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Content
List of figures
Abstract
Introduction
Literature survey
Problem statement
Simulation results
Conclusions
References
List of figures
Fig.3.a Pierce crystal oscillator.

Fig.4.1.1.a RC phase shift oscillator.

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Fig.5.2.a crystal.

Fig.5.2.b crystal model.

Fig.5.3.a Relative positions of series and parallel resonances.

Fig.5.3.b pierce crystal oscillator
Fig.5.3.c crystal model
Fig.5.6.a Block diagram
Fig.5.7.1.a Top level Schematic
Fig.5.7.2.a Inverter circuit schematic
Fig.5.7.3.a Shaper circuit schematic
Fig.5.8.a Test bench (schematic)
Fig.5.8.b Crystal model
Fig.5.8.c Test bench (adl)
Fig.5.8.d Test bench (adl)
Fig.6.1.a pmos (inverter)
Fig.6.1.b nmos (inverter)
Fig.6.2.a Transient result
Fig.6.2.b Transient result
Fig.6.3.a loop gain and phase
Fig.6.4.a Loop gain

Abstract
Today, the majority of electronic circuits (including microprocessors, microcontrollers, FPGAs, and CPLDs) are based on clocked logic, requiring a timing source.

The most commonly used frequency standard is the crystal oscillator; as the crystal oscillator gets vibrated with varying force and frequencies of vibration the phase noise of the signal changes.

As the phase noise increases, the signal to noise ratio decreases causing the likelihood of transmitting or receiving an incorrect signal to rise. This makes it critical to limit the phase noise increase that occurs in the frequency standard of the system.

Crystal oscillators use the mechanical vibration of a crystal to generate the clock signal. Due to the molecular composition of the crystal matter and the angle of which the crystal is cut, this type of oscillator is very precise and stable over a wide temperature range. The most commonly used crystal is the quartz crystal. It has a high quality factor which has less phase noise.

CMOS devices have a high input impedance, high gain, and high bandwidth. These characteristics are similar to ideal amplifier characteristics and, hence, a CMOS buffer or inverter can be used in an oscillator circuit in conjunction with other passive components. Now, CMOS oscillator circuits are widely used in high-speed applications because they are economical, easy to use, and take significantly less space than a conventional oscillator.

Introduction
Virtually all digital IC clock oscillators are of Pierce type, as the circuit can be implemented using a minimum of components: a single digital inverter, one resistor, two capacitors, and the quartz crystal, which acts as a highly selective filter element. The low manufacturing cost of this circuit and the outstanding frequency stability of the quartz crystal give it an advantage over other designs in many consumer electronics applications.

Resistors, inductors, capacitors, and an amplifier with high gain are the basic components of an oscillator. In designing oscillators, instead of using discrete passive components (resistors, inductors, and capacitors), crystal oscillators are a better choice because of their excellent frequency stability and wide frequency range. A crystal basically is an RLC network that has a natural frequency of resonance.

Fig.3.a Pierce crystal oscillator
Literature survey
4.1 Basic Oscillators
There are different types of oscillators to generate frequency.

4.1.1 RC oscillators
RC oscillators are built from resistors, capacitors, and an inverting amplifier. They come at a low cost and have a shorter startup time than the crystal oscillator, but variations in component values over temperature make it difficult to precisely determine the oscillation frequency.

RC Phase Shift Oscillator
In an RC Oscillator circuit the input is shifted 180o through the amplifier stage and 180oagain through a second inverting stage giving us “180o + 180o = 360o” of phase shift which is effectively the same as 0o thereby giving us the required positive feedback. In other words, the phase shift of the feedback loop should be “0”.In a Resistance-Capacitance Oscillator or simply an RC Oscillator, we make use of the fact that a phase shift occurs between the input to a RC network and the output from the same network by using RC elements in the feedback branch.

Fig.4.1.1.a RC phase shift oscillator
4.1.2 Crystal oscillators
Crystal oscillators use the mechanical vibration of a crystal to generate the clock signal. Due to the molecular composition of the crystal matter and the angle of which the crystal is cut, this type of oscillator is very precise and stable over a wide temperature range. The most commonly used crystal is the quartz crystal. Producing quartz crystals requires very stable temperature and pressure conditions over a few weeks. This makes crystal oscillators more expensive than RC oscillators.
4.1.3 Ceramic resonators
Ceramic resonators operate in the same way as crystal oscillators. They are easier to manufacture and therefore cheaper than quartz crystals, but suffer from inferior precision in the oscillation frequency. As will be seen in subsequent chapters, the quality factor for ceramic resonators is lower than for crystal oscillators, which usually results in a faster startup time. This can be more important than precision in frequency for some applications.

