Temperature coefficient resonance frequency

In its original application as timing reference, special care has been taken to minimize the perturbations on frequency of the selected mode of vibration caused by unavoidable variations in the environment, first of all temperature and acceleration. The breakthrough of quartz crystal resonators in timekeeping is very much correlated to the existence of a specific crysfal cuf, at which the device resonance frequency provides a zero temperature coefficient of frequency at 25 °C and a remarkable temperature stability around room... 

The temperature coefficient (at room temperature) of resonance frequencies of potassium hexachloro complexes increases progressively with decreasing atomic number of the central metal atom, i.e., with increasing electron deficiency of the central metal ions from Pt(IV) to W(IV) (-1,0,... 

All piezoelectric crystals should have a good temperature coefficient, that is. should show as little change in resonant frequency as possible under large variations in temperature. Ideally. Ihe piezoelectric constant of proportionality between the mechanical and electrical variables must be the same for both direct (pressure-to-electricily) and converse effects... 

Table 5.1 Microwave properties of the most important microwave dielectrics (SC= bulk single crystals , bc = bulk ceramics , tf = thin films , r/ = temperature coefficient of resonant frequency . The materials marked with are tuneable dielectrics.

In order to compare calculated and experimentally observed phase portraits it is necessary to know very exactly all the coefficients of the describing nonlinear differential Equation 14.3. Therefore, different methods of determination of the nonlinear coefficient in the Duffing equation have been compared. In the paraelectric phase the value of the nonlinear dielectric coefficient B is determined by measuring the shift of the resonance frequency in dependence on the amplitude of the excitation ( [1], [5]). In the ferroelectric phase three different methods are used in order to determine B. Firstly, the coefficient B is calculated in the framework of the Landau theory from the coefficient of the high temperature phase (e.g. [4]). This means B = const, and B has the same values above and below the phase transition. Secondly, the shift of the resonance frequency of the resonator in the ferroelectric phase as a function of the driving field is used in order to determine the coefficient B. The amplitude of the exciting field is smaller than the coercive field and does not produce polarization reversal during the measurements of the shift of the resonance frequency. In the third method the coefficient B was determined by the values of the spontaneous polarization... 

A common function of circuits is the provision of an accurate resonance state. For instance, for a resonance frequency to stay within a tolerance of 0.1% over a temperature range of 100 K a temperature coefficient of less than 10 MK 1 would be required. It might be achieved in the 10-100 kHz range by using a manganese zinc ferrite pot-core inductor (see Section 9.5.1) with a small positive temperature coefficient of inductance combined with a ceramic capacitor having an equal, but negative, temperature coefficient. This is clear from the resonance condition... 

A ceramic of relative permittivity 37 is in the form of a cylindrical DR for use at 1 GHz. Estimate the overall dimensions of the DR. The ceramic has a temperature coefficient of linear expansivity of 5MK-1 and a temperature coefficient of permittivity of — 16MK-1. Estimate by how much the resonance frequency will change for a 5°C change in temperature. [Answer diameter 2.5 cm 15 kHz]... 

Quartz Crystal Thermometer. The temperature coefficient of the resonant frequency of quartz (14-20 MHz), using the piezoelectric effect, is a function of temperature (1 kHz per degree). In the temperature range -80°C to 230°C, an electronically controlled quartz crystal thermometer can be accurate to 0.02°C and has a sensitivity of 10 microdegrees centigrade in temperature difference measurements. 

Further evidence for pi bonding is provided by the temperature coefficients of the resonance frequencies of these complex ions (see Table 6). The temperature coefficient is normally expected to be negative because of the decrease in the effective electric field gradient with increasing molecular bending vibrations (36,68, 69). Stretching vibrations do not reduce the principle electric field gradient (70). From Table 6... 

Table 6. Temperature coefficients of the resonance frequencies of some transition metal hexachloro complexions (58)...

With the progress in microwave telecommunication technology, dielectric materials have come to play an important role in the miniaturization and compactness of microwave passive components. The dielectric materials available for micro-wave devices are required to have predictable properties with respect to a high dielectric constant (K), high quality factor (Qf), and small temperature coefficient of resonant frequency (TCP). Numerous microwave dielectric materials have been prepared and investigated for their microwave dielectric properties and for satisfying these requirements. In particular, complex perovskite compounds A(B,B )03... 

Therefore the dielectric constant is changed with temperature and the resonant frequency will change with temperature, and the microwave devices cannot respond at a specific frequency if the dielectric materials in microwave frequencies show a large TCK and thermal expansion coefficient a due to the thermal expansion of dielectric materials and the temperature dependence of polarizability. In general, the a of dielectric ceramics, which is well known as the slope of the Cockbain equation, is about 10 ppm/°C. Therefore control of TCP can be achieved by adequate manipulations of TCK. It is an important requirement for practical applications to control the stable TCP, nearly zero, which is available to temperature-stable microwave devices. 

FIGURE 22.7 Temperature coefficient of resonant frequency (TCP) of PCCN, PCMT, PCFTN specimens with A-site and B-site bond valence. 

Another resonant-frequency thermometer is the quartz crystal resonator (Benjaminson and Rowland, 1972), which, if the crystal is properly cut, is quite linear from about 190 to 525 K. Although this thermometer has excellent resolution, it does exhibit hysteresis and drift. The principle of quartz crystal thermometry is based on the temperature dependence of the piezoelectric resonant frequency of a quartz crystal wafer of a given dimension. The angle of cut of the quartz crystal is selected to give as nearly a linear and yet sensitive correspondence between resonant frequency and temperature as possible. This angle of cut is referred to as an LC (linear coefficient) cut. The temperature sensitivity of the quartz crystal thermometer is about 1000 Hz/°C. 

The dielectric constant (6r) and the quality values Q at microwave frequency were measured using the Hakki-Coleman s dielectric resonator method , and modified and improved by Courtney. A vector network analyzer (E8363, Agilent Technologies, Loveland, CO, USA) was employed in the measurement. The temperature coefficient of resonant frequency (t/) was measured in the temperature range from -25 to h-85 °C. The X/ value was defined as follows ... 

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