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Quartz Crystal

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	Quartz Crystal - Technique Terms
	Quartz Crystal - Application notes
	Quartz Crystal - Design considerations
	Quartz Crystal - Reliability specifications

◆ Technical term ◆

Nominal Frequency:
The number of cycles of output waveform occurring per second. The unit of frequency is cycles per second, or Hertz, abbreviated Hz.

Fundamental Mode:
The main mode of the crystal. It is also called the first (1st) overtone.

Overtone Mode:
Odd numbers assigned for frequencies in terms of specified oscillation mode. Standard 3rd overtone mode, followed by 5th,7th,9th, etc.
It is not practical to go beyond 9th overtone.
Frequencies are not exactly 3, 5, 7 or 9 times the fundamental frequency.

Frequency Tolerance:
The allowable deviation from the normal frequency at room temperature. Frequency tolerance is expressed in percentage, typical 0.005% or in parts per millions (ppm), say ±50ppm.

Equivalent Series Resistance:
The value of impedance the crystal exhibits in the operating resonant circuit.

Drive Level:
The amount of power dissipation experienced by the crystal in the circuit. Drive level is expressed in milliwatt or microwatts. Excessive drive level will result in possible long-term frequency drift or crystal fracture.

Aging:
The relative frequency change over a certain period of time. This rate of change of frequency is normally exponential in character. Typically, aging is computed within first 30 days and is calculated over a long term (one year or ten years). The highest aging rate occurs within the first week of aging and decreases slowly after that.

Load capacitance:
(CL) is the amount of capacitance that the oscillator exhibits when looking into the circuit through the two crystal terminals. Load capacitance needs to be specified when the crystal is used in a parallel mode. Load capacitance is calculated as follows

Shunt Capacitance:
Shunt capacitance (C0) is the capacitance between the crystal terminals. It varies with package, usually it is smaller in SMD (4pF typical) and is 6pF in leaded crystals.

Spurious:
Unwanted resonances usually above the operating mode, specified in dB max or number of times of ESR. Frequency range must be specified. For example, spurious response can be minimum 6dB or 2.5XR in frequency window of F0±200kHz.

Operatable Temperature Range:
Temperature rang within which crystal units operate under specified conditions.

Mode of Vibration:
lt is a piezoelectric effect of quartz crystal. The mode of vibration of quartz crystal varies with crystal cuts such as thickness-shear for AT cuts and BT cuts, or length-width-flexure for tuning fork crystals (+2°X) cut, or face-sheer for CT, DT cuts. The most popular cut is the AT-cut which offers a symmetrical frequency shift over a wide temperature change.

Pullability:
Frequency change as a function fo load capacitance CL in a parallel resonant crystal. Pullability is a function of shunt capacitance C0, motional capacitance C1,and size of crystal.

Insulation Resistance:
Resistance between crystal's leads, or between lead and case (metal case). lt is tested with a DC voltage at 100V±15V and insulation resistance is in the range of 500M Ohms.

◆ Application Notes ◆
Crystal Equivalent Circuit

The equivalent circuit of a quartz crystal is shown to explain the basic elements governing crystal characteristics and performance. It consists of a motional capacitance C1, inductance L1, series resistance R1, and a shunted capacitance C0. The first 3 parameters are known as the motional parameters of the quartz element. See Fig. 1

Series Resonance
When a crystal is operatig at series resonance (Fs), it looks resistive in the circuit (Fig. 2). Thus, impedance at Fs is near zero. In a well designed series resonant circuit, correlation is not a problem and load capacitance does not have to be specified.

Parallel Resonance
When a crystal is operation at Parallel resonance (Fs)

As well as reactance changes, the frequency changes correspondingly, thus change the pullability of the crystal. The difference in frequency between the Fs and Fa depends on the Co/C1 ratio of the crystal unit, and the inductance L1. In parallel circuit design, load capacitance CL shall be specified. (Fig. 3)

The crystal equivalent circuit can be simplified as a series resistance Re with a reactance Xe. (Fig. 4)

Meanings of Crystal Equivalent Circuit
refer to Figure 5.

L1=results from the mass of the quartz blank.
L1(H)=4.22 X104X(1670)2/F (Hz)/ A(m3)
A=Area of the Electrode
F=Resonant Frequency
C1=results from the elasticity of the quartz blank.
C1(pF)=0.22XA(m)XF( Hz)/1670
C0=the capacitance forming by the electrodes and the mounting posts. Co varies with frequency and quartz blank size.
Typical Value is 1pF to 7pF.
R1= results from the bulk losses within the quartz blank due to mounting methods and stress.

Difference Between AT-Cut and BT-Cut
The typical AT-cut curve has an S-shape and the BT-cut has a parabola shape. Both are symmetrical to room temperatures (25°C±3°C). Please see figure 6.