4.2 Why a crystal oscillator over other models?
4.2.1 Stability
Stability is one of the most important requirements of any oscillator. This refers to the oscillator’s ability to generate a constant frequency under different conditions.

Several factors affect the stability of the frequency. These include variations in temperature, power supply voltage, and load.

This is where this type of oscillator shines. In LC and RC, you can improve the stability by careful selection of the circuit components.

Yet, frequency stability is inherent in the crystal itself. This is due to the great mechanical strength of certain crystals like quartz.

4.2.2 High Q
The Q factor or quality factor describes how ‘underdamped’ oscillators are. Oscillators with a high Q factor are slower to die out. This means that you need less energy to maintain a constant signal frequency. The high Q factor demonstrates the superior efficiency of these oscillators.

4.2.3 Frequency Customization and Range
You can customize the frequency at which the crystal vibrates. This is done by precise cutting of the crystal to a specific thickness, size, and shape. The frequencies can range from a few kilohertz to well over one hundred megahertz.

4.2.4 Low Phase Noise
The phase noise is another important feature of an oscillator’s performance. Phase noise is random, short-term fluctuations in the frequency domain. In communications systems, phase noise can reduce the signal quality.

Phase noise is generated by the amplification of the general noise in the circuit. This will produce several tones in different phases.

A crystal mostly vibrates in one axis and thus only one phase is dominant. This is the reason why a crystal oscillator can have very low phase noise
Problem statement
Design of a pierce crystal oscillator with frequency of 38.4 Mhz.

5.1 Theory
In principle, an oscillator can be composed of an amplifier, A, with voltage gain, a, and phase shift, ?, and a feedback network, F, with transfer function, f, and phase shift, ? (see Figure 1).

For ?f? × ?a? ? 1 the oscillating condition is fulfilled, and the system works as an oscillator.

f and a are complex quantities;
Consequently, it is possible to derive from equation 1
?f? × ?a? × expj(?+ ?)? 1 (1)
the amplitude
?f? × ?a? ? 1 (2)
and the phase
(? + ?) = 2 × ? (3)
To oscillate, these conditions of amplitude and phase must be met. These conditions are known as the Barkhausen criterion. The closed-loop gain should be ?1, and the total phase shift of 360 degrees is to be provided.

5.2 Crystal model and characteristics:
A crystal consists of a plate of piezo resistive material with a certain thickness d. Piezo resistive material allows exchange of mechanical and electrical energy. Examples are quartz and ZnO and some nitrides. Application of a mechanical pressure to it, generates a voltage across it and vice versa. This exchange of energy is particularly e?cient at one particular frequency, called the resonant frequency fs. This frequency is inversely proportional to the thickness of the quartz. Values of 100 kHz to 40–50 MHz are commonly fabricated. For higher values, the quartz becomes too thin and fragile.

Around this resonant frequency the electrical model of this crystal is a series resonant LRC circuit,( shown in the fig below) the resonant frequency of which is fm. It is damped by the series resistor Rm, which causes the quality factor Q to be ?nite.

• Cm is the motional capacitance. It represents the piezoelectric charge gained from a displacement in the crystal.• Rm is the motional resistance. It represents the mechanical losses in the crystal.• Lm is the motional inductance. It represents the moving mass in the crystal.• Cp is the shunt capacitance between the electrodes and stray capacitance from the casing
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Fig.5.2.a crystal
Fig.5.2.b crystal model
Note that at resonance, the impedance of the inductor equals that of the capacitance. Actually, at resonance the series RLC circuit is just Rm, itself. The inductor Lm and capacitor Cm cancel each other. In addition to this series RLC circuit, which represents the electro-mechanical operation of the crystal, a plate capacitance Cp has to be added. It is the capacitance between the two plates used to contact the crystal, with the dielectric constant of quartz (4.5 times larger than air). It includes the package and mounting capacitances as well.

5.3 Series and parallel resonance:
Physically there is no difference between series and parallel resonant crystals. Series resonant crystals are specified to oscillate at the series resonant frequency where the crystal appears with no reactance. Because of this, no external capacitance should be present as this would lower the oscillating frequency to below the natural resonance frequency. These crystals are intended for use in circuits with no external capacitors where the oscillator circuit provides 360° phase shift.Parallel resonant crystals require a capacitive load to oscillate at the specified frequency and this is the resonance mode require external load capacitors. The exact oscillation frequency for a parallel resonant crystal can be calculated, where CL is the load capacitance seen by the crystal. CL is therefore an important design parameter and is given in the datasheet for parallel resonant crystals.

