Understanding
Oscillator Specs
Hugo Fruehauf
FEI-Zyfer Inc.
August 2004
hxf@fei-zyfer.com
Agenda
• Definitions
• The Time and Frequency Domains
• Time Domain
• Frequency Domain
• General Comparisons
2
Frequency and Time Basics
•
I
F= T , where F = frequency (= number of “events” per unit time)
T = period (= time between “events”)
•
The unit for frequency is Hertz (Hz). One event or cycle per
second = 1 Hertz, 1000 cycles per second = 1000 Hz, etc.
•
The unit for time is of course seconds. Since 1967, the second
is defined by the cesium atomic oscillator.
Total Number of Events
Number of Events Per Unit of Time
•
Accumulated Clock Time =
•
Frequency Standard + Counting Mechanism = A Clock
3
Definition of Terms as Applied to Oscillators(1)
Aging (Implying Frequency Aging)
The change in frequency with time due to internal changes in the oscillator. It
is the frequency change with time while factors external to the oscillator
(environment, power supply, etc.) are kept constant. Generally aging, rather
than drift, is what one measures during oscillator evaluation.
∆Τ =
1 2
at
2
∆Τ = Time Error
a = aging
t = Elapsed Time
Drift (Implying Frequency Drift)
The change in frequency with time that one observes in an application. Drift is
due to aging plus changes in the environment and other factors external to the
oscillator.
Accuracy (Of Output Frequency)
The degree of conformity of a measured or calculated value to some specified
value or definition. In the case of time and frequency, the ultimate frequency
accuracy is defined by the 133Cs Atomic Resonance of 9,192,631,770 Hz.
Frequency Offset
The difference between the realized value and the nominal frequency value.
4
Definition of the ‘SECOND’
• The ‘SECOND’ is the duration of 9,192,631,770
periods of the radiation corresponding to the
transition between the two (unperturbed)
hyperfine levels of the ground state of the
133Cesium
atom
5
Accuracy (Precision) and Stability
f
Accurate but
not precise
Not accurate and
not precise
Precise but
not accurate
f
f
Accurate and
precise
f
0
Time
Stable but
not accurate
Time
Not stable and
not accurate
Time
Accurate but
not stable
Time
Stable and
accurate
6
Time Domain vs. Frequency Domain
A
f
(a)
Amplitude - Frequency
Amplitude - Time
t
(c)
(b)
A(t)
A(f)
Example (a) shows a sine wave and its second harmonic. A signal consisting of the sum of the two waves is
shown in the time domain (b), and in the frequency domain (c). In the time domain, all frequency components of a
signal are summed together. In the frequency domain, signals are separated into their frequency components and
the power level at each frequency is displayed.
7
Time and Frequency Noise vs. Time Error
Time Domain Stability
Freq. Aging vs. Time Error
(Time Noise)
4
3
1E-11
2
1E-12
1
~0.5µs
1E-13
10-1 100 101 102 103 104
Averaging Time (Sec.)
1E
Ag -11
in
g/
M
o.
1E-10
T(error) = 1/2 at 2
1
105
Freq. Domain Stability
2
3
4
Time In Days
Freq. Offset vs. Time Error
-80
dBc
~3µs
(Phase Noise)
-100
-120
f =
1
Τ
O
et
T(error) = ∆ f/f x t
~1µs
-140
-160
1
-1
E
1
~2µs
ffs
0
1
-1
10
0
10
1
10
2
10
3
10
4
10
5
10
2
3
4
Time In Days
Hertz From Carrier
8
How Do You Measure Time Domain Noise?
10-9
QUESTION: Why are the Total
and Allan deviations (shown on
top plot) recommended for time
domain noise characterization
of oscillators (shown on the
bottom plot)?
F
R
E
Q
U
E
N
C
Y
S
T
A
B
I
L
I
T
Y
- = Total Deviation
Ο = Allan Deviation
-10
10
10-11
10-12
ANSWER: The standard
deviation applied to the
measurement of the frequency
of an oscillator implies a false
assumption that there exists a
true mean frequency. The
Total and Allan deviations can
estimate frequency stability
even if the mean is changing,
such as the frequency step that
is shown in the figure.
