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 3 × 10−7 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.
REFERENCES
1.
Certain commercial equipment, instruments, or materials are identified in this paper for informational purposes only. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.
2.
D. W.
Allan
and J.
Barnes
, “A modified ‘Allan variance’ with increased oscillator characterization ability
,” in Thirty Fifth Annual Frequency Control Symposium. 1981
(IEEE
, 1981
), pp. 470
–475
.3.
D. W.
Allan
and H.
Daams
, “Picosecond time difference measurement system
,” in29th Annual Symposium on Frequency Control
(IEEE
, 1975
), Vol. 1
, pp. 404
–411
.4.
D. W.
Allan
and H.
Hellwig
, “Time deviation and time prediction error for clock specification, characterization, and application
,” in IEEE 1978 Position Location and Navigation Symposium
(IEEE
, 1978
), Vol. 1
, pp. 29
–36
.5.
M. G.
Bellanger
, J. L.
Daguet
, and G. P.
Lepagnol
, “Interpolation, extrapolation, and reduction of computation speed in digital filters
,” IEEE Trans. Acoust., Speech, Signal Process.
22
(4
), 231
–235
(1974
).6.
B. J.
Bloom
, T. L.
Nicholson
, J. R.
Williams
, S. L.
Campbell
, M.
Bishof
, X.
Zhang
, W.
Zhang
, S. L.
Bromley
, and J.
Ye
, “An optical lattice clock with accuracy and stability at the 10−18 level
,” Nature
506
(7486
), 71
–75
(2014
).7.
G.
Brida
, “High resolution frequency stability measurement system
,” Rev. Sci. Instrum.
73
(5
), 2171
–2174
(2002
).8.
A. C.
Cardenas-Olaya
, E.
Rubiola
, J.-M.
Friedt
, M.
Ortolano
, S.
Micalizio
, and C. E.
Calosso
, “Simple method for ADC characterization under the frame of digital PM and AM noise measurement
,” in 2015 Joint Conference of the IEEE International Frequency Control Symposium and the European Frequency and Time Forum (FCS)
(IEEE
, 2015
), pp. 676
–680
.9.
G.
Cibiel
, M.
Régis
, E.
Tournier
, and O.
Llopis
, “AM noise impact on low level phase noise measurements
,” IEEE Trans. Ultrason. Eng.
49
(6
), 784
–788
(2002
).10.
S. T.
Cundiff
and J.
Ye
, “Colloquium: Femtosecond optical frequency combs
,” Rev. Mod. Phys.
75
(1
), 325
(2003
).11.
See http://files.ettus.com/ for Ettus Research circuit schematics and technical information.
12.
See https://github.com/EttusResearch/uhd for Ettus Research code repository.
13.
T. M.
Fortier
, A.
Bartels
, and S. A.
Diddams
, “Octave-spanning Ti: Sapphire laser with a repetition rate >1 GHz for optical frequency measurements and comparisons
,” Opt. Lett.
31
(7
), 1011
–1013
(2006
).14.
T. M.
Fortier
, A.
Rolland
, F.
Quinlan
, F. N.
Baynes
, A. J.
Metcalf
, A.
Hati
, A.
Ludlow
, N.
Hinkley
, M.
Shimizu
, T.
Ishibashi
et al., “Digital-photonic synthesis of ultra-low noise tunable signals from RF to 100 GHz
,” Laser Photonics Rev.
(to be published), e-print arXiv:1506.03095 (2015
).15.
GNURadio: The free and open software radio ecosystem, GNURadio Team, April 2015, http://gnuradio.org/.
16.
C.
Greenhall
, D.
Howe
, and D. B.
Percival
, “Total variance, an estimator of long-term frequency stability
,” IEEE Trans. Ultrason. Eng.
46
(5
), 1183
–1191
(1999
).17.
J.
Grove
, J.
Hein
, J.
Retta
, P.
Schweiger
, W.
Solbrig
, and S. R.
Stein
, “Direct-digital phase-noise measurement
,” in Proceedings of the 2004 IEEE International Frequency Control Symposium and Exposition
(IEEE
, 2004
), pp. 287
–291
.18.
S.
Häfner
, S.
Falke
, C.
Grebing
, S.
Vogt
, T.
Legero
, M.
Merimaa
, C.
Lisdat
, and U.
Sterr
, “8 × 10−17 fractional laser frequency instability with a long room-temperature cavity
,” Opt. Lett.
40
(9
), 2112
–2115
(2015
).19.
T. P.
Heavner
, E. A.
Donley
, F.
Levi
, G.
Costanzo
, T. E.
Parker
, J. H.
Shirley
, N.
Ashby
, S.
Barlow
, and S. R.
Jefferts
, “First accuracy evaluation of NIST-F2
,” Metrologia
51
(3
), 174
(2014
).20.
N.
Hinkley
, J. A.
Sherman
, N. B.
Phillips
, M.
Schioppo
, N. D.
Lemke
, K.
Beloy
, M.
Pizzocaro
, C. W.
Oates
, and A. D.
Ludlow
, “An atomic clock with 10−18 instability
,” Science
341
(6151
), 1215
–1218
(2013
).21.
E.
Hogenauer
, “An economical class of digital filters for decimation and interpolation
,” IEEE Trans. Acoust., Speech, Signal Process.
29
(2
), 155
–162
(1981
).22.
J.
Jespersen
and J.
Fitz-Randolph
, From Sundials to Atomic Clocks: Understanding Time and Frequency
(Courier Corporation
, 1999
).23.
S. M.
Kay
, Modern Spectral Estimation: Theory and Application. 1988
(Prentice Hall
, 1999
).24.
T.
Kessler
, C.
Hagemann
, C.
Grebing
, T.
Legero
, U.
Sterr
, F.
