Fig. 1

Crystal units are the electronic devices using piezoelectric effect to generate electromechanical vibrations in resonators. Such vibrations are characterized by high quality factor Q and high resonance frequency stability, that are main reasons for using this resonators for frequency control and frequency selection in electronic equipment. From the electrical point of view, the crystal unit is represented by crystal unit equivalent circuit (see Fig. 1). The elements of this circuit are:

CRYSTAL UNITS - TERMS, DEFINITIONS AND CHARACTERISTICS
Term	Reference symbol	Definitions and characteristics
Motional resistance	R1 [Ω]	The resistance in the motional ( series ) arm of the equivalent circuit. It represents energy losses of vibrations in the resonator. Its value is according resonator type from Ohms up to hundreds of Ohms.
Motional inductance	L1 [mH, H]	The inductance in the motional ( series ) arm of the equivalent circuit. It represents mass inertia of the resonator. Its value is according resonator type from mH up to H
Motional capacitance	C1 [fF]	The capacitance in the motional ( series ) arm of the equivalent circuit. It represents elasticity of the resonator. Its value is according resonator type from order of 0.1 fF up to 10 fF.
Shunt capacitance	C0 [pF]	The capacitance in parallel with the motional arm of the equivalent circuit. It represents the resonator as a capacitor. Its value is according resonator type in order of pF.
Quality factor	Q	Quality factor is dimensionless parameter characterising losses of vibration energy in resonator, it can be calculated from equation:
Capacitance ratio	r	Capacitance ratio is the ratio of shunt capacitance to motional capacitance: The parameters of equivalent electrical circuit determine some characteristic features of crystal units (see below).
Motional (series) resonance frequency	fs [kHz, MHz]	Motional ( series ) resonance frequency ( fs), is the frequency, at which the susceptance of resonator is equal to 2πfsC0 or ( ωsC0) and conductance reaches maximum
Parallel resonance frequency (lossless)	fp [kHz, MHz]	Parallel resonance frequency (lossless) is the frequency at which the reactance of resonator is equal to 1/(2πfsC0) or 1/(ωsC0) and resistance reaches maximum.
Resonance frequency	fr [kHz, MHz]	Resonance frequency is the lower of the two frequencies of the crystal unit alone, under specified conditions, at which the electrical impedance of the crystal unit is resistive
Anti-resonance frequency	fa [kHz, MHz]	Anti-resonance frequency is the higher of the two frequencies of the crystal unit alone, under specified conditions, at which the electrical impedance of the crystal unit is resistive
Working frequency	fW [kHz, MHz]	Working frequency is the operational frequency of the crystal unit together with associated circuits
Load resonance frequency	fL [kHz, MHz]	Load resonance frequency is one of the two frequencies of a crystal unit in association with a series or with a parallel load capacitance, under specified conditions at which the electrical impedance of the combination is resistive. The load resonance frequency is the lower of the two frequencies when the load capacitance is in series and the higher when it is in parallel. In EN 60122-1:2002 (IEC 60122-1:2002) other characteristic frequencies of the crystal unit are defined.
Load capacitance	CL [pF]	Load capacitance is the effective external capacitance associated with the crystal unit which determines the load resonance frequency fL. It represents the influence of external circuits on resonator frequency.
Load resonance resistance	RL [Ω, kΩ, MΩ]	Load resonance resistance is the resistance of the crystal unit in series with a stated external capacitance at the load resonance frequency fL.
Fractional load resonance frequency offset	DL	Fractional load resonance frequency offset is the relative frequency change of resonance frequency caused by connection of load capacitance CL to the crystal unit.
Fractional pulling range		Fractional pulling range is the fractional frequency change caused by the load capacity change from value CL1 to CL2
Pulling sensitivity	S	Pulling sensitivity is the fractional pulling range related to 1 pF load capacity change at specified load capacity CL.
Operating temperature range	°C	Operating temperature range is the range of temperatures over which the crystal unit shall be within the specified tolerances
Operable temperature range	°C	Operable temperature range is the range of temperatures over which the crystal unit will not sustain permanent damage though not necessarily functioning within the specified tolerances
Storage temperature range	°C	Storage temperature range is the minimum and maximum temperatures, at which the crystal unit may be stored without deterioration or damage to its performance
Reference temperature	°C	Reference temperature is the temperature at which certain crystal measurements are made. For controlled temperature units, the reference temperature is the mid-point of the controlled temperature range. For noncontrolled temperature units, the reference temperature is normally 25°C ± 2°C
Frequency tolerance Fig. 2	[ ppm ]	Frequency tolerance is the maximum permissible deviation of the working frequency due to a specified cause or a combination of causes. The frequency tolerance is usually stated in parts per million (ppm =1×10-6) of the nominal frequency. The tolerances normally used are defined as follows: - deviation from nominal frequency at the reference temperature under specified conditions; - deviation over the temperature range from the frequency at the specified reference temperature, typical temperature-frequency dependency for AT and SC cut is shown in Fig. 2; - deviation as a result of ageing under specified conditions; - deviation from nominal frequency due to all causes (overall tolerance).
Level of drive	[ µW]	Level of drive is a measure of the conditions imposed upon the crystal unit. This may be expressed in terms of current through or power dissipated in the crystal element
Drive level dependency	( DLD )	Drive level dependency is the effect of changes in drive level conditions upon the resonance resistance or frequency of the crystal unit. This parameter can be specified by defining the ratio of resistance between two specified drive levels, or max. relative resistance and/or frequency change over specified drive level range.
Activity dip		Activity dip is undesirable change in the crystal unit`s load resonance frequency and/or resonance resistance, caused by the coupling of different modes in a narrow temperature range, at a specified load capacitance and level of drive ( see EN 60444-7 or IEC 60444-7 )
Frequency dip		Frequency dip is undesirable perturbation or fluctuation in the crystal frequency occurring in a narrow temperature range as a deviation of the load resonance frequency from the smooth regular frequency temperature characteristic described by a polynomial of up to the 5th order. It usually shows an associated resistance change and the effect is usually drive level dependent
Hysteresis		Hysteresis is the max. fractional frequency difference between two crystal unit frequency measurements at reference temperature (25 °C ± 3 °C) before and after passing through full operating temperature range.

The customer can specify even other parameters of demanded crystal units, such as follows:

• unwanted resonance rejection,
• specified frequency-temperature dependency,
• resistance to soldering heat at SMD-reflow process,
• severe mechanical and environmental resistance,
• etc.

Tab. 3 - Long-term stability (ageing) per year versus type and overtone quartz unit.