F
R
A
C
T
I
O
N
A
L
F
R
E
Q
U
E
N
C
Y
100
101
102
T(s)
103
104
105
8095
8085
8075
8065
8055
0
75
150
225
300
DAY
9
Given the Time Residuals from a
Precision Oscillator
x(t)
yi =
τ
x(t)
y1
y3
y4
x i +1 − x i
τ
yM
Etc.
y2
2
1 M
(y i − y )
σSTD DEV y (τ ) =
∑
M −1 i =1
Classical Variance
Does Not Converge as M
Increases
yi
2
M1
1
(
σ y (τ ) =
yi + 1 − yi )
∑
2(M − 1) i = 1
Allan Variance
Does Converge as M
Increases
10
Allan Variance Concept
Difference in Slope = ∆y = y2 - y1
x3
X = Time Difference
x2
x1
y2
y1
τ
σ 2y (τ ) =
τ
1
(∆ y )2 ~ τ µ
2
Time
11
Computing Allan Variance
The Two-Sample Deviation or square-root of the Allan Variance is the standard method of describing the shortterm stability of oscillators in the time domain. It is usually described by σy(τ), where:
1 m−1
∑ y −
2(m − 1) k =1 k +1
(
)
10-10
yk 2
In the example below:
10-12
10-13
Number of data values available, m=9
Number of differences averaged, m-1=8
Sampling time interval τ=1s
Data Values
(y)
892
809
823
798
671
644
883
903
677
1st Data Point
10-11
σy(τ)
σ2y (τ ) =
10-14
10-1 100 101 102 103 104
(τ)
First Differences
y k +1 − y k
First Differences Squared
-83
14
-25
-127
-27
239
20
-226
6889
196
625
16129
729
57121
400
51076
(
)
∑ (y
(y k +1 −
m −1
k =1
k +1
− yk
)
2
yk
)
= 133165
Based on these data:
2
σ y 2 (τ ) =
133165
= 8322.81
2(8 )
[σ y (τ )]
2
1/ 2
=
8322 . 81
σ y (τ ) = 91.23, τ = 1s
In this example, the data values
are parts in 1013.
12
Comparison of Qz, Rb, GPS, Cs, & Maser
Time Domain Stability
10-10
HP 5061A, Cs
Hi-Per Qz
HP 5071A, Cs
10-11
GPS-Disciplined
Qz/Rb
10-12
VR
1
(AllanVariance) 2, σy (τ )
Symmetricom
Cs III, Cs
EM
Y
10-13
10-14
KV
AR
ZP
CH
as s
-10
ive
06
Ma
Pa
KV
ssi
ser
AR
ve
ZA
M
ctiv
e M aser
ase
r
AV
Hi-Per Rb
HP 5071A, Cs
Hi-Per Option
10-15
1 Day
1 Hr
1 Week
1 Mo.
10 Hrs.
10-16
1
10
102
103
104
Averaging Time, T(Sec.)
105
106
13
-80
dBc/Hz down from REF.
Carrier REF. (Osc. Output Amplitude at the Intended Osc. Freq.)
