Calibration of a coaxial step attenuator at a setting of 30 dB (incremental loss)

Author: EA
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 + δLS + δLD + δLM + δLK + δLib - δLia + δL0b - δL0a

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
δLS dB correction obtained from the calibration of the reference attentuator
δLD dB change of the attenuation of the reference attenuator since its last calibration due to drift
δLM dB correction due to mismatch loss
δLK dB correction for leakage signals between input and output of the attenuator to be calibrated due to imperfect isolation
δLib dB correction due to the limited resolution of the reference detector at 30 dB
δLia dB correction due to the limited resolution of the reference detector at 0 dB
δL0b dB correction due to the limited resolution of the null detector at 30 dB
δL0a 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: 30.04025 dB
Standard Deviation: 0.018 dB
Standard Uncertainty: 9.13·10-3 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)

δLS: 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.

δLD: 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.

δLM: Type B U-shaped distribution
Value: 0.0 dB
Halfwidth of Limits: 0.0283 dB
MISMATCH LOSS: (see EAL-R2-S1:S7.6)

δLK: 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.

δLib: 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.

δLia: 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.

δL0b: 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.

δL0a: 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:

LX: attenuation of the attenuator to becalibrated
Quantity Value Standard
Uncertainty
Distribution Sensitivity
Coefficient
Uncertainty
Contribution
Index
LS 30.04025 dB 9.13·10-3 dB normal 1.0 9.1·10-3 dB 16.6 %
δLS 3.00·10-3 dB 2.50·10-3 dB normal 1.0 2.5·10-3 dB 1.2 %
δLD 0.0 dB 1.15·10-3 dB rectangular 1.0 1.2·10-3 dB 0.3 %
δLM 0.0 dB 0.0200 dB U-distr. 1.0 0.020 dB 79.7 %
δLK 0.0 dB 1.73·10-3 dB rectangular 1.0 1.7·10-3 dB 0.6 %
δLib 0.0 dB 289·10-6 dB rectangular 1.0 290·10-6 dB 0.0 %
δLia 0.0 dB 289·10-6 dB rectangular -1.0 -290·10-6 dB 0.0 %
δL0b 0.0 dB 2.00·10-3 dB normal 1.0 2.0·10-3 dB 0.8 %
δL0a 0.0 dB 2.00·10-3 dB normal -1.0 -2.0·10-3 dB 0.8 %
LX 30.0432 dB 0.0224 dB

Results:

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

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