
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: ................................................................................
1 mW
2. Frequency: .................................................................................
1 GHz
3. Calculate meter uncertainty: In free run, auto zero mode average = 16
Calculate noise contribution
•IfinFreeRunmode,Noise = Measurement noise x free run multiplier = 50 nW x 0.6 = 30 nW
•IfinTriggermode,Noise = Noise-per-sample x noise per sample multiplier
Convert noise contribution to a relative term
1
= Noise/Power = 30 nW/100 μW ........................ 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 = 300 nW/1 mW .............................. 0.03 %
5. Sensor calibration uncertainty
(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, | ρ
Sensor
| = (SWR–1)/(SWR+1) = .................................. 0.111
Max DUT SWR (frequency-dependent) = ........................................................
1.26
convert to reflection coefficient, | ρ
DUT
| = (SWR–1)/(SWR+1) = .................................... 0.115
8. Combined measurement uncertainty @ k=1
U
C
=
(
Max(ρ
DUT
) • Max(ρ
Sensor
)
)
2
+
(
sys
rss
)
2
...................................................
√2 2
2.23 %
Expanded uncertainty, k = 2, = U
C
•2= .........................................................
±4.46 %
1. The noise-to-power ratio is capped for powers > 100 μW, in these cases use: Noise/100 μW.
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