Overtones

     Quartz crystals naturally vibrate in several simultaneous resonance modes referred to the fundamental or overtone modes. Usually, one of these modes is designed to be dominant at the desired operating frequency.  The fundamental frequency of vibration is a function of the resonator physical dimension and angle of cut.  The overtone modes occur at odd numbered harmonics of the fundamental mode and include the 3^rd, 5^th, 7^th, 9^th, and 11^th. The maximum bandwidth obtainable in a filter and the maximum tuning range in an oscillator are inversely proportional to the capacitance ratio, r = C_o/C₁, and r increases as the square of the overtone.  Consequently, a wider bandwidth or larger tuning range can be obtained with a fundamental mode resonator than with a third or higher overtones.  Fundamental mode resonators are used for most filters, temperature compensated oscillators (TCXOs) and voltage controlled oscillators (VCXOs), where the required bandwidth or tuning range makes overtone devices undesirable.  Fundamentals are also used in many simple oscillators, such as clock oscillators at frequencies up to approximately 35 MHz.  At higher frequencies overtones are more economical for this application.

     Current crystal manufacturing processes limit the lapping of the quartz plate so that the highest fundamental mode frequency that may be reliably achieved is typically around 45 MHz.  At this frequency, the AT-cut quartz plate is less than 0.037 mm thick and further lapping using conventional techniques is not practical.  Several methods have been developed to increase the fundamental mode frequency achievable by removing some quartz mass from the center of the plate.  This so-called “inverted mesa” provides for an active area that is much thinner and is usually achieved by chemical or plasma/ion etching.  These processes can produce superior quality high frequency fundamental (HFF) mode crystal to 170 MHz and beyond.  Fundamental mode crystals typically have larger values of C1 than overtone mode crystals of the same frequency; therefore they are useful for applications such as VCXOs where greater pullability is required.  High frequency fundamental quartz blanks are also used extensively in filter applications where they provide better spurious mode response than overtone crystals of the same frequency.

      At a given operating frequency, quartz crystals aging and Q improve with higher overtone.  For this reason, ovenized oscillators (OCXOs) often use overtone resonators.  Usually the 3rd or 5th overtone is used.  The range of tuning required to accommodate the resonator frequency tolerance and aging characteristics limits the maximum useful overtone.

 while UTP indicates the Upper Temperature Turnover Point.

Spurious Modes

       Vibration at frequencies that are not fundamental or overtone modes are referred to as spurious or unwanted modes. The design of the wafer, electrode pattern and amount of metalization can be adjusted to suppress these unwanted modes.

     Spurious modes can be a problem if the response is as strong as the main mode.  When that happens, the oscillator may run on the spur instead of the main mode.  This is called mode hopping.  Spurious modes should be specified as either a resistance ratio to the main mode or dB suppression.  In general, a resistance ratio of 1.5 or 2.0 to 1, which is approximately equivalent to – 3 dB to –6 dB, is sufficient to avoid mode hopping for most oscillators. 

    Fundamental modes of a crystal can achieve the best spurious suppression, while overtone responses are more difficult to control.  Designs that require higher C₁ volumes for pullability reasons also can sacrifice spurious mode suppression.  For crystal filter applications, spurious mode suppression as low as –40 dB can be achieved with fundamental mode with low C₁ designs.

     The spurious modes occur above the main mode within a few hundred kilohertz. The response may look like the plot shown above.  In oscillator applications, the oscillator usually selects the strongest mode.  Some of the unwanted modes may have steep frequency vs. temperature characteristics.  Occasionally, as the temperature changes, at a certain temperature, the frequency of an unwanted mode coincides with the oscillator frequency, which causes so-called “activity dip”.  At the activity dip, excitation of the unwanted mode results in extra energy dissipation in the resonator, which results in a decrease in the Q, an increase in the equivalent series resistance, and a change in the frequency of the oscillator.  When the resistance increase is sufficiently large, the oscillation may stop, i.e., the oscillator fails.  When the temperature changes away from the activity dip temperature, the oscillation can restart.  Unwanted modes can be controlled by proper design and fabrication methods.  Maintaining the correct relationships among electrode and resonator plate dimensions (i.e., applying energy trapping rules), and maintaining the parallelism between the major faces of the resonator plate, can minimize the unwanted modes.