text: Analog electrical elements such as mixers, filters, transfer oscillators, isolating buffers, dividers, and even transmission lines contribute technical noise and unwanted environmental coupling in time and frequency measurements. Software defined radio (SDR) techniques replace many of these analog components with digital signal processing (DSP) on rapidly sampled signals. We demonstrate that, generically, commercially available multi-channel SDRs are capable of time and frequency metrology, outperforming purpose-built devices by as much as an order-of-magnitude. For example, for signals at 10 MHz and 6 GHz, we observe SDR time deviation noise floors of about 20 fs and 1 fs, respectively, in under 10 ms of averaging. Examining the other complex signal component, we find a relative amplitude measurement instability of 3e-7 at 5 MHz. We discuss the scalability of a SDR-based system for simultaneous measurement of many clocks. SDR's frequency agility allows for comparison of oscillators at widely different frequencies. We demonstrate a novel and extreme example with optical clock frequencies differing by many terahertz: using a femtosecond-laser frequency comb and SDR, we show femtosecond-level time comparisons of ultra-stable lasers with zero measurement dead-time.
  @cite_18: We are reporting on the design, performance, and application results of a phase and frequency comparator based on the direct phase-time measurement using a high performance event timer. The advantages of this approach are the simple implementation, a broad frequency range, and the clear interpretation of the measured results. Primarily we analyzed the background instability of the instrument in a common-clock test when a 200 MHz clock signal was connected to both inputs and the noise bandwidth was kept at 5 Hz by a preprocessing of the measured data. The results show that the Allan deviation of the background instability follows 4 × 10−14 τ for a wide range of averaging intervals from 0.1 s up to 104 s. These results are better than background instability of commercially available state-of-the-art instruments based on the phase difference multiplication. Finally the instrument was used for comparison of two H-masers. This experiment proofed that one of possible applications is a comparison of low-noise highly stable frequency sources and measurement of their frequency stability in the time-domain. The noise background of the instrument was negligible for averaging intervals longer than 100 ms.
  @cite_14: To measure the frequency stability of an atomic oscillator having high-frequency stability, a technique using a pair of mixers and a time interval counter is widely used. This technique shares the signals of a local oscillator, uses a pair of mixers to convert the signals of the reference oscillator and the signals of the test oscillator to beat signals, and then uses a time interval counter to measure the phase difference between the beat signals. In this paper, the authors propose a frequency stability measuring technique that uses a two-channel audio band digitizer in place of the time interval counter. This technique uses the local oscillator and pair of mixers to convert the test signals and reference signals to audio-band beat signals, and then performs an analog-to-digital conversion on the beat signals. When the phase difference between two beat signals is numerically calculated, not only the effect of the local oscillator's phase noise can be eliminated, but the DC offset voltage generated from the mixers is not a critical problem for frequency stability measurements. The authors developed a prototype frequency stability analyzer based on this technique and obtained an Allan deviation (square root of the Allan variance) of σy(τ) = 5 × 10−17 at τ = 1000 seconds as a result of measuring its residual noise at a frequency of 100 MHz. This technique can be used to analyze a wide range of properties such as the clock quality of digital devices that operate at high speed, as well as the frequency stability of atomic oscillators at arbitrary nominal frequencies. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 1, 87(1): 21–33, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002 ecja.10097
  @cite_8: We propose a novel measurement system that evaluates the frequency stability of high-precision oscillators such as atomic oscillators. This measurement system consists of a pair of high-speed analog-to-digital converters (ADCs) and digital-signal-processing (DSP) circuits on a field programmable gate array. The pair of high-speed ADCs simultaneously digitizes the two sinusoidal-voltage outputs from the oscillator under test and a reference oscillator. The DSP circuits calculate the phase difference between the two sinusoidal voltages. The frequency stability evaluated as the Allan deviation sigmay(tau) is calculated from the phase difference. The main advantage of this system is that the hardware configuration is much more compact than the conventional systems using a dual mixer and a local oscillator. Nonetheless, the system noise floor of the prototype at the nominal frequency of 5 MHz is sigmay(1000 s) = 6.8 times 10-17, which is sufficient to evaluate a commercial hydrogen maser oscillator and is better by a factor of 5 than our previously reported system. We have verified that the measurement accuracy of the prototype depends on the nominal frequency and the level of the sinusoidal voltages, but it does not depend on the initial phase difference and offset frequency.
