In standard applications such as microcontrollers, Digital European Cordless Telecommunications systems and other low cost crystal oscillators, the Pierce oscillator with a digital inverter used as an oscillator amplifier is most commonly used.
Next, the Pierce oscillator schematic is redrawn so that an AC simulation using the negative-resistance model method(1) can be used.
A schematic of a typical simple Pierce oscillator using a digital inverter as an oscillator amplifier is shown in Figure 1.
When using a CMOS or compatible digital inverter as an amplifier in the Pierce oscillator, it is necessary to set the inverter operating point close to its switching voltage.
(S-parameter models can be used in nearly every simulation software.) The model used for the simulation of the Pierce oscillator is split into small-signal conditions (oscillation start-up) and large-signal conditions (steady-state operation).
When simulating the Pierce oscillator, it is not possible to cut between the passive and active parts because the quartz crystal is located in the feedback loop of the oscillator.
To redraw the circuit's passive and active parts, it is necessary to delete the actual ground and add a virtual ground.(1,2) A standard Pierce oscillator with a bipolar junction transistor (BJT) can be redrawn as shown in Figure 7.
Converting a Pierce oscillator with a digital inverter from a two-port to a one-port model allows use of the negative-input-resistance method when simulating oscillation start-up reserve and oscillation frequency.
This type of oscillator features good frequency tolerance, low component count and simple circuit design for a Colpitts or Pierce oscillator, low circuit current consumption and low resonator price.
Two-port resonators are used principally in the Pierce oscillator, as shown in Figure 3.