30-11-2012, 04:50 PM
AVR4100: Selecting and testing 32kHz crystal oscillators for Atmel AVR microcontrollers
[attachment=41938]
Introduction
A crystal oscillator uses the mechanical resonance of a vibrating piezoelectric
material to generate a very stable clock signal. The frequency is usually used to
provide a stable clock signal or to keep track of time; hence, crystal oscillators are
widely used in RF and digital circuits.
Crystals are available from various vendors in a variety of shapes and sizes, and can
vary widely in performance and specifications. Understanding the parameters and the
oscillator circuit are essential for a robust application stable over variations in
temperature, humidity, power supply, and process.
All physical objects have a natural frequency of vibration, where the vibrating
frequency is determined by its shape, size, elasticity and speed of sound in the
material. Piezoelectric material distorts when an electric field is applied, and
generates an electric field when it returns to its original shape. The most common
piezoelectric material used in electronic circuits is quartz crystal, but ceramic
resonators are also used – usually in low-cost or less timing critical applications.
32kHz (32768Hz) crystals are usually cut in the shape of a tuning fork, and very
precise frequencies can be established.
The oscillator
The Barkhausen stability criteria are two conditions used to determine when an
electronic circuit will oscillate. They state that if A is the gain of the amplifying element
in the circuit and β(jω) is the transfer function of the feedback path, the circuit will
sustain steady-state oscillations only at frequencies for which:
Electrical model
The equivalent electric circuit of a crystal is shown in Figure 2-4. The series RLC
network is called the motional arm, and gives an electrical description of the
mechanical behavior of the crystal, where C1 represents the elasticity of the quartz, L1
represents the vibrating mass, and R1 represents losses due to damping. C0 is called
the shunt or static capacitance, and is the sum of the electrical parasitic capacitance
due to the crystal housing and electrodes. If a capacitance meter is used to measure
the crystal capacitance, only C0 will be measured (C1 will have no effect).
Equivalent series resistance (ESR)
The equivalent series resistance (ESR) is an electrical representation of the
mechanical losses, and at the series resonant frequency, fs, it is equal to R1 in the
electrical model. The ESR is a very important parameter, and can be found in the
crystal datasheet. The ESR will usually be dependent of the crystal’s physical size,
and small crystals (especially small SMD crystals) typically have higher losses and
ESR values than larger crystals.
Higher ESR values will load the inverting amplifier more, and too high an ESR may
cause unstable oscillator operation. Unity gain will not be achieved, and the
Barkhausen criterion will not be fulfilled.
[attachment=41938]
Introduction
A crystal oscillator uses the mechanical resonance of a vibrating piezoelectric
material to generate a very stable clock signal. The frequency is usually used to
provide a stable clock signal or to keep track of time; hence, crystal oscillators are
widely used in RF and digital circuits.
Crystals are available from various vendors in a variety of shapes and sizes, and can
vary widely in performance and specifications. Understanding the parameters and the
oscillator circuit are essential for a robust application stable over variations in
temperature, humidity, power supply, and process.
All physical objects have a natural frequency of vibration, where the vibrating
frequency is determined by its shape, size, elasticity and speed of sound in the
material. Piezoelectric material distorts when an electric field is applied, and
generates an electric field when it returns to its original shape. The most common
piezoelectric material used in electronic circuits is quartz crystal, but ceramic
resonators are also used – usually in low-cost or less timing critical applications.
32kHz (32768Hz) crystals are usually cut in the shape of a tuning fork, and very
precise frequencies can be established.
The oscillator
The Barkhausen stability criteria are two conditions used to determine when an
electronic circuit will oscillate. They state that if A is the gain of the amplifying element
in the circuit and β(jω) is the transfer function of the feedback path, the circuit will
sustain steady-state oscillations only at frequencies for which:
Electrical model
The equivalent electric circuit of a crystal is shown in Figure 2-4. The series RLC
network is called the motional arm, and gives an electrical description of the
mechanical behavior of the crystal, where C1 represents the elasticity of the quartz, L1
represents the vibrating mass, and R1 represents losses due to damping. C0 is called
the shunt or static capacitance, and is the sum of the electrical parasitic capacitance
due to the crystal housing and electrodes. If a capacitance meter is used to measure
the crystal capacitance, only C0 will be measured (C1 will have no effect).
Equivalent series resistance (ESR)
The equivalent series resistance (ESR) is an electrical representation of the
mechanical losses, and at the series resonant frequency, fs, it is equal to R1 in the
electrical model. The ESR is a very important parameter, and can be found in the
crystal datasheet. The ESR will usually be dependent of the crystal’s physical size,
and small crystals (especially small SMD crystals) typically have higher losses and
ESR values than larger crystals.
Higher ESR values will load the inverting amplifier more, and too high an ESR may
cause unstable oscillator operation. Unity gain will not be achieved, and the
Barkhausen criterion will not be fulfilled.