Resonant circuit

The heart of an NMR spectrometer is the probe, which is essentially a tuned resonant circuit with the sample contained within the main inductance (the NMR coil) of that circuit. Usually a parallel tuned circuit is used with a resonant frequency of coq = The resonant frequency is obviously the most important probe... 

Figure 1.8 A schematic representation of a typical resonant circuit for a dual H/ C probe. The capacitors A, B, C, and D perform various functions, such as symmetry and matching resonance.

The RF SQUID is formed from a single junction in a superconducting loop, which is inductively coupled to a resonant circuit. This is arranged to drive a current round the loop, so that the voltage across the circuit is a measure of the magnetic flux being measured. 

The ajTnbol Q is employed here to denote the quality factor of a resonant circuit, i.e., circulating energy divided by rate of energy loss. 

Piezoelectric microbalance The piezoelectric microbalance is a resonant frequency device. The piezoelectric effect is the development of a charge on some crystals such as quartz when a stress is applied the stress may be mechanical (e.g., added weight) or electrical. Such crystals may be used as part of a resonance circuit to provide very stable, narrow-band frequencies the quartz crystal is plated on two sides with a thin conducting layer and leads are connected to the resonance circuit so the crystal replaces an LC network. The obtained frequency of vibration (pu) depends on a number of parameters of the crystal but is usually 5-10 MHz. However, if a mass (Am) becomes attached to one side of the crystal, it changes the resonant frequency by an amount At , such that... 

The dielectric constant of a substance may be measured by determining the ratio of the capacity of a condenser filled with the substance and the capacity of the empty condenser. The electrical apparatus involves the condenser whose capacity is to be determined in parallel with a calibrated variable condenser, in a tuned resonant circuit the determination J3 made by adjusting the variable condenser to keep the resonance frequency constant, and this requires that the sum of the capacities of the two condensers be constant.1... 

FIGURE 3.13 Parallel resonance circuit and impedance graph indicating highest impedance at the frequency of resonance. 

The capacitor bank and the transformer form a parallel resonant circuit with the seventh harmonic current from the ASDs acting as the harmonic source. This condition is represented in Figure 4.19. Two adjustable speed drives typically draw a current of 550 A each, for a total load of 1100 A. If the seventh harmonic current is 5.0% of the fundamental (which is typical in drive applications), the seventh harmonic current seen by the parallel resonant circuit is 55 A = /7. 

The quality factor, Q, of an electrical system is a measure of the energy stored in the inductance and the capacitance of the system. The current amplification factor (CAF) of a parallel resonance circuit is approximately equal to the Q of the circuit ... 

FIGURE 4.19 Parallel resonance circuit formed by transformer inductance and capacitor bank capacitance at harmonic frequency /H. 

In the above example, by changing the capacitor bank to a 500-kVAR unit, the resonance frequency is increased to 490 Hz, or the 8.2 harmonic. This frequency is potentially less troublesome. (The reader is encouraged to work out the calculations.) In addition, the transformer and the capacitor bank may also form a series resonance circuit as viewed from the power source. This condition can cause a large voltage rise on the 480-V bus with unwanted results. Prior to installing a capacitor bank, it is important to perform a harmonic analysis to ensure that resonance frequencies do not coincide with any of the characteristic harmonic frequencies of the power system. 

Applying harmonic filters requires careful consideration. Series-tuned filters appear to be of low impedance to harmonic currents but they also form a parallel resonance circuit with the source impedance. In some instances, a situation can be created that is worse than the condition being corrected. It is imperative that computer simulations of the entire power system be performed prior to applying harmonic filters. As a first step in the computer simulation, the power system is modeled to indicate the locations of the harmonic sources, then hypothetical harmonic filters are placed in the model and the response of the power system to the filter is examined. If unacceptable results are obtained, the location and values of the filter parameters are changed until the results are satisfactory. When applying harmonic filters, the units are almost never tuned to the exact harmonic frequency. For example, the 5th harmonic frequency may be designed for resonance at the 4.7th harmonic frequency. 

By not creating a resonance circuit at precisely the 5th harmonic frequency, we can minimize the possibility of the filter resonating with other loads or the source, thus forming a parallel resonance circuit at the 5th harmonic. The 4.7th harmonic filter would still be effective in filtering out the 5th harmonic currents. This is evident from the series-tuned frequency vs. impedance curve shown in Figure 4.22. 

The investigated resonance circuit consists of a linear inductance Lo and the dielectric nonlinear capacitance C-nl (see Figure 14.1). Let us consider the case, that a ferroelectric triglycine sulfate crystal (tgs) is used as nonlinear capacitance. 

Rs describes the loss of the resonance circuit. The resonance circuit is driven by a sinusoidal voltage Uq cos ujet. The following differential equation describes the behavior of the circuit ... 

Figure 14.1 Dielectric nonlinear series-resonance circuit...

Dynamical systems may be conveniently analyzed by means of a multidimensional phase space, in which to any state of the system corresponds a point. Therefore, to any motion of a system corresponds an orbit or trajectory. The trajectory represents the history of the dynamic system. For one-dimensional linear systems, as in the case of the harmonic series-resonance circuit, described by the differential equation... 

Figure 14.9 Phase portraits of the resonance circuit with a TGS-crystal at different driving voltages below the phase transition and the corresponding Fourier spectra of the response functions with the periods T, 2T, 4T and deterministic chaos...

The selection of impedance or admittance for presentation of experimental results and data analysis is dependent on the type of equivalent electric circuit. For instance, for the analysis of -> charge-transfer processes and -> double-layer charging, the impedance may be preferred, while for the resonance circuits (e.g., in piezometric systems) the admittance may offer advantages. 

In order to limit size and weight of T, resonant circuits or low frequency (e.g. 0.1 cps) test voltage sources may be used [20] instead of the conventional transformer. 

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... 

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