SLLA549 July   2021 TCAN4550 , TCAN4550-Q1 , TCAN4551-Q1

 

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2 Crystal Oscillator Oscillation Concept

A crystal-based oscillator is formed by placing a crystal in the feedback loop of an oscillator circuit that provides sufficient gain and phase shift around the loop to start and sustain stable oscillations. A detailed explanation of crystal oscillator operation will not be covered here. However, to support the reader’s interpretation of the guidance and recommendations contained in this application note, some essential aspects of the crystal oscillator circuit model are presented and explained here. A simple model of a crystal is shown in Figure 2-1. The model has R-L-C series components, called motional resistance (Rm), motional capacitance (Cm), and motional inductance (Lm). The capacitor in parallel, C0, is called the shunt capacitance, and models the package capacitance. Figure 2-2 illustrates a simple oscillator model, consisting of an inverting amplifier and crystal, and its equivalent circuit model.

Figure 2-1 Oscillator Model
Figure 2-2 Cyrstal Oscillator Model

The circuit model in Figure 2-2 is useful for understanding the necessary conditions for oscillation. These are:

Equation 1. X X T A L +   X O S C = 0
Equation 2. R X T A L +   R n e g = 0

Where:

XXTAL = the imaginary part of the impedance represented by the crystal.

RXTAL = the real part of the impedance represented by the crystal.

XOSC = the imaginary part of the impedance represented by the oscillator.

Rneg = the real part of the impedance represented by the oscillator.

Mathematically, Rneg is a negative resistance. It represents a circuit that supplies power rather than dissipating power, for example, an amplifier. Consequently, a simple interpretation is that the amplifier must have enough gain to compensate for the losses represented by the crystal and load capacitance. The concept of negative resistance is important to crystal oscillator design and will be revisited later in this app note.