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AC simulation can be performed to gauge the effects of oscillatorcircuit components on tuning frequency.
SIMULATION of crystal-oscillator performance has long been a challenge for circuit designers. However, by making use of a negativeresistance model, the effects of individual components on an oscillator's tuning frequency can be evaluated through parametric analysis with SPICE simulators.
As an alternative to the conventional open-loop simulation method,1 Colpitts and Clapp oscillators can be simulated through negative-resistance analysis. These two oscillator types can be described in terms of two two-port networks.
Two-port network Z^sub pas^ describes the passive part of the oscillator while Z^sub act^ denotes the active part. In this case, the passive part of the oscillator has an impedance with a positive real part. Thus, it describes an attenuator in signal theory. If the active part is an amplifier and has one feedback link to its input, the real part of the input impedance can be positive or negative. If the real part is positive, it will also be an attenuator and the magnitude of the gain will be smaller than one. If, however, the real part is negative, the circuit will be an amplifier.
When the passive and active parts are connected (Fig. 1), the circuit can operate as an oscillator if the sum of the real parts of the entire impedance is negative. In this case, the noise voltage can be amplified. This implies the following conditions for the startup condition:
CIRCLE DIAGRAM
This formula can be solved through graphical methods.2,3 Figure 2 shows a circle diagram of the impedances of the active and passive circuits. For the passive part of a crystal oscillator, the locus of the complex impedance is a function of frequency and has only a weak dependence on the signal power. On the other hand, the active part is nearly independent of the frequency and is a function of the signal power. The two impedance curves intersect at certain points which yield information about the oscillator frequency.
After evaluating the possibility of performing an AC simulation with PSpice, it was determined that a power sweep of the active part is not possible. However, the passive part is described accurately with a simple quartz-crystal equivalent circuit. In contrast to the startup...