NIST Special Publication 250-29

(supersedes 1988 edition)

Remote Frequency Calibrations:

The NIST Frequency Measurement and 

Analysis Service

Michael A. Lombardi

Time and Frequency Division

Physics Laboratory

National Institute of Standards and Technology

325 Broadway

Boulder, Colorado 80305

June 2004

U.S. Department of Commerce

Donald L. Evans, Secretary

Technology Administration

Phillip J. Bond, Under Secretary for Technology

National Institute of Standards and Technology

Arden L. Bement, Jr., Director
Certain commercial entities, equipment, or materials may be identified in this 

document in order to describe an experimental procedure or concept adequately. Such 

identification is not intended to imply recommendation or endorsement by the 

National Institute of Standards and Technology, nor is it intended to imply that the 

entities, materials, or equipment are necessarily the best available for the purpose. 

National Institute of Standards and Technology Special Publication 250-29 

Natl. Inst. Stand. Technol. Spec. Publ. 250-29, 88 pages (June 2004) 

CODEN: NSPUE2 
iii 

Contents 

Introduction v 

Acknowledgements vi 

Chapter 1. History and Physical Description 1 

 A. History of the FMAS 1 

 B. Facilities 7 

 1. Configuration of Remote FMS Units 9 

 C. Organizational Control of the FMAS 11 

Chapter 2. Technical Description 13 

 A. Technical Description of Hardware 13 

 1. Computer Systems and Storage Devices 14 

 2. Frequency Measurement Hardware 14 

 a) Time Interval Counter (TIC) 15 

 b) Frequency Dividers 20 

 c) Multiplexer 22 

 d) Advantages and Limitations of Time Interval Method 23 

 3. GPS Receiver 24 

 a) GPS Antenna 27 

 4. Printer 28 

 5. Uninterruptible Power Supply (UPS) 28 

 6. Equipment Rack 28 

 B. Technical Description of FMS Software 28 

 1. Operating System 28 

 2. Remote FMS Software used at Customer Sites 28 

 a) GPS Software 29 

 b) Initialization of Measurement Software 32 

 c) Sequence of Time Interval Measurements 34 

 d) Estimation of Frequency Offset 38 

 e) Graphing and Data Analysis Software 42 

 f) Frequency Stability Analysis Software 44 

 g) Diagnostic Software 47 

 3. Host Software used at NIST 47 

Chapter 3. Operational Procedures 49 

 A. Hardware Maintenance 49 

 1. Verification of the FMS prior to shipment 49 

 2. Verification of the FMS after shipment 52 

Contents
iv 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

 B. Software Maintenance 53 

 C. Customer Maintenance 53 

 D. Failure Modes 53 

 1. Hardware Failures 53 

 2. Software Failures 55 

 3. GPS Signal Failures 55 

 E. Record Keeping 56 

 1. Customer Information Files 56 

 2. Raw Measurement Data Files 56 

 3. Processed Measurement Data Files 57 

 F. Security Issues 57 

 G. Calibration Reports 58 

Chapter 4. Customers 67 

 A. Number and Location of Customers 67 

 B. How the FMAS is Used by its Customers 68 

 C. Customer Interaction and Technical Support 69 

 1. Web Page 70 

 2. Seminars 70 

Chapter 5. Measurement Uncertainties 71 

 A. Uncertainties of Measurements made with GPS 71 

 B. Uncertainties of Measurements made without GPS 74 

 C. Discussion of Uncertainty Statement on Calibration Report 75 

 D. Establishing Traceability to the SI through UTC(NIST) 77 

References 81 
v 

Introduction 

The National Institute of Standards and Technology (NIST) provides its Frequency 

Measurement and Analysis Service (FMAS) to paying customers on a subscription basis. 

Subscribers to the service receive a complete frequency measurement system (FMS) that they 

install in their facility.* The service can measure any frequency from 1 Hz to 120 MHz in 1 

Hz increments. As many as five devices can be measured and calibrated at once, even if all 

five have different output frequencies. The FMAS uses Global Positioning System (GPS) 

signals as its link back to the United States national frequency standard, the Coordinated 

Universal Time Scale maintained at NIST, called UTC(NIST). Since GPS can be received 

anywhere on the Earth’s surface, the service can potentially be provided anywhere on Earth 

where telephone service is available. All measurements are made automatically and are 

traceable to the International System of units (SI) through UTC(NIST) at an uncertainty (k = 2) 

of 2 × 10-13 for an averaging time of one day. 

The FMAS was designed to continuously measure and calibrate a customer’s primary 

frequency standard, 24 h per day, 7 days per week. This continuous measurement provides the 

customer with confidence that their primary frequency standard is operating properly, and that 

its frequency uncertainty is continuously known with respect to the national frequency 

standard. Unlike other calibration services that only periodically complete the traceability 

chain, the FMAS continuously establishes traceability by measuring and reporting on the 

primary frequency standard’s performance at all times. 

NIST regularly checks each system by telephone modem to insure proper operation and to 

obtain the measurement data. NIST verifies the data from each system and mails each 

subscriber a monthly calibration report that certifies that their primary frequency standard is 

traceable to the SI through UTC(NIST) at a stated measurement uncertainty. If an FMS part 

fails, it is replaced by NIST using an overnight delivery service. 

This booklet describes the FMAS in detail. It provides a physical and technical description of 

the service, describes its theory of operation and its measurement uncertainties, and explains 

how NIST provides and maintains the service for its customers. 

 

* Throughout this document, the acronym FMAS will be used to refer to the calibration service, and the 

acronym FMS will be used to refer to the measurement system provided to the customers of the 

service. 

Introduction
vi 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

Acknowledgements 

Special thanks are due to George Kamas, Andrew Novick, and Lisa Nelson. Kamas conceived 

the idea of a remote frequency calibration service, launched the service in 1984, and served as 

its project manager until his retirement in 1993, when he was replaced by the author. Novick 

has provided engineering and technical support for the service from 1998 to 2004, a role 

previously filled by Nelson from 1994 to 1998. Without their dedicated efforts, operation of 

the FMAS would not have been possible. 
1 

Chapter 1 - History and Physical Description 

The FMAS is a network of individual frequency measurement systems located at each of its 

customer’s laboratories, and connected by telephone lines to the NIST laboratories in Boulder, 

Colorado. Each individual system includes a GPS satellite receiver and antenna, a time 

interval counter, and a computer that controls the measurements. The data collected from all 

customer sites are stored and archived at NIST, and calibration reports are sent each month to 

every customer. Several master units are also maintained by NIST. The master units, which 

comprise the same hardware and software as the customer’s units, continuously compare the 

received GPS signals to the national frequency standard. In this way, NIST can continuously 

monitor the frequency uncertainty of each customer’s unit, and the uncertainty of their primary 

frequency standard. 

This chapter begins by providing a history of the FMAS. It then provides a physical 

description of the FMAS components and facilities. 

A. History of the FMAS 

The FMAS has its origins in contractual work performed by NIST (then called the National 

Bureau of Standards, or NBS) for the United States Air Force, specifically the Rome Air 

Development Center (RADC), during the period from about 1980 to 1983. The project was 

led by NBS engineer George Kamas. The RADC’s contractual requirements called for a 

frequency measurement system that was versatile enough to measure a variety of different 

inputs, transportable enough to work at a variety of different field sites, and flexible enough to 

be reconfigured by the operator. In addition, it should be microprocessor controlled, so that it 

could run continuously without operator attention [1]. 

From the beginning, the plan was for each measurement system to receive its frequency 

reference over the air, using a radio receiver as a transfer standard. GPS was not originally 

considered for use with the FMS because only a few satellites had been launched, and low cost 

GPS receivers would not be available for several years. NBS’s own 60 kHz broadcast from 

WWVB was briefly considered and then dismissed, due to the then high cost of a quality 

receiver and the fact that the single transmitter (then producing only 13 kW) failed to 

adequately cover the entire United States. The now defunct Omega navigation system (turned 

off in 1996) was also briefly considered but ruled out due to its relatively poor performance 

and the lack of available commercial receivers. As a result, it was decided that LORAN-C, the 

100 kHz radionavigation system, was the optimal choice. The multiple, high power 

transmitters in the LORAN-C system covered all of the United States. In addition, the stable 

ground wave signals were locked to atomic oscillators maintained at the transmitter sites, and 

therefore served as an excellent frequency reference. Although NBS did not control the 

LORAN-C signals, it had been continuously monitoring the signals for years by comparing 

Chapter 1 

History and Physical Description 
2 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

them to the national frequency standard, so their performance was well documented. The 

results of these LORAN-C comparisons were published monthly in the Time and Frequency 

Bulletin [2]. 

During the RADC effort, several different frequency measurement systems were designed by 

NBS. Two basic approaches were used. The first approach relied on commercial test 

equipment controlled over the IEEE-488 bus by a dedicated instrument controller and a 

commercially available LORAN-C disciplined oscillator. The total cost per system with this 

approach exceeded $30,000 (estimated 1984 cost). The second approach relied on low cost 

personal computers as the controller of custom instruments that were specifically designed for 

the single purpose of measuring frequency. The frequency reference was a LORAN-C 

navigation receiver designed for fishing boat navigation, but modified to output stable pulses 

from the master station of the nearest LORAN-C chain. After incurring some initial 

development costs, it was possible to build a system using the second approach for well under 

$10,000. This made it realistic for NBS to launch a measurement service on a cost recovery 

basis, whereas the cost of building multiple units using the first approach would have been 

prohibitive. Several systems were built and tested by both NBS and the RADC, and it was 

decided to offer these systems on a subscription or lease basis to other calibration laboratories. 

This proposed frequency measurement and calibration service was based on a unique concept. 

Instead of the customer sending their device under test to NBS for calibration, NBS would send 

a measurement system to the customer. This concept, often called a remote calibration, is 

seldom possible or practical in other fields of metrology, but was already commonplace in the 

field of time and frequency, where radio broadcasts of standard frequency and time interval had 

existed for decades. For example, NBS/NIST radio station WWV has continuously broadcast 

standard frequency signals since 1923 [3]. However, this new service went beyond simply 

providing a signal. NBS would provide the entire measurement system and automate the 

calibration procedure. In addition, NBS would obtain the data over a telephone link and issue a 

monthly calibration report to each customer, making it perhaps the first NBS calibration service 

to calibrate and certify a customer’s standard without actually handling the device. 

During 1983, the NBS Frequency Measurement Service was announced at both the Frequency 

Control Symposium [4], and the Precise Time and Time Interval Meeting [5], two established 

meetings attended by the time and frequency community. A measurement system was shipped 

to the service’s first customer (the Federal Aviation Administration) on January 19, 1984. The 

initial response to the service was favorable, and by the end of 1984, a total of 18 calibration 

laboratories had subscribed to the new service, and measurement systems had been delivered to 

each of them. 

The new service was reviewed at a regional meeting of the National Conference of Standards 

Laboratories (NCSL) by one of its first customers in the latter part of 1984 [6]. The customer’s 

review identified a number of problems with the first implementation of the measurement 

system, most related to software, reliability, and LORAN-C reception. Overall, however, the 

review was favorable. It noted the advantages of the FMS over the 60 kHz WWVB phase 
3 

Chapter 1 - History and Physical Description 

comparator that this particular customer had previously used as their frequency reference, and 

commented that “support from NBS is superb.” NBS personnel quickly moved to correct the 

problem areas, and by the time a report was given about the new service at the 1985 national 

meeting of the NCSL [7], most problems were resolved, and a smoothly operating, reliable 

service was in place. 

A photograph of the original FMS system is shown in Figure 1.1. The instrument controller 

was an early personal computer, the Apple IIe, with a 6502 microprocessor running at 1 MHz 

and 64 kilobytes of memory. The unit had low-resolution graphics capability that allowed it to 

display phase graphs of the collected data on screen and to print them on a dot-matrix printer 

for archival 

purposes. The 

system’s operating 

system and all of its 

software resided on 

one single sided 

floppy disk with a 

capacity of about 

124 kilobytes. A 

second floppy disk 

drive, with the same 

capacity, stored all 

of the collected 

data. The controller 

interfaced to a timeof-day clock, a 300 

baud modem that 

was used to 

communicate with 

NBS, and a time 

interval counter 

(TIC). The custom 

designed TIC was 

controlled through a 

bidirectional 

parallel interface. It 

included a built-in 

multiplexer that 

allowed switching 

between four 

different incoming 

start/stop signals, so 

that different 

frequency sources 

Figure 1.1. The original FMS (1984).
4 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

could be selected and measured simultaneously, a feature still included in current FMS units. 

The TIC multiplied its incoming external time base signal up to 100 MHz, and then measured 

time interval by simply counting zero crossings of the time base while the gate was open. 

Resolution was thus limited to 10 ns, the period of the time base frequency. 

The original FMS contained two other instruments not under computer control. The first was 

the LORAN-C receiver that served as the frequency reference. The receiver was controlled by 

the operator through the front panel, although operation was essentially automatic after the 

initial installation. The receiver was connected to a 2.4 m tall fiberglass whip antenna. Since 

the incoming signal was at 100 kHz, signal loss was small, permitting long lengths of RG-58 

antenna cables (sometimes more than 100 m) to be used as the antenna download. The receiver 

output Group Repetition Interval (GRI) pulses to the TIC. The GRI is the interval between 

LORAN-C pulse groups. Depending upon the station being tracked, the GRI ranged from 49.9 

to 99.9 ms, producing an odd rate frequency ranging from about 10 Hz to about 20 Hz. The 

customer’s primary frequency standard was divided to match this frequency using the second 

instrument not under computer control, a frequency divider. The divider was configured by the 

operator using several different switches. In addition to producing the LORAN-C GRI 

frequency, the divider could accept several 1, 5, or 10 MHz inputs signals and divide them to 1 

Hz [8, 9]. The measurement uncertainty of the service was originally quoted as < 1 × 10-11 (at 

an averaging time of 1 day) using LORAN-C as a reference [5], and later reduced to 1 × 10-12

[9]. 

Throughout the 1980’s, new features were added to the basic FMS design, most of them at the 

request of customers. The customer base continued to increase, with about half of the units 

located at United States military installations. The service had 40 subscribers for the first time 

in 1987 and briefly rose to an all-time high of 60 customers in 1991. At this time a large 

number of military bases began to close, resulting in the loss of more than two-thirds of the 

military customers. Although a number of private industry customers were added, the total 

number of customers dropped back into the 40 to 50 range, an area where it remains in 2004. 

The second generation FMS unit (Figure 1.2) debuted in about 1990 [10]. LORAN-C was still 

used as the reference frequency, but a smaller, better performing receiver was used. The TIC 

and the frequency dividers were integrated into one box, and shortly afterwards on to a single 

expansion card, but the counter resolution was still limited to 10 ns. Modem speed was 

increased to 2400 baud. The software was ported from the Apple IIe to a PC-compatible 

platform and was made much more interactive and powerful, providing better graphics and data 

analysis features. As a result, the service’s name was changed from “Frequency Measurement 

Service” to “Frequency Measurement and Analysis Service,” so both the service and the 

agency now had new names (NBS had become NIST in 1988). 

 

Throughout the 1980’s, the attention of the time and frequency community had begun shifting 

away from LORAN-C and towards the Global Positioning System (GPS), an orbiting 

constellation of satellites that each carried atomic oscillators. The first experimental GPS 

satellite was successfully launched in 1978, GPS signals were routinely used by NBS for time 
5 

Chapter 1 - History and Physical Description 

and frequency 

comparisons by 1980 [11], 

and NBS had launched a 

GPS-based time service, 

called the Global Time 

Service, at about the same 

time the FMAS began in 

1984 [4]. GPS 

performance was superior 

to that of LORAN-C, the 

signals were easy to 

receive, and the coverage 

area was essentially 

worldwide. 

There were several 

reasons, however, that 

prevented the FMAS from 

quickly shifting away 

from LORAN-C and to 

GPS. One was that the 

FMAS was based on 

continuous measurement 

of the customer’s 

frequency standard, 24 h 

per day, 7 days per week. 

Until a sufficient number 

of GPS satellites were 

launched, there would be 

intervals when no 

satellites were in view, and 

when no measurement data 

could be collected. This was the situation in the early to mid-1980’s, and it was not until 

March 1994 that the entire constellation of 24 orbiting satellites was in place. A second reason 

was that early GPS receivers and antennas were much more expensive than the LORAN-C 

equipment being used, too expensive to use without substantially raising the subscription price 

of the FMAS. A third reason was that the United States Department of Defense (DoD) had 

classified GPS as an experimental system for military use. Consumer GPS products appeared 

throughout the 1980’s, but GPS was not completely accepted as a frequency reference by nonmilitary calibration laboratories until it was declared operational for civilian use. Initial 

Operational Capability (IOC) was formally declared by the DoD and the Department of 

Transportation (DoT) on December 8, 1993. Prior to IOC, GPS was considered a 

developmental system whose operation, including signal availability and accuracy, was subject 

to change at the discretion of the DoD [12]. 

Figure 1.2. The second generation FMS (1990).
6 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

By the time IOC for GPS was declared, work was underway on the third generation FMAS 

system, this one based on GPS. The first GPS unit was shipped by NIST in November 1994. 

While all new subscribers to the FMAS received a GPS based system, it was four years 

(November 1998) before the 

last LORAN-C system had 

been replaced with the new 

GPS units. The new GPS unit 

(see Figure 1.3) included many 

new features included a fivechannel GPS receiver. A new 

TIC with integrated frequency 

dividers was developed with a 

resolution of < 30 ps, an 

improvement of more than 

three orders of magnitude over 

the previously used counter 

[13]. Other new features 

included the capability to store 

and record short term 

measurements and produce 

Allan deviation graphs, faster 

data transfer to NIST (14.4 

kilobits/s), increased data 

storage capacity, and improved 

graphics [14, 15]. The 

measurement uncertainty (at k 

= 2) was reduced by a factor of 

two, to 5 × 10-13 for an 

averaging time of one day. 

The fourth generation FMS 

system (Figure 1.4) was 

introduced in 2000. With 

minor revisions, it is still the 

unit being provided by the 

FMAS at this writing (2004). 

