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  • 1Quartz crystal and frequency control element
  • Quartz is Silicon Dioxide(SiO2) composed of silicon atoms and oxygen atoms, a single crystal structure formed in the six square crystal system of 32 points. The single crystal quartz crystal structure has the piezoelectric effect. When the pressure is applied in some direction, the direction of vertical force will produce electrical potential. When the pair is applied to some axis of quartz crystal with an electric field, it will produce deformation or vibration in some other directions. To master the piezoelectric effect of single crystal quartz material, using its resonance frequency characteristics to play its precise degree as reference reference for various types of frequency signals, is the design of crystal oscillators. Because quartz crystals have high material Q values, most of the frequency control elements, such as resonators and oscillators, are based on quartz materials. The frequency control elements based on quartz can be divided into bulk wave vibration elements and surface acoustic wave based on the properties of their piezoelectric vibration. VE) vibration components, such as quartz crystal resonators, quartz crystal filters and quartz crystal oscillators, surface wave vibration elements such as surface wave filters and surface wave resonators. When quartz crystals are machined by a specific cutting mode, the surface is machined to finish the surface, and the specific outer size is the general name. Quartz wafers (quartz wafer or quartz blank). The quartz wafers are placed in the vacuum and deposited on the surface of the electrode and then fixed on the metal or ceramic base with conductive materials and encapsulated to become the commonly called quartz crystal resonators . Quartz resonators are used to resonate at the resonance time. The low impedance characteristics and the overlapping characteristics of the wave can make quartz crystal filters with adjacent double electrodes. Quartz oscillators are added to different electronic oscillators to make quartz oscillators with different characteristics. For example, quartz time pulse oscillator (CXO), Voltage Controlled Crystal Oscill (Ator, VCXO), temperature Compensated Crystal Oscillator(TCXO), constant temperature slot control quartz crystal oscillator (Oven Controlled Crystal Oscillator, OCXO)... Relative to the resonance of the body wave is the resonance of the surface acoustic wave. The surface oscillating waves produced by the surface of the quartz crystal on the inter-digital-transducer (IDT) mode can produce a short wavelength (high frequency) resonant surface acoustic resonance (SAW Resonator) or a surface acoustic wave filter (SAW Filter).
  • 2Piezoelectric properties of quartz crystal
  • The two silicon oxide molecule (SiO2) in the quartz material is in normal state, its electric dipole is a mutually balanced electrical neutrality. In the (two left) two silicon oxide is a simplified figure in the two-dimensional space. When we give the positive electric field and the negative electric field above the silicon atom and below the oxygen atom, the space system is to maintain the potential balance, two oxygen. The atoms will repel each other, form an induction electric field under the oxygen atom, and produce a negative electric field region above the silicon atom. On the contrary, when we give negative electric and positive electric fields above the silicon atom and below the oxygen atom, the two oxygen atoms are close to each other and the negative electric field is produced below the oxygen atom. An induced positive electric field is produced above the silicon atom. (Figure two). However, when the level of the oxygen atom changes, the other atom of the adjacent oxygen will produce the force of repel or attraction relatively, forcing the oxygen atom to return to its original space. Therefore, the power of the electric field and the force between the atoms will affect each other, the change of the electric field and the square of the water. The deformation is an interaction state. This interaction will form a vibrational state in which the quartz material has the smallest energy consumption. As long as the electric field continues to give energy, the quartz material will maintain a resonant frequency between the electric field and the electric field.
    The amplitude of the oxygen atom under this piezoelectricity and the intensity of the electric field and the electric field have a relative relation to the vector angle of the two silicon oxide. In practical application, the electric field is produced by the metal electrode plated on the quartz crystal. The vector angle of the electric field and the two silicon oxide is determined by the cutting angle of the quartz crystal rod.

    (Fig. 2) Simplified one dimensional piezoelectricity of SiO2
  • 3Vibration mode of quartz crystal
  • By different quartz cutting angles and electric field effects of different electrode shapes, quartz wafers exhibit various vibrational modes. The frequently produced vibration modes can be divided into perturbation modes (flexure mode), expansion mode , surface shear mode and thickness shear mode (thickness shear MOD). E). These vibration modes can be seen in a simple method in Table 1. In actual conditions, the quartz crystal is not necessarily only a single vibration mode, but there may be a variety of modes at the same time in the oscillation of a quartz crystal, and the other undesired vibration modes (unwanted Mo) can be suppressed via appropriate design. De) to achieve the optimization of the main vibration modes.

