This Example is taken from EA 4/02. See EA 4/02 Section S7 for more details.

The measurement involves the calibration of a coaxial step attenuator at 10 GHz using an attenuation measuring system containing a calibrated step attenuator which acts as the attenuation reference. The method of measurement involves the determination of the attenuation between a matched source and matched load. In this case the unknown attenuator can be switched between a setting of 0 dB and 30 dB and it is this change (called incremental loss) that is determined in the calibration process. The attenuation measuring system has a digital readout and an analogue null detector which is used to indicate the balance condition.

Model Equation:

LX = LS + dLS + dLD + dLM + dLK + dLib - dLia + dL0b - dL0a

List of Quantities:

Quantity	Unit	Definition
LX	dB	attenuation of the attenuator to becalibrated
LS	dB	=Lib - Lia attenuation difference of reference attenuator at 30 dB and 0 dB
dLS	dB	correction obtained from the calibration of the reference attentuator
dLD	dB	change of the attenuation of the reference attenuator since its last calibration due to drift
dLM	dB	correction due to mismatch loss
dLK	dB	correction for leakage signals between input and output of the attenuator to be calibrated due to imperfect isolation
dLib	dB	correction due to the limited resolution of the reference detector at 30 dB
dLia	dB	correction due to the limited resolution of the reference detector at 0 dB
dL0b	dB	correction due to the limited resolution of the null detector at 30 dB
dL0a	dB	correction due to the limited resolution of the null detector at 0 dB

LS:	Type A Method of observation: Direct Number of observation: 4 No. Observation 1 30.033 dB 2 30.058 dB 3 30.018 dB 4 30.052 dB Arithmetic Mean: 30.040250 dB Standard Deviation: 0.018 dB Standard Uncertainty: 9.132·10-3 dB Degrees of Freedom: 3

MEASUREMENTS: Four observations are made of the incremental loss of the attenuator to be calibrated between settings of 0 dB and 30 dB. (see EAL-R2-S1:S7.11)

dLS:	Type B normal distribution Value: 0.003 dB Expanded Uncertainty: 0.005 dB Coverage Factor: 2

REFERENCE ATTENUATOR: The calibration certificate for the reference attenuator gives a value of attenuation for the 30,000 dB setting at 10 GHz of 30,003 dB with an associated expanded uncertainty of 0,005 dB (coverage factor k=2). The correction of +0,003 dB with the associated expanded uncertainty of 0,005 dB (coverage factor k=2) is considered to be valid for attenuation settings of the reference attenuator which differ not more ±0,1 dB from the calibrated setting of 30,000 dB.

dLD:	Type B rectangular distribution Value: 0.0 dB Halfwidth of Limits: 0.002 dB

DRIFT OF THE REFERENCE: The drift of the attenuation of the reference attenuator is estimated from its calibration history to be zero with limits ±0,002 dB.

dLM:	Type B U-shaped distribution Value: 0.0 dB Halfwidth of Limits: 0.0283 dB

MISMATCH LOSS: (see EAL-R2-S1:S7.6)

dLK:	Type B rectangular distribution Value: 0.0 dB Halfwidth of Limits: 0.003 dB

LEAKAGE CORRECTION: Leakage signals through the attenuator to be calibrated have been estimated from the measurements at 0 dB setting to be at least 100 dB below the measurement signal. The correction for leakage signals is estimated from these findings to be within ±0,003 dB at the 30 dB setting.

dLib:

Type B rectangular distribution Value: 0.0 dB Halfwidth of Limits: 0.0005 dB

RESOLUTION OF THE REFERENCE ATTENUATOR SETTING: The digital readout of the reference attenuator has a resolution of 0,001 dB from which the correction for resolution is estimated to be within ±0.0005 dB.

dLia:

Type B rectangular distribution Value: 0.0 dB Halfwidth of Limits: 0.0005 dB

RESOLUTION OF THE REFERENCE ATTENUATOR SETTING: The digital readout of the reference attenuator has a resolution of 0,001 dB from which the correction for resolution is estimated to be within ±0.0005 dB.

dL0b:

Type B normal distribution Value: 0.0 dB Expanded Uncertainty: 0.002 dB Coverage Factor: 1.0

RESOLUTION OF THE NULL DETECTOR: The detector resolution was determined from a previous evaluation to have a standard deviation of 0,002 dB at each reading with assumed normal probability distribution.

dL0a:

Type B normal distribution Value: 0.0 dB Expanded Uncertainty: 0.002 dB Coverage Factor: 1

RESOLUTION OF THE NULL DETECTOR: The detector resolution was determined from a previous evaluation to have a standard deviation of 0,002 dB at each reading with assumed normal probability distribution.

Uncertainty Budgets:
L_X: attenuation of the attenuator to becalibrated

Quantity	Value	Standard Uncertainty	Distribution	Sensitivity Coefficient	Uncertainty Contribution	Index
LS	30.040250 dB	9.132·10-3 dB	normal	1.0	9.1·10-3 dB	16.6 %
dLS	3.000·10-3 dB	2.500·10-3 dB	normal	1.0	2.5·10-3 dB	1.2 %
dLD	0.0 dB	1.155·10-3 dB	rectangular	1.0	1.2·10-3 dB	0.3 %
dLM	0.0 dB	0.02001 dB	U-distr.	1.0	0.020 dB	79.7 %
dLK	0.0 dB	1.732·10-3 dB	rectangular	1.0	1.7·10-3 dB	0.6 %
dLib	0.0 dB	288.7·10-6 dB	rectangular	1.0	290·10-6 dB	0.0 %
dLia	0.0 dB	288.7·10-6 dB	rectangular	-1.0	-290·10-6 dB	0.0 %
dL0b	0.0 dB	2.000·10-3 dB	normal	1.0	2.0·10-3 dB	0.8 %
dL0a	0.0 dB	2.000·10-3 dB	normal	-1.0	-2.0·10-3 dB	0.8 %
LX	30.04325 dB	0.02242 dB

Results:

Quantity	Value	Expanded Uncertainty	Coverage factor	Coverage
LX	30.043 dB	0.045 dB	2.00	95% (t-table 95.45%)