The unit’s key new feature was a new time interval counter card with an integrated eightchannel GPS receiver [16]. The counter’s resolution and stability were identical to the previous 

TIC, but it included programmable frequency dividers. The third generation system had been 

limited to measuring frequencies of 1, 2, 2.5, 5, and 10 MHz. The programmable frequency 

dividers allowed the measurement of any frequency from 1 Hz to 120 MHz that was an even 

multiple of 1 Hz. This allowed the calibration of frequency sources used in telecommunication 

systems (1.544, 2.048, 44.736 MHz, for example), as well as specialized frequencies used in 

other industries [17]. The eight-channel receiver produced uncertainties slightly lower than 

Figure 1.3. The third generation FMS (1994).
7 

Chapter 1 - History and Physical Description 

those of the earlier five-channel version, and when the GPS system deactivated its selective 

availability program in May 2000 [18], the measurement uncertainty was further reduced to its 

current specification of 2 × 10-13. A complete technical description of this fourth generation 

FMS is provided in Chapter 2. 

Table 1.1 summarizes 

the features of the 

four generations of 

frequency 

measurement systems 

provided to 

customers by the 

FMAS. Note that the 

monthly service fee 

for the service has 

remained the same 

from 1990 to 2004. 

B. Facilities 

Since the FMAS is a 

remote calibration 

service, the actual 

measurements take 

place in the 

customer’s 

laboratory. However, 

the NIST Time and 

Frequency Division maintains areas designated as FMAS facilities, including a laboratory where 

GPS is continuously compared to UTC(NIST), a work area where new FMS units are assembled 

and tested, a storage room where an inventory of spare parts is maintained, and office space 

where billing and calibration records are maintained (Chapter 3.D). In addition, NIST maintains 

several FMS units in non-FMAS facilities, including units at radio stations WWV and WWVH. 

The FMAS laboratory is connected by coaxial cable to the UTC(NIST) time scale, receiving 

both 5 MHz and 1 pulse per second (pps) signals. Inside the FMAS laboratory, the 5 MHz 

signal is distributed using three 5-channel low-noise distribution amplifiers. The 1 pps signal is 

distributed using two 5-channel low-noise distribution amplifiers. The delay in the incoming 1 

pps signal has been calibrated and is known to be 375 ns with respect to UTC(NIST). 

Therefore, it is used as an absolute timing reference for GPS comparisons. 

Three GPS antennas, with their absolute position surveyed to an uncertainty of < 1 m, are 

located on the rooftop above the FMAS laboratory. The incoming 1575.42 MHz GPS L1 

signals are distributed within the laboratory by three antenna splitters. One is an eight-channel 

splitter with its own power supply, the other two are four-channel splitters powered by a DC 

voltage from one of the connected receivers. 

Figure 1.3. The fourth generation FMS (1994).
8 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

Maintaining a tightly controlled laboratory environment is not critical for the FMAS operation. 

The GPS receivers embedded inside the FMS are not particularly sensitive to temperature. 

Receiver delays can change by several nanoseconds or more (a frequency change of a few parts 

in 1014 over the course of a day) if large temperature fluctuations occur, but receiver delays will 

remain constant as long as the temperature remains constant [19]. Large receiver temperature 

fluctuations normally don’t occur, since the GPS receiver is enclosed in a case that maintains a 

nearly constant internal temperature. Even so, the temperature of the FMAS laboratory is 

continuously recorded, and average temperature is held near 24° C, with peak-to-peak variations 

of about 2° C, representing a fairly typical calibration laboratory environment. 

The FMAS work area includes a work bench with several cabinets containing tools and the 

hardware, cables, and miscellaneous parts needed for assembly. Standard laboratory test 

equipment including oscilloscopes, frequency counters, and signal generators are available in the 

work area and used for testing FMS units. Although functional tests are regularly performed on 

the test equipment, they do not need to be regularly calibrated, since the national frequency 

standard is used as the external time base frequency for all devices. 

The storage area contains the spare parts for the FMAS, including the larger parts such as rack 

chassis and equipment racks. When FMS units are returned by customers, they are moved to 

Feature 1st Generation 2nd Generation 3rd Generation 4rth Generation 

Year introduced 1984 1990 1994 2000 

Reference signal LORAN-C LORAN-C GPS GPS 

Measurement 

channels 

4 4 5 5 

TIC resolution 10 ns 10 ns < 30 ps < 30 ps 

Input 

frequencies 

1 pps 

1, 5, 10 MHz 

1, 2, 2.5, 5, or 10 

MHz 

1, 2, 2.5, 5, or 10 

MHz 

1 Hz to 120 MHz 

in 1 Hz steps 

Interactive data 

analysis 

software 

No No Yes Yes 

Data transfer 

to NBS/NIST 

(bits/s) 

300 2400 14400 14400 

Monthly service 

cost 

$300 $500 $500 $500 

Measurement 

uncertainty 

(1 d average) 

< 1 × 10-11 1 × 10-12 5 × 10-13 2 × 10-13

Table 1.1. A feature summary of the FMS units provided by NBS/NIST. 
9 

Chapter 1 - History and Physical Description 

this storage area. Parts that are determined to be in complete working order and that are still 

cosmetically acceptable are returned to inventory and sent to other customers. The other parts 

are disposed of or held in the storage area until they are picked up and removed by the NIST 

surplus property department. 

1. Configuration of Remote FMS Units 

One goal of the FMAS is to provide an identical FMS unit to each customer. This is desirable 

for two reasons. First, it is imperative that data are collected in the same way at all sites so that 

the assigned measurement uncertainties at each site are equivalent. Second, it is easier for NIST 

to stock replacement parts if all units use identical parts. Unfortunately, some commercially 

available parts of the FMS (particularly the computer parts) have very short product life cycles. 

For example, it is usually impossible to purchase the exact same model of printer that was 

purchased one year ago. For this reason, NIST attempts to procure multiple items at one time, 

and maintain an inventory of spare parts, although resources seldom permit “stockpiling” a large 

number of spares. When the inventory is depleted, an attempt is made to procure a functionally 

equivalent part (plug, pin, and software compatible) if the identical part is no longer available. 

The FMS units are shipped to the customer already assembled. To avoid damage, they are 

shipped in wooden crates by the NIST shipping and receiving department. The customer is 

responsible for mounting the GPS antenna, connecting cables, and so on, using procedures that 

are clearly explained in the Operator’s Manual [20] provided with each unit. Table 1.2 lists the 

items included in each shipment of the FMS unit which is pictured in Figure 1.4. 

Table 1.2. Items included in the FMS unit shipped to customers.

Item Description 

Equipment Rack Standard 19” (48.3 cm) equipment rack with side mounted 

carrying handles, 12.25” (31.1 cm) of interior rack space. 

Rack Mount Computer Chassis Includes 300 W power supply, 8-slot passive backplane 

with Personal Computer Interface (PCI) and Industry Standard Architecture (ISA) card slots, 10” (25.4 cm) LCD 

color video monitor, 3.5” (8.9 cm) floppy disk drive, internal cooling fans, bulkhead connectors mounted on rear 

panel (5 BNC connectors for input frequencies, 1 TNC connector for GPS antenna). 

Rack Mount Keyboard Sliding shelf keyboard, standard PC layout. 

Single Board Computer Includes 486 microprocessor or equivalent running at 66 

MHz or faster, 4 megabytes of RAM, ISA bus card edge 

connector, watchdog timer, RS-232, keyboard, speaker, and 

parallel printer interfaces. 
10 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

Item Description 

Solid State Flash Memory Disk 16 megabyte or higher capacity with embedded ROM-DOS 

operating system. Measurement software is preinstalled. 

 

Video Card Compatible with minimum requirements of VGA standard, 640 

× 480 resolution, 16 colors. 

 

Modem 14.4 kilobit per second modem (V.32 standard), compatible 

with existing software. 

 

Time Interval Counter Custom designed counter with 8-channel multiplexer, 24-bit 

frequency dividers, 30 ps resolution. Accepts 1, 5, or 10 MHz 

external time base signal, provides RS-232 interface for GPS 

receiver [16]. 

 

GPS Receiver Motorola Oncore 8-channel parallel tracking GPS receiver 

(mounts on time interval counter card). 

 

GPS Antenna Active GPS antenna with > 30 dB gain, mounting hardware, 

and cable. The cable is made to customer’s specification. Total signal loss on cable should not exceed 20 dB for the GPS 

L1 carrier frequency of 1575.42 MHz. Various types of coaxial cable are used to meet this requirement. 

 

Uninterruptible Power Supply 

(UPS) 

500 VA supply with four AC outlets. 

 

BNC Cables BNC to BNC cables provided for all 5 measurement channels. 

 

Printer and Supplies Inkjet printer with spare ink cartridges, printer cable, and paper. Must be compatible with Hewlett-Packard Deskjet graphics modes. 

 

Documentation NIST Frequency Measurement and Analysis System: Operator’s Manual [20]. 
11 

Chapter 1 - History and Physical Description 

C. Organizational Control of the FMAS 

The FMAS is managed, controlled, and maintained by the Services Group of the NIST Time and 

Frequency Division. The Group Leader of the Services Group reports to the Division Chief of 

the Time and Frequency Division, who in turn reports to the Director of the NIST Physics 

Laboratory. The Physics Laboratory is one of the seven operational units of NIST, which is an 

agency of the United States Department of Commerce. 
12 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

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13 

Chapter 2 - Technical Description 

This chapter describes the technical operation of the FMAS, including a discussion of the 

theory of operation and the specific hardware and software used to implement the service. 

A. Technical Description of Hardware 

The FMS blends commercially available equipment with hardware and software developed at 

NIST. Each piece of equipment was carefully chosen and designed to meet the measurement 

uncertainty requirements of the most demanding calibrations performed by our customers, but 

also to be inexpensive enough so that NIST can continually build, test, and replace FMS units, 

and still stay within its budgetary constraints. This section describes the hardware 

specifications and the theory of operation of each component. Figure 2.1 is a block diagram of 

the complete system. 

Chapter 2 

Technical Description 

Figure 1. Block diagram of the FMS. 
14 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

1. Computer System and Storage Devices 

The FMS computer and measurement hardware are enclosed inside a standard 19 in (48.3 cm) 

rack-mount equipment chassis with a 300 W power supply. The chassis includes internal 

cooling fans, and was designed for industrial and instrument control applications, where the 

computer is never turned off. The chassis houses a 10.4 in (26.4 cm) LCD color video monitor 

and a 3.5 in (8.9 cm) floppy disk drive on its front panel. The rear panel includes a number of 

bulkhead connectors (at least five BNC connectors for input frequencies, one TNC connector 

for the GPS antenna). Some FMS units have unused BNC connectors that allow future 

enhancements to be added. 

The single-board computer is mounted on an eight-slot passive backplane, containing both 

Industry Standard Architecture (ISA) and Personal Computer Interface (PCI) card slots. The 

passive backplane is also used to interface to the time interval counter and other peripheral 

cards. The computer includes a 486 microprocessor or equivalent running at 66 MHz or faster, 

4 megabytes of RAM, an ISA bus card edge connector, RS-232, keyboard, speaker, and 

parallel printer interfaces, and a watchdog timer. Data are stored on a solid-state flash disk 

with a capacity of 16 megabytes or higher. On some units this flash disk is integrated with the 

single board computer; on other units it resides on a separate bus card. The video interface 

(either integrated or on a separate card) is compatible with the minimum requirements of the 

VGA standard, supporting 640 × 480 resolution and 16 colors. The computer communicates 

with NIST via ordinary phone lines, using an analog 14.4 kilobit per second modem compatible 

with the V.32 standard. 

 

2. Frequency Measurement Hardware 

When FMS development began in the early 1980’s, there were already a number of established 

methods used by calibration laboratories to measure frequency using existing test equipment, 

nicely summarized and described by Kamas in the 1977 and 1979 editions of the Time and 

Frequency User’s Manual [21, 22] and by others [23-25]. The time interval method, or using a 

time interval counter (TIC) to make phase comparisons between a standard reference signal 

and an unknown signal, was chosen for the FMS. The time interval method had several 

advantages over alternative methods: it was relatively easy to automate; with a reasonable 

amount of averaging it was possible to make high resolution measurements and detect very 

small frequency changes; and a single measurement system (with the appropriate frequency 

dividers) could measure a wide range of frequencies, covering everything from timing pulses to 

the standard frequencies distributed by laboratories. 

A block diagram of a typical time interval measurement system is shown in Figure 2.2. Two 

signals, one from the device under test (DUT) and one from a reference, provide input to the 

TIC. Both signals are divided to 1 Hz. A signal from an external oscillator is provided to the 

TIC for use as its time base. Data collected by the TIC are output to a computer, where they 

are stored and analyzed. The following sections provide a more detailed look at the specific 

TIC, frequency dividers, and data handling process used by the FMS. 

 
15 

Chapter 2 - Technical Description 

a) Time Interval Counter (TIC) 

All TICs provide inputs for a start pulse and a stop pulse. The start pulse gates the TIC to start 

counting, and a stop pulse stops the counting. While the gate is open (Figure 2.3), the counter 

counts zero crossings from time base oscillator cycles. The resolution of the simplest TICs is 

equivalent to the period of a time base cycle, for example, 100 ns for a 10 MHz time base [26]. 

However, many TICs use interpolation schemes to divide the cycle period into smaller parts to 

obtain higher resolution. 

The FMS TIC is able to divide the 100 ns period into about 4000 parts to allow resolution near 

25 ps. This is done by using three counters inside the TIC circuitry: the main counter, the start 

interpolator counter, and the stop interpolator counter. The main counter provides the coarse 

resolution (100 ns), and the start and stop interpolator counters provide the fine resolution (< 

30 ps). The main counter is a 24-bit device that counts the zero crossings of the 10 MHz time 

base frequency. The values read from the 16-bit start and stop counters are used to determine 

where the start and stop pulses are located between successive time base zero crossings. The 

start interpolator counter measures the time interval between the start pulse and the first zero 

crossing from the time base, δt1. The stop interpolator counter measures the interval between 

the last zero crossing from the time base and the stop pulse, δt2. 

The interpolators consist of two integrators (A and B), a delay cell, a voltage comparator, and a 

16-bit digital counter. The integrators are charged with a constant current IREF. Using the start 

interpolator as an example, the delay cell introduces a delay equal to δt1 + T, where T = 100 ns 

and δt1 < 100 ns for the 10 MHz time base oscillator. This manipulation of the integrators and 

delay cell is done to scale, or magnify, δt1 into a larger time interval. The digital counter, in 

combination with the 10 MHz time base, is used to estimate the scaled δt1. 

Figure 2.2. A time interval measurement system. 
16 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

When the start pulse arrives, the charging current IREF is sent to integrator A, and the digital 

counter begins counting periods of the 10 MHz time base. The charging current is sent to 

integrator A for the period of δt1 + T, and then switched to integrator B. The voltage 

developed on integrator A, VA is held as reference voltage for the comparator while integrator 

B is being charged to a voltage of VB. When VB > VA, the comparator blocks the connection 

between the 10 MHz time base and the digital counter. The scaling factor for the interpolator, 

K, is determined as 

 , (1) 

 where CA and CB (CA < CB) are the ramping capacitances used in integrators A and B. 

The reading obtained from the start interpolator counter, Nstart, equals the number of 10 MHz 

pulses counted, and is linearly proportional to the time interval of δt1. The relationship 

between δt1 and Nstart can be expressed by the linear equation 

, (2) 

= − +1

C

C K

A

B

δ t1 = A⋅Nstart + B

Figure 2.3. Counting time base cycles. 
17 

Chapter 2 - Technical Description 

where the slope A and the intercept B are determined during the interpolator calibration. 

During the calibration, a series of readings is taken from the start interpolator counter and 

maximum and minimum values STmax and STmin are obtained by slewing the phase of a test 

signal with respect to the 10 MHz time base to simulate the range of possible values for δt1. 

Because the lowest possible reading from the start interpolator counter corresponds to δt1 = 0, 

and the maximum possible reading corresponds to δt1 = T, the slope and intercept of the 

interpolation are calculated as 

 , (3) 

 , (4) 

 

 Therefore, 

 , (5) 

 Because 

 , (6) 

the resolution of the interpolator counter is equal to T/K [13]. Using the time base and 

capacitance values used by the FMS TIC, where T = 100 ns, CA = 100 pF, and CB = 0.47 μF, 

the maximum possible resolution is about 21 ps 

 , (7) 

Obtaining 21 ps resolution would require the calibration software to sample Nstart across an 

optimal range where the difference between the maximum value and minimum value of δt1

would reach its theoretical limit of 4700 counts. In practice, it is not possible to sample the 

entire range, so the range is typically about 4000 counts. This results in TIC resolution (T / 

4000 counts) of approximately 25 ps. 

ST ST

T A

max − min

=

ST ST

ST T B

max min

min

−

⋅ =

ST ST

N ST t N start A start B

max min

min

1 −

− δ = ⋅ + =

ST ST

C

C K

A

B

max min = − +1 = −

12

9

21 10

4701

100 10

1

−

−

= ×

× =

+

C

C

A

B

T
18 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

The stop interpolator performs a nearly identical function as the start interpolator, except that it 

estimates the interval of T − δt2. Because of this, the main digital counter counts one more 

time base zero crossing after the arrival of the stop pulse [13]. 

The FMS TIC is calibrated once every 24 h using a two-part software algorithm. The first part 

calibrates the start and stop interpolator counters as described above. The second part of the 

calibration determines the differential path delay in the counter circuitry. The delay 

measurement is made by dividing the 10 MHz time base frequency by 256 to obtain a 

frequency of 39062.5 Hz and then supplying this frequency to both the start and stop inputs of 

the counter. The period of this frequency is 25600 ns. A series of time interval measurements 

are made, and the variation from the expected answer is computed. This variation indicates the 

counter delay, which is typically less than 1 ns. As long as this delay remains constant, it has 

no effect on the frequency measurement results. 

During the counter calibration, five values are obtained: the maximum values of the start and 

stop interpolator counters (STmax and SPmax), the minimum values of the start and stop 

interpolator counters (STmin and SPmin), and the counter delay (D). During a measurement, all 

three counters are read and three values are obtained: the main counter reading (Nmain), the start 

interpolator reading (Nstart), and the stop interpolator counter reading (Nstop). Equation 8 shows 

how these values are combined to produce a single counter reading (TICR). Note that T

represents the period of the time base frequency, which is a constant of 100 ns [13, 16]. 

