Certain limitations exist for modeling temperaturedependent crystal models when using standard Spice. The components typically used for quartz crystal models resistor, inductor, and capacitor) only offer a quadratic temperature coefficient (Fig. 1).

Also it’s not possible to access the temperature as a global variable in original Spice. Therefore, modeling a crystal is possible only at one temperature.

Now, though, the temperature characteristic of the quartz crystal can be simulated by accessing the global variable temperature via ABM-sources in Pspice version 8.0. It’s important to replace the inductor with an inductor model that uses controlled current and voltage sources. The value of the inductor can be replaced with a formula that directly accesses the global temperature variable, when using other simulation software such as ICAP/4. But, in Pspice simulations, it’s necessary to take the roundabout method by using controlled sources to get there.

The temperature-independent Spice Model for a quartz crystal is given in Lisitng 1. This model represents the equivalent circuit of Figure 1. The frequency-determining element is the series-resonance circuit C1 and L1. Therefore, the temperature dependency of the frequency can be observed by changing the value of C1 and/or L1.

Every parameter of a crystal is usually temperature-dependent (crystal frequency, C0, C1, R1,...). The variation of C1 and C0 can be neglected for the simulation. The changes of a real crystal’s series resistance R1 can’t be described with a simple formula. Therefore, we assumed a temperature-independent R1 value for the model, and assumed that the value of C1 and C0 is constant over temperature. Consequently, the frequency variation over temperature is realized by a variation of the inductance value. Unfortunately, it’s impossible to simply replace the inductance value by a formula that includes the global variable temperature. Thus, the entire inductor must be replaced by an ABMsource. This ABM-source allows use of the global variable temperature in Pspice Version 8. Shown is the typical structure of a crystal model using ABM sources to build the temperature coefficient (Fig. 2).

The inductor L1 has been replaced by the current source G3, which itself has a mirror function for the current through the reference inductor L3 at the operating point. The measured voltage V(out,in) is multiplied with a factor to change the inductor’s value. This factor, built using the voltage source E5, is a temperature-dependent function according to the cubic temperature behavior of the quartz crystal.

The library file for this crystal model has the following structure is shown in Listing 2. Tele Quarz offers a small program to simplify the construction of this model (Fig. 3). This program generates the crystal model with the wellknown equivalent circuit, including the effects of crystal parameters: frequency, load capacitance, C1, R1, and C0. As an option, this program also can generate the so-called “extended Pspice temperature model,” including the temperature coefficient of the quartz crystal. This program can be downloaded from the Tele Quarz home page at *www.telequarz.de*.