    〔Table 1〕Vibration Mode and Cut Angle.
  • 4Frequency and temperature characteristics of quartz crystal
  • Most of the quartz crystal products are used for reference frequency reference or frequency control elements on electronic circuits. Therefore, the characteristics of frequency and working environment temperature are a very important parameter. In fact, good frequency and temperature characteristics are also one of the main factors to choose quartz as a frequency component. By proper definition and design, the quartz crystal element can easily satisfy the frequency error range of one millionth (parts per million, PPM) unit level. If a LCR part is composed of a high frequency oscillating line in a discrete circuit, it can also reach the required reference frequency signal error in a small production scale. It is required at the ppm or sub-ppm level, but this method does not meet the scale of production to be achieved by the industry. The frequency of the quartz element is more simple than the discrete oscillating line. In (Figure four) several different frequency pairs of quartz crystal cutting angles are provided.

    〔Fig.4〕Frequency-temperature characteristics of various quartz cuts.

    In a variety of different cutting angles, AT angle cut quartz wafers are suitable for the frequency range of MHz to hundreds of MHz. It is the most widely used and most used cutting application of quartz crystal. In (Figure five), from the upper view of the quartz crystal rod X- axis, the A can be seen to rotate about 35 degrees to the Z- axis. T direction. This is also a good way of doing well in mass production technology.

    ( Fig.5 ) Orientation of AT plat

    (Figure six) is an expansion diagram of the temperature characteristic of the frequency of the AT cutting angle in the thickness vibration mode. In the diagram, the common room temperature perturbation 25 degree is used as the relative zero point, and the biggest advantage of the AT cutting is the frequency to the temperature change to the three order square curve. This characteristic, from (Figure six), can be seen in a fairly wide range of temperature, A The first and two order constants of the temperature curve of T cutting are zero, and the constant of the third order determines the value of frequency to temperature.

    (Fig. 6) AT - cut frequency-temperature characteristics.
  • 5The equivalent circuit and parameters of the quartz crystal resonators
  • (Figure seven) (a) and (b) are the basic structure diagrams of quartz oscillators of DIP type and SMD type respectively. (Figure seven) (c) is an electronic symbol for quartz oscillators used in electronic circuits. When quartz crystal resonators are far away from oscillating frequency regions, quartz crystal resonators are only a capacitive element, when the frequency is close to Shi Yingjing The oscillation frequency of the body is close to an inductive equivalent LCR oscillation circuit.

    (Fig. 7) (a) Metal can type resonator
    (b) Ceramic SMD type resonator
    (c) Symbol of crystal usnit

    (figure eight) is a Butterworth-Van Dyke (BVD) equivalent circuit that converts quartz crystal resonators to oscillating frequencies. In this diagram, there are four main parameters: static capacitance -Co, dynamic capacitance -C1, dynamic inductance -L1, and dynamic resistance -R1.

    〔Fig.8〕Effective Circuit of Crystal
  • 6Resonance Frequency
  • In terms of technical literature and product application, resonance of quartz crystal resonators has three sets of different definitions and resonance frequencies.

    1. Series resonant frequency and parallel resonant frequency ( fs , fp )
    (series resonance frequency and parallel resonance frequency)
    2. Resonance frequency and anti resonant frequency ( fr , fa )
    (resonance frequency and anti-resonance frequency)

    3. Maximum conductance frequency and minimum conductance frequency ( fm , fn )

    (maximum admittance frequency minimum admittance frequency).

    The admittance (admittance) diagram of these three sets of frequencies can be seen clearly from the plural coordinates of (Fig. nine).

    〔Fig.9〕 Complex Admittance of Resonators

    The frequency of FS and and FP is the frequency of the maximum conductance and the maximum impedance.
    The resonance frequency and the anti resonant frequency, FR and FA, are the two frequencies of zero (pure resistance), respectively. At this time, the impedance of FR is 1 / Rr and the impedance of FA is 1/ Ra..
    The series resonant frequency and the parallel resonant frequency, FS and FP, are the most important two frequency parameters when evaluating the equivalent lines of resonance. We can express the relationship between the series resonant frequency and the parallel resonant frequency (FS and FP) two, which we can express by the following formula:

    The C1 and L1 in the formula are dynamic capacitance and dynamic inductance in Figure seven respectively, and Co is static capacitance.

  • 7Exclusive name
  • (1) Nominal Frequency and Tolerance

    Under the correct matching of the oscillating lines, the frequency output from an oscillating line is called "nominal frequency". The frequency unit is generally expressed as MHz (megahertz, MHz) or kHz (Kilohertz, KHz).