 , (8) 

The resolution of the FMS TIC contributes measurement uncertainties of a few parts in 1011

over a 1 s interval, often averaging down to parts in 1015 after a few hours. Since these 

uncertainties are so low, the TIC resolution contributes no discernible uncertainty to 

measurements made over a 1 d interval. 

The uncertainty of TIC measurements is, however, potentially limited by factors other than 

resolution, including count ambiguity, trigger uncertainty, or time base uncertainty [26, 27]. 

Like most test instruments, a TIC generally has a +1 count or –1 count ambiguity in the least 

significant digit of its readout, contributing a resolution uncertainty to the measurement. 

However, since the FMS averages multiple readings, and since the count ambiguity is nearly 

random, this ±1 count error normally averages down to an insignificant level. 

Trigger uncertainty is a potentially more significant problem. It occurs when the TIC does not 

trigger at the expected voltage level on the input signal. Trigger uncertainty can be caused by 

incorrectly set trigger levels, or by input signals that are noisy, too large, or too small. Figure 

2.4 illustrates that while triggering is desired on point a, noisy signals can cause triggering on 

points b or c [26]. If clean input signals are provided by the customer, the FMS TIC eliminates 

most of the triggering problem with pulse shaping circuitry that converts the incoming signals 

D

SP SP

N T

ST ST

N T

TIC N T start stop

R main − − − − = + max min max min
19 

Chapter 2 - Technical Description 

on both sides of the counter to a nearly identical shape and amplitude. There are no user 

adjustable trigger levels, although the TIC software is preconfigured to expect either a 

sinusoidal or a square wave signal. It is still possible for the customer to introduce errors, 

however, by over driving or under driving the TIC. In order for the automated trigger level 

setting to function properly, the incoming signals must have a peak-to-peak amplitude in the 

200 mV to 3.5 V range at 50 W [20], and attenuators or amplifiers are sometimes needed to 

meet this requirement. 

Time base uncertainty is not an issue because the FMS uses the customer’s best available 

frequency standard as its external time base source. The FMS TIC uses a phase locked loop 

(PLL) circuit that locks a low cost 10 MHz crystal oscillator to either a 1, 5, or 10 MHz signal 

Figure 2.4. TIC trigger uncertainty due to noise. 
20 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

from the customer’s primary frequency standard. Typically, the customer has a stable 

frequency standard, with a frequency stability at 1 s no worse than 1 × 10-10, and often one or 

two orders of magnitude better. When 1 Hz pulses are used to start and stop the counter, the 

average time interval measured is 0.5 s, therefore the time base uncertainty is 0.5 s / 1010 = 5 ×

10-11 s, or 50 ps, which is roughly equivalent to the uncertainty contributed by the TIC’s ±1 

count ambiguity, and which will be negligible after it is averaged over multiple readings. It 

should be noted, however, that the frequency offset of the time base oscillator does introduce 

an uncertainty in the absolute accuracy of each individual time interval reading (TICR). 

However, since frequency is measured by looking at the difference between time interval 

readings (TICR2 − TICR1) over the measurement period, this uncertainty cancels out and 

becomes insignificant, since the time base contributes a nearly equal amount of uncertainty to 

each TIC reading. 

b) Frequency Dividers 

If standard oscillator frequencies such as 5 or 10 MHz are to be measured using a TIC, they 

first must be divided down to a lower frequency (Figure 2.2). There are least two reasons why 

frequency division is necessary. The first reason is that there is a limit to how fast the TIC can 

process and store measurements, sometimes called its sampling rate. The sample rate is limited 

by several factors including dead time, display time, data transfer time, and data processing 

time. Dead time refers to the delay that elapses between the completion of one reading (the 

arrival of a stop pulse) and the beginning of the next reading (the acceptance of the next start 

pulse). If the frequency of the input signals is too high, some information will be lost as a 

result of dead time [26]. For example, a TIC with a dead time specification of 200 ns would 

miss 50 % of the zero crossing if 10 MHz signals were connected to the start and stop inputs, 

since new zero crossings would arrive every 100 ns. In the case of the FMS TIC, the actual 

sampling rate is limited by the time interval interpolation scheme described earlier. If we make 

the assumption that the start and stop interpolator counters have the same scaling factor, then 

STmax = SPmax. Because it takes an interval of STmax × T to complete an interpolation, the 

maximum sampling rate, SRmax would equal 

 , (9) 

Using a value of 4700 for STmax, the maximum sample rate is approximately 2128 Hz, and 2 

kHz has been specified as the highest allowable input frequency that the TIC can sample 

without dead time [13]. 

The second reason for dividing down to a low frequency is to reduce the number of counter 

overflows and underflows. The maximum time interval recorded by the TIC is equal to the 

period of the stop frequency. Using once again the 10 MHz example, the maximum time 

interval recorded would be 100 ns. This would mean that each time the DUT had an 

accumulated phase change greater than 100 ns, the TIC reading would either overflow (go from 

100 back to 0), or underflow (go from 0 back to 100). In order to estimate the frequency offset, 

ST T SR ⋅ =

max

max

1
21 

Chapter 2 - Technical Description 

the software controlling the counter would have to keep track and correct for all the overflows 

and underflows. This could be a difficult task with some low performance oscillators; for 

example a DUT with a frequency offset of 1 × 10-6 would force, on average, 10 overflows or 

underflows every second. It also should be noted that the TIC can produce erroneous readings 

if the interval between the arrival of the start and stop pulses is too small. The FMS counter 

can measure a minimum interval of about 2 ns (the approximate delay in 40 cm of coaxial 

cable). If frequent overflows and underflows are allowed, a situation is likely to be reached 

where the interval between the two input signals is too small to measure, forcing the TIC into 

producing an erroneous reading. 

Like the system shown in Figure 2.2, most TIC systems used for frequency measurements 

divide the incoming signals to 1 Hz. However, a higher common frequency can be used. For 

example, the second and third generation FMS units described in Chapter 1 divided the 

incoming signals by 1000, stopping all counts with a 10 kHz reference signal obtained from the 

time base. This scheme was convenient, because it used nonprogrammable circuits embedded 

in the counter that did not require any software configuration. However, the maximum TIC 

reading was limited to 100 μs, the period of 10 kHz, so the software had to account for frequent 

overflows and underflows when measuring some DUTs. Also, the system could only measure 

frequencies whose period divided by 1000 equaled an even multiple of 100 μs, limiting the 

allowable inputs to 1, 2, 2.5, 5, and 10 MHz. 

The current FMS unit (Figure 2.1) includes programmable frequency dividers. The dividers 

are circuits that simply count and block n − 1 cycles of the incoming frequency, where n is the 

nominal frequency in hertz. For example, to divide 1 kHz to 1 Hz, 999 cycles of the incoming 

frequency are counted and blocked and every 1000th cycle is allowed to pass through. The 

FMS dividers use 24-bit counters, meaning that they can count frequencies as high as 224 Hz, or 

16.777 MHz. All incoming signals pass through a divide by 10 prescaler before reaching the 

divider circuit. If the incoming frequency is known to be 15 MHz or higher (configured by the 

customer in software), this prescaler is turned on; otherwise it is disabled. The signal then 

passes through to the 24-bit divider, where it is reduced to 1 Hz. If the incoming signal is 

specified by the customer as 1 Hz, the 24-bit divider is disabled in software. This allows nonsinusoidal timing pulses to be measured. 

In theory, the FMS can measure incoming signals as high as 167.77 MHz (Figure 2.5), since 

the combination of the prescaler and 24-bit divider could reduce this frequency to 1 Hz. 

However, due to potential problems of noise and crosstalk between adjacent counter channels 

(and no current customer demand for the measurement of frequencies in the 120 to 167.77 

MHz range), the upper range of the FMS has been specified as 120 MHz. 
22 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

c) Multiplexer 

Since the inception of the service, all FMS units have included multiplexer circuitry that allows 

the selection of different signals as the input to the time interval counter. The multiplexer is 

activated each time a new measurement channel is selected, and the channels are then read in 

sequence from the lowest number channel to the highest. This allows multiple frequency 

sources to be measured at the same time, a key feature in reducing the workload for calibration 

laboratories. 

Figure 2.5. Block diagram of the FMS TIC.
23 

Chapter 2 - Technical Description 

The current FMS TIC actually has two multiplexers. One allows the selecting between any of 

eight frequency inputs as shown in Figure 2.5, but only five inputs are activated in the current 

software. Each of these eight inputs includes a 24-bit programmable divider, and can be any 

frequency from 1 Hz to 120 MHz. The other multiplexer allows selection between four inputs: 

a 1 pps output from the GPS receiver, 1 pps obtained by dividing the time base PLL, or two 

external 1 pps signals (only one of these is selectable with the current software). 

Gold-plated SMA connectors are used for the eight frequency inputs and the time base input, as 

shown in the photo in Figure 2.6. Molex connectors are used for the two external 1 pps signals. 

The 1 pps output from the GPS receiver is directly obtained from a 10-pin connector on the 

receiver itself. 

d) Advantages and Limitations of Time Interval Method 

The time interval method employed by the FMS is very versatile, and has many advantages, 

including low cost, simple design, and excellent performance when measuring long term 

frequency accuracy or stability. The method has a much lower noise floor than the GPS 

reference frequency, and normally contributes no discernible uncertainty to calibrations lasting 

for 1 h or longer. This is evidenced by the fact that the Bureau International des Poids et 

Mesures (BIPM) produces its computation of the UTC time scale using data collected with 

TICs. In addition, the wide bandwidth of the time interval method allows the FMS to measure 

devices with frequency offsets ranging from 1 × 10-5 to less than 1 × 10-13 over a 1 d period, a 

range of approximately eight orders of magnitude. For a 10 MHz DUT, this means that the 

FMS can report frequency offsets as large as 100 Hz, or smaller than 1 μHz, allowing 

calibration of just about any type of instrument that a calibration laboratory is likely to 

encounter. 

Figure 2.6. Photograph of the FMS TIC. 
24 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

The main disadvantage of the time interval method is that it lacks the resolution to accurately 

measure frequency or to estimate short term stability at averaging times of less than about 100 

s. Calibration laboratories that need to measure the short term stability of oscillators generally 

use a system where the signal from the device under test is converted to a lower frequency by 

use of a heterodyne technique that mixes, rather than divides, the signal [28, 29]. The 

heterodyne technique increases the measurement resolution (often by a factor of 100 or more) 

and decreases the measurement noise. However, several things are lost with the heterodyne 

technique, such as the ability to measure 1 pps timing signals or other low frequency pulses, the 

ability to measure a wide range of frequencies, or in some cases, the ability to measure devices 

that have a large frequency offset from their nominal value. 

3. GPS Receiver 

The FMS uses the Motorola Oncore UT+ GPS receiver with firmware version 3.2. Motorola 

Oncore receivers have been used by numerous laboratories for time and frequency metrology 

applications [30 – 33]. The small receiver (50.8 × 82.6 × 16.3 mm) mounts directly on the TIC 

card [16], which provides the 5 V DC needed to power the device. The TIC card also supplies 

the necessary line drivers needed to convert the receiver’s built-in TTL serial interface to a 

conventional RS-232 interface that communicates with the computer at 9600 bits/s. 

Figure 2.7. GPS receiver block diagram. 
25 

Chapter 2 - Technical Description 

The GPS receiver searches for, acquires, and tracks satellites on eight parallel channels using 

the L1 carrier frequency (1575.42 MHz) and the coarse acquisition (C/A) code with a 1.023 

MHz chip rate. The receiver has an onboard MC68331 microprocessor unit (MPU), so that all 

processing related to satellite tracking is done by the receiver itself and not by the FMS 

computer system. A block diagram of the receiver is shown in Figure 2.7 [34]. 

Although the primary purpose of GPS is to serve as a positioning and radionavigation system, 

the entire system relies on precise timing. The satellite ranges used to calculate position are 

derived from travel time measurements of the GPS signals transmitted from each satellite to the 

GPS receiver. After the receiver position (x, y, z) is solved for, the solution is stored in RAM. 

Then, given the travel time of the signals (observed) and the exact time when the signal left the 

satellite (given), time from the atomic clocks (either cesium or rubidium) onboard the satellites 

can be transferred to the receiver clock. The basic measurement made by the GPS receiver 

reveals the difference between the satellite clock and the receiver clock. This measurement, 

when multiplied by the speed of light, produces not the true geometric range but rather the 

pseudorange, with deviations introduced by the lack of time synchronization between the 

satellite clock and the receiver clock, by delays introduced by the ionosphere and troposphere, 

and by multipath and receiver noise. The equation for the pseudorange observable is 

 , (10) 

where p is the pseudorange, c is the speed of light, ρ is the geometric range to the satellite, dt

and dT are the time offsets of the satellite and receiver clocks with respect to GPS time, dion is 

the delay through the ionosphere, dtrop is the delay through the troposphere, and rn represents 

the effects of receiver and antenna noise, including multipath. An estimate of dion is obtained 

from the GPS broadcast. The GPS receiver discussed here uses a digitally compensated crystal 

oscillator (DCXO) as its local clock oscillator. The DCXO is inexpensive and not particularly 

stable, causing the dt − dT term to change very rapidly. Therefore, the pseudorange 

measurement must be made every second in order to preserve GPS accuracy. If the receiver 

loses lock, even for 1 s, the measurements recorded by the FMS are discarded. 

 

The receiver exploits the coherency between the L1 carrier and the C/A code by using very 

narrow band (0.005 Hz) code tracking. The pseudorange data collected by the narrow band 

code tracking function are used to compute the satellite time for each satellite in view. The 

receiver compensates for propagation delay and applies satellite clock corrections received 

from the broadcast to produce a local time estimate for each satellite. Then it averages up to 

eight independent satellite time measurements and computes a single local time estimate, 

which represents the composite timing solution from all satellites in view. This average time 

estimate is then used to position the 1 pps signal to coincide with the rising edge of the next 

second. Although the reception of only one satellite signal is required to produce a timing 

solution, tracking multiple satellites reduces the amount of measurement noise. Assuming that 

the noise is white, the noise figure can be roughly estimated as 1/(√S), where S is the number of 

satellites being tracked. 

p = ρ + c × (dt − dT ) + dion + dtrop + rn
26 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

The receiver outputs a 1 pps timing signal with a 200 ms pulse width (20 % duty cycle) and a 

20 to 30 ns rise time from 0 to 5 V. The rising edge of the pulse is the on-time marker. The 1 

pps is set relative to an internal asynchronous 1 kHz clock derived from the DCXO. The 

receiver counts the 1 kHz clocks, and uses each successive 1000 clock cycles to define the time 

when the measurement epoch is to take place. The measurement epoch is the point in time 

when the receiver captures the pseudorange and pseudorange rate measurements for the 

computation of position, velocity, and time. Each measurement epoch is about 1 s later than the 

previous epoch, with the difference from 1 s resulting from the DCXO’s intentionally 

introduced frequency offset (which exceeds 1 × 10-5) and its inherent frequency instability (± 2 

× 10-6) [35]. 

The DCXO runs at a nominal frequency of 19.096 MHz. The output signal from this oscillator 

is divided by two to produce a 9.548 MHz signal, and the cycle synchronized most closely to 

the satellite broadcasts is used as the receiver’s 1 pps output within the selected 1 ms epoch. 

The period of this clock frequency is approximately 104 ns, so the 1 pps signal has a ± 52 ns 

ambiguity. Therefore, if the phase of the physical 1 pps signal produced by the receiver is 

plotted it looks like a “sawtooth.” The receiver returns a data message every second containing 

a “negative sawtooth” correction with a range of ± 52 ns and 1 ns resolution. This correction is 

always given for the upcoming 1 pps pulse, and is applied by the FMS software. Note that the 

correction is applied only in software; the physical 1 pps output is not corrected. Thus, if the 1 

pps signal is distributed by the FMAS customer, the ± 52 ns ambiguity will still be present. 

The receiver makes an additional correction to the 1 pps output to convert GPS time to UTC. 

The GPS satellites themselves use the GPS time scale as their timing reference. GPS time 

differs from UTC by the integer number of leap seconds that have occurred since the 

origination of the GPS time scale (January 6, 1980); this value is equal to 13 s as of March 

2004. It also differs by a small number of nanoseconds (nearly always < 25 ns) that 

continuously changes. The integer-second difference is needed to correct the time-of-day 

solution, since this information is used to time stamp data collected by the FMS. This small 

number of nanoseconds represents the difference between the GPS time scale on-time marker 

(OTM) and an estimation of the OTM for the UTC time scale maintained by the United States 

Naval Observatory, called UTC(USNO). The current difference between the UTC(USNO) 

estimate and GPS time is broadcast from the satellites, and this correction is applied to the 1 

pps signal. Therefore, the received 1 pps signal represents an estimation of UTC(USNO). The 

relative frequency offset between the UTC(USNO) estimate and UTC(NIST) is very small, 

typically a few parts in 1015 or less when measured over a one month interval. 

It is also possible to apply a software correction for receiver and antenna delays, and to 

calibrate the receiver for use as a time reference. Corrections can be applied to the 1 pps signal 

with a resolution of 1 ns. This is not normally done with FMS units, since the quantities being 

measured and reported are time interval and frequency, and not absolute time synchronization 

to UTC. The receiver and antenna delays are ignored, and their small variations are factored 

into to the overall measurement uncertainty (see Chapter 5). 
27 

Chapter 2 - Technical Description 

a) GPS Antenna 

The GPS antenna provided with the FMS was designed specifically for time and frequency 

applications. The antenna was designed for outdoor installation, and must be mounted on a 

rooftop location with a clear view of the sky in all directions. The antenna has a polycarbonate 

outer casing, and is cone shaped, with a height of about 163 mm and a diameter of 90 mm. It 

has a relatively narrow bandwidth of ± 10 MHz around the 1575.42 MHz L1 carrier frequency 

which helps reduce interference. The receiver provides power (5 V dc at less than 27 mA) to 

the antenna through the antenna cable. 

In GPS positioning applications, the antenna is usually located very close to the receiver 

(sometimes directly attached as in the case of GPS handheld receivers), so low-gain antennas 

are generally used. However, the FMS is usually installed in calibration laboratories where the 

antenna normally resides on a rooftop outside the laboratory, and the length of the antenna 

cable generally ranges from at least 10 m to 100 m or longer. Since the incoming 1575.42 

MHz signal is not down converted at the antenna, but rather inside the receiver (Figure 2.7), a 

relatively high-gain antenna is needed to drive long cable runs. The FMS antenna has a gain 

exceeding 30 dB, with 38 dB being typical for satellites at an elevation angle of 90o. For the 

receiver, the optimal gain of the antenna, cabling, and any in-line amplifiers and splitters is 10 

to 33 dB. Therefore, to be safe, no more than about 20 dB of loss can be tolerated in the 

antenna cable. 