Fig.5.3.a Relative positions of series and parallel resonances
561975-466725fm=12?Lm *Cm0fm=12?Lm *CmSeries resonance frequency:
Parallel resonance frequency:
43815020955fp=12?Lm *(CmCpCm+Cp)0fp=12?Lm *(CmCpCm+Cp)
The design is based on parallel resonance crystal oscillator:
296227410375900028384501075690
Fig.5.3.b pierce crystal oscillator Fig.5.3.c crystal model
5334006349CL=CL1*CL2CL1+CL200CL=CL1*CL2CL1+CL2
1285875149225Ceff=Cm*(CL+Cp)Cm+(CL+Cp)0Ceff=Cm*(CL+Cp)Cm+(CL+Cp)
619125434975fosc=12?Lm *Ceff0fosc=12?Lm *Ceff Frequency of oscillation
5.4 Specifications
Vdd:1.1V
Frequency:38.4MHz
CL:20pf
5.5 Calculations
fosc =38.4Mhz
let Cm=3.3fF?Ceff
from the above equations we have Lm=5.208mH
let Rm=20?
5.6 Block Diagram
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Fig.5.6.a Block diagram
5.7 Schematics
5.7.1 Top level Schematic
4667251625600
Fig.5.7.1.a Top level Schematic
5.7.2 Schematic (inverter)
43815082550
Fig.5.7.2.a Inverter circuit schematic
5.7.3 Schematic (shaper):
4572002082800
Fig.5.7.3.a Shaper circuit schematic
5.8 Test benches
Test bench (Schematic)
291465028295600048577567945
286702526416000
Fig.5.8.a Test bench (schematic)
Fig.5.8.b Crystal model
center3048000Test bench (adl)
center395160500Fig.5.8.c Test bench (adl)
Fig.5.8.d Test bench (adl)
Analysis & Simulation Results
6.1 DC analysis
Check the biasing input of inverter should be Vdd/2 and inverter should work as an amplifier means pmos and nmos should be in region 2(saturation).

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6667507683500118999069853467100235585
15430501460500
Fig.6.1.a pmos (inverter) Fig.6.1.b nmos (inverter)
Vin = Vdd/2 =1.1/2?544.437mV
Vds>Vsat (region 2 , saturation)
6.2 Transient analysis
right3340100To check the functionality i.e frequency.

Fig.6.2.a Transient result

Fig.6.2.b Transient result
Frequency = 38.4 Mhz.

6.3 AC analysis
To check the barkausen criteria.

Fig.6.3.a loop gain and phase
Basic principle of oscillation
Barkhausen condition:
Loop phase: 0 (or) 360deg
Loop gain>1
At the frequency of oscillation.

6.4 PSS & PSTB analysis
Done for large signal analysis.

Fig.6.4.a Loop gain
Loop gain is >1.

References
ANALOG DESIGN ESSENTIALS book By Willy M. C. Sansen Catholic University, Leuven, Belgium.

“CRYSTAL OSCILLATOR CIRCUITS” book by Robert J. Matthys. KRIEGER PUBLISHING COMPANY MALABAR, FLORIDA.

Use of the CMOS Unbuffered Inverter in Oscillator Circuits by Moshiul Haque and Ernest Cox Texas instruments Application Report SZZA043 – January 2004.

Pierce-Gate Crystal Oscillator, an introduction by Ramon Cerda, Director of Engineering, Crystek Corporation.

IEEE paper on “High-Performance Crystal Oscillator Circuits: Theory and Application” by ERIC A.VITTOZ senior, IEEE, MARC G.R.DEGRAUWE, member, IEEE, and SERGE BITZ. IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 23, NO. 3, JUNE 1988.

IEEE paper on “Analysis and design of low phase noise crystal oscillators” by Yan Wang ; Xianhe Huang held at 2012 IEEE International Conference on Mechatronics and Automation.

Intel Corp., Application Note AP-155, “Oscillators for Micro Controllers”, order #230659-001, by Tom Williamson, Dec. 1986.

IEEE paper on “The design and implementation of a 120-MHz pierce low-phase-noise crystal oscillator” by Xianhe Huang ; Yan Wang ; Wei Fu published in IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control ( Volume: 58 , Issue: 7 , July 2011 ).

IEEE paper on”A Differential Digitally Controlled Crystal Oscillator With a 14-Bit Tuning Resolution and Sine Wave Outputs for Cellular Applications” by Yuyu Chang, John Leete, Member, IEEE, Zhimin Zhou, Morteza Vadipour, Yin-Ting Chang, and Hooman Darabi, Senior Member, IEEE in IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 47, NO. 2, FEBRUARY 2012.

Oscillator design considerations by silicon labs.

Technical paper – Simulation of crystals and resonators by ACT World-leading supplier of frequency control solutions.

Design and build reliable, cost-effective, on-chip oscillator circuits that are trouble free. Putting oscillator theory into a practical design makes for a more dependable chip Application note by ZILOG.

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