Silicon Frequency Controller (SFC) Technology (Part 2)

　　R1: Dynamic impedance

　　C1: Dynamic Capacitor

　　L1: Dynamic inductor

　　C0: static capacitance

　　CL: Load capacitance

　　The frequency of the parallel oscillation mode can be obtained according to the following formula:

　　FL=[1/2π√(L1*C1))] 2eq eq *√[1+C1/(C0+CL)]

　　Where [1/2π√(L1*C1))] is the frequency of the crystal in serial oscillation mode

　　According to Taylor expansion:

　　FL=[1/2π√(L1*C1) 2eq eq ]*[1+C1/2(C0+CL)] (1)

　　It can be seen from the formula that the frequency is related to C0, C1 and CL.

　　In fundamental frequency resonance, C1 is 10-30fF, and is generally 20fF. The value of C0 is related to the size of the crystal, and is generally 5pF. However, the calculation of CL is related to the external capacitance of the crystal and the PCB design and materials. The following figure is a reference circuit diagram

　　Figure 3 Schematic diagram of crystal external load capacitance

　　From the above circuit, we can conclude that:

　　1/(C11+CS1)+1/(C12+CS2)=1/(CL) (2)

　　Among them, C11 and C12 are external capacitors, that is, two capacitors placed on both sides of the crystal and grounded in the circuit design. CS1 and CS2 are parasitic capacitors, which are related to the PCB circuit board routing, pads and chip pins. Generally, it is 5-10pF (it can be set to 8pF in the calculation of this article). For C11 and C12, there is no definite value (15pF-30pF), which is related to the actual design, for example, 18pF is taken.

　　If CL changes, the frequency of the parallel oscillation mode will also change, see Figure 4

　　Figure 4 Relationship between load capacitance change and frequency

　　From formula (1), the frequency change can be obtained as:

　　(FCL1-FCL2)/FCL1=C1/2 * [1/(C0+CL1)-1/(C0+CL2)] * 10E6 (3)

　　From formula (2) and formula (3), we can know that the accuracy of C11 and C12 will affect the accuracy of frequency. The specific data is shown in Table 1. The values ​​of the parameters are as mentioned above: C1=20fF, C0=5pF, CS1=CS2=8pF, C11=C12=18pF.

　　Table 1

In many applications, the capacitance accuracy is 5%. From the table above, we can see that its impact on frequency accuracy can reach 28PPM. This is easily overlooked in the design.

　　Other factors: such as the influence of reflow soldering, humidity, atmospheric pressure, etc. These factors have little influence and will not be detailed here.

　　The overall frequency accuracy of the crystal oscillator is the sum of the above five aspects.