Prior to shipment of the FMS, the customer is asked for the approximate length of antenna 

cable needed. In some cases, standard length cables are supplied to the customer; in other 

cases (particularly for long cable runs), custom length cables are constructed. As a general 

rule, RG-58 coaxial cable is used for short cable runs, and larger diameter, more rigid cables 

are used for long runs. In a few instances where the cable run has exceeded 100 m, in-line 

signal amplifiers have been supplied to FMS customers. Table 2.1 shows the signal loss of 

various cable types at the L1 carrier frequency. If the loss is too large for the receiver to work 

properly, the number in the table is shaded. Note that the loss figures are estimates; various 

manufacturers’ brands can have higher or lower loss figures. 

Table 2.1. Antenna cable signal loss at the L1 carrier frequency as a function of cable type and 

length. 

Length 

RG-58 

(dB loss) 

RG-8 

(dB loss) 

RG-213 

(dB loss) 

LMR-400 

(dB loss) 

 10 6.4 3.3 3.6 1.7 

 25 16.0 8.1 9.0 4.3 

 50 32.0 16.3 18.0 8.6 

100 64.0 32.6 35.9 17.3 

150 96.0 48.9 53.9 25.9 

Cable Type 
28 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

4. Printer 

An inkjet printer with a parallel interface is used to print daily phase graphs from each of the 

five measurement channels currently in use. During normal operation, the printer is left on at 

all times and the phase graphs are produced automatically. The printer can also be used to print 

out data tables or statistics compiled from the data if the customer desires [20]. Replacement 

ink cartridges are provided by NIST. 

5. Uninterruptible Power Supply (UPS) 

A small 500 VA uninterruptible power supply (UPS) with four AC outlets is provided with 

every FMS unit. The UPS is intended to keep the FMS running through short power outages, 

not to exceed about 15 min. The FMAS customer is responsible for providing backup power 

for all of the frequency sources being tested, and in some cases, the FMS itself is placed on the 

laboratory’s backup power, and the supplied UPS is not needed. 

6. Equipment Rack 

A standard 19 in (48.3 cm) equipment rack with side mounted carrying handles is provided as 

the outer housing of the FMS. The rack has 12.25 in (31.1 cm) of interior rack space. The top, 

bottom, and side panels are constructed of 0.05 in (1.27 mm) thick aluminum. The printer is 

generally placed on top of the equipment rack. In addition to housing the hardware, the 

equipment rack provides some additional RF shielding for the measurement components. 

B. Technical Description of FMS Software 

The FMS software consists of the operating system, the remote software deployed at customer 

sites, and the host software which resides at the NIST Boulder Laboratories and is used 

exclusively by NIST personnel. 

1. Operating System 

The operating system is ROM-DOS 6.22 published by Datalight, Inc. ROM-DOS is similar to 

and compatible with the MS-DOS and PC-DOS operating systems formerly published by 

Microsoft and IBM, respectively. ROM-DOS is an embedded operating system that resides in 

flash memory on an ISA bus card. An individual ROM-DOS license is purchased by NIST for 

every FMS unit produced. 

2. Remote FMS Software used at Customer Sites 

An identical set of software programs is preinstalled by NIST on every FMS unit. The use of 

this software from the customer’s perspective is described in the NIST Frequency Measurement 

and Analysis System: Operator’s Manual [20]. This section provides a technical description 

of how the software works. 

The software was written in the BASIC programming language, with the exception of a few 

routines written in assembly language. Most routines were written to run in graphics mode, 

with a 640 × 480 screen resolution using 16 colors. All applications (data and executable code) 

reside in the standard DOS memory space of 640 kilobytes. 
29 

Chapter 2 - Technical Description 

a) GPS Software 

When an FMS unit is first installed at a customer’s site, or whenever it is restarted, a software 

program named GPS2000 is executed. This software performs the site survey on the GPS 

antenna, configures the GPS receiver, and tests its integrity. When these tasks are completed, it 

loads the main measurement module, called FM2000. 

Receiver Cold Start - GPS2000 can perform a cold start or warm start of the receiver. A cold 

start is used when an FMS unit is first installed at a customer’s site, and no information exists 

about the antenna position. To initiate a cold start, GPS2000 is run with the /COLD parameter. 

This parameter is included in the batch file shipped with the system, but deleted by NIST after 

the initial installation. The cold start performs the following functions: 

• Initializes all of the receiver parameters to their default values and erases any 

existing almanac and ephemeris data. 

• Sends time and date information from the computer clock to the GPS receiver 

clock to give the receiver a rough estimate of the current time. 

• Configures the receiver to output data messages to the computer via the RS-232 

port once per second. 

• Sets the mask angle so that the receiver only tracks satellites with an elevation 

angle of 15o or higher. 

At this point, the receiver begins searching the sky for a satellite. Once a satellite is found, the 

navigation message is downloaded, and the almanac and ephemeris data contained in the 

message are stored on disk. The GPS navigation message is transmitted at a data rate of 50 Hz 

and contains 25 frames. Each frame consists of 1500 bits and takes 30 s to transmit and 

receive. The entire message contains 37500 bits, takes 750 s to transmit and receive, and is 

continually repeated, so a new message begins every 12.5 min. Each frame has five subframes. 

Subframes four and five contain the data that are stored on disk; subframe four contains the 

almanac data for satellites with psuedo random noise (PRN) numbers from 25 through 32, and 

subframe five contains almanac data for satellites with PRN numbers from 1 through 24. The 

stored data occupy 1124 bytes of disk space, and consists of 34 unique formatted messages 

(each 33 bytes long) that correspond to the subframe and page number of the navigation 

message [36]. Once the signal from a single satellite has been parsed, the almanac data enable 

the receiver to search for other satellites. Since the navigation message repeats every 12.5 min, 

the process of downloading an almanac file typically takes from 12.5 to 25 min after the sky 

search is completed. 

Other information in the navigation message is used by the receiver as part of the time and 

frequency solution, and is briefly summarized here. The first two words in every subframe, 

called the telemetry word (TLM) and the handover word (HOW), provide synchronization 

signals for the receiver clock. Bits 20 to 22 of the HOW contain the subframe ID code. 
30 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

Subframe 1 contains the GPS week number, six bits that describe the health of the satellite, an 

estimate of the signal dispersion due to the ionosphere, and the coefficients of a polynomial 

that estimates the difference between the satellite clock and GPS time. The polynomial 

coefficients give the predicted time offset, frequency offset, and frequency aging of the satellite 

clock with respect to an origin time that is also part of the message. 

Subframes 2 and 3 contain the ephemeris parameters, which are used by the receiver to 

compute the satellite position. As with the time parameters in Subframe 1, this computation is 

made with respect to a transmitted origin time. The ephemeris for each satellite is described 

using six Keplerian elements. The first three Keplerian elements define the shape of the orbit. 

They are the length of the semi-major axis of the ellipse, a, the eccentricity, e, and the time, τ, 

at which the satellite crosses the perigee, which is the point on the orbit nearest the Earth (the 

semi-major axis crosses the ellipse at perigee). The second three Keplerian elements define the 

orientation of the orbit in space with respect to the Earth-centered, Earth-fixed (ECEF) 

coordinate system in which the x–y plane is the equatorial plane of the Earth and the z-axis is 

perpendicular to this plane. These three parameters are the orbit inclination angle, i, the 

longitude (or right ascension) of the ascending node, Ω, and the angle between the ascending 

node and the direction of perigee measured in the orbital plane, ω [37]. 

Subframes 4 and 5 contain the previously described almanac data that are stored to disk. The 

almanac provides a set of reduced precision ephemeris information for all satellites in the 

constellation, not just for the satellite whose navigation message is currently being received. 

Subframe 4 also includes parameters that relate GPS time to UTC(USNO), normally a 

difference of < 25 ns, and provides information regarding previous and future scheduled leap 

seconds. The leap seconds are added to UTC but not to GPS time, so that the difference 

between the two time scales changes by 1 s whenever a leap second occurs (Chapter 2.A.3). 

Once a valid UTC time-of-day message has been obtained from the GPS receiver, the date and 

time of the computer clock are synchronized to GPS. 

During the period when the navigation message is being downloaded, the software stays in a 

continuous loop where a number of receiver parameters are monitored through the RS-232 

interface. The loop is not exited until all of these parameters have acceptable values. During 

this time, the GPS antenna is surveyed by averaging position fixes. The allowable positioning 

uncertainty of the antenna survey needed to meet the frequency uncertainty specifications of 

the FMS are fairly modest, 10 m for the 2D position (longitude and latitude), and 20 m for the 

3D position (altitude). Table 2.2 summarizes the receiver parameters that are monitored during 

the acquisition process. 

Once the site survey is completed, the receiver is placed in position hold mode using the values 

obtained for latitude, longitude, and altitude. From this point forward, no further position fixes 

are computed unless the antenna is resurveyed (a new survey is not normally necessary unless 

the antenna is moved or if data collected by the FMS reveals a position error). The receiver’s 1 

pps signal is turned on. The position data are stored for future use in a binary disk file in 

milliarcsecond format, and occupy only 12 bytes of disk space. The GPS2000 software counts 

down for 10 s (display shown in Figure 2.8) and then loads the FM2000 software. 
31 

Chapter 2 - Technical Description 

Receiver Warm Start – As previously mentioned, GPS2000 can perform either a cold start or 

warm start of the receiver. A warm start is performed whenever the FMS unit is powered on or 

rebooted after the initial installation. In this case, it is not necessary to download a new 

almanac or resurvey the antenna, since the almanac and position data can be read from disk and 

sent to the receiver via the RS-232 port. However, the receiver parameters listed in Table 2.2 

Receiver parameter Acceptable value 

Almanac Almanac stored in RAM is complete and 

integrity has been verified. 

Receiver status errors None 

Position dilution of position (PDOP) <= 3 

Satellites being tracked >= 4 

Time solution 

(this is a coarse estimate computed by the 

receiver and is not determined by actual 

measurement) 

< 80 ns 

3D position fix Completed and integrity verified 

Table 2.2. Parameters monitored by the FMS during GPS signal acquisition.

Figure 2.8. The GPS receiver configuration screen. 
32 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

are still checked to verify receiver integrity, a process that normally takes a few minutes or less. 

Once this integrity check is completed, the GPS2000 software counts down for 10 s (display 

shown in Figure 2.8) and then loads the FM2000 software. 

b) Initialization of Measurement Software 

Each time the FMS is restarted, the FM2000 software will automatically begin making 

measurements without any operator attention, provided that information about the frequency 

sources being measured has been previously entered. Three pieces of information are 

necessary [20, pp. 10-12]: 

 

• The name of the device being tested. 

 

• The nominal frequency of the device being tested (entered in units of hertz). 

• The reference for the measurement (either GPS or the customer’s primary 

standard). 

Each time the FM2000 software starts, normal software housekeeping is performed (arrays are 

dimensioned; subroutines and variables are defined, etc.). Then the measurement process is 

ready to begin. The first step is to read several data files, including a file name named 

CHANNELS that contains the three pieces of information described above. When the data 

files have been read and processed, the following message is displayed on screen: 

Finished Reading Configuration Data 

Communications are established with the GPS receiver, and the computer’s time-of-day clock 

is synchronized to GPS, a process that will be repeated every 10 min while the system is 

running. When the time-of-day synchronization is complete, this message appears: 

Finished Synchronization of System Clock to GPS 

From this point forward, the FMS continually reads and writes data to and from the TIC 

previously described in Chapter 2.A.2.a. The TIC occupies 32 bytes of the computer’s I/O 

addressing space. These bytes are designated as registers R0 to R31. R0 is at the base address 

of the counter. The base address may be set to either 200h or 300h using an on-board jumper. 

R1 is equal to the base address + 1, R2 is equal to the base address + 2, and so on. 

Table 2.3 provides a listing of the registers so that the measurement software can be adequately 

described. Note that eight measurement channels actually exist on the TIC, but only five are 

used by the FMS. The TIC’s functions can be programmed using the control registers (R0 

through R5, and R16 through R23). Registers R28 through R31 are used to program the 

counter’s field programmable gate array using a RBF (raw binary file). This file is uploaded to 

the counter before any other functions are usable. Registers R6, R7, R15, and R24 to R27 are 

not used. 
33 

Chapter 2 - Technical Description 

Table 2.3. TIC control registers.

Register Read Write 

R0 

Control register 0 Control register 0 

R1 

Read waveform type (channels 0 to 7) Set waveform type (channels 0 to 7) 

R2 

Count done and signal present Enable count done interrupt 

R3 

Select dividers to set (channels 0 to 7) Select dividers to set (channels 0 to 7) 

R4 

Control register 4 Control register 4 

R5 

Read time base frequency and start and 

stop Input 

Set time base frequency and start and stop 

input 

R6 

Not used Not used 

R7 

Not used Not used 

R8 

Start counter readout (bits 0-7) Divide value for start input (bits 0-7) 

R9 

Start counter readout (bits 8-15) Divide value for start input (bits 8-15) 

R10 

Stop counter readout (bits 0-7) Divide value for start input (bits 16-23) 

R11 

Stop counter readout (bits 8-15) Divide value for stop input (bits 0-7) 

R12 

Main counter readout (bits 0-7) Divide value for stop input (bits 8-15) 

R13 

Main counter readout (bits 8-15) Divide value for stop input (bits 16-23) 

R14 

Main counter readout (bits 16-23) Not used 

R15 

Not used Not used 

R16 

Run dividers (channels 0 to 7) Run dividers (channels 0 to 7) 

R17 

Load dividers (channels 0 to 7) Load dividers (channels 0 to 7) 

R18 

Reset start input (channels 0 to 7) Reset start input (channels 0 to 7) 

 

R19 

Read prescalers (channels 0 to 3) Set prescalers (channels 0 to 3) 

R20 

Read prescalers (channels 4 to 7) Set prescalers (channels 4 to 7) 

R21 

Clear prescalers (channels 0 to 7) Clear prescalers (channels 0 to 7) 

R22 

Select channel (0 to 7) Select channel (0 to 7) 

R23 Bypass dividers (Channels 0 to 7) Bypass dividers (Channels 0 to 7) 

R24 Not used Not used 

R25 Not used Not used 

R26 Not used Not used 

R27 Not used Not used 

R28 

Data transfer register 7 to 0 Data transfer register 

R29 

Bit mover status Start JTAG mode 

R30 

Byte shift register 0-7 Start transfer 

R31 

Bit count/move state Device clear 
34 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

The TIC is prepared for measurements by first setting the time base frequency and then setting 

the frequency dividers. The time base frequency (1, 5, or 10 MHz) is set by writing to R5. 

This allows the counter’s 10 MHz time base PLL to lock to the signal from the customer’s 

primary frequency standard. Once this is accomplished, the 10 MHz PLL is divided to 1 pps 

using a series of writes to R11, R12, and R13 (the 24-bit divider occupies three 8-bit registers). 

This 1 pps signal from the customer’s primary frequency standard is always compared to GPS 

on channel one of the FMS. 

The nominal frequencies of the devices connected to FMS channel numbers two through five 

(if present) are also divided to 1 pps. Prior to setting the dividers, three steps must be 

performed. The first step is to select the waveform type for each of these channels by writing 

to R1. If the nominal frequency is 100 kHz or higher, it is assumed that the waveform is 

sinusoidal. If not, it is assumed that the waveform consists of TTL pulses. The second step is 

to determine if the nominal frequency is 1 Hz. If so, the divider on that channel is bypassed by 

writing to R23. The third step is to determine if the nominal frequency exceeds 15 MHz. If so, 

the divide by 10 prescaler for that channel is turned on by writing to R20. Now that all signal 

housekeeping has been performed, the divider is set by first selecting the appropriate divider 

for each channel with a write to R3, and then sending the 24-bit divide ratio to R8, R9, and 

R10. The divide values are loaded by writing to R17, and the divide counters are started by 

writing to R16. The following message is then displayed on screen: 

Finished Setting Frequency Dividers 

The next step is to calibrate the TIC, a process generically described in Chapter 2.A.2.a. The 

TIC is placed in calibrate mode by writing to R0. A write to R5 puts the 39062.5 Hz calibrate 

frequency on both the start and stop inputs to the TIC. Then the gate level is set by charging 

and discharging capacitors on the counter board with a series of writes to R0. A series of 

iterative loops are used to repeatedly arm and read the TIC at a number of different signal 

levels so that the start and stop interpolators can be calibrated. The counter is armed by writing 

to R0, and a “count done” condition is indicated by reading from R2. Once a “count done” 

occurs, the 24-bit main counter is read from R12, R13, and R14. The 16-bit start interpolator 

counter is read from R8 and R9, and the 16-bit stop interpolator counter is read from R10 and 

R11. When the TIC calibration is finished, the following message is displayed on screen: 

Finished Calibration of Time Interval Counter 

If the FMS was taking measurements the last time it was restarted, it will now automatically 

begin taking measurements again. If not, the user can start the measurement process by 

selecting MEASURE from the menu [20, p. 15]. 

c) Sequence of Time Interval Measurements 

Measurements are made sequentially from each of the five channels with devices connected. 

The measurements run nearly continuously unless the FMS is stopped (either by the operator or 

by a power outage). Measurements stop only for a short time once every 24 h; normally at 
35 

Chapter 2 - Technical Description 

1600 UTC (the customer can change this time). During this stoppage, the collected data are 

graphed and printed, and the TIC is recalibrated. The collected data are stored every hour, and 

the computer clock is resynchronized to GPS every 10 min. Table 2.4 shows a simplified 

measurement sequence that repeats every N s, where N is the number of channels in use. 

Table 2.4. Time Interval Measurement Sequence.

Step Action Description 

1 Read each measurement channel 

once. 

Each measurement channel is read once. Prior 

to each measurement, the start and stop inputs to 

the TIC are selected by configuring the multiplexer by writing to R5. The multiplexer used 

for channels two through five is always selected 

as the start input. A write to R22 selects which 

channel on the multiplexer is passed through to 

the TIC. The TIC is then armed and read after 

the “count done” flag goes high on R2. 

