May 1967 Electronics World
Wax nostalgic about and learn from the history of early electronics. See articles
Electronics World, published May 1959
- December 1971. All copyrights hereby acknowledged.
This article from the May 1967 edition of Electronics World
shows you just how long the
Electronics company has been around! In fact, here is an
excerpt from their website: "Frequency Electronics, Inc. was
founded in 1962 and is now a well-established public company
in Long Island, New York, and trades on the NASDAQ Stock Exchange
under the symbol FEIM." Mr. Irwin Math, who wrote the article,
has surely retired by now. The discussion on short- and long-term
stability is as relevant today as it was 45 years ago.
Selecting Frequency and Time Standards
By Irwin Math / Project Engineer, Frequency Electronics, Inc.
How precision oscillators and clocks are rated and exactly
what they are capable of. A discussion of stability and other
important standard specifications.
Highly precise frequency
and time standards are becoming more and more widely used in
today's sophisticated scientific world. The missile and space
age demands, for example, are far in excess of the requirements
of only a few years ago. In fact, the stability of the research
laboratory's frequency standard of 10 years ago is now taken
for granted in the oscillators of many types of modern industrial
As a result, all too often the engineer
or technician will specify a complex, ultra-stable frequency
standard when a much less stable one would have been sufficient
for his application. Similarly, he can often mistakenly interpret
a lower order oscillator as easily as one of much higher quality.
For these reasons, the engineer and technician as well as anyone
with even a casual interest in the measurement field should
have a good
of just how precision oscillators and clocks
are rated and exactly what they are capable of doing.
Long-Term and Short-Term Stability
In the "good
old days", it was enough to ask for a 1-MHz oscillator with
a stability of ±0.001%. Anything better than 0.1% was considered
rather good. But today things have changed. All but the simplest
of oscillators that are used as standards are rated in parts
per 10". For example, a 1-MHz oscillator with a stability of
± 1 Hz is rated at 1 MHz ±1 part in 106
or 1 part
per million. Similarly, a good frequency standard may have a
stability of ±1 part in 1010
The general expression for frequency stability is S=ΔF/F
where F is the nominal frequency and ΔF is the allowable variation.
Therefore, the actual frequency variation of our frequency standard
(considering its output is 1 MHz nominal) is ±0.0001 Hz or ±1
x 10-10 of the nominal frequency.
Fig. 1. Measuring long-term stability by
means of peak readings.
However, this information is not enough. While it does indicate
stability, it does not specify over what period of time this
stability must be measured, The complete stability of a frequency-standard
oscillator must be given in two parts: the long term and the
The long-term stability of an oscillator is basically the
average change in frequency over a long fixed period of time
as compared to some absolute reference. Usually, long-term stability
is measured in one of two ways. The first of these, as indicated
in Fig. 1, depends on readings of frequency taken continuously
for several days. The maximum peak-to-peak deviation over any
24-hour period is measured and the stability is then defined
as ± one-half this maximum. For example, since both oscillators
in Fig. 1 have a peak-to-peak variation of 1 part in 108
per day, their long-term stability would be specified as ±5
parts per 109 per day. Notice, though, that oscillator
#2 has a much longer average rate of frequency change than does
oscillator # 1. Therefore, while they both are ±5 parts in 109
per day oscillators, oscillator #2 is obviously superior.
Fig. 2. Measuring long-term stability by
The second method, and by far the more accurate one, is based
on the average change of frequency over a given time interval.
As shown in Fig. 2, the stability of oscillators #1 and #2 is
now determined by the slope of their average frequencies. Now
it is easy to see that oscillator #2 is substantially better
than oscillator #1.
Fig. 3. Automatic recording of an oscillator
with a short-term stability of plus or minus 5 parts in 109
To further clarify the measurement and eliminate any remaining
doubt, a few oscillator manufacturers incorporate both the average
long-term frequency change and the day-to-day change in their
long-term stability specification. For example, a 1-MHz oscillator
such as the one shown in Fig. 4 with a rated long-term stability
of ±1 part in 1010 is one whose maximum daily and
average frequency will change by no more than ±1 cycle per 10
billion cycles per day or 0.0001 cycle per day.