Riehle
, M. J.
Martin
, L.
Chen
, and J.
Ye
, “A sub-40-mHz-linewidth laser based on a silicon single-crystal optical cavity
,” Nat. Photonics
6
(10
), 687
–692
(2012
).25.
G.
Paul Landis
, I.
Galysh
, and T.
Petsopoulos
, “A new digital phase measurement system
,” in 33rd Annual Precise Time and Time Interval (PTTI) Meeting
, Technical Report, DTIC Document,2001
.26.
J.
Levine
, “Invited review article: The statistical modeling of atomic clocks and the design of time scales
,” Rev. Sci. Instrum.
83
(2
), 021101
(2012
).27.
L.-S.
Ma
, P.
Jungner
, J.
Ye
, and J. L.
Hall
, “Delivering the same optical frequency at two places: Accurate cancellation of phase noise introduced by an optical fiber or other time-varying path
,” Opt. Lett.
19
(21
), 1777
–1779
(1994
).28.
J.
Mitola
, “The software radio architecture
,” Commun. Mag., IEEE
33
(5
), 26
–38
(1995
).29.
K.
Mochizuki
, M.
Uchino
, and T.
Morikawa
, “Frequency-stability measurement system using high-speed ADCs and digital signal processing
,” IEEE Trans. Instrum. Meas.
56
(5
), 1887
–1893
(2007
).30.
N. R.
Newbury
, “Searching for applications with a fine-tooth comb
,” Nat. Photonics
5
(4
), 186
–188
(2011
).31.
J.
Phillips
and K.
Kundert
, “Noise in mixers, oscillators, samplers, and logic an introduction to cyclostationary noise
,” in CICC. Proceedings of the IEEE 2000 Custom Integrated Circuits Conference
(IEEE
, 2000
), pp. 431
–438
.32.
N.
Poli
, C. W.
Oates
, P.
Gill
, and G. M.
Tino
, “Optical atomic clocks
,” Riv. Nuovo Cimento
36
(12
), 555
–624
(2013
).33.
W. H.
Press
, S. A.
Teukolsky
, W. T.
Vetterling
, and B. P.
Flannery
, Numerical Recipes in C
(Cambridge University Press
, 1996
), Vol. 2
.34.
I.
Prochazka
, P.
Panek
, and J.
Kodet
, “Note: Precise phase and frequency comparator based on direct phase-time measurements
,” Rev. Sci. Instrum.
85
(12
), 126110
(2014
).35.
W. J.
Riley
, “Handbook of frequency stability analysis
,” NIST Special Publication 1065 (U.S. Government Printing Office, Washington, DC, 2008).36.
S.
Römisch
, S. R
Jefferts
, and T. E.
Parker
, “A digital time scale at the National Institute for Standards and Technology
,” in General Assembly and Scientific Symposium, 2011 XXXth URSI
(IEEE
, 2011
), pp. 1
–4
.37.
E.
Rubiola
, “On the measurement of frequency and of its sample variance with high-resolution counters
,” Rev. Sci. Instrum.
76
(5
), 4703
(2005
).38.
E.
Rubiola
and F.
Vernotte
, “The cross-spectrum experimental method
,” e-print arXiv:1003.0113 (2010
).39.
L. B.
Ruppalt
, D. R.
McKinstry
, K. C.
Lauritzen
, A. K.
Wu
, S.
Phillips
, S. H.
Talisa
et al., “Simultaneous digital measurement of phase and amplitude noise
,” in IEEE International Frequency Control Symposium (FCS)
(IEEE
, 2010
), pp. 97
–102
.40.
L. C.
Sinclair
, I.
Coddington
, W. C.
Swann
, G. B.
Rieker
, A.
Hati
, K.
Iwakuni
, and N. R.
Newbury
, “Operation of an optically coherent frequency comb outside the metrology lab
,” Opt. Express
22
(6
), 6996
–7006
(2014
).41.
P.
Stoica
and R. L.
Moses
, Spectral Analysis of Signals
(Pearson/Prentice Hall Upper Saddle River
, New Jersey
, 2005
).42.
D. B.
Sullivan
, D. W.
Allan
, D. A.
Howe
, and F. L.
Walls
, “Characterization of clocks and oscillators
," in US Department of Commerce, National Institute of Standards and Technology
, NIST Technical Note 1337 (U.S. Government Printing Office, Washington, DC, 1990).43.
P.
Tavella
and C.
Thomas
, “Comparative study of time scale algorithms
,” Metrologia
28
(2
), 57
(1991
).44.
M.
Uchino
and K.
Mochizuki
, “Frequency stability measuring technique using digital signal processing
,” Electron. Commun. Jpn. (Part I: Commun.)
87
(1
), 21
–33
(2004
).45.
Th.
Udem
, R.
Holzwarth
, and T. W.
Hänsch
, “Optical frequency metrology
,” Nature
416
(6877
), 233
–237
(2002
).46.
I.
Ushijima
, M.
Takamoto
, M.
Das
, T.
Ohkubo
, and H.
Katori
, “Cryogenic optical lattice clocks
,” Nat. Photonics
9
(3
), 185
–189
(2015
).47.
J. E.
Volder
, “The CORDIC trigonometric computing technique
,” IRE Trans. Electron. Comput.
EC-8
(3
), 330
–334
(1959
).48.
L.
Šojdr
, J.
Čermák
, and R.
Barillet
, “Optimization of dual-mixer time-difference multiplier
,” in EFTF 2004. 18th European Frequency and Time Forum
(IET
, 2004
), pp. 588
–594
.49.
F. L.
Walls
and D. W.
Allan
, “Measurements of frequency stability
,” Proc. IEEE
74
(1
), 162
–168
(1986
).2016
U.S. Government
You do not currently have access to this content.
