Winter 2005 Issue

Some Notes on
Crystals and Oscillators

What is inside that container called a crystal? On what frequency does that crystal oscillate? Here KØVXM discusses some of the basics
of crystals.

By Chuck Hoover,* KØVXM
 

Oh, Happy Day! The crystal you ordered for your latest pet project finally arrived. Deftly, you install it. Confidently, you apply power. Smugly, you measure it with your Radio-Shack counter. Oh . . . oh (or worse), you discover that it’s oscillating, but it’s not on frequency. In fact, it’s a long way off! Before you fire off an angry e-mail to the crystal supplier, pour a cup of coffee and read on.

First, the following remarks apply only to thin, flat, round AT-cut plates with deposited electrodes, which are designed for oscillator service and mounted in conventional holders (see photo A). This means that I will be discussing crystals with frequencies above about 10 MHz, thus encompassing a large majority of crystals.

Second, I will not delve into the realm of mathematics. Some math is unavoidable, of course, but a four-function calculator will handle everything nicely.
Figure 1 is the equivalent circuit of a crystal. C, L, and R are the representations of motional capacitance (very small), motional inductance (very large), and resistance (generally small). The motional capacitance is expressed in femto Farads (10–15), or thousandths of a pico Farad. The motional inductance is expressed in Henries. Because the resistance is generally less than 100 ohms and the reactance of the motional elements is quite high, the Q of the crystal is also high. The term Co is the capacitance because of the electrodes, the holder, and the mounting structure (see photo B). This capacitance is generally between 3 and 5 pico Farads. This is a “real” capacitance. Simply insert the crystal into capacitance meter and read the value.

Crystals can be run on their fundamental frequency and odd overtones (third, fifth, seventh, etc.). The overtones are close to, but not exactly, the integral multiple of the fundamental. The values of the motional elements change with the overtone of operation. For example, a crystal operated on the fundamental overtone may have a motional resistance of 10 ohms and a motional capacitance of 30 femto Farads (see note 1), while the same crystal, running on the third overtone, will have a motional resistance of 30 ohms and a motional capacitance of 3.3 femto Farads. When it is operated on the fifth overtone, the resistance will increase to 50 ohms and the capacitance will fall to 1.2 femto Farads. On the seventh overtone, the resistance will be 100 ohms and the capacitance will be 0.6 femto Farads.

It is possible to excite crystals on higher overtones (ninth, eleventh, etc.) However, the resistance becomes so great that the oscillators become difficult to start, or will take off and run at some frequency not under crystal control. A few years ago, seventh overtone operation was included in this category.
 

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