2 Store each counter reading. The readings are stored in the array named lastcount. If no reading was available (TIC timeout 

condition), a value of 9999 is stored in the array. 

3 Check to see whether GPS receiver 

is locked. 

Check GPS receiver status message. If receiver 

is unlocked, record date and time information in 

the file named coast.dat. 

4 Check keyboard input. See if user has entered a keystroke to stop the 

measurements (Ctrl-X), or to force the collected 

data to be graphed (Ctrl-P). Branch out of loop 

if either condition exists. 

5 Print time on screen. Print current time of computer clock on screen 

(ambiguous to a few tenths of a second). 

6 Check time. If it is the top of the hour (00 minutes, 00 seconds), the data collected during the past hour 

need to be saved to disk. If the scheduled plot 

time has occurred, the data need to be graphed 

and the TIC recalibrated. Branch out of loop if 

either condition exists. 

7 Get “sawtooth” correction (2.3) 

from GPS receiver via RS-232. 

The “sawtooth” correction has a range of ± 52 ns 

and is applied to the next measurement made 

using GPS as a reference. 
36 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

Step Action Description 

8 Read all measurement channels 

again. 

The reading from the current channel is stored in 

the count array. If no reading was available (TIC 

timeout condition), a value of 9999 is stored in 

the array. Reset divider on selected measurement 

channel by writing to R16 if the TIC is approaching an overflow or underflow condition. 

9 Print reading from current channel on screen. 

Print the reading in the “Count” column on the 

FMS screen (Figure 2.9), rounded to a resolution 

of 100 ps. If the reading is believed to be valid, 

print in white numerals. If the reading is invalid 

and is to be discarded, for example if GPS is the 

reference and the receiver is unlocked, print in 

red numerals. If no signal is available on either 

the start or stop channel, print NO SIGNAL. 

10 Take the difference of the last 

two counter readings made from 

the same channel. 

First, ensure that the last two readings are valid 

(no timeout conditions, divider resets, GPS 

unlocked, etc). Then, take the difference between the two readings, and print in the 

“Difference” column on the FMS display with 

100 ps resolution. If the time difference between 

the last two readings exceeds 100 μs, print a 

string of asterisks in red in place of the value. 

This means that the frequency offset is unusually 

large (larger than 2 × 10-5 even if all five channels are connected), and that the data will be discarded, since something is probably wrong with 

the DUT. 

11 Add valid differences to the accumulated phase difference for 

the channel. 

Valid differences for each channel are added to 

the array named total, which has five elements, 

one for each channel. This array stores the accumulated phase difference for each channel, which 

is saved each hour. After the data are stored (see 

step 6), all five elements of the total array are 

reinitialized to 0 and the process repeats starting 

with step 1. 

12 Copy values in count array to 

lastcount array. 

Once the current count is processed, it becomes 

the last count. Thus, the stored difference values 

represent n2 − n1, n3 − n2, n4 − n3, and so on. 

13 Repeat process Return to step 3 and repeat process until the top 

of the hour. 

Table 2.4., continued.
37 

Chapter 2 - Technical Description 

While the FMS is taking data, a screen similar to Figure 2.9 is displayed. The top part of the 

measurement screen is a bar graph that provides the customer with a quick indication of how 

each oscillator is performing. The bars represent channels one through five (from top to 

bottom). The bars are color coded, with their colors corresponding to the boxes next to the 

channel names shown near the bottom of the measurement screen. 

When the FMS is first started, the bars extend only to the number "5" on the far left side of the 

screen. After the system has been running for between 1 and 2 hours, the bars will extend 

further (assuming that the oscillator's performance is better than 1 × 10-5) and show the 

estimated frequency offset of each oscillator. The numbers at the top of the screen (ranging 

from 5 to 13) denote frequency offset values ranging from 1 × 10-5 to 1 × 10-13. The longer the 

bar, the smaller the frequency offset of the device under test. Each bar also contains either a 

plus sign "+" or a minus sign "−". A plus sign means that the oscillator frequency is higher 

than nominal; a minus sign means the oscillator frequency is lower than nominal. 

When the FMS has run for less than 24 h, the frequency offset estimate is based on all of the 

available data; for example, 12 h of data if the FMS has run for 12 h. However, when the FMS 

Figure 2.9. The FMS display. 
38 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

has collected data for more than 24 h, only the most recent 24 h of data are used to estimate the 

frequency offset. A new data point is stored to disk every hour. When this occurs, a new 

frequency offset estimate is calculated and the length of the bars might change. 

The screen area below the bar graph (see Figure 2.9) contains information about the most 

recent time interval readings, expressed in nanoseconds. The small red box contains the 

current date and the current time (UTC). The "Difference" column shows the difference 

between the last two counter readings for a given channel. The "Count" column shows the 

most recent counter reading for each channel. The FMS reads each counter channel in 

numerical order. The arrow points to the channel currently being read [20]. 

d) Estimation of Frequency Offset 

The FMS reports the frequency offset of each device under test, or the difference between the 

measured frequency and its nominal, or nameplate value. A frequency offset estimate is 

reported every day for each measurement channel that is in use. Another frequency offset 

estimate for the customer’s primary oscillator is made for the entire month, and reported on the 

monthly calibration reports. The measurement uncertainty value shown on the calibration 

reports refers to the uncertainty of the monthly frequency offset estimate. The standard 

equation for estimating frequency offset is 

 , (11) 

where foff is the dimensionless frequency offset, fmeas is the actual frequency in hertz reported by 

the measurement, and fnom is the nominal frequency in hertz that the device would ideally 

produce. Note that in practice fmeas has an associated measurement uncertainty, but fnom is 

always an ideal value with no uncertainty. This equation is often simplified in the literature as 

 , (12) 

where foff is the dimensionless frequency offset, ∆f is the difference between the measured and 

nominal frequency in hertz, and f is the nominal frequency in hertz. This is perhaps easiest to 

illustrate with a frequency counter. For example, if a 10 MHz oscillator (107

 Hz) produced a 

frequency counter reading that was high by 1 Hz, the equation becomes 

 (13) 

 

Note that since the nominal frequency was included in both the numerator and denominator in 

Eq. 11, the value for foff is now dimensionless, and not in units of hertz. 

nom

meas nom

off

f

f f f − =

f

f foff

∆ =

7

7 1 10 1

10

− foff = = ×
39 

Chapter 2 - Technical Description 

As previously discussed, the FMS measures time interval, but produces frequency information. 

This is possible since the relationship between frequency and time interval is known. 

Dimensionally, frequency is the reciprocal of time interval. A mathematical definition of 

frequency is 

 , (14) 

where T is the period of the signal in seconds, and f is the frequency in hertz. This can also be 

expressed as 

 . (15) 

If we perform mathematical differentiation on the frequency expression with respect to time 

and substitute in the result, we can show that the average fractional difference in frequency is 

equivalent to the average fractional difference in time, or that ∆f/f is equivalent to −∆t/T 

, (16) 

 therefore, 

 , (17) 

where ∆t is the difference between two time interval measurements (such as the one described 

by Eq. 8), and T is the elapsed time between the two measurements. To keep the sign correct, 

note that the first reading must be subtracted from the second, therefore 

. (18) 

To illustrate this, consider a simple example where an initial reading is made from a TIC and a 

second reading is made 1 s later, with the value increasing by 100 ns. This produces the same 

value for foff previously shown in Eq. 13 

 (19) 

T f 1 =

f T −1 =

f T

t

T

t f T t∆ = − ∆ − ∆ = − − ∆ = 2

2

T

t

f

f foff∆ = − ∆ =

T

t

T

TIC TIC foff

∆ = − − = 2 1

7

9 1 10

10

100 − foff = = ×
40 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

A frequency estimation of frequency offset can be made by recording a single TIC reading, 

waiting for a specified length of time, one hour for example, and then recording a second TIC 

reading. If the two readings are substituted into Eq. 18, the result is an estimate of the average 

frequency offset for the one hour interval. Of course, knowledge of how the frequency 

performed during the one hour interval has been lost. It is possible that the frequency was 

very noisy and unstable and thus deviated by large amounts during the hour, but coincidentally 

the two time interval readings were very close to the same value. For this reason, the FMS 

collects data throughout the interval. One data point is stored each hour by summing phase 

differences collected throughout the hour (Table 2.4). These one-hour phase accumulations 

are stored by the FMS using the file format pictured in Figure 2.10. This file is appended to 

every hour, and a new file is started every month. 

 

Cesium 1 vs GPS 

Not Used 

Rubidium 1 

Rubidium 2 

Cesium 2 

52852.000 -0.00256 8888.00000 2.11985 0.16894 0.01159 

52852.042 0.00836 8888.00000 2.12173 0.17673 0.01141 

52852.083 0.00827 8888.00000 2.10792 0.18175 0.00117 

52852.125 -0.00504 8888.00000 2.09820 0.17746 0.00092 

52852.167 -0.00143 8888.00000 2.09068 0.17019 0.00411 

52852.208 -0.00365 8888.00000 2.08916 0.17076 0.00800 

52852.250 0.01039 8888.00000 2.08408 0.16152 0.00409 

52852.292 -0.01364 8888.00000 2.08591 0.15282 0.00089 

52852.333 -0.01128 8888.00000 2.08197 0.15751 0.00358 

52852.375 0.01394 8888.00000 2.08085 0.15117 0.00287 

52852.417 -0.00531 8888.00000 2.08104 0.15520 0.00300 

52852.458 -0.00754 8888.00000 2.07624 0.14917 0.00259 

52852.500 0.01645 8888.00000 2.07451 0.15213 0.00236 

52852.542 -0.01189 8888.00000 2.06955 0.15074 0.00363 

52852.583 0.01042 8888.00000 2.07619 0.15165 0.00249 

52852.625 0.00374 8888.00000 2.07261 0.14912 0.00899 

52852.667 -0.00215 8888.00000 2.07330 0.15631 0.00393 

52852.708 -0.03227 8888.00000 2.07839 0.15835 0.00627 

52852.750 0.01137 8888.00000 2.10058 0.16400 0.00368 

52852.792 -0.01093 8888.00000 2.10818 0.17305 0.01005 

52852.833 0.01953 8888.00000 2.11426 0.17597 0.00591 

52852.875 -0.02473 8888.00000 2.12401 0.16804 0.00477 

52852.917 -0.00231 8888.00000 2.12180 0.16970 0.01072 

52852.958 0.00409 8888.00000 2.10731 0.16868 0.00442 

52853.000 -0.07642 8888.00000 2.09216 0.17042 0.00855 

The file header contains the channel names for each measurement channel in use, followed by 

six data columns. The leftmost column contains the time stamp for the data (x values), 

depicted as the Modified Julian Date (MJD) plus the fractional part of the UTC day when the 1 

h sample was completed. For example, 53057.500 indicates that this row of measurements 

was taken on MJD 53057 in the 1 h interval from 1100 to 1200 UTC. The other five columns 

Figure 2.10. FMS phase data file. 
41 

Chapter 2 - Technical Description 

(y values) contain the accumulated phase differences taken from the five measurement channels 

during the 1 h interval. The units for these data are microseconds, but since five digits are 

carried to the right of the decimal, the resolution is 10 ps. If a channel is unused, a value of 

8888.00000 is stored. 

To estimate frequency offset for a given measurement channel, the FMS software loads the 

phase data file, and creates a new two-dimensional array (x, y). The x values are the time 

stamps for each data point; the y values are generated by starting with an initial data point or 

“anchor value” of 500 000 μs, and then algebraically adding each phase difference yi to the 

previous data point. A least squares line is then fit to the new array, and the slope of the least 

squares line is substituted for ∆t in Eq. 18. The slope and y-intercept for the least squares lines 

are calculated as 

 (20) 

 

 , (21) 

 where 

 (22) 

 

 , (23) 

where n is the number of data points used in the estimate. 

To estimate the “goodness of fit” of the least squares line to the phase data, the linear 

correlation coefficient, r, is calculated. The possible values for r range for −1 to +1, with r = 1 

or r = −1 indicating that there is a nearly perfect linear relationship between the x and y values, 

that all data points lie on the least squares line, and that the frequency offset estimate is very 

accurate. The linear correlation coefficient is calculated as 

 . (24) 

SS xx

SS xy βˆ = 1

β y βˆ x 1 ˆ

0 = −

n

y )

i x )( i (

yi xi y y) i x x)( i SS ( xy

n

i

n

i n

i

n

i

∑ ∑

= ∑ − − = ∑ − = =

= =

1 1

1 1

∑

∑

= ∑ − = − =

=

=

n

i

n

i n

i n

xi

xi x x SS xx i

1

1

2

2

1

2

( )

( )

ss ss

ss

r

xx yy

xy =
42 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

The least squares line is drawn on all graphs produced on channel one of the FMS. If r = 1 or r 

= −1, the least squares line is nearly identical to the recorded phase data, and will overlap the 

data on the graph. This is nearly always the case when the measurement ran for 24 h or longer 

and foff is > 1 × 10-12. Values for foff and r are printed on all graphs produced by the FMS. A 

channel one example that includes the least squares line is provided in Figure 2.11. Note that 

the frequency offset estimate on this graph is very small, −4.46 × 10-14, and that r = −0.59. 

These results show that the uncertainty of the frequency offset estimate is limited by GPS 

noise, but that the trend contributed by the frequency offset is still clearly visible. 

e) Graphing and Data Analysis Software 

The FMS software produces phase graphs from all five channels every 24 h, unless this feature 

has been turned off by the customer. In addition, the customer can graph up to 3600 h (150 d) 

of data on demand, since all data recorded by the FMS are stored on a solid-state disk and can 

be retrieved at any time. 

The phase graphs use the standard Cartesian x/y format. The x-coordinate is elapsed time-ofday, measured in hours. This is the quantity T shown earlier in Eq. 10. The tick marks on the xaxis are automatically scaled in intervals ranging from 1 h to 24 h, depending upon the amount 

of data being plotted as shown in Table 2.5. 

Figure 2.11. Sample FMS phase graph. 
43 

Chapter 2 - Technical Description 

The change in phase, DF, is plotted as the y-coordinate. However, since phase is expressed in 

units of time (microseconds), this is actually the change in time, or the ∆t quantity described 

earlier. The maximum and minimum values of the yi data series are found, and the range (ymax

− ymin) is calculated. The tick marks on the y-axis are then scaled using the “1-2-5-10” scaling 

sequence sometimes used by oscilloscopes and other test instruments. For example, a range of 

3 μs would result in a y-axis scale of 5 μs, since the range is > 2 μs but < 5 μs. The minimum 

y-axis scale is 1 ns. 

The data are normalized to 0 by subtracting the midpoint of the data from every value in the 

data set, making the midpoint 0. The midpoint is calculated as 

 , (25) 

where ymid is the midpoint and ymax and ymin are the maximum and minimum values in the yi

data series, respectively. After the data are normalized, x-axis intercepts the y-axis at 0, and the 

data are scaled ± 0 as shown in Figure 2.12. The normalization of the data makes the phase 

graphs easier to interpret, and also make senses because no absolute time information is 

contained in the yi series, therefore labeling the y-axis with unnormalized numbers would serve 

no purpose. Although the time interval readings are made at a 1 Hz rate, the alignment of the 1 

pps signal is arbitrary for nearly all FMS measurements, because it is obtained by dividing a 

higher frequency signal. If the frequency dividers are stopped and restarted, a different cycle 

of the frequency passes through the divider and the 1 pps is realigned. Therefore, it is the 

change in phase and not the absolute phase difference that is being measured, and ∆t is always 

relative to an arbitrary starting point, and not to an absolute time reference. 

The phase graphs can be customized with a variety of editing and analysis features [20]. It is 

possible for the customer to “zoom-in” or “zoom-out” on a particular data segment by 

decreasing or increasing the scale of either the x or y-axes. It is also possible to remove 

outliers, one data point at a time, by deleting either ymax or ymin from the phase graph. The FMS 

software also includes a “Filter” function, which was designed to remove all of the outliers and 

y

y y

ymid min

max min

2

( )

+ − =

Table 2.5. Tick intervals for x-axis used by FMS phase graphs.

Length of data run (h) x-axis tick interval (h) 

 1 to 24 1 

 25 to 96 2 

 97 to 192 4 

 193 to 384 8 

 385 to 576 16 

 > 576 24 
44 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

phase steps from a phase graph with a single keystroke. This feature works utilizing a simple 

“3-sigma, 2-pass” filter. First, the mean and standard deviation (σ) of the yi data series are 

computed; then data points that fall more than 3σ from the mean are removed and the process 

is repeated. To avoid removing valid data, the software will not attempt to filter data sets 

where the range is < 1 μs, where the number of values in the data series is less than 9, where 

the computed frequency offset is < 1 × 10-12, or where the absolute value of r exceeds 0.99. 

Data points deleted from the phase graph are not deleted from the disk, and customers can 

restore the phase graph to its original status whenever they wish. The FM2000 software also 

allows the customer to view the data set and its associated statistics in tabular form. 

f) Frequency Stability Analysis Software 

The FM2000 software contains a module that allows customers to collect phase data from any 

of the five measurement channels for up to 1 h (3600 s). The data are collected at a 1 Hz rate 

and not averaged, so that the customer can examine, graph, and store raw phase data. This 

feature is useful for several applications. It can be used to identify potential noise sources, such 

as periodic steps or outliers that might be present in the frequency produced by a defective 

Figure 2.12. FMS phase graph with data normalized to 0. 
45 

Chapter 2 - Technical Description 

device. It can be used to graph the “warm-up” curve of an oscillator that has just been turned 

on. It is also useful for a quick calibration or adjustment of oscillators with a frequency offset 

larger than about 1 × 10-10, where a 24 h measurement might not be practical or necessary. 

Customers can also graph the Allan deviation of the collected phase data. The Allan deviation, 

σy(t), is a standardized statistic used to estimate frequency stability [38]. Because the FMS 

makes time measurements to compute frequency, it estimates the Allan deviation with the 

equation for time series data using overlapping samples 

 , (26)

where xi is a set of phase measurements in time units that consists of individual measurements, 

x1, x2, x3, and so on; N is the number of original time residual measurements spaced by τ0 (1 s); 

m is the number of original frequency measurements of sample time τ0 (m = N − 1); and t = 

mτ0. The FMS uses the octave method of computing σy(t), where every τ value is twice the 

length of the previous τ. Figure 2.13 shows an Allan deviation graph created with the FMS. 