  @cite_48: The noise of a device under test (DUT) is measured simultaneously with two instruments, each of which contributes its own background. The average cross power spectral density converges to the DUT power spectral density. This method enables the extraction of the DUT noise spectrum, even if it is significantly lower than the background. After a snapshot on practical experiments, we go through the statistical theory and the choice of the estimator. A few experimental techniques are described, with reference to phase noise and amplitude noise in RF microwave systems and in photonic systems. The set of applications of this method is wide. The final section gives a short panorama on radioastronomy, radiometry, quantum optics, thermometry (fundamental and applied), semiconductor technology, met allurgy, etc. This report is intended as a tutorial, as opposed to a report on advanced research, yet addressed to a broad readership: technicians, practitioners, Ph.D. students, academics, and full-time scientists.
  @cite_0: Abstract : The Naval Research Laboratory (NRL) is developing a digital phase measurement system. The measurement system uses high speed Analog to Digital Converters (ADC) to make tens of millions of measurements per second, Digital Signal Processing (DSP) hardware for intermediate calculations, and a PC for the final phase calculations. Performance of the present configuration is limited by a 12-bit analog-to-digital converter. Averaging times can be as small as 0.0001 seconds. Multiple input frequencies to over 10 MHz can be measured simultaneously. Modular construction will allow for expansion to many channels. Absolute phase measurements are possible. Inputs to channels can be switched between frequencies and then returned to an original frequency without losing phase coherency of the measurements. This system to be used in the laboratory and may be used on the GPS satellites to monitor a hot backup clock. The basic system measures the coefficient of a Discrete Fourier Transform (DFT) at the assumed frequency of the input signal. This paper will describe the special purpose DSP hardware and software used to measure the signal and transform the measurements into conventional clock parameters.
  @cite_40: A novel, all-digital measurement system has been developed at the National Institute of Standards and Technology (NIST) as an alternative to the traditional analog approach to measuring time differences between the outputs of atomic standards used in the implementation of an ensemble time scale. The novel approach has been demonstrated viable for time scale applications and we are now working toward a full implementation of the system in an all-digital time scale.
  @cite_45: The last years improvements of electronic circuits has allowed the appliance of digital systems in phase noise measurement techniques where low noise and high accuracy are required, yielding flexibility in the implementation and setup of measurement systems. By definition, any measure performed is always affected and limited by the noise of the measurement instrument itself. Considering that the Analog to Digital Converter (ADC) is the core and front end of digital systems, its residual noise has an important impact on the system performance. Consequently, the selection of the proper ADC becomes a critical issue for the system implementation. Currently, the information available in literature deeply describes the ADC features mainly at frequencies offsets far-from-carrier. Nevertheless for time and frequency applications the performance close to the carrier is an important concern as well. In this paper, a simple method for ADC characterization is proposed based on the Phase Locked Loop (PLL) definition and on Phase and Amplitude Modulation (PM AM) measurements, focused in obtaining the relevant information of ADC noise contributions for phase noise measurement applications. The purpose of such a method is to find the parameters of a state ADC noise model using a technique which avoids the use of complex hardware and allows having a low computational costs performance.
  @cite_2: We have completed a phase 1 SBIR project to develop technology for direct phase-noise measurements. This new approach to phase-noise measurements uses fast analog-to-digital converters to digitize the input RF signal and performs all down-conversion and phase detection functions by digital signal processing. It has several significant advantages over analog phase-noise measurement techniques: there is no external phase-lock loop; oscillators can be compared at all different frequencies; amplitude and phase noise may be measured simultaneously; the spectrum and Allan variance may be computed simultaneously; and complex calibration techniques are eliminated.
  @cite_46: 
summary: Some limitations in DMTD can be addressed by replacing certain analog processing steps with digital implementations. The TIC can be dramatically redesigned @cite_18 with much higher effective @math . One group @cite_14 replaced the TIC by digitizing the mixed and filtered signals at @math and later eliminated the mixers with high-speed direct sampling of the input signals @cite_8 . Others have replaced mixer-based spectral down-conversion with aliasing through under-sampling @cite_40 . Early consideration of a direct-sampling system @cite_0 very similar to the present work showed plausible limits due to quantization effects alone can be @math for averaging intervals @math . While high-speed samples can be processed entirely in software @cite_46 or with custom hardware @cite_2 , this work explores oscillator metrology using an inexpensive, commercially available, unmodified software defined radio (SDR). We note a similar approach for characterizing ADCs @cite_45 . We employ an ADC noise cancelation technique in the time domain, which perhaps is analogous to cross-spectral analysis @cite_48 in the frequency domain.