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At least 253 records · Page 14

Test Cases for the Benchmark Active Controls: Spoiler and Control Surface Oscillations and Flutter

As a portion of the Benchmark Models Program at NASA Langley, a simple generic model was developed for active controls research and was called BACT for Benchmark Active Controls Technology model. This model was based on the previously-tested Benchmark Models rectangular wing with the NACA 0012 airfoil section that was mounted on the Pitch and Plunge Apparatus (PAPA) for flutter testing. The BACT model had an upper surface spoiler, a lower surface spoiler, and a trailing edge control surface for use in flutter suppression and dynamic response excitation. Previous experience with flutter suppression indicated a need for measured control surface aerodynamics for accurate control law design. Three different types of flutter instability boundaries had also been determined for the NACA 0012/PAPA model, a classical flutter boundary, a transonic stall flutter boundary at angle of attack, and a plunge instability near M = 0.9. Therefore an extensive set of steady and control surface oscillation data was generated spanning the range of the three types of instabilities. This information was subsequently used to design control laws to suppress each flutter instability. There have been three tests of the BACT model. The objective of the first test, TDT Test 485, was to generate a data set of steady and unsteady control surface effectiveness data, and to determine the open loop dynamic characteristics of the control systems including the actuators. Unsteady pressures, loads, and transfer functions were measured. The other two tests, TDT Test 502 and TDT Test 5 18, were primarily oriented towards active controls research, but some data supplementary to the first test were obtained. Dynamic response of the flexible system to control surface excitation and open loop flutter characteristics were determined during Test 502. Loads were not measured during the last two tests. During these tests, a database of over 3000 data sets was obtained. A reasonably extensive subset of the data sets from the first two tests have been chosen for Test Cases for computational comparisons concentrating on static conditions and cases with harmonically oscillating control surfaces. Several flutter Test Cases from both tests have also been included. Some aerodynamic comparisons with the BACT data have been made using computational fluid dynamics codes at the Navier-Stokes level (and in the accompanying chapter SC). Some mechanical and active control studies have been presented. In this report several Test Cases are selected to illustrate trends for a variety of different conditions with emphasis on transonic flow effects. Cases for static angles of attack, static trailing-edge and upper-surface spoiler deflections are included for a range of conditions near those for the oscillation cases. Cases for trailing-edge control and upper-surface spoiler oscillations for a range of Mach numbers, angle of attack, and static control deflections are included. Cases for all three types of flutter instability are selected. In addition some cases are included for dynamic response measurements during forced oscillations of the controls on the flexible mount. An overview of the model and tests is given, and the standard formulary for these data is listed. Some sample data and sample results of calculations are presented. Only the static pressures and the first harmonic real and imaginary parts of the pressures are included in the data for the Test Cases, but digitized time histories have been archived. The data for the Test Cases are also available as separate electronic files.

Bennett, Robert M.↗

Model of Wave Driven Flow Oscillation for Solar Cycle

At low latitudes in the Earth's atmosphere, the observed zonal flow velocities are dominated by the semi-annual and quasi-biennial oscillations with periods of 6 months and 20 to 32 months respectively. These terrestrial oscillations, the SAO and QBO respectively, are driven by wave-mean flow interactions due to upward propagating planetary-scale waves (periods of days) and small-scale gravity waves (periods of hours). We are proposing (see also Mayr et al., GRL, 2001) that such a mechanism may drive long period oscillations (reversing flows) in stellar and planetary interiors, and we apply it to the Sun. The reversing flows would occur below the convective envelope where waves can propagate. We apply a simplified, one dimensional, analytical flow model that incorporates a gravity wave parameterization due to Hines (1997). Based on this analysis, our estimates show that relatively small wave amplitudes less than 10 m/s can produce zonal flow amplitudes of 20 m/s, which should be sufficient to generate the observed variations in the magnetic field. To produce the 22-year period of oscillation, a low buoyancy frequency must be chosen, and this places the proposed flow in a region that is close to (and below) the base of the convective envelope. Enhanced turbulence associated with this low stability should help to generate the dynamo currents. With larger stability at deeper levels in the solar interior, the model can readily produce also oscillations with much longer periods. To provide an understanding of the fluid dynamics involved, we present numerical results from a 2D model for the terrestrial atmosphere that exemplify the non-linear nature of the wave interaction for which a mechanical analog is the escapement mechanism of the clock.

Mayr, Hans G.↗

Unsteady Pressures in a Transonic Fan Cascade Due to a Single Oscillating Airfoil

An extensive set of unsteady pressure data was acquired along the midspan of a modern transonic fan blade for simulated flutter conditions. The data set was acquired in a nine-blade linear cascade with an oscillating middle blade to provide a database for the influence coefficient method to calculate instantaneous blade loadings. The cascade was set for an incidence of 10 dg. The data were acquired on three stationary blades on each side of the middle blade that was oscillated at an amplitude of 0.6 dg. The matrix of test conditions covered inlet Mach numbers of 0.5, 0.8, and 1.1 and the oscillation frequencies of 200, 300, 400, and 500 Hz. A simple quasiunsteady two-dimensional computer simulation was developed to aid in the running of the experimental program. For high Mach number subsonic inlet flows the blade pressures exhibit very strong, low-frequency, self-induced oscillations even without forced blade oscillations, while for low subsonic and supersonic inlet Mach numbers the blade pressure unsteadiness is quite low. The amplitude of forced pressure fluctuations on neighboring stationary blades strongly depends on the inlet Mach number and forcing frequency. The flowfield behavior is believed to be governed by strong nonlinear effects due to a combination of viscosity, compressibility, and unsteadiness. Therefore, the validity of the quasi-unsteady simplified computer simulation is limited to conditions when the flowfield is behaving in a linear, steady manner. Finally, an extensive set of unsteady pressure data was acquired to help development and verification of computer codes for blade flutter effects.

Lepicovsky, J.↗

Investigation of an Oscillating Surface Plasma for Turbulent Drag Reduction

An oscillating, weakly ionized surface plasma has been investigated for use in turbulent boundary layer viscous drag reduction. The study was based on reports showing that mechanical spanwise oscillations of a wall can reduce viscous drag due to a turbulent boundary layer by up to 40%. It was hypothesized that the plasma induced body force in high electric field gradients of a surface plasma along strip electrodes could also be configured to oscillate the flow. Thin dielectric panels with millimeter-scale, flush- mounted, triad electrode arrays with one and two-phase high voltage excitation were tested. Results showed that while a small oscillation could be obtained, the effect was lost at a low frequency (less than 100Hz). Furthermore, a mean flow was generated during the oscillation that complicates the effect. Hot-wire and pitot probe diagnostics are presented along with phase-averaged images revealing plasma structure.

Wilkinson, Stephen P.↗

A New Forced Oscillation Capability for the Transonic Dynamics Tunnel

A new forced oscillation system has been installed and tested at NASA Langley Research Center's Transonic Dynamics Tunnel (TDT). The system is known as the Oscillating Turntable (OTT) and has been designed for the purpose of oscillating, large semispan models in pitch at frequencies up to 40 Hz to acquire high-quality unsteady pressure and loads data. Precisely controlled motions of a wind-tunnel model on the OTT can yield unsteady aerodynamic phenomena associated with flutter, limit cycle oscillations, shock dynamics, and non-linear aerodynamic effects on many vehicle configurations. This paper will discuss general design and components of the OTT and will present test data from performance testing and from research tests on two rigid semispan wind-tunnel models. The research tests were designed to challenge the OTT over a wide range of operating conditions while acquiring unsteady pressure data on a small rectangular supercritical wing and a large supersonic transport wing. These results will be presented to illustrate the performance capabilities, consistency of oscillations, and usefulness of the OTT as a research tool.

Piatak, David J.↗

Low Frequency High Amplitude Temperature Oscillations in Loop Heat Pipe Operation

This paper presents a theory that explains low frequency, high amplitude temperature oscillations in loop heat pipe (LHP) operation. Oscillations of the CC temperature with amplitudes on the order of tens of degrees Kelvin and periods on the order of hours have been observed in some LHPs during ambient testing. There are presently no satisfactory explanations for such a phenomenon in the literature. It is well-known that the operating temperature of an LHP with a single evaporator is governed by the compensation chamber (CC) temperature, which in turn is a function of the evaporator heat load, sink temperature, and ambient temperature. As the operating condition changes, the CC temperature will change during the transient but eventually reach a new steady temperature. Under certain conditions, however, the LHP never really reaches a true steady state, but instead displays an oscillatory behavior. The proposed new theory describes why low frequency, high amplitude oscillations may occur when the LHP has a low evaporator power, a low heat sink temperature (below ambient temperature), and a large thermal mass attached to the evaporator. When this condition prevails, there are some complex interactions between the CC, condenser, thermal mass and ambient. The temperature oscillation is a result of the large movement of the vapor front inside the condenser, which is caused by a change in the net evaporator power modulated by the large thermal mass through its interaction with the sink and CC. The theory agrees very well with previously published test data. Effects of various parameters on the amplitude and frequency of the temperature oscillation are also discussed.

Ku, Jentung↗

Nonlinear Oscillations and Flow of Gas Within Closed and Open Conical Resonators

A dissonant acoustic resonator with a conical shaped cavity was tested in four configurations: (A) baseline resonator with closed ends and no blockage; (B) closed resonator with internal blockage; (C) ventilated resonator with no blockage; and (D) ventilated resonator with an applied pressure differential. These tests were conducted to investigate the effects of blockage and ventilation holes on dynamic pressurization. Additionally, the investigation was to determine the ability of acoustic pressurization to impede flow through the resonator. In each of the configurations studied, the entire resonator was oscillated at the gas resonant frequency while dynamic pressure, static pressure, and temperature of the fluid were measured. In the final configuration, flow through the resonator was recorded for three oscillation conditions. Ambient condition air was used as the working fluid. The baseline results showed a marked reduction in the amplitude of the dynamic pressure waveforms over previously published studies due to the use of air instead of refrigerant as the working fluid. A change in the resonant frequency was recorded when blockages of differing geometries were used in the closed resonator, while acoustic pressure amplitudes were reduced from baseline measurements. A sharp reduction in the amplitude of the acoustic pressure waves was expected and recorded when ventilation ports were added. With elevated pressure applied to one end of the resonator, flow was reduced by oscillating the cavity at the fluid fundamental resonant frequency compared to cases without oscillation and oscillation off-resonance.

Daniels, Christopher↗

The Dynamics of Coupled Oscillator Phase Control

Arrays of coupled oscillators have been proposed as means of realizing high power rf sources via coherent spatial power combining. In such applications, a uniform phase distribution over the aperture is usually desired. However, it has been shown that by detuning some of the oscillators away from the oscillation frequency of the ensemble of oscillators, one may achieve other useful aperture phase distributions. Of particular interest among those achievable are linear phase distributions because these result in steering of the output rf beam away from the broadside direction. The theory describing the behavior of such arrays of coupled oscillators is quite complicated since the phenomena involved are inherently nonlinear. However, a simplified theory has been developed which facilitates intuitive understanding. This simplified theory is based on a "continuum model" in which the aperture phase is represented by a continuous function of the aperture coordinates. A challenging aspect of the development of this theory is the derivation of appropriate boundary conditions at the edges or ends of the array.

Pogorzelski, R. J.↗

Evidence for Harmonic Content and Frequency Evolution of Oscillations During the Rising Phase of X-ray Bursts From 4U 1636-536

We report on a study of the evolution of burst oscillation properties during the rising phase of X-ray bursts from 4U 1636-536 observed with the proportional counter array (PCA) on board the Rossi X-Ray Timing Explorer (RXTE) . We present evidence for significant harmonic structure of burst oscillation pulses during the early rising phases of bursts. This is the first such detection in burst rise oscillations, and is very important for constraining neutron star structure parameters and the equation of state models of matter at the core of a neutron star. The detection of harmonic content only during the initial portions of the burst rise is consistent with the theoretical expectation that with time the thermonuclear burning region becomes larger, and hence the fundamental and harmonic amplitudes both diminish. We also find, for the first time from this source, strong evidence of oscillation frequency increase during the burst rise. The timing behavior of harmonic content, amplitude, and frequency of burst rise oscillations may be important in understanding the spreading of thermonuclear flames under the extreme physical conditions on neutron star surfaces.

Bgattacharyya, Sudip↗

Semiconductor Reference Oscillator Development for Coherent Detection Optical Remote Sensing Applications

The NASA Earth Science Enterprise Advanced Technology Initiatives Program is supporting a program for the development of semiconductor laser reference oscillators for application to coherent optical remote sensing from Earth orbit. Local oscillators provide the frequency reference required for active spaceborne optical remote sensing concepts that involve heterodyne (coherent) detection. Two recent examples of such schemes are Doppler wind lidar and tropospheric carbon dioxide measurement by laser absorption spectrometry, both of which are being proposed at a wavelength of 2.05 microns. Frequency-agile local oscillator technology is important to such applications because of the need to compensate for large platform-induced Doppler components that would otherwise interfere with data interpretation. Development of frequency-agile local oscillator approaches has heretofore utilized the same laser material as the transmitter laser (Tm,Ho:YLF in the case of the 2.05-micron wavelength mentioned above). However, a semiconductor laser-based frequency-agile local oscillator offers considerable scope for reduced mechanical complexity and improved frequency agility over equivalent crystal laser devices, while their potentially faster tuning capability suggest the potential for greater scanning versatility. The program we report on here is specifically tasked with the development of prototype novel architecture semiconductor lasers with the power, tunability, and spectral characteristics required for coherent Doppler lidar. The baseline approach for this work is the distributed feedback (DFB) laser, in which gratings are etched into the semiconductor waveguide structures along the entire length of the laser cavity. However, typical DFB lasers at the wavelength of interest have linewidths that exhibit unacceptable growth when driven at the high currents and powers that are required for the Doppler lidar application. Suppression of this behavior by means of corrugation pitch-modulation (using a detuned central section to prevent intensity peaking in the center of the cavity) is currently under investigation to achieve the required performance goals.

distributed feedback (DFB) laser↗

Crystal oscillators using negative voltage gain, single pole response amplifiers

A simple and inexpensive crystal oscillator is provided which employs negative voltage gain, single pole response amplifiers. The amplifiers may include such configurations as gate inverters, operational amplifiers and conventional bipolar transistor amplifiers, all of which operate at a frequency which is on the roll-off portion of their gain versus frequency curve. Several amplifier feedback circuit variations are employed to set desired bias levels and to allow the oscillator to operate at the crystal's fundamental frequency or at an overtone of the fundamental frequency. The oscillator is made less expensive than comparable oscillators by employing relatively low frequency amplifiers and operating them at roll-off, at frequencies beyond which they are customarily used. Simplicity is provided because operation at roll-off eliminates components ordinarily required in similar circuits to provide sufficient phase-shift in the feedback circuitry for oscillation to occur.

Kleinberg, Leonard L.↗

Monlithic nonplanar ring oscillator and method

A monolithic nonplanar ring oscillator having an optically isotropic solid-state laser body for propagating laser radiation about a nonplanar ring path internal to the laser body is disclosed. The monolithic laser body is configured to produce a 2N reflection nonplanar ring light path, where N is an integer greater than or equal to 2, comprising 2N-1 total internal reflections and one reflection at a coupler in a single round trip. Undirectional traveling wave oscillation of the laser is induced by the geometry of the nonplanar ring path together with the effect of an applied magnetic field and partial polarizer characteristics of the oblique reflection from the coupler. The 6-reflection nonplanar ring oscillator makes possible otpimal unidirectional oscillation (low loss for the oscillating direction of propagation and, simultaneously high loss for the nonoscillating direction of propagation) in monolithic NPROs using materials with index of refraction smaller than the square root of 3, for example, laser glass.

Nilsson, Alan C.↗

Intra-seasonal Oscillations Inferred from SABER (TIMED) and MLS (UARS) Temperature Measurements

In the zonal mean meridional winds of the upper mesosphere, intra-seasonal oscillations with periods between 1 and 4 months have been inferred from UARS measurements and independently predicted with the Numerical Spectral Model WSM). The wind oscillations tend to be confined to low latitudes and appear to be driven, at least in part, by small-scale gravity waves propagating in the meridional direction. Winds across the equator should generate, due to dynamical heating and cooling, temperature oscillations with opposite phase in the two hemispheres. Investigating this phenomenon, we have analyzed SABER temperatures from TIMED in the altitude range between 55 and 95 km to delineate with an empirical model, the year-long variability of the migrating tides and zonal mean components. The inferred seasonal variations of the diurnal tide, characterized by amplitude maxima near equinox, are in substantial agreement with UARS observations and results from the NSM. For the zonal mean, the dominant seasonal variations in the SABER temperatures, with annual (12 months) and semiannual (6 months) periodicities, agree well with those derived from UARS measurements. The intra-seasonal variations with periods between 2 and 4 months have amplitudes close to 2 K, almost half as large as those for the dominant seasonal variations. Their amplitudes are in qualitative agreement with the corresponding values inferred from UARS during different years. The SABER and UARS temperature variations reveal pronounced hemispherical asymmetries, consistent with meridional wind oscillations across the equator. The phase of the semi-annual temperature oscillations from the NSM agrees with the observations from UARS and SABER. But the amplitudes are systematically smaller, which may indicate that planetary waves are more important than is allowed for in the model. For the shorter-period intra-seasonal variations, which can be generated by gravity wave drag, the model results are generally in better agreement with the observations.

