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The electric equivalent circuits of a crystal unit is generally represented as shown in Fig.7, and the four equivalent constants are labeled as follows: L1: Equivalent series inductance C1 : Equivalent series capacitance R1: Equivalent series resistance C0: Shunt capacitance |
Fig. 7 Electric Equivalent Circuit of a Crystal Unit |
The main characteristics of a crystal unit is derived by using these equivalent constants. As an example, Fig. 8 shows the frequency characteristic of impedance. Typical frequencies and performances of crystal units are shown below. |
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The general crystal oscillation circuit is capacitive, and can be treated as series circuits with a negative resistance (-R) and load capacitance (CL) as shown in Fig. 9 | Fig. 9 Relationship between a Crystal Unit and the Oscillation Circuit |
When the load capacitance values are CL and series , fL and fS, respectively, the following relationship is established. Fig. 10 shows an example. An overtone crystal with a smaller C1 value than a fundamental wave has a smaller frequency change rate with respect to CL than a fundamental wave. The C1 value of small-size crystal units is smaller than that of large-size crystal units with the same frequency. For this reason, frequency change rate to the load capacitance is smaller for a small-sized crystal units. When the load capacitance (CL) is connected to the crystal unit in series as shown in Fig. 9, the equivalent resistance increases according to the following formula. |
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