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CUTTING ANGLES AND VIBRATION MODE LOAD RESONANT FREQUENCY(fL)
BASIC CHARACTERISTICS TERMINOLOGIES
CUTTING ANGLES AND FREQUENCIES OSCILLATION CIRCUITS
TEMPERATURE CURVES FOR AT-CUT AND TUNING FORK(kHz) REGARD TO DRIVING LEVEL OF X'TAL
EQUIVALENT CIRCUIT AND PARAMETERS REGARD TO OSC LOGIC LEVEL OF OSC
CAPACITANCE RATIO(r) PPM AND Hz , HOW TO EXCHANGE


SERIES RESONANT FREQUENCY(fs)& PARALLEL RESONANT FREQUENCY(fp) -R VS FREQ. AND LOAD
   
   


Mode of Vibration
Cut
Frequency Range(kHz)
Frequency Formula(kHz)
Capacitance Ratio
(Typical)
Thickness-shear 
 

 
AT Fundamental
800~5000
2000~80000
1670/t
1670/t

300~450
220

AT 3rd Overtone
20000~90000
1670* n/t
n* 250
n: Overtone Mode
AT 5th Overtone
40000~130000
AT 7th Overtone
100000~200000
AT 9th Overtone
150000~230000
BT Fundamental
2000~35000
2560/t
650
Length-width-flexure 
+2° X
16~100
700*w/l
450
Length-width-flexure 
XY 
NT
1~35 
4~100
5700*t/l
5000*w/l
600 
900
Length-extensional 
+5° X
40~200
2730/l
140
Face-shear 
CT
250~1000
3080/l
400
DT
80~500
2070/l
450
SL
300~1100
460/l
450
 
Note : With At-cut 3rd overtone and 5th overtone, lower frequency are available.
 
Theoretical Frequency-temperature Curves of Various Cuts
 
 
 

 

C0: Shunt Capacitance 
L1: Motional Inductance
C1: Motional Capacitance
R1: Equivalent Series Resistance
The ratio of the shunt capacitance to the motional capacitance
It is barometer of the change in oscillation frequency caused by the change in load capacitance.
 
There are two frequencies when the crystal's impedance is pure resistance. The low frequency is series resonance frequency fs and the high frequency is parallel resonance frequency fp.
To provide condition, crystal and load capacitance are connected in series or parallel, the fL is 
one frequency of the two frequencies when the connected impedance is only resistance. In series capacitance the low frequency is load resonance frequency. In parallel capacitance, the high frequency is load resonance frequency.
The main mode of the crystal. It is called the first (1st) overtone usually.

Odd numbers assigned for frequencies in terms of specified oscillation mode Standard 3rd overtone mode , followed by 5th , 7th , 9th etc.
It is not actual to produce 9th overtone.

The load capacitance is the circuit equivalent capacitance looking the circuit system from the two wire leads of crystal. The operation frequency in the circuit is defined by load capacitance and crystal.
Equivalent resistance for series resonance frequency.
Shunt (parallel) capacitance(C0) is the capacitance between the crystal terminals. It is difference in package, usually it is less than 7.0pF
The capacitance is the motional capacitance (series) in the euqivalent electric circuit.
The inductance is the motional inductance (series) in the euqivalent electric circuit.
The resistance is motional resistance (series) in the equivalent electric circuit.
Electric-power or current level under the specified conditions of a crystal unit.
Drive level is expressed in terms of milliwatt or microwatts. 
Excessive drive level will result in the crystal fracture or make the frequency drift in a long time.
The "Q" of a crystal unit is the Quality Factor or the motional arm resonance. The maximum stability that can be attained by the crystal is directly related to Q. The highter the Q , the smaller the band width (¡÷ f ) and the steeper the reactance slope (fs-fp). External circuit reactance value changes have less effect on a high Q crystal (less pullability) than lower Q devices.