Frequency Domain Noise
(Phase Noise)
-100
f =
1
Τ
-120
-140
Measure Energy in 1 Hz Bandwidth
-160
10-1
(1 mHz)
100
(1 Hz)
101
(10 Hz)
102
(100 Hz)
103
(1 KHz)
104
(10 KHz)
105
(100 KHz)
Hertz From Carrier
dBc = Decibels (referenced to the carrier)
14
Phase Noise Under Vibration
Vibration Induced Phase Noise
Vibration Induced
Side Band
L(f)
(Slope 6 dB/Octave)
L(f)
Quiescent Oscillator Performance
f-From Carrier
Acceleration Power
Spectral Density
Acceleration Power
Spectral Density
Quiescent Oscillator Performance
f-From Carrier
f-Vibration
Sinusoidal Vibration
f-Vibration
Random Vibration
15
Typical Specs for the Precision Quartz Oscillators
Basic Parameters
TCXO
OCXO (0.5” High) OCXO (0.75” High)
DOCXO
(Temp. Comp. XO) (Oven Control XO) (Oven Control XO) (Double Oven XO)
10 MHz, Sine
0.5 Vrms, 50 Ω
1 E-9
5 E-10
5 E-10
1E-11
1E-11
1E-10
5E-12
1E-11
1E-11
- 55 dBc/Hz
-115 dBc/Hz
-130 dBc/Hz
- 80 dBc/Hz
-135 dBc/Hz
-145 dBc/Hz
- 90 dBc/Hz
-135 dBc/Hz
-145 dBc/Hz
- 90 dBc/Hz
-135 dBc/Hz
-145 dBc/Hz
-75 dBc/Hz
-125 dBc/Hz
-145 dBc/Hz
--5E-7/yr
5E-10/day
2E-7/yr
2E-10/day
2E-8/yr
2E-10/day
2E-8/yr
5E-11/day
5E-10/yr
Temp Range
Frequency Stability
0° to 75°C
5E-7
0° to 75°C
2E-8
0° to 70°C
2E-10
0° to 60°C
3E-10
Power Consumption
Warm-up Time
50 miliwatts
50 milisec
2 watts
10 min, 1E-8
3.5 watts
10 min, 1E-8
8 watts
4 min, ~1E-9
--12 Vdc± 10%
1E-9 for +/-10%
--12 Vdc± 10%
1E-9 for +/-10%
2E-11/Gauss
15 to 28 Vdc
2E-11 for +/-10%
2.0” x 2.0” x 0.75” H
3
3 in
< 0.22 lbs
2.0” x 2.0” x 1.0” H
3
4 in
< 0.3 lbs
3.0” x 3.0” x 1.4” H
3
13 in
0.75 lbs
Short Term Stab.
Phase Noise,
1s
10s
100s
1Hz
100Hz
1000Hz
Aging/Day/Month/Year
Magnetic Field Sensitivity
Input Volts Range
Supply Volts Sensitivity
--5 Vdc± 0.25%
1E-8 for +/-10%
Size
Volume
Weight
1.0” x 0.7” x 0.22” H
3
0.154 in
< 0.1 lbs
--12 Vdc± 10%
1E-9 for +/-10%
1.5” x 1.5” x 0.5” H
3
1.125 in
< 0.15 lbs
0° to 75°C
2E-9
2.5 watts
10 min, 1E-8
10 MHz, Sine
0.5 Vrms, 50 Ω
Rubidium Osc.
10 MHz, Sine
0.5Vrms, 50 Ω
Output
10 MHz, Sine
0.5 Vrms, 50 Ω
For Reference Only
5E-12
1E-11
1E-11
10 MHz, Sine
0.5 Vrms, 50 Ω
3E-11
7E-12
3E-12
16
1 sec
100 ms
10 ms
1 ms
100 µs
10 µs
1 µs
100 ns
10 ns
1
Hr.
O
et
ffs
x
-5
x
-6
10
-9
-7
10
10
-8
10
x
10
1
et
ffs
1
x
x
4
1
et
ffs
O
1
et
ffs
t1
fse
Of
2
O
O
30
10
Min.
1 ns
Accumulated Time Error
10 sec
Frequency Aging and Offset vs. Time Error
Dr
ift
0
-1
10
10
2
-1
t1
fse
0
x1
3
-1
0
x1
t1
fse
Dr
ift
1x
Dr
ift
10 -1
2
1x
10 -1
1
Dr
ift
Dr
ift
1x
10 -1
0
1x
10 -9
1x
1x
1x
10 -7
Dr
ift
1x
1x
10 -4
10 -5
10 -6
10 -8
x
4
-1
t1
1
Year
5
-1
10
4
x
1
-1
10
x
Of
Of
fse
1 3 2 1 5 4 3 2 1 16
Month
Week
Day
1
Dr
ift
x
10 -1
5
Of
2
et
10 -1
4
1
1x
ffs
1x
10 -1
3
1
Dr
ift
1x
t
fse
Of
Dr
ift
Dr
ift
O
Dr
ift
t
fse
Of
Elapsed Time
8
Dr
i ft
Note: • Aging Lines Represent “Aging/Day”
• Offset Lines are Independent of a Time Period
• Add Aging and Expected Offset for ~ Total Time Error
17