Quality factor microwave

A microwave pulse from a tunable oscillator is injected into the cavity by an anteima, and creates a coherent superposition of rotational states. In the absence of collisions, this superposition emits a free-mduction decay signal, which is detected with an anteima-coupled microwave mixer similar to those used in molecular astrophysics. The data are collected in the time domain and Fourier transfomied to yield the spectrum whose bandwidth is detemimed by the quality factor of the cavity. Hence, such instruments are called Fourier transfomi microwave (FTMW) spectrometers (or Flygare-Balle spectrometers, after the inventors). FTMW instruments are extraordinarily sensitive, and can be used to examine a wide range of stable molecules as well as highly transient or reactive species such as hydrogen-bonded or refractory clusters [29, 30]. 

The formal definition of this quality factor, Q, is the amount of power stored in the resonator divided by the amount of power dissipated per cycle (at 9.5 GHz a cycle time is l/(9.5 x 109) 100 picoseconds). The dissipation of power is through the resonator walls as heat, in the sample as heat, and as radiation reflected out of the resonator towards the detector. The cycle time is used in the definition because the unit time of one second would be far too long for practical purposes within one second after the microwave source has been shut off, all stored power has long been dissipated away completely. 

Good X-band resonators mounted into a spectrometer and with a sample inside have approximate quality factors of 103 or more, which means that they afford an EPR signal-to-noise ratio that is over circa three orders of magnitude better than that of a measurement on the same sample without a resonator, in free space. This is, of course, a tremendous improvement in sensitivity, and it allows us to do EPR on biomolecules in the sub-pM to mM range, but the flip side of the coin is that we are stuck with the specific resonance frequency of the resonator, and so we cannot vary the microwave frequency, and therefore we have to vary the external magnetic field strength. 

Microwaves. Among the lowest frequencies of interest in collisional absorption are radio- and microwaves. As will be seen below, the absorption coefficient a is extremely small at low frequencies because absorption falls off to zero frequency as of2 see Chapter 5 for details. As a consequence, it has generally been necessary to use sensitive resonator techniques for the measurement of the loss tangent, tan <5 = s"/s, where s and s" are the real and imaginary part of the dielectric constant. The loss tangent is obtained by determination of the quality factors Qa, Qo, of the cavity with and without the gas filling, as (Dagg 1985)... 

Replacing the field plates of Fig. 14.7 with the resonant microwave cavity shown in Fig. 15.4 allowed an increase in the circulating microwave power by Q, the quality factor, of the cavity.8 The cavity is a piece of WR-90 (X band) waveguide 20 cm long which is closed at both ends. The inside dimensions of the cavity are... 

Functional oxide materials play an important role for applications in microwave communication and sensor systems. Whereas silicon and GaAs represent the basic materials for the digital part of communication and sensor systems, the analogue parts require high quality factors and low losses, which cannot be fulfilled by semiconductors. Oxide insulators provide extremely low microwave losses expressed by the value of its loss tangent tan 5 = Im(er)/Re(er). The functionality of oxides in microwave devices or circuits can be classified as follows ... 

Apart from ybco, thin films with reasonable microwave properties have been prepared from the thallium-based compounds Tl2Ba2CaCu208 (Tc 105 K) and Tl2Ba2Ca2Cu30io (Tc 115 K) [10], hts films with reasonable and qualified microwave properties nowadays can be grown on wafers up to more than 4 in diameter, the most common size are 2 and 3 for microwave applications. A very important step was the preparation of double-sided coating, which have turned out to be essential for planar microwave devices, where the metal ground plane needs to be superconducting in order to achieve high quality factors. 

In general, electromagnetic resonators are of common use for material characterization at microwave frequencies. In addition, a resonator represents a basic element of a multipole filter or an oscillator circuit. Any type of electromagnetic resonator is characterized by the resonant frequency /o and the unloaded quality factor Qo of the selected resonant mode and its spectrum of spurious modes. In order to measure the resonator properties or to use a resonator as part of a filter structure, the resonator needs to be equipped with one or two... 

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... 

Where f is the frequency of the incident microwave radiation and Q is the dimensionless cavity quality factor. Thus for a typical cavity Q of 20,000 at 10 GHz the operational bandwidth is on the order of 0.5 MHz. Therefore a typical rotational spectrum that covers 7.5-18.5 GHz must be stepped in 500 kHz step sizes over that spectral range. The result is a recording device that must take 22,000 steps to record an 11 GHz spectral region leading to data acquisition times that can take upwards of 14 hours. This analysis time can be reduced to minutes if spot checks are performed by tuning the cavity only to the rotational transition of a known species, however, in tliis mode of operation, only the species of interest will be detected, i.e., molecular species with transitions outside the spectral window being monitored will not be detected. 

The microstructure observation of the sintered ceramics surface was performed by means of scanning electron microscopy (SEM, JEOL JSM 6400, Japan). The crystalline phase of sintered ceramics was identified by X-ray diflfaction (XRD, RIGAKU D/max 2.B) with CuKa radiation (X=l. 541SA at 40 kV and 30 mA) and scanned from 20° to 70° with scanning speed of 4°/min. The bulk densities of the sintered pellets were measured by the Archimedes method. The dielectric constant ( ,) and the quality factor values (Qxf) at microwave frequencies were measured using the Hakki-Coleman dielectric resonator method which had been modified and improved by Courtney The dielectric resonator was positioned between two brass plates. Microwave... 

Dielectric data for microwave dielectric materials, namely, the relative dielectric permittivity (e,), the product of the quality factor Q and the frequency (Q x/), the frequency of the measurement (/), and the temperature coefficient of the resonance frequency (xf) based on rare earth aluminates are listed in Table 30. Measurements carried out using low-frequency (MHz) impedance methods are... 

The quality of the resonant EPR cavity is measured by its efficiency for integrating microwave energy. A measure of this efficiency is described by the quality factor (2-factor),... 

A resonator can be considered as a bandpass filter. The exeitation bandwidth Avis determined by the resonator quality factor and is given by Qi = v/Av. For example, at X-band with v= 9.8 GHz and 100, a total bandwidth of approximately 100 MHz or 3.5 mT is exeited. In addition to the resonator, the excitation width of the m.w. pulse needs to be considered. With the maximum available microwave power and value the B field strength is sueh that a n/2-pulse requires typically 10 ns (a rectangular pulse of width L has a sine function in the frequeney domain with a full width at half height of s3.79/(23iL) Hz). 

The permittivity of Fe203 was measured using the cavity perturbation technique [17]. The main components of the measurement system include a resistive heating furnace and a cylindrical TMort) resonant mode cavity. The system measures the differences (frequency shift and change of quality factors) in the microwave cavity response between a cavity with an empty sample-holder and the same cavity with a sample-holder plus the sample at each specified temperature. These differences are recorded in a Hewlett Packard 8753B vector network analyzer and then used to calculate the permittivity. The details about this technique and apparatus used for the measurements can be found in the published literature [17,18]. 

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