Calibration of a power sensor at a frequency of 18 GHz
Author: EAThis Example is taken from EA 4/02. See EA 4/02 Section S6 for more details.
The measurement involves the calibration of an unknown power sensor with respect to a calibrated power sensor used as a reference by substitution on a stable transfer standard of known small reflection coefficient. The measurement is made in terms of calibration factor, which is defined as the ratio of incident power at the reference frequency of 50 MHz to the incident power at the calibration frequency under the condition that both incident powers give equal power sensor response. At each frequency one determines the (indicated) ratio of the power for the sensor to be calibrated respectively the reference sensor and the internal sensor that forms part of the transfer standard, using a dual power meter with ratio facility.
Model Equation:
K_{X} = (K_{S} + δK_{D}) * (M_{Sr} * M_{Xc}) / (M_{Sc} * M_{Xr}) * p_{Cr} * p_{Cc} * p

List of Quantities:
Quantity  Unit  Definition 

K_{X}  unknown calibration factor  
K_{S}  calibration factor of the reference power sensor  
δK_{D}  drift of calibration factor of the reference power sensor since its last calibration  
M_{Sr}  mismatch factor of the reference power sensor at the reference frequency of 50 MHz  
M_{Xc}  mismatch factor of the unknown power sensor at the calibration frequency of 18 GHz  
M_{Sc}  mismatch factor of the reference power sensor at the calibration frequency of 18 GHz  
M_{Xr}  mismatch factor of the unknown power sensor at the reference frequency of 50 MHz  
p_{Cr}  correction of the observed ratio for nonlinearity and limited resolution of the power meter at power ratio level of the reference frequency  
p_{Cc}  correction of the observed ratio for nonlinearity and limited resolution of the power meter at power ratio level of the calibration frequency  
p  =p_{iX}/p_{iS,} ratio of the output power ratios indicated at the power transfer system in realizing equal response for the unknown and the reference power sensor 
K_{S}: 
Type B normal distribution Value: 0.957 Expanded Uncertainty: 0.011 Coverage Factor: 2 
δK_{D}: 
Type B rectangular distribution Value: 0.001 Halfwidth of Limits: 0.002 
M_{Sr}: 
Type B Ushaped distribution Value: 1.0 Halfwidth of Limits: 0.0008 
M_{Xc}: 
Type B Ushaped distribution Value: 1.0 Halfwidth of Limits: 0.0168 
M_{Sc}: 
Type B Ushaped distribution Value: 1.0 Halfwidth of Limits: 0.014 
M_{Xr}: 
Type B Ushaped distribution Value: 1.0 Halfwidth of Limits: 0.0008 
p_{Cr}: 
Type B normal distribution Value: 1.0 Expanded Uncertainty: 0.00142 Coverage Factor: 1.0 
p_{Cc}: 
Type B normal distribution Value: 1.0 Expanded Uncertainty: 0.000142 Coverage Factor: 1.0 
p: 
Type A Method of observation: Direct Number of observation: 3
Arithmetic Mean: 0.97597 
Uncertainty Budgets:
K_{X}: unknown calibration factorQuantity  Value 
Standard Uncertainty 
Distribution 
Sensitivity Coefficient 
Uncertainty Contribution 
Index 

K_{S}  0.95700  5.50·10^{3}  normal  0.98  5.4·10^{3}  11.0 % 
δK_{D}  1.00·10^{3}  1.15·10^{3}  rectangular  0.98  1.1·10^{3}  0.5 % 
M_{Sr}  1.000000  566·10^{6}  Udistr.  0.93  530·10^{6}  0.1 % 
M_{Xc}  1.0000  0.0119  Udistr.  0.93  0.011  46.9 % 
M_{Sc}  1.00000  9.90·10^{3}  Udistr.  0.93  9.2·10^{3}  32.6 % 
M_{Xr}  1.000000  566·10^{6}  Udistr.  0.93  530·10^{6}  0.1 % 
p_{Cr}  1.00000  1.42·10^{3}  normal  0.93  1.3·10^{3}  0.7 % 
p_{Cc}  1.000000  142·10^{6}  normal  0.93  130·10^{6}  0.0 % 
p  0.97597  4.80·10^{3}  normal  0.96  4.6·10^{3}  8.1 % 
K_{X}  0.9330  0.0162 
Results:
Quantity  Value 
Expanded Uncertainty 
Coverage factor 
Coverage 

K_{X}  0.933  0.032  2.00  95% (ttable 95.45%) 