    In actual mass production and oscillating line applications, there are some frequency dispersion errors relative to the center frequency in the room temperature environment (25oC). The maximum dispersion of this type of frequency admissible error is generally expressed as ppm (parts per million) or% (percent).

    (2) Fundamental and Overtone Vibrations Mode

    The quartz crystal resonators at the AT cutting angle exist mainly in the oscillating mode of the thickness shear. In the resonance, the high order frequency doubling resonances also exist between the electrode regions of the quartz crystal in addition to the basic wave oscillation, but the electrode of the piezoelectric material is the opposite of the electrical phase. Therefore, the frequency doubling of only odd times can occur, and the frequency doubling resonance of the even number of times (even number) will not exist in the quartz crystal resonance (Figure ten).

    (Fig.10) Only odd number harmonic vibrations can be excited in crystal resonator

    (3) Load Capacitance, CL

    The "load capacitance" on an oscillating line is defined as all capacitance values encountered in an oscillating line from two terminals of a quartz crystal resonance. On line, the load capacitance can be connected with a quartz crystal resonance in parallel or in series. An oscillating line connected in parallel mode. The size of the load capacitance (CL) affects the nominal frequency characteristics.

    The resonant frequency of this load capacitance parallel circuit is expressed in fL. :

    (4) Frequency-Temperature Stability

    The frequency of quartz changes because of the temperature change, which is due to the different thermal expansion coefficient of the quartz material in the axis of each coordinate. When the temperature changes, the axial lattice distance of each axis varies a little. When the different cutting angles are quoted, the variations of the different oscillation modes are also different.
    The design of the shear oscillating mode with the thickness of the AT cutting angle is generally used as the frequency of 25 degrees centigrade as the reference temperature point to define the stability of the frequency variation within the temperature range of the working environment. At the same time, the temperature range of the working environment should be defined together with the corresponding working environment temperature range.

    The frequency of a quartz frequency element has a characteristic of temperature stability, as well as the nominal frequency error, with ppm or% as a measurement unit. The frequency temperature characteristic curve of the component has a great relationship with the cutting angle of quartz, the oscillating mode, the surface treatment and the outer size. In addition, the load capacitance (CL) on the oscillating line, The characteristics of driving power (drive level) will also affect the stability of the output frequency of the oscillation circuit to the temperature change.

    (5)Equivalent Series Resistance , ESR

    When the quartz crystal oscillates in series at FS, the C1 and L1 are counterpart to the opposite phase, and the dynamic branched arm (motional arm) of the entire resonance (admittance) is close to the minimum impedance value R1. at this time the whole quartz crystal resonance is only a resistive element. The resistance value R1 is the mechanical energy loss of the whole component. It contains quartz material, and all the energy loss of materials and packaging materials.

    (6) Motional Capacitance C1 and Motional Inductance L1

    In Formula 1, the dynamic capacitance C1 and dynamic inductance L1 are interrelated with the frequency of series vibration and FS.
    In the actual measurement system, we can only measure the dynamic capacitance C1 and the serial frequency of FS. The dynamic inductance L1 is calculated by formula (4).

    (7) Static Capacitance or Shunt Capacitance, Co

    The static capacitance, Co, is mainly free to use quartz wafers as the main capacitance of the dielectric material and the two electrodes; the other a small part of the static capacitance comes from the capacitance between the conductive materials connected by the quartz chip and the wiring and the capacitance of the package shell.
    The static capacitance is measured at a range of far lower than the oscillating frequency to avoid the dynamic capacitance affected by the oscillating frequency. Formula (5) is a mathematical expression of the static capacitance.

    In the formula (5), A represents the area of the electrode; D represents the thickness of the quartz crystal; the epsilon is the relative dielectric value of the quartz crystal; Cm+p is the other capacitance value produced by the material.

    (8) Drive Level

    The driving power of quartz crystal refers to the power consumed by the quartz crystal resonators. Generally, it is expressed in a microwatt. The design of the oscillating line must provide the appropriate power to make the quartz crystal resonate to start and maintain the oscillation. The oscillation of the quartz crystal is the electrical impedance of the physical high frequency mechanical vibration and the oscillation. The value is below 10~100 ohm (depending on the frequency range and size). If the oscillating line provides high driving power, the nonlinearity of the quartz crystal and the interface between the quartz / electrode / material will deteriorate, and the oscillation frequency FL and the equivalent impedance R1 will be over changed. The quartz crystal is overdriven for a long period of time. With the low consumption of power demand and the trend of product reduction, the electrical impedance values of quartz crystal resonators are reduced and stable as a whole with the technology of quartz products in recent years. The energy is on the quartz crystal resonators. For most applications, the oscillating lines provide the maximum power of 10 ~ 100 microwatt (depending on the size and frequency of the quartz resonance) to the quartz resonators.

