

Mode of Vibration

Cut

Frequency Range(kHz)

Frequency Formula(kHz)

Capacitance Ratio
(Typical)

Thicknessshear

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

Lengthwidthflexure

+2° X

16~100

700*w/ l

450

Lengthwidthflexure

XY
NT

1~35
4~100

5700*t/ l
5000*w/ l

600
900

Lengthextensional

+5° X

40~200

2730/l

140

Faceshear

CT

250~1000

3080/l

400

DT

80~500

2070/l

450

SL

300~1100

460/l

450



Note : With Atcut 3rd overtone and 5th overtone, lower frequency are available. 

Theoretical Frequencytemperature 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. 
Electricpower 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 (fsfp). 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 CL in 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:


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.)


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 
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. 
