A crystal oscillator, a device with multifaceted parameters, hinges significantly on capacitance and resistance. But how exactly do these parameters influence its functionality? Let’s unpack this.
Load Capacitance: The load capacitance of a crystal oscillator is critical for its standard oscillation. Typically, external capacitors are employed to balance the equivalent capacitance at the crystal oscillator's ends with the load capacitance. When precision is key, even the capacitance from the IC input terminal to the ground is considered. Usually, the connected capacitor is double the needed load capacitance, aiming to approximate the load capacitance value. The formula, load capacitance of the crystal oscillator = [(Cd*Cg)/(Cd+Cg)]+Cic+△C, encapsulates this relationship.
Crystal Oscillator Pins: The pins on various logic chips can be likened to a capacitive three-point oscillator. Inside, there's usually an inverter, or a series of odd-numbered inverters. A resistor, typically several MΩ to tens of MΩ for CMOS chips, is connected between the output pin XO and input pin XI of the crystal oscillator. Often, this resistor is integrated into many chip pins, negating the need for an external connection. Its role? To maintain the inverter in a linear state at the start of oscillation, acting like an amplifier with substantial gain.
Quartz Crystal and Parallel Resonant Circuit: The quartz crystal, situated between the input and output of the crystal oscillator pin, effectively forms a parallel resonant circuit. The oscillation frequency aligns with the crystal’s parallel resonant frequency. Flanking the crystal are two grounded capacitors, essentially the voltage-dividing capacitors of the three-point circuit. The ground point serves as the voltage dividing point. From the parallel resonant circuit’s perspective, these create a positive feedback, ensuring continuous oscillation.
Capacitor Considerations: In chip design, these capacitors are pre-formed, typically equal in capacity but small, possibly limiting frequency range adaptability. When added externally, their values, several PF to tens of PF, depend on frequency and crystal characteristics. It's crucial to note that their series values, connected parallel to the resonant tank, can impact the oscillation frequency. A feedback coefficient of 0.5 is usually sufficient for oscillation. However, if oscillation struggles to initiate or remains unstable, adjusting the ground capacitance at the input and increasing the output capacitance can enhance feedback.
Resistor’s Role: The resistor linking the input and output of the crystal oscillator introduces negative feedback, ensuring the amplifier works in a high-gain linear region. It also limits current, protecting the crystal oscillator from potential damage by the inverter’s output overdrive. This resistor transforms a logic inverter into a high-gain linear region device. In saturation, the gain disappears, and without gain, oscillation ceases. For oscillation purposes, especially with CMOS, this resistor, often exceeding 1M, must be externally connected. With TTL, the complexity varies with type. If the chip specifies a crystal oscillator pin, like in some microprocessors, external addition is unnecessary due to internal integration.
In essence, the resistor adds a feedback loop to the circuit’s inverter, forming an amplifier. When the crystal is embedded, the AC equivalent of this feedback loop resonates at the crystal's frequency. Given the crystal's high Q value, substantial resistance variations minimally affect the output frequency.