must also be included. The load
capacitance presented to the crystal
by the printed circuit board and other
devices can also be absorbed by C P .

256
R2

268

-
+

260

F
F

258

262
264

D
254
D

C1
Q

250

T1
P

252

259

Most electronic systems rely on a precise reference frequency or time base
for their operation. Examples include
wireless and wireline communication
transceivers, computing devices, instrumentation, and the electronic watch.
The crystal oscillator has served this
purpose for nearly a century. In this
article, we study the design principles
of this circuit.

266
a2

(b)

(a)
Digital Object Identifier 10.1109/MSSC.2017.2688679
Date of publication: 21 June 2017

Figure 2: the MoS crystal oscillators patented by (a) luscher and (b) Walton.

IEEE SOLID-STATE CIRCUITS MAGAZINE

S p r i n g 2 0 17

Table of Contents for the Digital Edition of IEEE Solid-State Circuits Magazine - Spring 2017