# Application Notes

## Quartz Crystal Theory

#### Crystal Units : Terms and Definitions

1. Equivalent Circuit
2. Operating Modus
3. Shunt Capacitance
4. Frequency-Temperature Characteristics
5. Calibration Tolerance
6. Stability
7. Overall Frequency Tolerance
8. Aging
9. Pullability
10. Overtone Crystals
11. Spurious Response
12. Drive Level
13. Insulation Resistance
14. Quality Factor
• Application Note--Oscillator Circuit
• Application Note--Selecting a crystal for microprocessor
• Application Note--Negative Resistance Measurements

#### Crystal Units : Terms and Definitions

The piezoelectric effects is defined that pressure applied on quartz crystal generates voltage and voltage applied across a quartz crystal produces mechanical vibration. The frequency of these vibration is determined by several factors:

• The physical dimensions of the piece of quartz crystal wafer.
• The plane or cut of the piece in relation to the crystalline axes of the quartz.
• The ambient temperature.
• The operating circuit.

1) Equivalent Circuit
Although the theoretical analysis of this piezoelectric effect is a relatively complex electro-mechanical function, it can be shown as a simple equivalent circuit.

The equivalent crystal circuit is useful in explaining the electrical characteristics of a quartz crystal unit operating near its fundamental resonant frequency. The series circuit consisting of L1, C1 and R1 is related to elastic vibration, while the element Co connected in parallel to the series arm as a capacitance attributable to the dielectric body of the quartz crystal wafer.

The resistance R1 is a resonance resistance of the crystal unit at the series resonance frequency. (See fig. 1).

2) Operating Modus
A crystal unit can be used in a circuit to operate in either of two modes, in series or parallel mode.

A) Series Resonance: Crystal units operating at series resonance appear resistive in the circuit and the value of the crystal unit is nearly equal to the motional resistance R1. Most crystals are manufactured at series resonance unless a load capacity is specified.

B) Parallel Resonance: Crystals operating at parallel resonance appear inductive in the circuit. The crystal frequency will be determined by the equivalent electrical parameters of the crystal and the load capacity CL which is a factor for determining the "conditions" of a crystal unit when used in the oscillator circuit. In an ordinary oscillation circuit, the crystal unit is used in a range where it functions as an inductive reactance.

In other words, when the oscillation circuit is seen from both terminals of the crystal unit, this oscillation circuit can be expressed as a series circuit of a negative resistance -R and a capacitance CL. At that time this capacitance is called the load capacitance.

The relationship between load capacitance is small, the amount of frequency variation is large, and when the load capacitance is increased, frequency variation lowers. If the load capacitance is lessened in the circuit to secure a large allowance for the oscillation frequency, the frequency stability will be greatly influenced even by small change in the circuit. The load capacity can be chosen from standard values specified on the datasheets.

3) Shunt Capacitance
Shunt capacitance (Co) is the capacitance between the crystal terminals. It varies with package, usually it is smaller in SMD crystal units and is 6-7pF in leaded crystal units.

4) Frequency-Temperature Characteristics
To use a crystal unit as an oscillator, its oscillated frequency is required to be stable against temperature variations. A quartz crystal has crystallographic axis, and crystal cut is defined according to the cutting angle against a crystallographic axis and its associated mode of vibration. The frequency-temperature characteristics of an AT-cut crystal unit which is most commonly used are expressed by cubic curves. (See fig.2) A quartz crystal wafer is cut at an angle at which a required frequency tolerance is obtained in the given operating temperature range. Actually, however, there can be some dispersion in apparent cutting angle due to the result of cutting and polishing accuracy in the successive process. Therefore it is required to optimize processing accuracy.

5) Calibration Tolerance
The calibration tolerance is the maximum allowable deviation from nominal frequency at a specified temperature typically at 25°C. It is normally specified in parts per million (ppm) or percentage of nominal frequency.

6) Stability
The stability is the maximum allowable deviation from nominal frequency, referencing as 0 at 25°C, over a specified temperature range and is specified in parts per million or percentage of nominal frequency. This parameter depends on the angle of quartz wafer cut as previous explained.

7) Overall Frequency Tolerance
The overall frequency tolerance is the maximum allowable deviation from nominal frequency due to change in temperature, time and other environmental conditions.

8) Aging
Quartz Crystal aging applies to the cumulative change in frequency which results in a permanent change in operation frequency of the crystal unit. The rate of change of frequency is fastest during the first forty five days of operation. Many interrelated factors are involved in aging, some of the most common factors are:

• Internal contamination
• Excessive drive level
• Crystal surface change
• Various thermal effects
• Wire fatigue
• Frictional wear

Proper circuit design incorporation low operating ambient, minimum drive level and static aging will greatly reduce not all but most severe aging problem. Typical aging figures for resistance welded crystal nits operating in the 10MHz range are 2 parts per million (ppm) per year.

9) Pullability
The pullability of a crystal refers to a crystal operating in the parallel mode and is a measure of the frequency change as a function of load capacitance. Pullability is important to the circuit designer who wishes to achieve several operating frequencies with a single crystal by means of changing in values of load capacitance.

10) Overtone Crystals
The crystal is usually operated at its fundamental frequency but can be operated on its 3rd, 5th, 7th and 9th harmonics with slight adjustment to the circuit. Overtone crystals are specially processed for plane parallelism and surface finish to enhance its performance at the desired overtone harmonics vibration.