In a resonant circuit composed of an L, C, and R, a quantity that represents the sharpness of a resonant curve, a curve that shows the relationship between the circuit current and power frequency.
It is means that when a crystal is operating at parallel resonance, and the frequency change as a function of load capacitance Cin a parallel resonant crystal. Pullability is a function of shunt capacitance C0, motional capacitance C1 , and size of crystal.
Frequency responses other than the main or desired respones, which the crystal elements have , specified in dB max. Frequency range must be specified.
Resistance between crystal's leads, or between lead and case. It's standard values is 
500M
 Ω min //DC100V.
Aging is very important to crystal unit. If we do not do that, the highest aging rate occurs within the first week, not one year later. The operating frequency will be over range early.
When designing an oscillator circuit, negative resistance (-R) is very important parameter to consider. To maintain stable oscillation at a constant frequency, it must have enough negative resistance (|-R|) to compensate for the resistance of the crystal.
Add resistor "VR" to the crystal unit in series and ensure that the oscillation starts or stops.
The approximate negative resistance of the circuit is the value obtained by adding the effective resistance "RL" the maximum resistance "VR" when the oscillation starts or stops after gradually making VR value larger.
The best value of Negative Resistance (-R) is 3~5 times of X'tal ESR(R1).
If the Negative Resistance (-R) is too small, could make Crystal unstable.
 

The following circuits are standard oscillation circuits.
The difference of IC circuit constants or circuit configuration due to the difference of IC makers may exert some influence upon the oscillation of a crystal unit.






Frequency
Range (KHz)

C1=C2 (pF)

R1
(KΩ)
Rf
(MΩ)
Load
Capacitance(pF)
20~60
15
0~100
10
12.5
60~150
15
0~100
10
12.5




 

Frequency
Range (MHz)

C1=C2
(pF)

R1
(Ω)
Load
Capacitance(pF)
3~4
33
4.7k
20
4~5
33
3.3k
20
5~6
33
2.2k
20
6~9
22
1.0k
16
9~10
22
470
16
10~15
15
470
12
15~20
15
470
12
20~25
10
470
10
*Reference to 74HCU04 

Frequency
Range (MHz)

C1=C2
(pF)

R1
(Ω)
Load
Capacitance(pF)
25~30
15
1.0k
12
30~40
10
680
10
40~50
7
330
8
*Reference to 7SHU04








Frequency Range (MHz)

C1
(pF)

C2
(pF)
L1
(uH)
R1
(Ω)
Load
Capacitance(pF)
30~40
10
18~10
2.2
820
10
40~50
7
15~10
1.5
470
8
50~60
5
15~10
1.0
330
8
 
*Reference to 7SHU04
 

The drive level of Crystal / Oscillator greatly affects to electrical performance.

If the drive level too high over 1000uW, the crystal oscillator dissipates heat effect and electrical
 
performance may be decreased.
If the drivel level is too low, will bring the DLD issue or can not oscillation.
As below table for crystal selection reference:

Holder type

Fund.(MHz)

3rd(MHz)
DL
CL
49U
1.8432~48.000
26.000~90.000
1000uW(Max.)
8pF(Min.)
49S/49SMD
3.000~54.000
36.000~150.00
300uW(Max.)
8pF(Min.)
7.0x5.0mm
6.000~40.000
40.000~70.000
300uW(Max.)
8pF(Min.)
6.0x3.5mm
7.000~54.000
40.000~200.00
300uW(Max.)
8pF(Min.)
5.0x3.2mm
7.600~54.000
40.000~156.25
300uW(Max.)
8pF(Min.)
3.2x2.5mm
10.000~60.000
60.000~156.25
200uW(Max.)
7pF(Min.)
2.5x2.0mm
12.000~80.000
 
100uW(Max.)
7pF(Min.)
2.0x1.6mm
16.000~60.000
 
100uW(Max.)
7pF(Min.)
1.6x1.2mm
24.000~60.000
 
50uW(Max.)
7pF(Min.)
 
1) ppm → Hz :
ppm is equal to per million (10^-6) . For example , the normal frequency is 12MHz , the frequency tolerance is ±10ppm, it shows the following equation :


so the frequency range is from 11.999880MHz to 12.000120 MHz
2) Hz → ppm :
For example , the normal frequency is 20MHz , the actually oscillation frequency is 20.000600MHz , it shows the following equation :


so the frequency tolerance is 30ppm.
 
 

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