When it comes to the calculation of crystal load capacitance, it's a critical factor in ensuring the proper operation of oscillators in electronic circuits. The two capacitors labeled C1 and C2 in the diagram are referred to as the load capacitance of the crystal oscillator. These capacitors are connected between the two pins of the crystal and ground. Their values typically range from a few picofarads up to about 30 pF, and they play a key role in determining both the resonant frequency and output amplitude of the oscillator. When ordering a crystal, manufacturers often ask for the load capacitance value to ensure compatibility with your design.
The formula for calculating the crystal load capacitance is: Crystal Load Capacitance = (C1 × C2) / (C1 + C2) + Cic + ΔC. Here, C1 and C2 are the external capacitors connected to each leg of the crystal and to ground. The term "Cic" represents the internal capacitance of the integrated circuit, while ΔC accounts for the parasitic capacitance on the PCB. For example, if a crystal specifies a 12 pF load capacitance, you might use 22 pF capacitors on each side, accounting for an additional 2 pF of parasitic capacitance on each pin.
In practical terms, this means that if the desired load capacitance is 15 pF, the two external capacitors should be around 27 pF each. This ensures that the equivalent capacitance seen by the crystal matches the required load value.
Many logic chips implement a three-point capacitor oscillator configuration at the crystal input and output pins. Inside the chip, these pins usually contain an inverter or a series of inverters. A resistor is often placed between the output (XO) and input (XI) of the crystal oscillator. For CMOS devices, this resistor can range from several megaohms to tens of megaohms. Some chips already include this resistor internally, so no external component is needed. The purpose of this resistor is to bias the inverter into a linear region, allowing it to function as an amplifier during startup.
The quartz crystal itself is connected between the input and output of the oscillator pin, forming a parallel resonant circuit. The two capacitors connected to ground act as a voltage divider, creating a feedback path that sustains oscillation. If the two capacitors are equal, the feedback coefficient is 0.5, which generally meets the oscillation condition. However, if the circuit is unstable or doesn’t start easily, adjusting the capacitance—by reducing the input-side capacitor and increasing the output-side one—can help improve feedback and stability.
To summarize, here are a few important points to keep in mind:
Matching capacitors are used to adjust the effective capacitance across the crystal to match the specified load capacitance. In many cases, the external capacitors are set to twice the required load capacitance, which helps achieve a closer match.
Load capacitance refers to the total external capacitance seen across the crystal in the circuit. It’s a test and operational parameter. When designing, it's often fine-tuned to achieve a precise frequency close to the specified value.
Increasing the load capacitance tends to lower the oscillation frequency, while decreasing it raises the frequency.
Load capacitance includes all internal and external capacitances connected to the crystal’s two leads. It acts like a series capacitor in the resonant circuit. Different load capacitances result in different oscillation frequencies. Even crystals with the same nominal frequency may have different load requirements because they can resonate in either series or parallel mode. Therefore, swapping crystals without matching the load capacitance can cause malfunctions in the circuit.
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