Frequency measurement

Frequency measurement

The determination of the number of cycles of a periodically varying quantity occurring in unit time. Many physical systems demonstrate cyclic behavior; that is, one or more of their properties vary in a characteristic fashion before returning to the initial value and then repeating the cycle. Examples are the angular positions of the planets and satellites in the solar system, the pressure in a cylinder in a reciprocating engine, and the heights and fields associated with surface, acoustic, and electromagnetic waves. The duration of a single cycle, the period, may vary widely, from 10^-27 s for the electromagnetic field associated with a cosmic gamma ray to 10⁸ years for the rotation of a galaxy in space. The frequency, which is the inverse of the period, is the number of cycles, including fractions, occurring in unit time. The unit of frequency is the hertz (Hz), named after Heinrich Hertz, who investigated the nature of electromagnetic radiation. Measurement of the characteristic frequencies of a system, and their variation with time or under changing conditions, yields valuable information on its properties and behavior. Together with temperature and voltage, frequency ranks as one of the quantities most often measured in modern science and technology. See Cerenkov radiation, Electromagnetic radiation, Wave motion

The measurement of an unknown frequency requires a standard producing a fixed, stable, and known frequency, and a system or technique for the comparison of the unknown frequency with the standard. In the past, a wide variety of analog techniques and material standards have been employed. An example is the use of a tuning fork to adjust a musical instrument, usually a piano. Analog frequency measurement techniques possessed two major disadvantages: The frequency of the standards depended upon the material properties and dimensions of critical components, which meant that they were prone to drift and affected by variations in the ambient temperature. In addition, optimum accuracy was achieved only when the unknown and standard frequencies were close or harmonically related.

Developments in electron-tube and, later, solid-state electronics improved matters. These included the quartz crystal oscillator, in which a thin slice of crystalline quartz acts as the resonant element in an electronic feedback circuit. As a result of the sharpness of the resonance and the stability of the properties of the quartz, this device provides a stable frequency in the range from 10 kHz to 100 MHz and remains the most common secondary frequency standard in use. In addition, a range of circuits were developed to generate more complex harmonic and subharmonic frequencies from a standard source. This led ultimately to the frequency synthesizer which, with an array of phase-locked loops, could be set to produce one of a very wide range of output frequencies. In use, however, it was still necessary to measure the beat or heterodyne frequency from the unknown frequency. See Piezoelectricity

Fast, inexpensive solid-state digital circuits have replaced analog frequency measurement techniques and many of their associated standards. The underlying principle of the digital technique is simple: the electrical signal from the sensor or transducer observing the physical system under test generally contains, from Fourier analysis, the fundamental frequency and components at integral harmonics of this frequency. It is filtered to select the fundamental and converted into a rectangular waveform, representing transitions between the binary logic levels 0 and 1. A frequency measurement then consists of counting the number of positive- or negative-going transitions between the two levels in a known time.

In parallel with the production of counters capable of operating at frequencies up to around 1 GHz, frequency standards based upon selected atomic transitions rather than the properties of bulk materials have been developed. These have the advantage that the frequency produced from a particular transition is in principle universal; that is, it is largely independent of the design of the standard and the materials used in its construction, and of changes in the ambient conditions. The combination of high-speed digital counters and of very stable atomic reference sources allows a wide range of frequencies to be determined simply, inexpensively, and very accurately.

As a result, much work has been carried out on the definition and measurement of other physical quantities in terms of frequency. Clearly, time and frequency are closely related; not only are the measurement, calibration, and dissemination techniques largely interchangeable, but any frequency standard may be converted into a standard of time, that is, a clock, by adding an appropriately designed counter. The unit of time, the second, is itself defined as the duration of 9 192 631 770 cycles of the electromagnetic radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom. The primary standards of voltage and resistance are now also realized in terms of frequency using, respectively, the superconducting Josephson effect and the von Klitzing (quantum Hall) effect. See Electrical units and standards, Resistance measurement, Time, Voltage measurement

To calibrate the internal quartz oscillators in frequency counters, and to enable frequency measurements to be made at the highest accuracies, up to and occasionally beyond 10^-12, standards laboratories require a selection of very stable frequency standards. The four types in common use are the temperature-stabilized or ovened quartz crystal oscillator, the rubidium gas cell, the cesium atomic beam standard, and the hydrogen maser. Their performance depends essentially upon the quality factor Q—the ratio of the resonant or transition frequency f_T to its half-bandwidth—and the sensitivity of f_T to changes in the properties of materials or in the ambient and operating conditions.

Quartz oscillators are employed in most of the atomic standards to reduce the short-term noise and to provide a convenient output frequency (usually 10 MHz). In these, f_T is set by atomic transitions whose properties are in principle fixed and universal. In practice, small interactions with the containment system and the operating conditions mean that this ideal is not completely realized. In the rubidium gas cell, the transition is perturbed by collisions with other buffer gas atoms whose temperature and composition may change in time; in the hydrogen maser, collisions of the hydrogen atoms with the inert coating inside the containing bulb produce the so-called wall shift, which depends upon the condition of the coating. Atoms in the cesium beam standard are very well isolated from each other and the container, and this is reflected in the low drift rates and temperature coefficients observed. See Atomic clock