11) Spurious Response
It is also possible for a crystal to vibrate at a frequency that is not related to its fundamental or overtone frequencies. Such unwanted frequencies are referred to as spurious. The circuit designer should protect the circuit from spurious by ensuring that the oscillation feedback circuit achieves its highest gain at the desired operating frequency.

12) Drive Level
Since a crystal unit performs mechanical vibration, too much vibration may lead to unstable oscillation frequency, and finally such may result in a sever damage to the quartz crystal wafer in the worst case scenario. When designing an oscillation circuit, the drive level should be examined so as to use an oscillator below the level specified by our datasheets. Fig. 4 shows an example method of confirming a drive level. This method employs a current probe to measure the crystal oscillator current. In this case the drive level is as follows:

13) Insulation Resistance
Resistance between 2 soldering terminals of crystal unit, or between lead and case (metal case). It is tested with a DC voltage at 100V ±15V and insulation resistance is in the range of 500M ohm.

14) Quality Factor
Quality factor is a quality function of motional inductance, resonant frequency and equivalent series resistance (ESR). It is typical in the range of ten's to hundred's of thousands.

Application Note : Oscillation Circuit

A typical oscillation circuit composed of a crystal unit is introduced below. Element constants used are for example.

CL=(C1xC2)/C1+C2)+stray capacitance
Stray capacitance may vary from 2pF to 6pF.

1. The Rd in the circuit diagram is indispensable, when used in a C-MOS oscillation circuit, to keep the drive level within the specified value and to obtain stable oscillation frequency.
2. C1 and C2 should be used within the range of 10 ~ 31pF. If C1 and C2 are used below or above 30pF, oscillation may be easily affected by circuit condition, drive level may be increased or negative resistance may be decreased, thus resulting in unstable oscillation.
3. The layout for crystal oscillation circuits should be arranged as short as possible
4. The stray capacitance between circuits and ground patterns should be reduced.
5. Crossing of crystal oscillation circuit patterns over other circuit patterns should be avoided.
6. Ultrasonic wave cleaning may cause deterioration of the crystal units.

Application Note : Selecting a crystal for microprocessor

Unless otherwise specified in the microprocessor datasheet, this application note can be used as a general guidance in selection of a crystal which can be used with many leading manufacterers of microprocessors.

Most microprocessors includes an inverter design with a positive feedback resistor (typical 1MO) with an optional series resistor with value varied from 10 ohm to 1K ohm (see Fig. A)

It has an input port (normally called XIN, XI, XTALI or similar nature) and an output port (XOUT, XO, XTALO or similar nature) for crystal unit connection between those two ports. Most chips are designed with an option either driven by an external clock oscillator fed to the crystal input port, or with an external crystal.

Depending on resonance frequency, crystals can be selected as fundamental or an overtone mode. Normally frequencies above 28MHz requires the third overtone mode for price advantage and delivery.

In parallel mode, where the crystal reactance is inductive, two external capacitors (C1) and (C2) are required for a necessary phase shift in oscillation. C1 and C2 are required regardless if the crystal is in fundamental mode or overtone mode. Value of C1 and C2 are specified by the chip manufacturer and vary from 6pF to 47pF.

C1 and C2 may not be balanced, i.e., equal in value, but sometimes are offset in a particular ration (C1/C2) for best performance, depending on crystal and amplifier characteristics and board lay-out. Fig. B shows a typical configuration for a fundamental mode operation.

In an overtone mode, an additional inductor L1 and capacitance Cc is required to select the third-overtone mode while suppressing or rejecting the fundamental mode. Chose L1 and Cc values in the third overtone crystal circuit to satisfy the following condition.

The L1, Cc components from a series resonant circuit at a frequency below the fundamental frequency, which makes the circuit look inductive at fundamental frequency. This condition does not favor to oscillation at fundamental mode.

The L1, Cc and C2 components from a parallel resonant circuit at a frequency about half-way between the fundamental and third overtone frequency. This condition makes the circuit capacitive at the third overtone frequency, which favors the oscillation at the desired overtone mode. (See Fig. C)

In a standard overtone mode, C2 value varies from 10pF to 30pF. Cc value should be chosen at least 10 times the value of C2, so its equivalent C-equiv. Will be approximately the value.

Typical values of L1 for different crystal frequencies:

Fig. D shows a typical circuit configuration for a 40.320MHz, third overtone mode operation.

Application Note : Negative Resistance Measurement

When a crystal unit is actuated as an inductive reactive reactance in an oscillation circuit, the relationship between the crystal unit and oscillation circuit is shown in Fig. E. To improve the starting conditions of the oscillation circuit, it is perferable to increase the value of negative resistance -R- which parameter of the of the oscillation circuit. The starting conditions will become worse if a circuit without much allowance in negative resistance (less negative resistance) is combined with a crystal unit having a larger resonance resistance. The oscillation circuit should be designed to a goal such that the value of negative resistance is 5 to 10 times the resonance resistance.

It is also necessary that the center value of load capacitance (the determine the absolute value of oscillation frequency) and the variable range (fine adjustment range of oscillation frequency) are maintained at the optimum values in the oscillation circuit.

Procedures of Negative Resistance Measurements

• Open either end of the crystal unit in the main circuit used, and insert a variable resistor in series to the crystal unit, as shown in Fig. E.
• Change the resistance value to examine the limits of oscillation and resistance in ohms observed at that time. In this case the power circuit must be turned on and off, without fail.
• Negative resistance (-R) in the circuit is the sum of the value obtained by the above and the resonance resistance R1 of the crystal.
• This measurement should be carried out at both the upper and lower limits of the operating frequency