mode, and overtone frequencies are therefore not exact harmonics of the fundamental. High frequency crystals are often designed to operate at third, fifth, or seventh overtones. Manufacturers have difficulty producing crystals thin enough to produce fundamental frequencies over 30 MHz. To produce higher frequencies, manufacturers make overtone crystals tuned to put the 3rd, 5th, or 7th overtone at the desired frequency, because they are thicker and therefore easier to manufacture than a fundamental crystal that would produce the same frequency—although exciting the desired overtone frequency requires a slightly more complicated oscillator circuit. A fundamental crystal oscillator circuit is simpler and more efficient and has more pullability than a third overtone circuit. Depending on the manufacturer, the highest available fundamental frequency may be 25 MHz to 66 MHz. A major reason for the wide use of crystal oscillators is their high Q factor. A typical Q value for a quartz oscillator ranges from 104 to 106, compared to perhaps 102 for an LC oscillator. The maximum Q for a high stability quartz oscillator can be estimated as Q = 1.6 × 107/f, where f is the resonant frequency in megahertz. One of the most important traits of quartz crystal oscillators is that they can exhibit very low phase noise. In many oscillators, any spectral energy at the resonant frequency is amplified by the oscillator, resulting in a collection of tones at different phases. In a crystal oscillator, the crystal mostly vibrates in one axis, therefore only one phase is dominant. This property of low phase noise makes them particularly useful in telecommunications where stable signals are needed, and in scientific equipment where very precise time references are needed. Environmental changes of temperature, humidity, pressure, and vibration can change the resonant frequency of a quartz crystal, but there are several designs that reduce these environmental effects. These include the TCXO, MCXO, and OCXO which are defined below. These designs, particularly the OCXO, often produce devices with excellent short-term stability. The limitations in short-term stability are due mainly to noise from electronic components in the oscillator circuits. Long-term stability is limited by aging of the crystal. Due to aging and environmental factors (such as temperature and vibration), it is difficult to keep even the best quartz oscillators within one part in 1010 of their nominal frequency without constant adjustment. For this reason, atomic oscillators are used for applications requiring better long-term stability and