Design Technique for Analog Temperature Compensation of Crystal Oscillators Mark A.Haney Thesis submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Master of Science In Electrical Engineering Dr.Dennis G.Sweeney Dr.Charles W.
Ira Jacobs Blacksburg, Virginia Keywords:
TCXO, Temperature Compensation, Crystal Oscillator Copyright 2001, Mark Haney Abstract For decades, the quartz crystal has been used for precise frequency control.
In the increasingly popular field of wireless communications, available frequency spectrum is becoming very limited, and therefore regulatory agencies have imposed tight frequency stability requirements.
There are generally two techniques for controlling the stability of a crystal oscillator with temperature variations of the environment.
They are temperature control and temperature compensation.
Temperature control involves placing the sensitive components of an oscillator in a temperature stable chamber.
Usually referred to as an oven-controlled crystal oscillator (OCXO), this technique can achieve very good stability over wide temperature ranges.
Nevertheless, its use in miniature battery powered electronic devices is significantly limited by drawbacks such as cost, power consumption, and size.
Temperature compensation, on the other hand, entails using temperature dependent circuit elements to compensate for shifts in frequency due to changes in ambient temperature.
A crystal oscillator that uses this frequency stabilization technique is referred to as a temperature-compensated crystal oscillator (TCXO).
With little added cost, size, and power consumption, a TCXO is well suited for use in portable devices.
This paper presents the theory of temperature compensation, and a procedure for designing a TCXO and predicting its performance over temperature.
The equivalent electrical circuit model and frequency stability characteristics for the AT-cut quartz crystal are developed.
An oscillator circuit topology is introduced such that the crystal is operated in parallel resonance with an external capacitance, and equations are derived that express the frequency stability of the crystal oscillator as a function of the crystals capacitive load.
This relationship leads to the development of the theory of temperature compensation by a crystals external load capacitance.
An example of the TCXO design process is demonstrated with the aid of a MATLAB script
.Table of Contents of of of of 1 : 2 : Frequency-Temperature Crystal Temperature 3 : Theory of Temperature with a Capacitive Compensation by Load 4 : Measurement of Crystal Circuit 5 : TCXO Oscillator Component 6 : TCXO Implementation and of A: MATLAB B: Users Guide to MATLAB 1: Determine Crystal 2: Determine Nominal Load 3: Determine Frequency-Temperature 4: Determine Values for NTC 5: Determine Values for Thermistor-Capacitor 6: Measure the of Figures Figure 2.1:
Equivalent circuit of a quartz 2.2:
Graph of a crystals reactance vs. 2.3:
Typical frequency-temperature curves for AT-cut 4.1: Network to measure crystal 5.1:
Basic structure of Colpitts 5.2:
Colpitts oscillator followed by a grounded collector PNP 5.3:
Complete TCXO 6.1: DC bias of the 6.2: Circuit used to measure frequency-temperature characteristic curve of 6.3: Cubic approximation for frequency-temperature data of 6.4: Graph of capacitive load required for compensation, , vs. 6.5: Schematic of 6.6: Comparison of total capacitance of the circuit () with required capacitance for compensation ()....41Figure 6.7: Predicted frequency error of TCXO 6.8: Schematic of the TCXO that was 6.9: Comparison of total capacitance () with required capacitance () for the TCXO circuit that was 6.10: Predicted frequency error of TCXO circuit that was 6.11: Experimental results of the TCXO frequency error over List of Equations Equation 2.1:
Impedance of a quartz 2.2: Impedance of a quartz crystal in analysis friendly 2.3: Condition for 2.4:
Solution for resonant frequencies of a quartz 2.5:
Assumption used for simplification of resonant frequency 2.6:
Approximate resonant frequency 2.7:
Series resonant 2.8:
Approximation for antiresonant 2.10: Simplified approximation for antiresonant relationship of AT-cut 3.1:
Parallel resonant frequency of a crystal due to an external capacitive 3.2:
Parallel resonant frequency expressed as a frequency offset from ..18Equation 3.3: Capacitive load expressed as a function of the frequency offset from ...19Equation 3.4: Total frequency offset from
due to the capacitive load and change in 3.5:
Capacitive load required for resonance at ...19Equation 3.6:
Capacitive load required for resonance at
in terms of the crystals motional and static capacitances, and its nominal capacitive 3.7:
Total load capacitance required for temperature 4.1: Calculation for the motional resistance of a 4.2: Calculation for the motional capacitance of a 4.3: Calculation for the motional inductance of a 5.1:
Expression for the capacitance of a negative temperature coefficient 5.2: Resistance-temperature relationship for an NTC 5.3:
Series impedance of the thermistor-capacitor 5.4:
Equivalent parallel impedance of the thermistor-capacitor 5.5: