Fred L. Walls

Measurement of the Short-Term Stability of Quartz Crystal Resonators and the Implications for Crystal Oscillator Design and Applications

A new technique is presented which makes it possible to measure the inherent short-term stability of quartz crystal resonators in a passive circuit. Comparisons with stability measurements made on crystal controlled oscillators indicate that noise in the electronics of the oscillators very seriously degrades the inherent stability of the quartz resonators for times less than 1 s. A simple model appears to describe the noise mechanism in crystal controlled oscillators and points the way to design changes which should improve their short-term stability by two orders of magnitude. Calculations are outlined which show that with this improved short-term stability it should be feasible to multiply a crystal controlled source to 1 THz and obtain a linewidth of less than 1 Hz. In many cases, this improved short-term stability should also permit a factor of 100 reduction in the length of time necessary to achieve a given level of accuracy in frequency measurements.

Measurements of frequency stability

The characterization of frequency stability in the time domain and frequency domain are briefly defined and their relationships explained. Techniques for making precise measurements of frequency fluctuations in oscillators, multipliers, dividers, amplifiers, and other components are discussed. Particular attention is given to methods of calibration which permit accuracies of 1 dB or better to be achieved when measuring in the frequency domain. Common pitfalls to avoid are also covered, and efficient time-domain techniques are explained.

Fundamental limits on the frequency stabilities of crystal oscillators

The frequency instabilities of precision bulk acoustic wave (BAW) quartz crystal oscillators are reviewed. The fundamental limits on the achievable frequency stabilities, and the degree to which the fundamental limits have been approached to date are examined. Included are the instabilities as a function of time, temperature, acceleration, ionizing radiation, electromagnetic fields, humidity, atmospheric pressure, power supply, and load impedance. Most of the fundamental limits are zero or negligibly small, a few are finite. We speculate about the progress which may be achievable in the future with respect to approaching the fundamental limits. Suggestions are provided about the paths that may lead to significant stability improvements.<<ETX>>

Laser-pumped rubidium frequency standards: new analysis and progress

We have achieved a stability of 3/spl middot/10/sup -13/ /spl tau//sup -1/2/ for 3</spl tau/<30 s with a laser-pumped rubidium gas-cell frequency standard by reducing the effects due to noise in the microwave and laser sources. This result is one order of magnitude better than the best present performance of lamp-pumped devices.

Origin of 1/f PM and AM noise in bipolar junction transistor amplifiers

In this paper we report the results of extensive research on phase modulation (PM) and amplitude modulation (AM) noise in linear bipolar junction transistor (BJT) amplifiers. BJT amplifiers exhibit 1/f PM and AM noise about a carrier signal that is much larger than the amplifiers thermal noise at those frequencies in the absence of the carrier signal. Our work shows that the 1/f PM noise of a BJT based amplifier is accompanied by 1/f AM noise which can be higher, lower, or nearly equal, depending on the circuit implementation. The 1/f AM and PM noise in BJTs is primarily the result of 1/f fluctuations in transistor current, transistor capacitance, circuit supply voltages, circuit impedances, and circuit configuration. We discuss the theory and present experimental data in reference to common emitter amplifiers, but the analysis can be applied to other configurations as well. This study provides the functional dependence of 1/f AM and PM noise on transistor parameters, circuit parameters, and signal frequency, thereby laying the groundwork for a comprehensive theory of 1/f AM and PM noise in BJT amplifiers. We show that in many cases the 1/f PM and AM noise can be reduced below the thermal noise of the amplifier.

