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
Arithmetic Mean: 30.04025 dB |
| 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%) |