Resonant circuit methods

Distributed circuit methods use coaxial lines, waveguides and resonant cavities at microwave frequencies. The circuits are designed for measuring an attenuation factor and a phase factor, from which sample dielectric properties can be calculated. The sample may form the dielectric medium between the two conductors of a coaxial line (Scaife et al, 1971), or an open coaxial line is brought into contact with the sample surface (Roussy and Pearce, 1995). Fagan et al, (2004) used an open coaxial line method to demonstrate that the moisture and salt contents of processed cheese could be predicted by measuring dielectric properties over a range of frequencies. 

At radio frequencies a medium- to low-loss material can be most sensitively examined by making it part of a resonant circuit. The Hartshorn and Ward (1936) method, for which the basic circuit is shown in Fig. 5.11, has been highly developed (Reddish et al., 1971) for very accurate measurements in the 105to 108Hz range. Here a disc specimen is held in a micrometer electrode system (see Fig. 5.6, where the specimen is represented by a capacitance Cx in parallel with a resistance Rx) and connected directly to a coil of fixed... 

Instead of the SSFP method, pulsed excitation is used [Bot2, Scol]. However, the lines are broadened for slow modulation frequencies, and sideband artefacts result if the modulation frequency is increased beyond 1 / Tf [Fei 1, Man 1 ]. The sidebands appear at multiples of the modulation frequency. If the modulation frequency is increased beyond the spectral width, they can be filtered out. To achieve such high-gradient modulation frequencies, the gradient coils need to be part of a resonant circuit. Modulation frequencies of up to 60 kHz can be achieved on small-gradient systems. 

Electron concentrations have been measured by radiofrequency resonant circuits " in which the flame is placed inside a coil or condenser which is part of a resonant circuit. Electron concentrations have also been obtained by cyclotron resonance/ microwave scattering/ microwave absorp-tion/ microwave interferometry/ and microwave cavity reso-nance. " All of these methods for measuring electron concentration have the advantage of not perturbing the flame, but suffer from the disadvantage of poor spatial resolution. Also, measurements can be made only over a relatively limited range of concentrations—typically, one or two orders of magnitude. 

Single-ended tetrode and pentode stages can be neutralized using the method shown in Fig. 5.45. The input resonant circuit is placed above ground by a smaU amount because of the addition of capacitor Qn. 

M. Randic, A. T. Balaban, and D. Plavsic, Applying the conjugated circuits method to Clar structures of [ ]phenylenes for determining resonance energies, Phys. Chem. Chem. Phys. 13 (2011) 20644-20648. 

There are, however, practical limitations to diis method of determining Ti. First, it must be remembered diat the modulation eoil and its assoeiated parasitic capacitance behave as a resonant circuit. The frequency range over whieh the coil may be used will therefore be limited. Second, the receiver diode and the associated selective amplifier also limit the applicable frequency range. And, finally, the typical cavity quality factor of approximately 10 imposes a rather narrow bandpass to the measurement, typically 1 MHz. In practice, then, only spin-lattice re-... 

For a characterization of materials with a low mechanical resistance and for routine measurements in industrial production, it would be of great importance to have a method which allows a contact-less, non-destmctive measurement of the resistance. One of the more recently developed techniques that is capable of such non-contact resistance measurement is the eddy current technique (Kraftmakher, 2000 Schroeder, 1998), which is mainly used in the semiconductor industry for wafer characterization (ASTM, 1996b) and is only recently entering display manufacturing as well (ASTM, 2002c). The technique is based on the effect that the quahty factor of a resonant circuit is reduced when a conducting... 

The dielectric constant and dissipation factor of flat sheets or slabs of both rigid and flexible cellular plastics can be determined by this method, at frequencies from 60 to lOOMHz. The basic apparatus consists of a bridge and a resonant circuit. Since cellular plastics do not have surfaces suitable for the attachment of conven-... 

When considering expansions, some caution has to be exercised in allowing for a possibility that an apparently different form of an expansion may turn out to be mathematically equivalent. This has already been seen with Herndon s resonance theory and the conjugated circuits method, which can both lead to the same expressions for the molecular resonance energy. The distinction between such expansions may be in the interpretation of the terms used. This is well illustrated with a comparison of the quantum chemically computed diamagnetic susceptibilities of alkanes and the graph theoretical analysis of the same diamagnetic susceptibilities briefly outlined below. 

Since the circuits comprise amplifying stages and resonating circuits, it is to be expected that the overall circuit response will be different for different frequencies. Can you suggest a method of determining this frequency dependence ... 

Most NC-AFMs use a frequency modulation (FM) teclmique where the cantilever is mounted on a piezo and serves as the resonant element in an oscillator circuit [101. 102]. The frequency of the oscillator output is instantaneously modulated by variations in the force gradient acting between the cantilever tip and the sample. This teclmique typically employs oscillation amplitudes in excess of 20 mn peak to peak. Associated with this teclmique, two different imaging methods are currently in use namely, fixed excitation and fixed amplitude. 

Quasi-resonant converters are a separate class of switching power supplies that tune the ac power waveforms to reduce or eliminate the switching loss within the supply. This is done by placing resonant tank circuits within the ac current paths to create pseudo-sinusoidal voltage or current waveforms. Because the tank circuits have one resonant frequency, the method of control needs to be modified to a variable frequency control where the resonant period is fixed and the control varies the period of the non-resonant period. The quasi-resonant converters usually operate in the 300 kHz to 2 MHz frequency range. 

ZVS QR topologies appear to be the more popular of two methods of quasi-resonant technologies. This is mainly due to two reasons first, its typical variation in frequency over its input and load variations is 4 f as opposed to fO f for the ZCS topologies secondly, it has a better heavy load performance. Also, some of the more troublesome parasitic elements within the circuit can be more easily harnessed. 

Figure 4-15 The two methods of loading a resonant tank circuit.

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