∑ [ ] −

= + − + +

−

= N m

i

i m i m i x x x

m y

2

1

2

2 2 2 2(N 2 )τ

1 σ (τ )

Figure 2.13. FMS Allan deviation graph. 
46 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

These graphs use a “log-log” format, with the y-axis scale indicating the dimensionless 

frequency stability, and the x-axis scale indicating the averaging time τ in logarithmic format 

(log τ 3 = 103

 s = 1000 s). 

The FMS was designed to measure the long term accuracy and stability of frequency sources, 

and should not be considered as an alternative to measurement systems designed specifically to 

measure the short term stability of oscillators. When measuring devices that contain an ovencontrolled quartz oscillator (OCXO) at τ ≤ 100 s, there is a good possibility that the FMS noise 

floor, limited by the TIC, will be higher than the DUT noise floor. In these instances, the Allan 

deviation reveals only the FMS stability, and not the DUT stability. It also should be noted that 

many quartz and rubidium oscillators reach their noise floor at a τ of < 100 s, so by the time 

that FMS noise has averaged down to a sufficient level, information about the short-term 

stability of these devices has been lost. As mentioned earlier, laboratories that need to measure 

the short term stability of oscillators should use a system based on a heterodyne technique that 

mixes, rather than divides, the signal [28, 29]. However, at τ values > 100 s the FMS should 

produce essentially the same Allan deviation results as a heterodyne type system. 

Customers can also produce graphs of the daily frequency offset of their primary frequency 

standard (Figure 2.14). On these graphs, the x-axis scale indicates the day of month (one 

month of data is contained on each graph), and the y-axis scale indicates the dimensionless 

frequency offset. A straight line of markers indicates that the oscillator is stable and able to 

Figure 2.14. FMS frequency history graph (one month). 
47 

Chapter 2 - Technical Description 

produce nearly the same frequency day after day. In Figure 2.14, UTC(NIST) is being 

compared to GPS, and the daily frequency offset estimate seldom exceeds 1 × 10-13. A similar 

graph is provided to the customer on the monthly calibration report (Chapter 3.G). 

g) Diagnostic Software 

Diagnostic routines are included in the FM2000 software that allow the customer or NIST (via 

modem) to view the current status of GPS satellite reception. The GPS status screen includes 

information about all satellites currently being tracked; including their PRN number, elevation 

angle above the horizon, health indicator, time offset in nanoseconds relative to the receiver’s 

composite timing solution, and signal strength. The signal strength information is particularly 

important, since it can be used to identify and troubleshoot reception problems. Signal strength 

is reported as carrier to noise power density ratio (C/No), or the ratio of the power level of a 

signal carrier to the noise power in a 1 Hz bandwidth. In order for the FMS to meet its 

specifications, the C/No value should be in the 40 to 50 dB-Hz range, with 51 the maximum 

value that can be reported by the receiver. Values of less than about 38 indicate that the 

receiver is close to losing lock. 

Additional diagnostic software allows the user to force a calibration of the TIC, a process 

generically described in Chapter 2.A.2.a. The forced TIC calibration displays the calibration 

results in tabular form. These results are not displayed during the automatic calibration that 

takes place every 24 h, but it might be necessary to look at them in some instances. 

3. Host Software Used at NIST 

Two customer software applications written at NIST are used to process the measurement data 

downloaded from each customer’s site (Chapter 3.A.2). The first application, called 

FMSFILER, accepts as input the raw frequency data files (Chapter 3.E.2) downloaded from 

every customer, and then outputs processed data files (Chapter 3.E.3) that contain an 

uncertainty statement generated using the technique described in Chapter 5.C. FMSFILER

assigns a status code to every calibration. A calibration is defined as a measurement made over 

a 24 h interval, so during the average month, each customer records about 30 calibrations. This 

status code is either a 0, which means that the calibration is valid, or a 9, which means that the 

value reported was either out of tolerance, unrealistic, incomplete, or missing, or that the FMS 

was being operated improperly. The report preparer at NIST then uses FMSFILER to review 

all calibration results with status codes of 9. If the calibration is considered by NIST personnel 

to be valid, the status code is changed from 9 to 0. If not, the status code is changed to a value 

ranging from 1 to 6, and a comment is added to annotate the situation. The allowable status 

codes are described in the section on calibration reports (Chapter 3.G). During a typical month, 

about 97 % of all calibrations are automatically marked with a status code of 0, and only about 

3 % require additional review by the NIST staff. Of the approximately 3 % that require 

additional review, over half are changed to a status code of 0 (marked valid) after the NIST 

review is completed. 

The second application, called TREPORT, accepts the processed data files (Chapter 3.E.3) and 

prints out a three-page calibration report for every customer. While most of the processing has 
48 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

already been done by FMSFILER, a graph of the daily frequency values is generated by 

TREPORT. The format of the monthly calibration reports is described in detail in Chapter 3.G. 

 

 
49 

Chapter 3 - Operational Procedures 

This chapter discusses the hardware and software maintenance required by the FMAS. It also 

discusses failure modes, record keeping, security issues, and how calibration reports are 

created and sent. 

A. Hardware Maintenance 

This section describes how the FMS hardware is maintained and checked both before and after 

its shipment to the customer. 

1. Verification of the FMS prior to shipment 

Each FMS unit is completely tested prior to shipment to the customer’s site. Since the unit has 

just been assembled, all parts need to be full tested to confirm that they are fully functional and 

meet the FMS specifications. All FMS systems are “burned-in” for a long period of time, 

usually several weeks or more, before shipment to the customer. 

The performance of each FMS unit is verified in one of two ways. The first way involves 

using the same frequency source, usually UTC(NIST) since it is readily available in the FMAS 

laboratory, as the start and stop input to all five measurement channels. This represents a 

“self-test” of the measurement system. Since the same input is being compared to itself, in 

theory, the frequency offset should be 0, but in practice, some noise is always produced by the 

measurement system. When a self-test is performed, this measurement system noise is 

examined to see whether it is within acceptable limits (typically low parts in 1015 or high parts 

in 1016 after one day of averaging). Units are not shipped until the amount of self-test noise is 

deemed acceptable. 

The second type of test involves measuring a signal with a known frequency offset [39]. This 

signal is generated by locking a direct digital synthesizer (DDS) to UTC(NIST) and producing 

a 10 MHz signal offset by 1 mHz. This signal then has a known frequency offset of 1 × 10-13

relative to UTC(NIST), so the FMS should return that value when measuring the signal over an 

interval of a few hours or longer. An example of this measurement is shown in Figure 3.1. 

Note that since UTC(NIST) distributes a 5 MHz standard frequency, a low-noise frequency 

doubler is used to produce the 10 MHz DDS time base input. 

The same type of test can be used to validate GPS performance on channel one of the FMS 

(Figure 3.2). However, if a 1 × 10-13 offset is used, it will take more than 1 day of averaging 

(usually about one week) to get a “clean”, accurate measurement of the frequency since the 

peak-to-peak GPS variations (one-hour averages) have a typical daily amplitude near 20 ns, 

and this offset represents a daily phase change of just 8.64 ns [39]. 

Chapter 3 

Operational Procedures 
50 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

Figure 3.1. Verifying an oscillator to oscillator comparison with a known frequency offset. 

Figure 3.2. Verifying a GPS to oscillator comparison using a known frequency offset. 
51 

Chapter 3 - Operational Procedures 

In addition to having the measurement integrity verified, each FMS unit must pass a series of 

other tests prior to shipment. A checklist of these tests is prepared for each unit and stored at 

NIST for diagnostic and information purposes. The other items on the checklist are 

summarized in Table 3.1. 

Description of item Information logged 

Computer MPU type, clock speed, amount of RAM, flash disk 

capacity, I/O port addresses and IRQ settings, software installation verified, cooling fans tested, 

floppy drive tested, modem tested by calling unit, 

results from a standardized speed test used to verify 

performance. 

GPS receiver Model number and firmware revision number. 

Fully tested, including its ability to provide power to 

the GPS antenna. 

GPS antenna Type of antenna, type of antenna cable, and length 

of antenna cable. 

Time Interval Counter Serial number and results of counter calibration. All 

channels and dividers are tested, and peak-to-peak 

values recorded in nanoseconds for counter self test 

on channels 2 through 5. 

Printer Tested by printing graphs from all five channels in 

succession. 

Keyboard Keys tested, rack mounting hardware tested so that 

it moves in and out smoothly. 

Signal connectors Tested for continuity and for proper labeling. 

Video monitor, printer, and UPS Tested for functionality. Serial numbers and NIST 

property numbers (when applicable) are recorded. 

Accessories A list of accessories packed with the system. 

Table 3.1. Items checked and logged prior to each FMS shipment. 
52 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

2. Verification of the FMS after shipment

After the FMS is installed by the customer and is successfully taking measurements, it is 

called by NIST personnel at least twice each month (at the beginning of each month and at 

mid-month) to verify correct operation. Systems that need more attention are called more 

often. If a phone connection cannot be established, NIST assumes that something is wrong 

(either with the FMS or the phone line) and the customer is immediately contacted. 

During a remote system check, NIST personnel can view the identical measurement screen 

seen by the customer. In most cases, the measurements are stopped briefly, and data are 

downloaded for inclusion in the monthly calibration reports. If necessary, diagnostic software 

can be run to make sure that all FMS components are working properly. On rare occasions, 

new software is installed, or a new survey of the GPS antenna is initiated. A log sheet is filled 

out during every system check. Table 3.2 lists the information logged by NIST during each 

remote system check. 

Table 3.2. Information logged at NIST during each remote check of an FMS unit.

Item logged or downloaded Description 

Frequency offset The frequency offset of the customer’s primary standard during the last 24 h is logged. 

If this value looks unusual, steps are taken to 

determine the cause of the anomaly. 

Date of last system restart This date is recorded to see if the system has 

been restarted lately. Under normal conditions, the system does not need to be restarted. Frequent restarts might mean that 

there are frequent power outages in the laboratory, or that the system is malfunctioning or 

being used improperly. 

Dates and times when the GPS receiver was 

unlocked 

Whenever the GPS receiver is unlocked (an 

extremely rare event for most customers), the 

date and time are recorded and logged. 

Manufacturer and model number of primary 

frequency standard 

Normally, this information does not change, 

or if it does, the change is usually reported in 

advance by the customer. However, it needs 

to be checked for reporting purposes. 

Miscellaneous information Anything unusual seen during the system 

check (including difficulties in connecting by 

phone) is recorded and logged. 
53 

Chapter 3 - Operational Procedures 

B. Software Maintenance 

The software maintenance is simplified by the fact that all remote FMS units contain identical 

software, although the software might be configured slightly differently from unit to unit to 

allow for minor hardware differences. Also, since the software runs 24 hours per day under a 

variety of conditions at customer sites, any errors are easily recognized. When software “bugs” 

are found, or new features are added, new software is uploaded and installed over the modem 

link. If the change impacts the customer in any way, NIST will contact the customer and 

inform them of the change. This contact is normally done with a written notice sent by mail. 

Multiple documented copies of the master source code are kept at NIST, along with associated 

documentation for compilers, programmable hardware, and other items that influence the 

software architecture of the FMS. 

C. Customer Maintenance 

With a few small exceptions, the FMS requires no customer maintenance. The customer is 

responsible for ensuring that the GPS antenna is still mounted properly on the roof, that there is 

paper in the printer (if daily phase graphs are desired), that the backup power for their 

frequency sources is functioning, and that the telephone line connected to the FMS is still 

functioning properly. However, since NIST inspects each system by modem regularly, they 

can alert the customer to most potential problems. Most of the time, the customer can assume 

that everything is fine unless they “have heard from NIST.” 

When parts fail, they are immediately replaced using an overnight delivery service. Since 

NIST personnel do not travel to the customer’s sites, the installation of the new part is normally 

performed by the customer. Most installations are very simple to perform. However, if the 

customer is not comfortable with the installation or if NIST cannot determine which part has 

failed, NIST sends a completely new FMS to the customer, and the data collected by the old 

unit are transferred to the new unit. 

D. Failure Modes 

FMAS failures can be divided into three groups: hardware failures, software failures, and GPS 

signal failures. Each type of failure is discussed in this section. 

1. Hardware Failures 

The FMS hardware is very reliable, but most problems regarding the FMS are related to 

hardware failures. NIST quickly works to correct FMS hardware problems (Chapter 3.C), and 

any hardware failures that impact the measurements are annotated on the calibration report. 

Table 3.3 summarizes the various types of hardware failures experienced in the past by FMS 

customers. The various failures are listed in descending order or occurrence, with the failures 

most likely to occur listed at the top of the table. 
54 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

Table 3.3. Hardware failures experienced by FMS units at customer sites.

Part name Symptom/Cause Critical to 

measurements? 

Action taken by 

NIST 

Video monitor No measurement display at customer’s site. CRT monitors often 

fail after being left on for several 

years or more. The LCD monitors 

being used now have a longer life 

expectancy. 

No, the measurements continue 

without a display. 

Replacement part 

sent. 

Printer No printouts, poor quality printouts, 

or paper jamming. This is usually 

due to a mechanical failure in the 

printer. 

No, the measurements continue 

without a printer. 

Replacment part 

sent. 

Telephone line NIST cannot connect via modem 

due to a non-working telephone 

line. 

No, the measurements continue. The customer is 

responsible for getting the telephone 

line repaired. 

Computer 

“freezes” 

Computer display is frozen, measurements stop. This can be due to a 

general computer failure, but is 

sometimes due to overloading the 

time interval counter, operating the 

unit in a high RF environment, or 

using poor quality signal cables. 

Yes, the measurements stop. The computer is 

reset, if problems 

continue it is replaced. If TIC is 

being overdriven, 

attenuators are installed on input signals. 

Computer 

power 

supply 

FMS will not power up. Power supplies eventually fail, although the 

mean time between failure (MTBF) 

is typically 50 000 to 100 000 h 

(roughly five to ten years). 

Yes, measurements stop. Replacement part 

sent. 

GPS receiver/

antenna 

No data on channel one. Antenna 

and cable failures are more common 

than receiver failures since those 

components are located outdoors, 

but occasional damage to receivers 

occurs due to electrical storms. 

Yes, traceability 

to NIST is lost, 

but measurements on channels two through 

five continue. 

Replacement part 

sent. A lightning 

arrestor is installed 

on antenna if electrical storms are a 

problem in the area. 

UPS FMS will not power up, or is being 

rebooted intermittently. A bad UPS 

unit can cause numerous problems. 

Yes, measurements stop or are 

constantly interrupted. 

Replacement part 

sent. 
55 

Chapter 3 - Operational Procedures 

2. Software Failures 

When software failures occur, the software is fixed, and new software is uploaded and installed 

over the modem link (3.B). If these failures adversely impacted the measurements, or caused 

FMS downtime, these failures are annotated on the next calibration report. 

3. GPS Signal Failures 

A signal failure occurs if the FMS cannot receive the GPS signal. The most common reason 

for this is a hardware failure concerning the GPS receiver or antenna (Table 3.3). However, in 

some cases, GPS reception is weak or intermittent due to local interference, or in very rare 

instances, the GPS satellites actually transmit bad data. 

If local interference is the problem, NIST works with the customer to solve it. Often, this 

requires relocating the antenna. One case of interference involved an antenna located in the 

line-of-sight of a radar testing range at a U.S. military facility. Another case involved a GPS 

antenna located too close to another GPS antenna that was equipped with a preamplifier. The 

second GPS antenna had a crack in the coaxial antenna cable and was essentially 

rebroadcasting the L1 signal from about 1 m away, blocking GPS reception entirely. Most 

problems are caused by placing the antenna in an area where a clear sky view is not available in 

all directions, resulting in signals from satellites in parts of the sky being blocked. Most 

interference problems are solved shortly after the FMS is installed at the customer’s site. 

Part name Symptom/Cause Critical to 

measurements? 

Action taken by 

NIST 

Modem Will not answer telephone calls 

from NIST. Most problems can be 

solved by rebooting. Modem failures are rare, but the modem circuits 

can sometimes be damaged by a 

power surge over the telephone line. 

No, measurements continue 

without modem. 

Replacement part 

sent. Sometimes 

surge protection is 

applied to the phone 

line. 

Disk Drive Data cannot be stored or are corrupted, FMS normally (but not always) stops. Since a solid state disk 

is used, drive failures are rare. 

Yes, measurements stop or 

data are lost. 

Replacement part 

sent. Data from old 

drive are transferred 

to new drive, if possible. 

Distribution 

amplifier or 

cables from 

primary 

standard 

Weak or intermittent signal causes 

the time base PLL on the FMS to 

miss a zero crossing, resulting in 

phase steps in data that are an even 

multiple of 100 ns. 

Yes, measurements are contaminated by unwanted noise. NIST assists customer in finding the 

source of the problem. 

Table 3.3, continued.
56 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

If a single GPS satellite is broadcasting bad data, there is a good chance that it will not be 

noticeable to the FMAS customer. The FMS GPS receiver drops bad satellites from the time 

and frequency solution if they are marked as unhealthy by the GPS status message. It also 

drops satellites from the solution if their clock signals substantially disagree with the data being 

received from the other satellites, a feature known as TRAIM (Time Receiver Autonomous 

Integrity Monitoring) [34]. However, for a short time, bad data might be processed by the 

FMS. For example, a satellite clock might go bad minutes or hours before GPS master control 

updates the status message. Or, the TRAIM feature might be tricked by a situation where most 

or all of the satellites are broadcasting bad data. In these extremely rare instances, NIST 

personnel will discover a problem in the GPS data received at more than one customer site, 

since the same signals will be simultaneously received at multiple laboratories. To verify that 

the GPS broadcast was bad, NIST personnel consult several sources, including the NANU 

(Notice Advisory to Navstar Users) messages published by the United States Coast Guard. 

These messages inform users of any changes or unusual events that impact the GPS 

constellation [40]. Information from the NANUs is used to annotate the situation on the 

customer’s calibration report. 

E. Record Keeping 

The FMAS records are described below. They include customer information files, raw 

measurement data files, and processed measurement data files. 

