HP 53131A, Assembly And Service Manual

Page: 241 / 254

Chapter 8 HP 53181A Specifications
Measurement Specifications (Continued)
Assembly-Level Service Guide 8-7
8
Frequency Measurement Example:
Given an HP 53181A with a High Stability Oven that was calibrated 3 days ago, measure a 15 MHz square wave signal (which has negligible
trigger error) with a 1 second gate time. Compute the measurement error to within 2-sigma confidence.
Which is to say that the HP 53181A would display results in the range 15 MHz ±63.1 mHz. Note however that the dominant error is the Time
Base Error. If an even higher stability time base is available to the instrument or if the instrument can be source locked to the 15 MHz signal,
then this error term can be substantially reduced. The measurement resolution under these conditions is ±0.8 MHz (1 sigma) which
determines the number of digits displayed.
Measurement Specifications (Continued)
Measurement Error Systematic Uncertainty 2 RMS Resolution
× ±
=
Time Base Error
±
t
acc
Gate Time
----------------------------
±
 
 
2
4 t
res
2
2 Trigger Error
2 × ( )
+
×
Gate Time Number of Samples
×
-------------------------------------------------------------------------------------------
t
jitter
Gate Time
----------------------------
+
 
 
 
× ±
 
 
 
=
Frequency
×
Number of Samples 200,000 since Frequency is greater than 200kHz and gate time equals 1 second
=
Time Base Error Temperature Stability 3 Days Daily Aging Rate
×
+ =
2.5 10
9 –
3 5 10
10 –
× ( ) ×
+
×
=
4.0 10
9
– ×
=
Measurement Error 4.0 10
9 – × ±
1 10
10 – ×
s
1s
---------------------------
±
 
 
2
4 500 10
12 –
s
× ( )
2
2 0
× ( )
+
×
1s 200 000
, ×
-------------------------------------------------------------------------------
50 10
12 –
s
×
1s
------------------------------
+
 
 
 
× ±
 
 
 
15MHz
×
=
4.1
±
10
9 – ×
2 4.47 10
12 – ×
50 10
12 – ×
+
( ) × ± ( )
15MHz
×
=
4.1
±
10
9 –
×
1.09 10
10 –
× ± ( )
15MHz
×
=
63.1 mHz
±
=