The short-term stability of an oscillator is its frequency
stability over periods of time from a few seconds to fractions
of a second. This type of specification is important when the
oscillator is used as the source for a frequency multiplication
system, especially into the thousands of MHz. If, for example,
a 1-MHz oscillator with a second-to-second variation of ±1 part
in 106 were multiplied to 1000 MHz, the variation
would now be ±1000 Hz per second.
As in long-term measurements, there are two general methods.
One is similar to long term in that readings of frequency are
taken. The time interval, however, is much shorter. Fig. 3 is
a recording of an oscillator with a short-term variation of
±5 parts in 109 per second. Notice that in any 1-second
interval, the frequency never deviates by ±5 parts in 109
from the nominal. This type of recording is used for intervals
as low as 0.1 second. Smaller intervals require too fast a recorder
speed and are measured by the second method.
This method involves a statistical approach. The oscillator
to be measured is fed to a low-noise mixer along with a very
stable reference frequency.
The difference of the two signals is then fed to a counter
which measures the period (or wavelength) of this signal. A
typical setup is shown in Fig. 5. The difference frequency actually
triggers a gate, allowing a very stable 10-MHz signal to drive
the counter. Since the period of the difference signal determines
how many cycles of 10 MHz will be fed into the counter, great
accuracy can be achieved. Assuming that the difference signal
is 1 Hz, this means that 10,000,000 cycles will pass into the
counter through the gate for each cycle of input. Therefore,
only 1/10,000,000 of a second change in the difference signal
will cause the counter to indicate a change. Since such great
resolution is possible by this technique, extremely short intervals
of time can be measured and interpreted as short-term stabilities.
Fig. 4. A typical high-quality frequency
standard which has a long-term stability of plus or minus 1
part in 1010.
Usually an oscillator with good short-term stability will
not exhibit a good long-term characteristic and vice versa.
As a result, where both long- and short-term stability must
be as good as possible, the technique shown in Fig. 6 is used.
A very good long-term standard and a very good short-term standard
are fed to a phase detector. The d.c. output of the phase detector
is then fed back to a voltage-variable capacitor in the short-term
standard which causes its frequency to "lock" to the frequency
of the long-term unit. This "phase-locking" technique now produces
an output with excellent long- and short-term stabilities.
Fig. 5. Test setup employed for short-term measurements.
The stability of an oscillator with changes in ambient operating
temperature is another important factor to consider when specifying
high-stability oscillators. Fig. 7 is a curve of the temperature
versus frequency characteristics of a typical high-quality crystal.
It can be seen that changes in crystal temperature result in
significant changes in frequency.
It is therefore extremely important to isolate the crystal
from the effects of varying temperatures. Vacuum bottles (dewars)
are often employed in the highest stability units and, in most
cases, the crystal itself is in a well-regulated, temperature-controlled
Similarly, changes in operating voltage, line voltages, and
load impedances are all important and should be considered when
choosing oscillators. The effects of these parameters are stated
in terms of the maximum frequency changes they produce in the
Other Important Criteria
Some of the other more
important criteria which should be considered when selecting
equipment of this nature are:
1. Construction - the
equipment should be able to withstand mechanical shock and also
occupy the least amount of space, especially where it is to
be part of a physically complex system.
2. Power consumption
- in portable, airborne, or other such applications, it is desirable
to obtain the lowest power consumption of the oscillators in
order to realize the longest usable life.
3. Measurements should be the result of exhaustive tests
on many units of the type to be used, where possible.
Finally, perhaps the most important "specification" to many
technical personnel is cost. While mechanical construction and
ambient temperature isolation will determine the cost of a unit
to an extent, the primary cost factor is the ultimate stability
of the unit. The greater the stability required (both long-
and short-term) the more elaborate the circuitry required and
better the crystal must be. For example, while a ±1 part in
108 oscillator is available for $200, a ±1 part in
1010 oscillator can easily cost $2000.
Fig. 6. A phase-locked oscillator system
Fig. 7. Typical frequency vs. temperature
characteristic for a high-quality crystal. Oven is set to "turnover-point"