Working Frequency Matching for Evaluating Oscillating Circuits (Evaluation Method 1 for Oscillating Circuits)

Before actual evaluation of matching, please confirm the following three parameters of the quartz crystal unit used for evaluation:

1. Standard load capacitance value

Load capacitance refers to the capacitance of an oscillating circuit when viewed from both ends of a quartz crystal unit.

The principle is the numerical value specified by the circuit designer.

2. Quartz crystal unit oscillation frequency (FL) of standard load capacitor

The oscillation frequency (FL) refers to the oscillation frequency when a quartz crystal unit is driven by an oscillation circuit with a standard load capacitor.

Using data at room temperature without considering factors such as stray capacitance.

3. Equivalent circuit constant of quartz crystal unit

The oscillation frequency (Fr) of the quartz crystal unit itself without considering the equivalent series impedance (R1), equivalent series capacitance (C1), equivalent series inductance (L1), equivalent parallel capacitance (C0), and load capacitance.

Inductance testers or network analyzers are commonly used to test the equivalent circuit constants of quartz crystal units. The method of determining the equivalent circuit number after testing quartz crystal units using a network analyzer is the most ideal. However, if the testing of quartz crystal units cannot be carried out by the circuit designer due to incomplete equipment or other reasons, it is recommended that the circuit designer request testing from the manufacturer of the purchased crystal units.

【2】 The evaluation of oscillation frequency (frequency matching) begins with the actual evaluation work here.

Firstly, confirm the oscillation frequency of the quartz crystal unit (evaluation crystal unit) and the oscillation circuit installed together on the substrate.

This is called "confirming frequency matching status". By mastering the difference between the oscillation frequency when installed on the substrate and the oscillation frequency when using a standard load capacitor, one can confirm the deviation between the actual capacitance of the substrate (circuit side capacitance) and the pre specified standard capacitance. The substrate capacitance referred to here includes the capacitance (load capacitance) when viewing the oscillating circuit from a quartz crystal unit, as well as stray capacitance caused by substrate conductive patterns, etc.

Next, prepare the necessary testing instruments to evaluate the matching of quartz crystal units and oscillation circuits.

The basic testing instruments required for evaluation include DC power supply, frequency meter, oscilloscope, FET probe, and current probe. Figure 1 shows an example of the basic composition of the testing instrument.

Firstly, place the FET probe on the HOT terminal of the quartz crystal unit (Figure 2), and display the waveform on the oscilloscope and the frequency on the frequency meter.

For example, when the oscillation frequency (Fr) of a quartz crystal unit without considering the load capacitor is 12MHz, if the oscillation frequency (FL) of the standard load capacitor is 12.000034MHz, assuming that the oscillation frequency (FR) obtained by installing the quartz crystal unit on the substrate and using a FET probe is 12.000219MHz, the difference between the two (the oscillation frequency (FR) after installing the quartz crystal unit on the substrate and the oscillation frequency of the quartz crystal unit under the standard load capacitor) is+185Hz, resulting in a difference of+15.4ppm.

The closer this difference is to zero, the higher the frequency accuracy.

There are two methods to make the difference between FR and FL close to zero.

The first method is to purchase quartz crystal units with an oscillation frequency (center frequency) offset of+15.4ppm from the current quartz component manufacturer. Another method is to slightly adjust the load capacitance of the oscillation circuit to obtain the corresponding oscillation frequency.

In the next section, we will introduce the matching method for micro adjustment of load capacitance.

【3】 The method of fine-tuning the load capacitance to match the frequency requires the aforementioned data when calculating the load capacitance.

·Equivalent circuit constant of quartz crystal unit (Fr R1 、C1 、L1 、C0） 

·Oscillation frequency (FR) installed on the substrate

Calculate the load capacitance (CL) using the following equation based on these data.

     Equation (1)

The specific calculation examples are as follows:

Assuming the rated frequency of the quartz crystal unit is 12MHz and the load capacitance (CL) of the oscillation circuit is 7.8pF. The rated frequency here refers to the oscillation frequency (FL) under the conditions of using an oscillation circuit with a specified load capacitor.

Assuming that the following constants were obtained after testing the quartz crystal unit using a network analyzer:

FR=12.000219 MHz

Fr＝11.998398 MHz

R1＝33.7 ohm  L1＝70.519 mH C1=2.495 fF

C0=1.11 pF

Here it is reiterated that Fr is the oscillation frequency of the quartz crystal unit itself. By substituting these constants into equation (1), CL=7.11pF can be calculated.

The difference between the calculated value and the previously specified oscillation circuit load capacitance (CL) of 7.8 pF is 0.69 pF. As long as the difference is adjusted to zero, the pre specified load capacitance of the oscillation circuit is equal to the capacitance when installing quartz crystal units on the printed substrate.

Therefore, theoretically, the frequency tolerance also becomes zero, and the predetermined oscillation frequency can be obtained.

When adjusting the load capacitance of the oscillation circuit, the Cg and Cd in Figure 3 will be changed to comply with the pre specified standard capacitance. At this point, the approximate values of Cg and Cd can be calculated using the following equation (2).

Here, Ci represents the actual load capacitance (CL) of the oscillating circuit, while Cs represents the wire pattern of the printed substrate and the parasitic capacitance of the components. Ci can be calculated using the following equations (3) and (4) as long as it is equal to the pre specified standard capacitance CL (single crystal unit capacitance CL).

Cg and Cd are the values obtained by subtracting Cs from the specified single crystal unit load capacitance. The calculated values are only approximate. It is recommended to confirm the oscillation frequency and perform frequency matching when adjusting Cg and Cd in practice.

If the Cg and Cd of the oscillation circuit are difficult to change, frequency matching can be achieved by adjusting the load capacitance of the crystal unit. In this case, the quartz crystal unit manufacturer can adjust the crystal unit capacitor to a circuit capacitor and purchase it, and then conduct a matching evaluation to confirm the results. However, it should be noted that the load capacitance of the circuit is inversely proportional to the change in oscillation frequency. Therefore, when the load capacitance of the oscillation circuit is small, it is easily affected by small characteristic changes in the oscillation circuit, leading to a deterioration of frequency stability. So, the key is to set appropriate conditions based on the purpose of the machine.