Variable frequency oscillator

With the advent of inexpensive, fast frequency counters, which count the individual cycles over a precisely fixed period (usually 1 s) and display the frequency digitally, it is more convenient to connect the radio-frequency output of the variable-frequency oscillator directly to the frequency counter and determine the total capacitance with the aid of Eq. (27). This technique is highly suitable for the present experiment if a WTW Dipol-meter or another LC oscillator is available or can be constructed. (With the Dipolmeter only the variable-frequency oscillator is used.) A simple LC oscillator circuit that can be constructed from inexpensive components has been described by Bonilla and Vassos this circuit, with a small modification to provide for one side of the tank to be grounded, is shown in Fig. 2. In this circuit, as in the WTW Dipolmeter circuit, all tank capacitances are in parallel. [This is not true of the circuit described in Ref. 4 of Exp. 30, as that circuit incorporates some series capacitance. If that circuit is employed, Eqs. (28) to (30) are not valid and Eqs. (30-3) to (30-5) must be used instead, unless the null mode is employed.]... 

In practice it is difficult to design a variable frequency oscillator that has the required accuracy. Since the resonant frequency depends on the magnetic field, we vary the resonant... 

The signal generator may be a 60-Hz transformer, a 1000-Hz oscillator, or a variable-frequency oscillator. If earphones are used as a null, the 1000-Hz oscillator is preferred. The null indicator can also be a sensitive microammeter or more elaborate null-point indicators. 

In the vibrating reed technique one end of a small sample is clamped in a gramophone record cutter head driven by a variable frequency oscillator. The amplitude of vibration is measured opto-electrically. enabling tan <5 to be calculated from the width of the resonance, sihce tan = Af. fr where f is the resonant frequency and A/ the bandwidth. 

A block diagram of the spectrometer is shown in Figure 16. The master oscillator (MO) is frequency-stabilized (FS) to two lower frequency standards. A one-GHz signal (1 GHz) is produced by multiplying a 20 MHz oven-controlled crystal oscillator which has a frequency stability of 1 x 10 parts per day. A variable frequency oscillator (VFO) is also used for continuous frequency adjustment... 

Some of these problems can be overcome by quickly switching, or hopping, the friendly carrier frequency over a wide band. This is the fundamental concept behind frequency-hopped spread spectrum systems, as shown in Fig. 12.73. A number of excellent texts discuss this topic such as Sklar (1988) Peterson, Ziemer, and Borth (1995) and Simon et al. (1985). The system design is very similar to conventional NB systems. The only modification to the transmitter is that the conventional fixed frequency oscillator is replaced by a variable frequency oscillator that can change frequency very quickly under electronic control. In Fig. 12.73 the message source and variable frequency oscillator are fed into a DSB modulator (a simple multiplier), although any form of NB modulation can be used. The oscillator frequency used at any instant in time is... 

We therefore conclude that by allowing the angular frequency of the simple harmonic oscillator to vary with the quantum number n, we obtain the spectrum of the Morse oscillator. Again the second term in Eq. (20) is in agreement to the fact that most perturbing potentials near their origin can be approximated by the harmonic oscillator potential. We shall refer to the oscillator of Eq. (20) as the Variable Frequency Oscillator (VFO). 

The pickup coil is affixed to the sample tube using a saddle-shaped configiua-tion (Figure 13). A Q-meter cannot be used to determine the quality factor of this device when it is inserted in the cavity resonator, and so Qb is determined by measuring pass bandwidth M2 at -3 dB while the coil is tuned to Q by using an external coil weakly coupled to a variable-frequency oscillator (Pescia, 1965) it follows that Qb= /Mi- Finally, because of the delicate nature of its measurement, Hi is not directly measured but rather steps are taken to ensure that it remains constant. 

The dielectric constant may be measured by a Q-Meter within the frequency range in which it operates and with a suitable sample holder [73]. The g-Meter is one of the common instruments in radio frequency measurement for determining the inductance, the capacitance, the Q of electronic components, and the resonant frequencies of circuits. The g-Meter includes a variable frequency oscillator with the output coupled to a series resonant circuit (Figure 24.12) [73]. 

The variable frequencies of suites V and VIII on one side, and VI and VIII on the other, correspond to oscillations resulting from the coupling of the v(C-X) vibration with the cjf mode in the case of 2- or 5-substituted derivatives and with the mode in the case of 4-substituted derivatives. For 2,5-disubstituted thiazoles the ojf, vibration is only slightly different from that of thiazole itself and the 5 oscillation is coupled with both v(C(2iX) and vfC(5,X or Y) modes, giving rise to three frequencies, two of which are higher and classified in suites V and V, the third, being lower, is assigned to suite VIII. 

RO, Fig. 3d) (2) higher-frequency, smaller amplitude, quasi-harmonic oscillations (QHO, Fig. 3a) and (3) double-frequency oscillations containing variable numbers of each of the two previous types. By far the most familiar feature of the BZ reaction, the relaxation oscillations of type 1 were explained by Field, Koros, and Noyes in their pioneering study of the detailed BZ reaction mechanism.15 Much less well known experimentally are the quasiharmonic oscillations of type 2,4,6 although they are more easily analyzed mathematically. The double frequency mode, first reported by Vavilin et al., 4 has been studied also by the present author and co-workers,6 who explained the phenomenon qualitatively on the basis of the Field-Noyes models of the BZ reaction. 

Cantilevers in AFM function as force transducers converting unknown force to measurable deflection. The value of the unknown force can then be expressed by Hookean mechanics following spring constant calibrations. In addition to static point loads, cantilevers can also be vibrated, e.g., by an oscillation piezo to which the fixed end of the beam is attached (or by other approaches). Excitation frequency, oscillation amplitude, and phase relationships are variables that govern dynamic tapping (intermittent contact) imaging. This problem will be discussed in the next section. 

There is the relationship between the interannual variability in the index of the SCS Warm Water and the monsoon break over the SCS. The SCS Warm Water, and the warm pools in both the western equatorial Pacific and the Indian Oceans are in the same coupled system on a large scale, sharing a long period of oscillation of about 4.8 years. During the years when colder water occurs in the SCS, an atmospheric anticyclone maintains itself to the east of the Philippines in summer. A low frequency activity associated with the anticyclone results in low frequency oscillation in the precipitation field over this region, whereas the weak subtropical high over the western Pacific travels eastward in summer, which is responsible for the anomalous distribution of meridional vapor transport. 

Free vibration methods such as the torsion pendulum are covered by ISO 4663 and are limited to cry low strains and frequencies, and are in much less frequent use these days than the forced vibration nonresonant systems on which this chapter will focus. The early Du Pont DMA and German Myrenne used input energy to maintain the resonant oscillation amplitude, but the main limitations were variable frequency according to the sample size (which had to be glassy or plastic) or one frequency only (1 Hz) respectively. 

Chapter 14 shows how modeling can propose mechanisms to explain experimentally observed oscillations in the cardiovascular system. A control system characterized by a slow and delayed change in resistance due to smooth muscle activity is presented. Experiments on this model show oscillations in the input impedance frequency spectrum, and flow and pressure transient responses to step inputs consistent with experimental observations. This autoregulation model supports the theory that low-frequency oscillations in heart rate and blood pressure variability spectra (Mayer waves) find their origin in the intrinsic delay of flow regulation. 

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