1. Customer Information Files 

There are three database files that contain customer information, as listed below. This 

information is stored on a single computer at NIST, and backed up both to removable media 

and to an internal network location (the combined file size is less than 1 megabyte). All files 

are accessed using software developed at NIST. The file format is dBase. 

• Main File – This file contains the customer’s name, address, phone number, and 

information about their primary frequency standard (manufacturer and model number). It 

also contains a list of all NIST property that is on-site at the customer’s location. 

Information from this file is automatically extracted and copied into the processed 

measurement files (see below). 

• Billing File – This contains the billing address for each customer, the customer purchase 

orders, and the expiration dates. The software automatically generates the information 

necessary to bill the customer. 

• Parts Inventory File – This file contains the spare parts inventory stored at NIST, 

including the property number of each item. If a customer needs to send a part back to 

NIST, that information is also recorded here. 

2. Raw Measurement Data Files 

Since the FMS is a remote calibration service, all measurements are made and stored at the 

customer’s location on local media. The measurement data are downloaded, stored, and 
57 

Chapter 3 - Operational Procedures 

backed up at NIST, but a copy remains on the customer’s system. Therefore, if those data are 

lost at NIST, it is usually possible to download them again. The raw data consist of two files 

(both are ASCII text files): 

• Phase Data File - This file is appended to every hour, and a new file is created monthly. It 

contains the time and date stamps for the measurements, the names of the devices being 

measured, and the phase measurements made from up to five oscillators (Figure 2.10). The 

average monthly file size is about 60 kilobytes. If 50 FMS systems are in operation, this 

means about 3 megabytes of phase data are stored each month. 

• Frequency Data File - This file is appended to daily, and a new file is created monthly. It 

stores the estimated frequency offset of the customer’s primary oscillator, and other data 

that indicate the confidence level of the measurement. The average monthly file size is 

about 1 kilobyte. The file name is MMMYY.##, where MMM is a three character prefix 

for the current month, YY is the two digit year code, and ## is the customer number. 

3. Processed Measurement Data Files 

These files are also ASCII text files. They are generated from the raw frequency data files by 

the FMSFILER software developed at NIST (Chapter 2.B.3). The processed file includes the 

customer’s name and address; a description of the device under test, the daily frequency offset 

values, a statement of measurement uncertainty, and comments entered by NIST personnel that 

explain out of tolerance conditions. The processed files are run through the TREPORT

software application developed at NIST (Chapter 2.B.3) that generates the actual calibration 

reports mailed to customers. The file name is MMMYYUNC.##, where MMM is a three 

character prefix for the current month, YY is the two digit year code, “UNC” is a tag that 

denotes the file contains an uncertainty statement, and ## is the customer number. Copies of 

the calibration report are not stored, but any calibration report can be regenerated almost 

instantly from the processed file. 

The processed files are backed up periodically at NIST on removable media, and also copied to 

the NIST internal network for further redundancy. If the processed files are lost, they could be 

regenerated at NIST from the raw files, but the process might be fairly labor intensive (it 

typically takes 8 to 12 h per month to generate the processed files for all FMS customers). 

However, once a calibration report is sent, it should not be necessary to access the processed 

files again, unless a customer asks for a calibration report to be resent (an event that happens 

only several times each year). 

F. Security Issues 

Security is not a large concern with the FMS units located at customer sites, and no security 

violations have ever occurred. It is important to note that the units are not networked in any 

way with other computers in the facility. Instead, they are simply connected to ordinary analog 

telephone lines and accept only incoming phone calls; their software does not allow them to 

make a call. 
58 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

Each FMS comes with remote communications software preinstalled. When a call is received 

from NIST, a series of commands allows NIST personnel to download the data. It is 

conceivable that an outside caller using identical remote communications software could call 

the system, somehow learn and enter the commands, and download, change, or delete the 

software or the calibration data. However, the chance of this happening is extremely small, 

because the FMS phone numbers and command structure are unpublished and kept in a secure 

area at NIST. Even if someone were able to “log-on” to an FMS, there is relatively little 

damage they could do. They could not use the FMS to obtain entry into another computer, 

since the FMS is not on a network. Downloaded data consist of columns and rows of numbers 

that contain no sensitive information and would likely mean nothing to a potential intruder. 

Deleted data or software could easily be restored since backup copies are kept at NIST, and 

NIST personnel would be able to tell whether the data had been tampered with. 

G. Calibration Reports 

All FMAS customers receive a monthly calibration report by mail. These reports are nearly 

always mailed before the 7th day of the month following the month when the calibrations were 

performed. For example, the February report is nearly always mailed before March 7th. 

A sample calibration report is shown in Figure 3.3. The report is three pages long, and the 

content contained on each page is summarized in the following sections. 

• Page 1

This page contains a header with the NIST service identification number (76100S) as listed in 

the NIST Calibration Services User’s Guide [41], and the address of the NIST Time and 

Frequency Division. 

The top portion of page 1 contains some general information about each customer including: 

the customer’s address, the main point of contact, and the manufacturer, model number, and 

type of the customer’s primary frequency standard (called the device under test). The rest of 

page 1 contains a brief description of the calibration method, and some general information 

about the FMAS. This text will change slightly from time to time as changes are made to the 

service. 

The bottom of page 1 contains a footer (also found on pages 2 and 3) that lists the issue date of 

the report, the report number, the NIST service identification number [41], and the page 

number. The report number is a six-digit number that uniquely identifies the report. The 

format for the report number is ##YYMM, where ## is the customer number, YY is a two-digit 

year code, and MM is the number of the month. 

• Page 2

This page contains a table that lists the daily frequency offset values for the customer’s primary 

frequency standard. Each frequency offset value is the result of a 24 h calibration (Chapter 

2.B.2.d). The table also lists the correlation coefficient r as a measure of confidence for each 

calibration, and a status code for each calibration. The status codes are explained in Table 3.4. 
59 

Chapter 3 - Operational Procedures 

If a status code other than 0 is assigned, it is accompanied by a brief comment that explains the 

situation. If a status code of 0 is assigned it means that the calibration is considered valid, and 

no further comment is necessary. 

• Page 3

This page contains a graph showing the daily frequency offset values for the customer’s 

primary frequency standard. The x-axis shows the days of the month, with each tic mark 

representing 1 d. The y-axis shows the frequency offset, with the middle of the y-axis 

representing a frequency offset of 1 × 10-12 or less. The plot accommodates oscillators that are 

high in frequency (the top half of the plot), or low in frequency (the bottom half). Frequency 

offsets larger than ± 1 × 10-8 are off the scale and plotted along the top or bottom line of the 

graph. 

An uncertainty statement, consisting of a table of values (see Chapter 5.C for computational 

details), is below the frequency graph. These values are described in Table 3.5. 

Table 3.4. Calibration report status codes.

Code Description 

0 Valid Calibration - NIST has determined that all components of the FMS worked properly during the calibration and that the calibration results are valid. This usually means 

that the result was within a k = 2 coverage area with respect to the average frequency. 

However, in some cases a valid calibration falls outside of the k = 2 range. 

1 No Data - No data were recorded. The measurement system was either turned off or 

malfunctioning or no DUT signal was present. 

2 GPS Reception Error - NIST has determined that the customer had a problem with 

GPS reception during the calibration. The cause could be either due to a malfunctioning receiver, antenna, or cable, or due to a source of interference. 

3 GPS Broadcast Error - NIST has determined that a GPS satellite was broadcasting invalid data that adversely influenced the calibration. Note that this situation rarely occurs. 

4 Measurement System Error - NIST has determined that the FMS had failed or was malfunctioning due to a hardware or software failure. 

5 DUT error – The customer’s primary frequency standard was out of normal tolerance 

during the calibration. 

6 DUT change – The customer has replaced their primary frequency standard with another device. 
60 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

The bottom of page 3 contains logos for the United States Department of Commerce and NIST, 

and signatures and telephone numbers from the preparer of the calibration report and the 

manager of time and frequency services at NIST. The customer is invited to contact these 

individuals if they have questions about the report. 

Table 3.5. Items listed on FMAS uncertainty statement.

Item Description 

Days when data were recorded The number of days in the month when a calibration of 

the customer’s primary frequency standard was performed. In most cases, this equals the number of days in 

the month since the calibrations are continuous. 

Days within tolerance (k = 2) The number of days when the customer’s primary frequency standard was within two standard deviations of 

its average frequency. 

Mean Frequency Offset (MFO) The mean (or average) frequency offset for the customer’s primary frequency standard for the specified 

month. 

Uncertainty (U), (k = 2) The measurement uncertainty assigned to the calibration 

of the customer’s primary frequency standard. This 

number will seldom be smaller than ± 2 × 10-13, since it 

is limited by the GPS propagation noise that is still present after 1 d of averaging. 

FOlower = MFO – U The lower band performance limit of the customer’s primary frequency standard during the month. There is a 

95.4 % probability that the frequency offset remained 

above this value and below FOupper throughout the entire 

month. 

FOupper = MFO + U The upper band performance limit of the customer’s primary frequency standard during the month. There is a 

95.4 % probability that the frequency offset remained 

below this value and above FOlower throughout the entire 

month. 
61 

Chapter 3 - Operational Procedures 

Figure 3.3.a. FMAS calibration report (page 1).
62 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

Figure 3.3.b. FMAS calibration report (page 2).
63 

Chapter 3 - Operational Procedures 

 

 

 

 

 

Figure 3.3.c. FMAS calibration report (page 3).
64 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

The FMAS calibration report contains the necessary elements listed in Section 5.10 

(“Reporting the Results”) of ISO/IEC Standard 17025 [42]. Table 3.6 lists the ISO/IEC 17025 

reporting requirements and where they are included on the FMAS calibration report. 

Table 3.6. ISO Standard 17025 requirements for reporting of calibration results. 

ISO/IEC 

17025 

section 

Description FMAS report 

page number 

5.10.2.a Title 1 

5.10.2.b Name and address of issuing laboratory, and location where 

calibrations were carried out 

1 

5.10.2.c Unique identification of the calibration certificate on every 

page 

1, 2, 3 

5.10.2.d Name and address of client 1 

5.10.2.e Identification of method 1 

5.10.2.f Description of item being calibrated 1 

5.10.2.g Date of performance of the calibration 1, 2, 3 

5.10.2.h Sampling plan or procedures NA 

5.10.2.i Calibration results 2, 3 

5.10.2.j Names, functions, and signatures of persons authorizing the 

calibration certificate 

3 

5.10.2.k Statement that results relate only to items being calibrated NA 

5.10.2.Note 1 Page numbers and total number of pages 1, 2, 3 

5.10.2.Note 2 Statement specifying that certificate should not be reproduced 

without consent of issuing laboratory 

3 

5.10.4.1.a Environmental conditions that have an influence on measurement results 

1 

5.10.4.1.b Measurement uncertainty statement 3 

5.10.4.1.c Evidence that the measurements are traceable 1, 3 

5.10.4.2 Statement of compliance NA 

5.10.4.3 Results before and after calibration instrument repair, when 

applicable 

2 

5.10.4.4 No recommendation on calibration interval shall be given NA 
65 

Chapter 3 - Operational Procedures 

5.10.8 Format of Certificate accommodates each type of calibration 

carried out 

1, 2, 3 

5.10.8.Note 1 Layout designed for ease of assimilation by reader 1, 2, 3 

5.10.8.Note 2 Headings should be standardized 1, 2, 3 

5.10.9 Amendments to certificates shall meet all requirements of 

ISO/IEC 17025 

NA 

5.10.7 Electronic transmission of results NA 

5.10.6 Results obtained from subcontractors must be identified NA 

5.10.5 Opinions and interpretations shall be documented 2 

Table 3.6, continued.. 
66 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

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67 

Chapter 4 - Customers 

This section describes the number and location of FMAS customers, the type of customers, the 

potential capacity of the service, and the ways that NIST interacts with and supports the 

customers. 

A. Number and Location of Customers 

From 1987 to 2004, the number of FMAS customers has fluctuated between about 35 and 60. 

The 60 customer peak was reached in 1990, prior to the closure of a number of United States 

Navy calibration laboratories. Figure 4.1 shows the approximate location of FMAS customers 

in the United States as of March 2004. A few customers are located outside the United States 

(not shown in the figure), since the use of GPS signals allows the FMS to be operated 

anywhere in the world. Historically, about 70 % of the FMAS customers operate cesium 

Chapter 4 

Customers 

Figure 4.1. Approximate locations of FMAS customers in the United States.
68 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

oscillators as their primary frequency standard, denoted by the letter “C” in Figure 4.1. The 

letter “R” denotes that a rubidium oscillator is used as the primary standard, “G” represents the 

use of a GPS disciplined oscillator, and “Q” represents the use of a quartz oscillator. 

NIST is always ready to accept new FMAS customers. Most customers subscribe for multiple 

years, and customer turnover is low, but reaching potential new customers is not particularly 

easy. How many potential FMAS customers are there in the United States? Answering this 

question requires identifying the needs of an FMAS customer. It is probably safe to assume 

that any customer or potential customer of the FMAS is required (for legal, contractual, 

practical, or policy reasons) to maintain a continuously running, traceable frequency source 

with a known uncertainty that they can use as a reference for calibrations or other 

measurements. Their known uncertainty requirement is probably never larger than about 1 ×

10-9 and often smaller than 1 × 10-10 since customers with lesser requirements probably cannot 

justify the subscription costs. In addition, the FMAS customer is probably required to provide 

documentation that these requirements are being met; a requirement satisfied by the monthly 

calibration certificate issued by NIST. Based on these assumptions, the number of potential 

FMAS customers in the United States, including those who already subscribe, can be roughly 

estimated as somewhere between 200 and 250 laboratories. To support this estimate, the NCSL 

International Directory of Standards Labs, an on-line database [43], lists 998 United States 

standards laboratories, including 457 with time and frequency capabilities as of March 2004. 

However, it is believed that roughly half of these laboratories require uncertainties too large to 

justify the cost or use of the FMAS. For example, some perform only simple calibrations of 

timing devices, such as stopwatches, and/or simple frequency calibrations of tuning forks used 

by law enforcement officers. Other listed laboratories are not potential FMAS customers since 

they provide only consulting services related to time and frequency metrology, and do not 

maintain an actual standard. 

B. How the FMAS is Used by its Customers 

Most FMAS customers are calibration and testing laboratories, located at either government or 

commercial facilities. These laboratories use the FMS to continuously monitor and measure 

their primary frequency standard and to establish documented measurement traceability back to 

the SI. This primary frequency source is then distributed throughout a laboratory or facility 

and used as a reference for other measurements. For example, a laboratory might send the 

output of its 10 MHz standard through a multi-channel distribution amplifier, so that signals 

can be distributed to the workbench of every engineer or technician involved in tests or 

measurements. The 10 MHz signal can then be used as the traceable time base or external 

trigger source for test equipment such as frequency counters, signal generators, and 

oscilloscopes. At the same time the 10 MHz signal is being used as the working reference 

standard for other measurements, it is being continually measured and monitored by the FMS, 

and its performance is reported upon by NIST. 

Since it has a total of five channels, the FMS can also be used by the customer to measure and 

calibrate four other devices without interrupting the continuous calibration of their primary 

frequency standard. For example, the FMAS customer might be a commercial calibration 
69 

Chapter 4 - Customers 

laboratory that routinely calibrates a large number of frequency counters. When a frequency 

counter is sent to the lab for calibration, its time base can be measured on the FMS, and the 

collected data can be used by the NIST customer to create a calibration report for their

customer. It’s fairly typical for a device to spend just one or two days connected to an FMS 

channel, and then be returned to service after its frequency uncertainty has been measured and 

documented. 

To support their calibration workload, many laboratories specify a frequency uncertainty 

requirement for their primary standard. This generally ranges from 1 × 10-9 to 1 × 10-12. A 

number near 1 × 10-11 should meet nearly all workload calibration requirements [44] and is a 

fairly typical requirement for a high quality laboratory. This is because the 1 × 10-11

requirement exceeds the manufacturer’s specification by about a factor of 10 for nearly all of 

the items they are likely to be asked to calibrate, thus establishing a desirable test uncertainty 

ratio of 10:1. Therefore, the FMS uncertainty of 2 × 10-13 (Chapter 5) should exceed the 

present needs of nearly all calibration labs, both for distributing frequency and for calibrating 

other devices. 

The FMAS can also be a very useful tool for customers seeking laboratory accreditation in 

frequency calibrations, since it provides a documented and controlled method for performing 

traceable calibrations. The two major accreditation bodies in the United States are the 

American Association for Laboratory Accreditation (A2LA) and the National Voluntary 

Laboratory Accreditation Program (NVLAP). At this writing (March 2004), six FMAS 

customers have received accreditation for frequency calibrations from NVLAP and three from 

A2LA. The NVLAP Calibration Laboratories Technical Guide for Time and Frequency 

Measurements [45] notes that: 

“The FMAS can benefit NVLAP customers seeking 

accreditation in the frequency calibration field. In some 

cases, it can eliminate or reduce the need for proficiency 

testing (and its associated fees) in the frequency calibration 

area.” [45, p.15] 

In addition to calibration and testing laboratories, the FMAS is also used by telecommunication 

companies, manufacturers of time and frequency related equipment, and others who need a 

convenient, traceable way to measure frequency. One of the most interesting applications 

involved using the FMS to measure the performance of a time and frequency distribution 

system (including cesium and rubidium oscillators) on board a United States Naval ship in a 

high magnetic field environment [46].

C. Customer Interaction and Technical Support 

The majority of FMAS technical support is still handled by telephone, although an increasing 

amount is now handled through email. Customers are encouraged to call NIST whenever they 

have a question or problem related to the service, or any other concern related to time and 

frequency metrology. Most problems are given immediate attention and quickly resolved, and 

very few customer complaints regarding the quality of technical support have been received 
70 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

during the 20 year span (1984 to 2004) that the service has been operational. NIST also 

interacts with customers through its web page and through its seminars, as described below. 

