8-9
fr = reference (i.e., the “correct”) frequency
Text Box: Frequency
Frequency
Text Box: t
t
Text Box: Time Error
Time Error
Text Box: 1
1
2
Text Box: 3
3
Text Box: t
t
Text Box: 1
1
Text Box: 2
2
Text Box: 3
3
fr
Text Box: t
t
Text Box: Frequency
Frequency
Text Box: Time Error
Time Error
Text Box: t
t
Text Box: fr
fr
Text Box: Frequency
Frequency
Text Box: Time Error
Time Error
Text Box: t
t
Text Box: t
t
Text Box: fr
fr
Text Box: 3
3
Text Box: t
t
Text Box: Time Error
Time Error
Text Box: 1
1
Text Box: 2
2
Text Box: t
t
Text Box: fr
fr
Text Box: 1
1
Text Box: 2
2
Text Box: 3
3
Text Box: Frequency
Frequency
Frequency Error vs. Time Error
ft = fo + Afrt
where ft = f at time t, fo = initial f at time zero, A is the aging (e.g., 5 x 10-10 per day), and fr = the reference frequency.  The time error T(t) is given by the equation two pages back.  Neglecting the noise term,
T(t) = T0 + ([fo- fr]/fr] t + 1/2At2)

The plot of To vs. t is a parabola (for finite A), for which the vertical displacement is To.  The above illustration shows the relationship between frequency and time errors, for positive and negative constant frequency errors, and for positive and negative aging.


"Timekeeping and Frequency Calibration," Hewlett-Packard Co. Application Note 52-1
<http://www.tmo.hp.com/tmo/Notes/English/>