Huang, F. T.↗

Extreme Temperature Operation of a 10 MHz Silicon Oscillator Type STCL1100

The performance of STMicroelectronics 10 MHz silicon oscillator was evaluated under exposure to extreme temperatures. The oscillator was characterized in terms of its output frequency stability, output signal rise and fall times, duty cycle, and supply current. The effects of thermal cycling and re-start capability at extreme low and high temperatures were also investigated. The silicon oscillator chip operated well with good stability in its output frequency over the temperature region of -50 C to +130 C, a range that by far exceeded its recommended specified boundaries of -20 C to +85 C. In addition, this chip, which is a low-cost oscillator designed for use in applications where great accuracy is not required, continued to function at cryogenic temperatures as low as - 195 C but at the expense of drop in its output frequency. The STCL1100 silicon oscillator was also able to re-start at both -195 C and +130 C, and it exhibited no change in performance due to the thermal cycling. In addition, no physical damage was observed in the packaging material due to extreme temperature exposure and thermal cycling. Therefore, it can be concluded that this device could potentially be used in space exploration missions under extreme temperature conditions in microprocessor and other applications where tight clock accuracy is not critical. In addition to the aforementioned screening evaluation, additional testing, however, is required to fully establish the reliability of these devices and to determine their suitability for long-term use.

Patterson, Richard L.↗

Assessment of Operation of EMK21 MEMS Silicon Oscillator Over Wide Temperature Range

Electronic control systems, data-acquisition instrumentation, and microprocessors require accurate timing signals for proper operation. Traditionally, ceramic resonators and crystal oscillators provided this clock function for the majority of these systems. Over the last few years, MEMS (Micro-Electro-Mechanical Systems) resonator-based oscillators began to surface as commercial-off-the-shelf (COTS) parts by a few companies. These quartz-free, miniature silicon devices could easily replace the traditional crystal oscillators in providing the timing/clock function for many digital and analog circuits. They are reported to provide stable output frequency, offer great tolerance to shock and vibration, and are immune to electro-static discharge [ 1-2]. In addition, they are encapsulated in compact lead-free packages and cover a wide frequency range (1 MHz to 125 MHz). The small size of the MEMS oscillators along with their thermal stability make them ideal candidates for use in space exploration missions. Limited data, however, exist on the performance and reliability of these devices under operation in applications where extreme temperatures or thermal cycling swings, which are typical of space missions, are encountered. This report presents the results of the work obtained on the evaluation of an Ecliptek Corporation MEMS silicon oscillator chip under extreme temperatures.

Patterson, Richard L.↗

Saturn's Equatorial Oscillation: Evidence of Descending Thermal Structure from Cassini Radio Occultations

Ground-based and Cassini CIRS thermal-infrared data have characterized the spatial and temporal characteristics of an equatorial oscillation in Saturn's middle atmosphere above the 100-mbar level. The CIRS data indicate a vertical pattern of alternating warm and cold anomalies at the equator. From the thermal wind equation this implies a concomitant reversal of zonal winds with attitude, relative to the cloud-top winds, with peak-to-peak amplitude approximately 200 meters per second. The ground-based observations do not having the altitude range or vertical resolution of the CIRS observations, but they cover several years and indicate an oscillation cycle of 1 years, roughly half of Saturn's year. Equatorial oscillations in Earth's middle atmosphere have primarily exhibited either quasi-biennial or semi-annual "periodicities," and both types have been extensively observed and modeled. They exhibit a vertical pattern of alternating warmer and cooler zonal-mean temperatures and zonal winds analogous to that described above for Saturn. Moreover, the pattern of winds and temperatures descends with time. Momentum deposition by damped vertically propagating easterly and westerly waves is thought to play a key role in forcing both types of oscillation, and it can plausibly account for the descent. Here we report the direct observation of this descent in Saturn's equatorial atmosphere from Cassini radio occultation soundings in 2005 and 2009. The retrieved temperatures are consistent with a descent of 0.6 x the pressure scale height over this time period. The descent rate is related to the magnitude of the wave forcing, radiative damping, and induced meridional circulations. A simple calculation implies that vertical wave fluxes of zonal momentum approximately 0.05 square meters per square second could account for the observed vertical descent on Saturn, which is comparable to the magnitude of the wave fluxes associated with the terrestrial quasi-biennial oscillation.