AT-cut and BT-cut have the same vibration mode thickness shear Fundamental frequencies higher than 24MHz (in HC49U) or 28MHz (in HC49US) can be designed with either AT-cut or BT- cut. For the same frequency. Quartz blank of a BT-cut is relatively thicker than a AT-cut, therefore offers better yield and lower cost. However, special precautions must be made before selecting the appropriate cuts because they possess different motional parameters and frequency vs. Temperature characteristics.

F(AT Fundamental in kHz)=1670/t(t in mm)
F(BT Fundamental in kHz)=2560/t

Negative Resistance -R
Negative resistance is an important parameter to consider when designing an oscillator. Fig. 7 shows an equivalent circuit for an oscillator -R represents negative resistance. To maintain stable oscillation at a constant frequency, the oscillator must have enough negative resistance |-R|>10 Re) to compensate for the resistance (loss) of the resonator.

Change of Load Capacitance and Pullability
When a crystal is operating at parallel resonance (Fs1 ratio of the crystal unit.

The same crystal with frequency at 3rd-overtone mode will have much less pulling because its motional capacitance C1 is approximately 1/9 of C1 at fundamental.

In some applications, the frequency pullability due to load change must be controlled either to maximum or minimum. ln most PLL design, pulling must be specified to a minimum in order to lock to a reference frequency. In other applications, where accuracy at calibration is specified, the frequency pulling due to load change must be at maximum. Unit of trim sensitivity is ppm/pF.

If CL is small or C1 is large, the sensitivity of frequency increases. It is very difficult to design and control tight frequency accuracy at small load capacitance without considering correlation in reading between equipment. Fundamental high frequencies between 24MHz to 50MHz which require minimum frequency pulling must be designed with AT-cut instead of BT-cut.

Overtone Crystal
The overtone modes of a crystal are typically oddmultipies of the fundamental mode.
See Figure9

Drive Level of a Crystal
Drive level is the amount of power dissipated by the crystal. The Drive level is specified in mW or W. Drive level varies with frequency, load capacitance, and size of quartz blank. Standard parallel circuit: drive level varies between 50 W & 1mW.

Drive level can be measured in a couple of ways. A simple way which is not highly recommended is to insert a series resistor with a value equal to the crystal resistance. Measuring voltage drop of that resistor and the power can be calculated using the formula:

Another direct method to measure the drive level is by using an AC current probe with an amplifier to measure the AC current through the crystal. Please, refer to Figure 10.

Measure peak-to-peak current on a scope. Record the value. Measure Re(ESR) of the crystal. Calculate the power by using the formula: P=I2XRe

P=Power dissipated in crystal (W)
I= rms current (I=Ipp/2 x 0.707)
Re=ESR in Ohms

Basic Parameters of a Crystal

◆ Design Considerations ◆

The following considerations must be well studied in order to select the right crystal for your applications:

1) ASIC CHARACTERISTICS:

Negative resistance.
Small-signal gain analysis.
Input and output resistance.
Propagation delay between input and output of inverter.
Gain-phase analysis.
Supply voltage operational margin.
Circuit configuration.
Feedback resistor value (if integrated within the ASIC).
Built-in load capacitance on X1 and X2 ports.
Sensitivity of inverter operation versus stray inductance or capacitance due to layout or attachment methods.

2) CRYSTAL CHARACTERISTICS:

Mode of Operation (Fundamental vs Overtone. )
Series vs Parallel.
If parallel: State Load Capacitance
If overtone: specify design without inductor or conventional tuning tank LC circuit.
Maximum resistance.
Drive Level dependency.
Operating temperature.
Frequency accuracy at 25°C
Frequency stability over temperature.
Aging
Pulling characteristics.
Spurious responses.

3) CIRCUIT CONSIDERATIONS:

Select the best value for therefore (feedback resistor).
Recommend Value:
Low kHz Range: between 10 M Ohms 20 MOhms
MHz Range: between 100k Ohms to 1 M Ohms.
Select Series Resistance Value (Rd) for impedance matching. Rd selection varies with ASIC negative resistance, output resistance and load impedance.
Typical value for Rd:
0(Short) to 1 k from 4 MHz to 30 MHz.
Study the Voltage Gain from output to input Vi/Vo = C2/C1. It is very common to select equal values of C1 and C2 in the circuit, but sometimes it is necessary to make the output load capacitance (C2) higher to compensate for the signal losses through the crystal and feed back loop.
Maximum Crystal Resistance Allowed:
Low resistance is desirable for better operational margin and stability. However, crystal resistance varies with frequency, blank size. Low crystal resistance could affect yield and therefore cost.
Typical Crystal Aging: 5ppm per year maximum.
Aging over 10 years: 10ppm to 15 ppm maximum.
Tighter aging (up to 1 ppm to per year max.) is available. Tighter aging requiring extremely high design, manufacturing, and/or post-tests need additional steps, thus affecting cost.
Inductorless Third (3rd) Overtone:
The inductorless 3rd-Overtone circuit is similar to the fundamental frequency circuit except the feedback resistor value is made much smaller (typical value varies between 2k to 6k).
In this case, the component of inductive admittance due to the resistor is greater than the admittance of the loading capacitance at the fundamental frequency, thereby preventing oscillation at the fundamental frequency, In the meantime, the inductive admittance at the overtone is less than the admittance of the load capacitor thus enabling the oscillation at the third-overtone. (See figure 11.)