1. Web Page 

The FMAS web page on the NIST Time and Frequency Division web site is primarily used to 

inform new customers about the service. However, the page also is useful to current 

customers. It contains current pricing and financial information about the service that can be 

used by purchasing departments that are renewing or extending the service agreement. It also 

contains an electronic copy of the NIST Frequency and Measurement and Analysis System: 

Operator’s Manual [20], and other technical articles that serve as useful reference material for 

FMAS customers. The page can be found at http://tf.nist.gov/service/fms.htm 

2. Seminars 

FMAS customers are entitled to attend a free training seminar. Although the FMS does not 

really require any training to install and use (experience has shown that it is a task easily 

handled by any calibration laboratory technician), these seminars are useful for explaining the 

concepts behind the service, and serve as an introductory course in time and frequency 

metrology. These seminars typically last for two days. In the past, many of these seminars 

were scheduled on an ad hoc basis at the NIST laboratories in Boulder, Colorado, and this 

option is still utilized when necessary. From 1999 to 2004, they have been held each January 

immediately prior to the Measurement Science Conference (MSC) in California. Future 

seminars are expected to be held at MSC, and/or at the National Conference of Standards 

Laboratories International (NCSLI) headquarters training facility in Boulder, Colorado. A 

portable equipment rack containing various time and frequency related instrumentation, 

including a FMS unit, has been constructed for use as a teaching tool in these seminars. 

FMAS customers who require or desire more advanced time and frequency training are 

encouraged to attend the annual NIST Time and Frequency Metrology Seminar. This seminar is 

a comprehensive four-day course that explores the course material in more detail than the 

introductory courses. It has been held each summer at the NIST Boulder Laboratories since 

1976, typically attracting forty or more students (a registration fee is charged to FMAS 

customers who attend this seminar). 
71 

Chapter 5 - Measurement Uncertainties 

This chapter discusses the measurement uncertainty of the FMS unit, the uncertainties of 

measurements made with and without GPS, and how the service establishes traceability to the 

SI through UTC(NIST). 

The FMS uncertainties are reported in a manner that utilizes elements of the ISO and NIST 

guides [47, 48]. In general terms, frequency uncertainty is usually expressed in terms of 

accuracy and stability. Accuracy is a Type B uncertainty that quantifies the offset from an 

ideal value, such as the frequency offset quantity previously discussed. Stability is a Type A 

uncertainty that indicates how well a device produces the same frequency offset over a given 

period. Stability estimates are calculated from a set of frequency offset measurements and 

show frequency fluctuations with respect to an average frequency offset. The offset values are 

obtained by sampling or averaging over the stated time interval tau (t). Standard deviation (σ) 

can be used to measure frequency stability for white noise processes, but a common “nonclassical” statistic used to estimate frequency stability is the previously described Allan 

deviation, σy(τ) [38]. 

The FMAS defines a calibration as a 1 d (24 h) measurement. Therefore, measurement 

uncertainty is specified at an averaging time of 1 d. This is done for both practical and 

technical reasons. For example, 1 d is a long enough period to calibrate nearly anything that a 

lab will be asked to calibrate, but not too long to be considered impractical. Longer 

measurement runs and more averaging would obviously result in lower measurement 

uncertainties, but the uncertainties are already low enough to meet the customer’s 

requirements. Measurement uncertainty is contributed by GPS (Chapter 5.A) and by the FMS 

itself (Chapter 5.B). A 1 d calibration is generally sufficient to reduce the k = 2 noise floor of 

both GPS (2 × 10-13) and the FMS (2 × 10-15) below the noise floor of the DUT, resulting in a 

clean measurement of the DUT with an uncertainty that is not inflated by either reference or 

measurement system noise, and that meets or exceeds the laboratory’s requirements. 

A. Uncertainties of Measurements made with GPS 

When estimating the measurement uncertainty of GPS with respect to UTC(NIST), it should 

first be noted that both time scales are steered to agree with the international UTC time scale 

maintained by the Bureau International des Poids et Mesures (BIPM). As a result, the GPS 

signals and UTC(NIST) are essentially phase locked to each other with a very long time 

constant used for the steering. Over long time periods, the Type B uncertainty contributed by 

the frequency offset is insignificant, < 1 × 10-15, and for practical purposes it can be regarded 

as 0. Figure 5.1 illustrates this by showing a GPS to UTC(NIST) comparison for the entire 

year of 2003. The graph shows many short term frequency fluctuations, but the frequency 

offset for the entire year, estimated using the slope of a linear least squares line, is −1.7 × 10-16. 

Chapter 5 

Measurement Uncertainties
72 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

When looking at the GPS data in Figure 5.1, or at GPS data collected by the FMS over its 1 d 

calibration interval, it becomes obvious that the uncertainty in the frequency offset estimate is 

almost always several times larger than the average frequency offset itself. This is because 

GPS is always steered to be accurate relative to UTC, so continuous corrections are being made 

to compensate for the Type B uncertainty. Thus, the uncertainty of a GPS measurement made 

over a 1 d interval is essentially equivalent to the Type A uncertainty, which is limited by GPS 

propagation noise. 

The Type A frequency uncertainty of the FMS GPS receiver was estimated with two different 

statistical techniques, Allan deviation and standard deviation, both involving a comparison with 

UTC(NIST). The test was run for one month (31 d). A data set consisting of 31 daily 

frequency offset estimates was created using the least squares line technique described in 

Chapter 2. A frequency graph of these data is shown in Figure 5.2. The average frequency 

offset (as indicated by the straight line) is < 4 × 10-14 and would continue to get smaller over a 

longer data run. 

 

GPS - UTC(NIST)

-10

-5

0

5

10

15

20

25

30

35

40

Daily Averages (January 1 to December 31, 2003)

Nanoseconds

Figure 5.1. GPS versus UTC(NIST) during 2003 (1 d averages). 
73 

Chapter 5 - Measurement Uncertainties 

The two statistics should produce essentially the same result if the noise processes are white, an 

assumption that is basically true for the dominant FMS noise source at 1 d, which is GPS 

propagation noise. First, the Allan deviation, σy(τ) at τ = 1 d was calculated as 8.77 × 10-14, 

then doubled to produce a k = 2 coverage area of 1.75 × 10-13. Next, the standard deviation (σ) 

was calculated as 8.71 × 10-14, then doubled to produce a k = 2 coverage area of 1.74 × 10-13. 

These numbers are rounded up to 2 × 10-13 and used as the FMS frequency offset uncertainty 

estimate (k = 2) for a 1 d calibration using GPS as a reference. Note that these data were 

collected after only a coarse survey of the receiving antenna was done as described in Chapter 

2.B.2.a. A better antenna survey, which is not always possible at customer sites, would result 

in a slightly lower frequency uncertainty. 

It should be noted that the linear regression technique used to estimate the daily frequency 

offset “smooths” the data and makes the 1 d uncertainty estimate slightly lower than it would 

be if the entire raw data set were used. Figure 5.3 shows the Allan deviation graph for all of 

the 1 h averages collected by the FMS during the 31 d interval. This graph uses the “all tau” 

method, so σy(τ) is calculated for all possible τ values. Note that the first τ value is 1 h, the 

averaging time of the FMS. At τ = 24 h, σy(τ) equals 1.31 × 10-13, or 2.62 × 10-13 when 

expanded to k = 2, slightly higher than the “smoothed” data. Not all of the data for the month 

 Figure 5.2. Graph of daily frequency offset estimates (GPS – UTC(NIST)). 
74 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

is used to estimate the Type A uncertainty because the FMS treats each 1 d period as an 

independent calibration, and a frequency offset estimate is reported daily. Therefore, a day 

with “bad” data affects only a single daily calibration. A “bad” data point can be removed if 

necessary so that it does not affect the uncertainty analysis for the entire month (Chapter 5.C.). 

B. Uncertainties of Measurements made without GPS 

The uncertainty of measurements made without GPS (oscillator to oscillator comparisons) is 

estimated as 2 × 10-15 (k = 2) for an averaging time of 1 d. The limiting factors for these 

measurements are either noise introduced by the frequency dividers or noise introduced by the 

time base PLL on the TIC when it is used to generate the stop pulse. This is the scenario that 

exists whenever a customer compares a secondary oscillator to their primary oscillator. The 

PLL circuit has small frequency variations over time due to temperature and voltage 

fluctuations in the power supply. The TIC’s built-in frequency dividers are usually present in 

all comparisons made with the FMS, unless an incoming 1 pps test signal is compared to an 

external 1 pps signal, a configuration seldom used by FMAS customers. Frequency dividers 

always add some measurement noise or jitter to the counter readings [28], but this problem 

was minimized in the FMS design, where the majority of the counter’s digital circuitry is 

included in a programmable logic device (PLD). The PLD allows measurement noise and 

 Figure 5.3. Frequency stability (Allan deviation) of FMS GPS receiver. 
75 

Chapter 5 - Measurement Uncertainties 

delays to be reduced since the counter and divider circuitry is housed in a single integrated 

circuit [16], an advantage over using discrete components. 

The TIC itself introduces significant resolution uncertainties at short averaging times, but these 

are indiscernible after 1 d of averaging. As previously discussed, the TICs single shot 

resolution is near 25 ps, which limits its ability to detect frequency changes smaller than a few 

parts in 1011 at an averaging time of 1 s. However, the TIC noise, which is typically white 

phase noise, averages down to a few picoseconds at about 100 s, and the noise floor is typically 

a few parts in 1016 at an averaging time of 1 d, or below the noise floor of the frequency 

dividers or time base PLL. 

From a practical perspective, the most important characteristic of any frequency measurement 

system is its ability to resolve small frequency differences between two oscillators. If the noise 

floor of the measurement system has been accurately determined, it should be able to make a 

clean measurement of a frequency offset that is a factor of 10 larger than the noise floor. In the 

case of the FMS, its noise floor estimate of 2 × 10-15 (k = 2) suggests that it should be easily 

able to resolve a frequency offset of 2 × 10-14 over the standard 1 d calibration period. To test 

this premise, an 80 MHz direct digital synthesizer (DDS) was phase locked to UTC(NIST), and 

its output signal was offset in frequency by −1 μHz (−1.25 × 10-14). This signal was then 

connected to channels 2 and 3 of the FMS, where it was divided to 1 pps and used as the start 

pulse on both channels. On channel 2, the stop pulse was obtained by locking the TIC PLL 

circuit to UTC(NIST), and then dividing the 10 MHz output to 1 pps. On channel 3, the stop 

pulse was obtained directly from UTC(NIST) using an external divider. The phase graphs 

from the two measurements are shown in Figures 5.4 and 5.5. 

The measurement was run for 16 d (384 h). Note that the two graphs look very similar. There 

is some noise visible along the measurement trace, but the trend contributed by the frequency 

offset is obvious. At least some of the noise is due to the instability of the DDS used to 

generate the start pulse on both channels, and is not attributable to the FMS itself. At τ = 1 d, 

σy(τ) is estimated as approximately 2 × 10-15 for both measurements. The test demonstrates that 

the FMS has a sufficiently low noise floor to easily reveal and measure a 1.25 × 10-14 frequency 

offset, with both techniques producing a result within 2 × 10-16 of the expected value. 

C. Discussion of Uncertainty Statement on Calibration Report 

The uncertainty statement on the NIST calibration report provides the frequency uncertainty of 

the customer’s primary frequency standard, and not the measurement uncertainty of the FMS, 

which was discussed in sections B and C above. It reports the average frequency offset and a 

range of possible frequency offset values for the customer’s primary frequency standard based 

on a k = 2 coverage area (2σ). Therefore, there is a 95.4 % probability that the frequency offset 

will remain within this estimated range during the month for which values are reported. The 

estimated range for the frequency offset values is limited by GPS noise, and can generally not 

be made narrower than ± 2 × 10-13 with respect to the average frequency. In many cases, the 

range is made wider due to the frequency aging and drift of the customer’s primary frequency 

standard, and in some cases, due to frequency adjustments made by the customer. 
76 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

 

 Figure 5.4. Measuring a 1.25 × 10-14 frequency offset with TIC PLL as stop pulse. 

 Figure 5.5. Measuring a 1.25 × 10-14 frequency offset with an external 1 pps stop pulse.
77 

Chapter 5 - Measurement Uncertainties 

An uncertainty statement is shown in tabular form in Table 5.1. This statement is identical to 

the uncertainty statement that appears on page 3 of the calibration report pictured in Figure 

3.3.c, and previously described in Table 3.5. 

The daily frequency offset values become the yi data set, which contains from 28 to 31 values, 

depending upon the length of the current month. The mean frequency offset for the month, 

MFO, and the standard deviation are calculated by utilizing a simple “3-sigma, 2-pass” filter. 

The mean and standard deviation (σ) of the yi data series are computed, data that fall more than 

3σ from the mean are removed, and the process is repeated. Therefore, the MFO and σ are 

calculated from the second pass, in some cases with outliers removed. The uncertainty, U, is 

set equal to 2σ and is added to and subtracted from MFO to obtain the upper and lower bounds 

of the uncertainty range, FOupper and FOlower. Then, all values in the yi data set, including those 

that were excluded from the original calculation of MFO and σ, are checked to see if they fall 

outside the upper and lower bounds of the uncertainty range. If so, they are marked as out of 

tolerance and require annotation by the person preparing the calibration report (Chapter 3.G). 

In the uncertainty statement listed in Table 5.1, it was determined that the customer’s primary 

standard was high in frequency on average by 1.74 × 10-12 during the one month interval, and 

that there was a 95.4 % probability that the frequency offset stayed between +1.54 and +1.95 

parts in 1012 with respect to the nominal frequency. 

D. Establishing Traceability to the SI through UTC(NIST) 

One of the main benefits of the FMAS is that it simplifies a laboratory’s task of establishing 

traceability to the SI. Calibration laboratories are generally required to establish traceability of 

their own measurement standards and measuring instruments to the SI by means of an 

unbroken chain of calibrations or comparisons linking them to relevant primary standards of 

the SI units of measurement. The link to SI units may be achieved by reference to national 

measurement standards [42]. One obvious way to establish traceability then is for a calibration 

laboratory to make a measurement that directly compares its primary standard to the national 

standard. This could be done if the laboratory sends its primary standard to its National 

Metrology Institute (NMI) for calibration. Even then, however, traceability would only be 

established at a given point in time, and would have to be periodically reestablished [49]. For 

example, if a house standard were calibrated by an NMI ten years ago, it would not be 

considered sufficient evidence to establish traceability today. 

In frequency metrology, transfer standards such as GPS make it possible to continuously 

establish traceability by making continuous comparisons against the national standard. This is 

often done via common-view comparisons, which have been performed by NMIs using GPS 

 Table 5.1. Sample FMAS calibration report uncertainty values. 

Days when data were recorded 31 Uncertainty (U), (k = 2) +2.05E-13 

Days within tolerance (k=2) 31 FOlower = MFO – U +1.54E-12 

Mean Frequency Offset (MFO) 1.74E-12 FOupper = MFO + U +1.95E-12 
78 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

satellites since 1980 [11], and prior to that time with signals from LORAN-C, television, 

WWV, and other sources. The common-view method is conceptually simple. Since it is often 

impossible to bring two oscillators to the same physical location to compare them, both 

oscillators are continually compared to signals originating from a reference transmitter, R. 

Receivers at each oscillator site (A and B) simultaneously receive the signal from R, compare 

the received signal to their oscillator, and store the measurement data. Thus, one site measures 

the frequency offset between R and oscillator A, the other site measures the frequency offset 

between R and oscillator B. The two sites then exchange their data and subtract one data set 

from the other. The resulting data reveals the frequency offset between oscillator A and 

oscillator B, since the frequency offset of R falls out of the equation [18]. Through the use of 

common-view GPS, a direct comparison to the national frequency standard can be made, 

meaning that the traceability chain back to the NMI contains only one link [39]. 

The FMAS is based on a hybrid form of the common-view technique. NIST continuously 

monitors the GPS satellites with several “master” FMS units identical to those used by 

customers and with a number of other receivers, so the GPS signals are in common-view. At 

NIST, the master FMS GPS receivers are being continually compared to UTC(NIST), the 

national frequency standard, so the frequency uncertainty of an FMS unit is well characterized. 

Continuous evidence that GPS uncertainties are at or below the 2 × 10-13 specification claimed 

by the FMAS is provided to the public in the NIST GPS Data Archive, which publishes daily 

measurement values for GPS − UTC(NIST) for all satellites in the constellation 

(http://tf.nist.gov/service/gpstrace.htm) using the same type of receiver used by the FMS. 

However, the FMAS is not a true common-view service because the data collected at the 

customer’s site are not subtracted from the data collected at NIST. This has the advantage of 

allowing measurement results to be reported to the customer in real time because no continuous 

data exchange is required with NIST before results can be shown. 

In the FMAS model, the traceability chain back to the NMI consists of two links. The first link 

is the comparison between the local device under test and GPS. The second link is the 

comparison between GPS and UTC(NIST) performed by NIST [39]. This same general model 

(Figure 5.6) for establishing traceability to the SI through an NMI can be applied to any other 

signal that is monitored, but not controlled by the NMI [50]. Note that in Figure 5.6 links B 

and C represent the two links back to the NMI, and link A represents the link from the NMI 

back to the SI. In a true common-view system, the unlabeled diagonal line would serve as a 

single link back to the NMI (replacing links B and C), but exchanging and differencing data 

would be required. 

Subscribing to the FMAS is obviously not the only way that a laboratory can establish 

traceability in frequency to the SI. The use of GPS disciplined oscillators (GPSDOs) is now 

widely accepted as a proper way to establish traceability. However, one key component of 

establishing traceability involves quantifying the measurement uncertainty of each link in the 

traceability chain. This can be a difficult problem, because the uncertainties of all GPS 

measurements are receiver dependent, and different models of GPSDOs produce different 

results, even when operated under identical conditions [51-52]. It is also not always obvious to 
79 

Chapter 5 - Measurement Uncertainties 

a laboratory whether a GPS receiver is working properly or meeting its specifications [44]. 

The FMAS solves these problems since the uncertainties of its GPS measurements have been 

well characterized and are highly repeatable. All customers use identical hardware and 

hardware operated in a controlled, identical fashion and the achievable uncertainties are 

essentially identical at all customer sites. NIST has confirmed this through many years of 

experience performing remote frequency calibrations at numerous geographic locations. 

 Figure 5.6.. The generic traceability model used by the FMAS. 
80 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

Products or companies named in this document are cited only in the interest of providing a 

complete technical description of the FMS, and identification neither constitutes nor implies 

endorsement by NIST or by the U. S. government. Other products may be found to work as 

well. 

 
81 

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Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

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84 

Remote Frequency Calibrations: The NIST Frequency Measurement and Analysis Service 

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