Flasar, F. M.↗

Equatorial Oscillations in Jupiter's and Saturn's Atmospheres

Equatorial oscillations in the zonal-mean temperatures and zonal winds have been well documented in Earth's middle atmosphere. A growing body of evidence from ground-based and Cassini spacecraft observations indicates that such phenomena also occur in the stratospheres of Jupiter and Saturn. Earth-based midinfrared measurements spanning several decades have established that the equatorial stratospheric temperatures on Jupiter vary with a cycle of 4-5 years and on Saturn with a cycle of approximately 15 years. Spectra obtained by the Composite Infrared Spectrometer (CIRS) during the Cassini swingby at the end of 2000, with much better vertical resolution than the ground-based data, indicated a series of vertically stacked warm and cold anomalics at Jupiter's equator; a similar structurc was seen at Saturn's equator in CIRS limb measurements made in 2005, in the early phase of Cassini's orbital tour. The thermal wind equation implied similar patterns of mean zonal winds increasing and decreasing with altitude. On Saturn the peak-to-pcak amplitude of this variation was nearly 200 meters per second. The alternating vertical pattern of wanner and colder cquatorial tcmperatures and easterly and westerly tendencies of the zonal winds is seen in Earth's equatorial oscillations, where the pattern descends with time, The Cassini Jupiter and early Saturn observations were snapshots within a limited time interval, and they did not show the temporal evolution of the spatial patterns. However, more recent Saturn observations by CIRS (2010) and Cassini radio-occultation soundings (2009-2010) have provided an opportunity to follow the change of the temperature-zonal wind pattern, and they suggest there is descent, at a rate of roughly one scale height over four years. On Earth, the observed descent in the zonal-mean structure is associated with the absorption of a combination of vertically propagating waves with easlerly and westerly phase velocities. The peak-to-peak zonal wind amplitude in the oscillation pattern and the rate of descent constrain the absorbed wave flux of zonal momentum. On Saturn this is approximately 0.05 square meters per square seconds, which is comparable to if not greater than that associated with the terrestrial oscillations. We discuss possible candidates for the absorbed waves on Saturn. On Earth the wave forcing of the equatorial oscillation generales secondary circulations that can affcct the temperature and wind structure at latitudes well away from the equator, and we discuss possible evidence of that on Saturn.

Flasar, F. Michael↗

Amplitude-Stabilized Oscillator for a Capacitance-Probe Electrometer

A multichannel electrometer voltmeter that employs a mechanical resonator maintained in sustained amplitude-stabilized oscillation has been developed for the space-based measurement of an Internal Electrostatic Discharge Monitor (IESDM) sensor. The IESDM is new sensor technology targeted for integration into a Space Environmental Monitor (SEM) subsystem used for the characterization and monitoring of deep dielectric charging on spacecraft. Creating a stable oscillator from the mechanical resonator was achieved by employing magnetic induction for sensing the resonator s velocity, and forcing a current through a coil embedded in the resonator to produce a Lorentz actuation force that overcomes the resonator s dissipative losses. Control electronics employing an AGC loop provide conditions for stabilized, constant amplitude harmonic oscillation. The prototype resonator was composed of insulating FR4 printed-wireboard (PWB) material containing a flat, embedded, rectangular coil connected through flexure springs to a base PWB, and immersed in a magnetic field having two regions of opposite field direction generated by four neodymium block magnets. In addition to maintaining the mechanical movement needed for the electrometer s capacitor-probe transducer, this oscillator provides a reference signal for synchronous detection of the capacitor probe s output signal current so drift of oscillation frequency due to environmental effects is inconsequential.

Blaes, Brent R.↗