4) Tuning Tank LC Overtone Circuit
In an overtone mode, an additional inductor L1 and capacitance Cc is required to select the 3rd-overtone mode, while suppressing or rejecting the fundamental mode. Choose Lc and Cc component values in the 3rd-overtone crystal circuit to satisfy the following conditions:

The Lc/Cc component form a series resonant circuit at a frequency below the fundamental frequency which makes the circuit look inductive at the fundamental frequency. This condition does not favor to oscillation at the fundamental mode.
The L1/Cc and C2 components from a parallel resonant circuit at a frequency about half-way between the fundamental and 3rd-overtone frequency. This condition makes the circuit capacitive at the 3rd-Overtone mode, (See figure 12).
The LC tank may be located at either input or output of the inverter. However, the LC tank at the output is preferred, because it helps to clean up all unwanted modes before signal goes through the crystal.

5) CONTROL UNWANTED MODES IN CRYSTALS:
Unwanted modes are resonant modes in addition to the desired modes (Fundamental, Third-Overtone, Fifth-overtone, etc.). The frequencies of these unwanted modes are usually slightly higher than the desired modes within couple of hundreds kilohertz. In oscillator applications, it is necessary to control unwanted modes as lower as possible to prevent circuit oscillating in the Spurious mode. See Figure 13. The design of large electrodes on crystal to produce large pulling is a common cause of promotion spurs.

Unwanted modes are usually specified in terms of resistance or in terms of the ratio of resistance of the unwanted mode to the resistance of the main mode over a bandwidth of desired frequency. A resistance ratio of 2:1 or a minimum of 3dB separation is usually adequate.

◆ Reliability Specifications ◆

Seam Sealed Ceramic Surface Mount Crystal Package

MECHANICAL CHARACTERISTICS
VIBRATION
20G, 10~2000Hz sweep for 20 minutes, 1.52mm, 4 hours for each direction.
Ref. MIL-STD-883E Method 2007.2

MECHANICAL SHOCK
1000G, 0.5mS, 3 times for each direction
Ref. MIL-STD-883E Method 2002.3

DROP TEST
75cm Height.3 times on 2mm stainless plate.
Ref.JIS C6701

SOLDERABILITY
95% Coverage by using 63/37 solder at 230±5°C solder pot immersion 3±0.5 seconds.
Ref.MIL-STD-883E Method 2003.7

RESISTANCE TO SOLDER HEAT
10 Seconds 5 seconds immersion into 260±5°C solder pot. Ramp rate is 1 to 4°C/sec; above 183°C is 90~120 seconds.
Ref. MIL-STD-202 Method 210, test condition J.

GROSS LEAK TEST
5kgf/cm Helium bombing for 2 hours, bubble test in 125±5°C FC # 40 for 60 Second or equivalent auto test method.
Ref. MIL-STD-883E Method 1014.10

FINE LEAK TEST
5kgf/cm Helium bombing for 2 hours, leak rate less than 1 10 exp (-8)atm.c.c./sec.
Ref.MIL-STD-883E Method 1014.10

DIMENSION CHECK
X, Y, Z, Three dimensional, according to specifications
Ref. MIL-STD-883E Method 2016

DPA (INTERIOR CHECK)
Visual and 50X Stereo-microscope.
Ref. MIL-STD-883E Method 2013.1

ENVIRONMENTAL CHARACTERISTICS

THERMAL SHOCK
-55°C~125°C for 100 cycles, dwell time: 30 minutes,
Transit time less than 10 minutes
Ref. MIL-STD-883E Method 1011.9

HIGH TEMPERATURE STORAGE
125±3°C 1000±12hours.
Ref. MIL-STD-883E Method 1055.4

LOW TEMPERATURE STORAGE
-55±3°C static 1000±12hours.
Ref. MIL-STD-833E Method 1013

HIGH TEMPERATURE AND HIGH HUMIDITY STORAGE
85°C, RH 95%, 1000±12hours.
Ref. MIL-STD-833E Method 1004.7

FREQ. Vs. TEMPERATURE
-40°C ~85°C , from low temp. 5°C step up to high temp

Glass Sealed Ceramic Surface Mount Crystal Package

MECHANICAL CHARACTERISTICS
VIBRATION
20G, 10~2000Hz sweep for 20 minutes, 1.52mm, 4 hours for each direction.
Ref. MIL-STD-883E Method 2007.2

MECHANICAL SHOCK
100G, 0.5mS, 3 times for each direction
Ref. MIL-STD-883E Method 2002.3