    (9) Quality Factor, Q

    For quartz crystal resonators, the electrical quality factor Q is a very important characteristic. The electrical quality factor can be expressed by the following formula (6).

    The quality factor of quartz crystal resonator can reach over 100 million.

    (10) Pullability and Trim Sensitivity

    The resonance frequency of quartz crystal is applied on a parallel oscillating line. The oscillation frequency has a great relationship with the load capacitance CL. This can be seen in the previous formula (3). (Figure eleven) is a diagram of the change curve of the load capacitance CL on the FL frequency of the parallel oscillating line. 

    The frequency "traction rate" refers to the frequency variation of the frequency FL1 of the load capacitance CL1 to the frequency FL2 of the load capacitance CL2. In (Figure eleven) the frequency change value of FL1 (CL=24pF) and FL2 (CL=10pF). In this example, the frequency traction rate is 220 ppm. if we approach the CL1 and CL2 load capacitance values The tangent value of the curve is the sensitivity of a load capacitance .

    In (Figure eleven), the frequency sensitivity of CL=24 pF is 10 ppm/pF, and the frequency sensitivity of CL=10 pF is 20 ppm/pF. in parallel lines. The smaller the load capacitance is, the higher the sensitivity of the frequency to the load capacitance. The higher the load capacitance, the lower the sensitivity of the frequency to the load capacity change. This is the quartz crystal common. When the oscillator is used on the VCXO line, a smaller load capacitance is used in the circuit design. On the other hand, a higher load capacitance will be used in the circuit design when the more accurate frequency signals are required.

    (Fig. 11) Frequency variation vs. load capacitance

    (11) AGING

    "Aging" refers to the variation in the frequency of the quartz crystal resonators with the frequency of time in a certain period of time, with a unit of parts per million (PPM). The characteristic curves of aging in frequency and time are generally the changes in the exponential pattern. The frequency aging changes most. The large period is the first month after the quartz frequency component is made. After that, the frequency changes gradually decrease with time. There are several major factors affecting the aging characteristics of the frequency. For example, the packaging method, the type of material, the process temperature, the process control, the heat treatment process and the size and frequency of the product. Most of them need to define the short term (1~3 months) or long term (1~10) frequency aging needs.


    In addition to the temperature range in the previous working environment, another temperature related feature is the "Storage Temperature Range". This parameter refers to the maximum and minimum temperature range that the product can store in a static state. In this temperature range, the product must be guaranteed to be stored for a long time. It is also possible to work well in the working temperature range and conform to the specifications. This characteristic is closely related to the design and process design of the quartz crystal resonators, and should be carefully defined.

    (13) Negative Resistance , - R

    Negative impedance is the impedance characteristic value of the oscillating line at the oscillating frequency from the two terminals of the quartz crystal resonance. The oscillating line must provide sufficient amplification gain to compensate for the mechanical loss of the quartz crystal resonators at resonance. Negative impedance is not a quartz oscillator. Product parameter is an important characteristic parameter of oscillating line. From the point of resonance, it is the "negative impedance" of oscillating line.

  • When the quartz resonators are integrated with an oscillating line or an integrated circuit (IC) together in a package, the power supply voltage is supplied externally, forming an active component output frequency signal, the so-called quartz crystal oscillator. The quartz crystal oscillator can be provided by different oscillating lines and output lines within a single package element. The reference frequency of different characteristic requirements (reference frequency). For example, a quartz time pulse oscillator SPXO (Simple Package Crystal Oscillator) or CXO (Clock Crystal Oscillator), a programmable quartz crystal oscillator PCXO, voltage controlled quartz crystal oscillator Ntrolled Crystal Oscillator), temperature compensates the quartz crystal oscillator TCXO (Temperature Compensated Crystal Oscillator) and the constant temperature slot to control the quartz crystal oscillator OCXO (Oven Controlled Crystal).

    In order to meet the application needs, the oscillating lines within the quartz crystal oscillator are different in the basic or three frequency doubling modes. To reach the output frequency of the hundreds of megahertz, the post stage of the oscillating line can use the phase locked loop mode or the frequency doubling mode to increase the frequency of the quartz oscillation at a lower frequency. Bit and output waveforms also have different needs, such as CMOS, LVPECL, LVDS... .. And so on. These specifications should be carefully defined.
    In Figure twelve, several stability diagrams of quartz oscillator output frequency for temperature changes are provided.

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