Environmental sensitivities of quartz oscillators

The frequency, amplitude, and noise of the output signal of a quartz oscillator are affected by a large number of environmental effects. The physical basis for the sensitivity of precision oscillators to temperature, humidity, pressure, acceleration and vibration, magnetic field, electric field, load, and radiation is examined. The sensitivity of quartz oscillators to radiation is a very complex topic and poorly understood. Therefore, only a few general results are mentioned. The sensitivity to most external influences often varies significantly both from one oscillator type to another and from one unit of a given type to another. For a given unit, the sensitivity to one parameter often depends on the value of other parameters and on history. Representative sensitivity to the above parameters is given.<<ETX>>

RF Spectrum of a Signal after Frequency Multiplication; Measurement and Comparison with a Simple Calculation

A novel experimental technique is introduced and used to measure the effect of frequency multiplication on the RF spectrum of an oscillator. This technique makes it possible to produce the RF spectrum at X band¿where measurements are relatively straightforward¿that would have been produced by frequency multiplication of the 5-MHz source to any frequency from 9.2 GHz to 100 THz (1014 Hz). A simplified theory is developed and shown to reproduce the experimental results for the relative power in the carrier and noise pedestal, and the shape and the width of the carrier and noise pedestal, to within the measurement uncertainty of 2 or 3 dB, from 5 MHz to 10 THz. The calculations are easily made using analytical techniques from the measurement of the spectral density of phase fluctuations of the source, the effective input spectrum density and the bandwidth of the multiplier chain, and the frequency multiplication factor. It is shown that present 5-MHz-crystal-controlled oscillators are useful as a precision source to ~500 GHz. Suggestions for extending their range to ~100 THz are made.

Noise figure vs. PM noise measurements: a study at microwave frequencies

This paper addresses two issues: (i) it compares the usefulness of phase-modulation (PM) noise measurements vs. noise figure (NF) measurements in characterizing the merit of an amplifier, and (ii) it reconciles a general misunderstanding in using -174 dBc/Hz (relative to carrier input power of 0 dBm) as thermal noise level. The residual broadband (white PM) noise is used as the basis for estimating the noise figure (NF) of an amplifier. We have observed experimentally that many amplifiers show an increase in the broadband noise of 1 to 5 dB as the signal level through the amplifier increases. This effect is linked to input power through the amplifiers nonlinear intermodulation distortion. Consequently, this effect is reduced as linearity is increased. It is important to note that NF is sometimes used as a selection criteria for an amplifier but yields no information about potentially important close-to-carrier 1/f noise of an amplifier, whereas PM and amplitude modulation (AM) noise measurements do. We have verified theoretically and experimentally that the single-sideband PM (and AM) noise floor due to thermal noise is -177 dBc/Hz, relative to a carrier input power of 0 dBm.

Fundamental limits on the frequency instabilities of quartz crystal oscillators

The frequency instabilities of precision bulk acoustic wave (BAW) quartz crystal oscillators, and the contributions from the instabilities of resonators, sustaining circuits, and ovens, are reviewed. The fundamental limits on the achievable frequency stabilities, and the degree to which the fundamental limits have been approached to date are examined. Included are the instabilities as a function of time, temperature, acceleration, ionizing radiation, electromagnetic fields, humidity, atmospheric pressure, power supply and load impedance. Most of the fundamental limits are zero or negligibly small, a few are finite. The authors speculate about the progress which may be achievable in the future with respect to approaching the fundamental limits. Suggestions are provided about the paths that may lead to significant stability improvements.<<ETX>>

High spectral purity X-band source

An X-band source that is specifically designed for high order frequency multiplication and precision spectroscopy is presented. The wideband phase noise is controlled by frequency-locking a dielectric resonator oscillator source to a high-Q cavity with a DC loop. This avoids the need for modulation on the source signal that might interfere with high order multiplication. The phase noise close to the carrier can be controlled by phase-locking the 10.6 GHz signal to a harmonic of a low-noise quartz crystal controlled oscillator. Modulation sideband due to the power line and harmonics are suppressed far below the random noise by enclosing the entire source in a magnetic shield. The phase noise is lower than previously published levels of phase noise for a free-running, room temperature, X-band source. In principle the 10.6 GHz signal could be multiplied to approximately 250 THz before carrier collapse would occur. At 250 THz the free-running linewidth would be approximately 2.8 kHz. At a frequency of 30 THz a linewidth on the order of 10 Hz is expected if the phase noise near the carrier is controlled by a harmonic of a low-noise 5 MHz oscillator.<<ETX>>