10
Worked Example
Uncertainty calculations for a power measurement (settled, average power)
[Specification values from this document are in bold italic, values calculated on this page are underlined.]
Process:
1. Power level: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1mW
2. Frequency: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 GHz
3. Calculate meter uncertainty: In free run, auto zero mode average = 16
Calculate noise contribution
• If in Free Run mode, Noise
= Measurement noise x free run multiplier = 50 nW x 0.6 = 30 nW
• If in Trigger mode, Noise
= Noise-per-sample x noise per sample multiplier
Convert noise contribution to a relative term
15
= Noise/Power = 30 nW/100 uW . . . . . . . . 0.03%
Instrumentation linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.8%
Drift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . –
RSS of above three terms => Meter uncertainty
= . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.8%
4. Zero Uncertainty
(Mode and frequency dependent) = Zero set/Power
= . . . . . . . . . . . . . . . . . . . . . . . . . 0.03%
5. Sensor calibration uncertainty
300 nW/1 mW
(Sensor, frequency, power and temperature dependent) = . . . . . . . . . . . . . . . . . . . . . . . 4.0%
6. System contribution
, coverage factor of 2 => sys
rss
= . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.08%
(RSS three terms from steps 3, 4 and 5)
7. Standard uncertainty of mismatch
Max SWR (Frequency dependent) = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.25
convert to reflection coefficient, |
r
Sensor
| = (SWR–1)/(SWR+1) = . . . . . . . . . . . . . . . . . . 0.111
Max DUT SWR (Frequency dependent) = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.26
convert to reflection coefficient, |
r
DUT
| = (SWR–1)/(SWR+1) = . . . . . . . . . . . . . . . . . . . . 0.115
8. Combined measurement uncertainty @ k=1
. . . . . . . . . . . . . . . . . . . . . 2.23%
Expanded uncertainty, k = 2, = U
C
• 2 = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ±4.46%
15. The noise to power ratio is capped for powers > 100 uW, in these
cases use: Noise/100 µW instead.