Uncertainty of a Measurement

Measurement Uncertainty Calculator

Included at the Anritsu download center is a Microsoft Excel tool for calculating power uncertainty. It contains two tabs; one that provides measurement uncertainty for each sensor (selectable from a drop-down menu), and another tab that provides additional uncertainty components and calculated values for the power sensor.

Uncertainty Components

Power measurements have many component parts that affect overall measurement uncertainty when measuring power with the sensor:

• Measurement Uncertainty: Measurement uncertainty includes the uncertainty associated with the correction of frequency and the linearity response of the sensor over the entire dynamic range. Anritsu follows the industry standard condition of calibrating the power-sensing element at a reference power of 0 dBm (1 mW) and an ambient temperature of 25 °C.

• Temperature Compensation: Sensor Temperature Compensation describes the relative power level response over the dynamic range of the sensor. Temperature Compensation should be considered when operating the sensor at other than room temperature.

• Noise, Zero Set, and Zero Drift: These are factors within the sensor that impact measurement accuracy at the bottom of the power sensor’s dynamic range.

• Mismatch Uncertainty: Mismatch uncertainty is typically the largest component of measurement uncertainty. The error is caused by the differing impedances between the power sensor and the devices to which the power sensor is connected. Mismatch uncertainty can be calculated as follows:

% Mismatch Uncertainty = 100[|1 + Γ1Γ2|2 – 1]

dB Mismatch Uncertainty = 20log|1 + Γ1Γ2|

where:

Γ1 is the reflection coefficient of the power sensor

Γ2 is the reflection coefficient of the device

Uncertainty examples are shown in Table: MA24108A and MA24118A Measurement Uncertainty Example and Table: MA24126A Measurement Uncertainty Example.

Uncertainty Examples

Two measurement uncertainty calculations are shown for the MA24108A and MA24118A sensors in Table: MA24108A and MA24118A Measurement Uncertainty Example. The power sensor is used to measure the power of a 3 GHz, +12.0 dBm and –35 dBm CW signal from a signal source with a 1.5:1 VSWR. The example is based on an aperture time of 20 ms and 64 measurement averages.

Uncertainty Term | Uncertainty Specification at +12 dBm (%) | Uncertainty Specification at –35 dBm (%) | Probability Distribution | Divisor | Adjusted Uncertainty at +12 dBm (%) | Adjusted Uncertainty at –35 dBm (%) |

Sensor Linearity (<+18 dBm) | 3.0 | 3.0 | Rectangular | √3 | 1.7 | 1.7 |

Noise | 0.0 | 1.6 | Normal at 2σ | 2 | 0.0 | 0.8 |

Zero Set | 0.0 | 3.2 | Rectangular | √3 | 0.0 | 1.8 |

Zero Drift | 0.0 | 0.9 | Normal at 2σ | 2 | 0.0 | 0.6 |

Calibration Factor Uncertainty | 1.5 | 1.5 | Normal at 2σ | 2 | 0.8 | 0.8 |

Mismatch Uncertainty | 4.0 | 4.0 | Rectangular | √3 | 2.3 | 2.3 |

Combined Uncertainty (RSS), Room Temperature | 3.0 | 3.6 | ||||

Expanded Uncertainty with K=2, Room Temperature | 6.0 | 7.3 | ||||

Temperature Compensation | 1.4 | 1.4 | Rectangular | √3 | 0.8 | 0.8 |

Combined Uncertainty (RSS, 0 to 50 °C) | 3.1 | 3.6 | ||||

Expanded Uncertainty with K=2 (RSS, 0 to 50 °C) | 6.2 | 7.5 |

Two measurement uncertainty calculations are shown for the MA24126A sensor in Table: MA24126A Measurement Uncertainty Example. The power sensor is used to measure the power of a 3 GHz, +12.0 dBm and –35 dBm CW signal from a signal source with a 1.5:1 VSWR. The example is based on an aperture time of 20 ms and 64 measurement averages.

Uncertainty Term | Uncertainty Specification at +12 dBm (%) | Uncertainty Specification at –35 dBm (%) | Probability Distribution | Divisor | Adjusted Uncertainty at +12 dBm (%) | Adjusted Uncertainty at –35 dBm (%) |

Sensor Linearity (<+18 dBm) | 3.0 | 3.0 | Rectangular | √3 | 1.7 | 1.7 |

Noise | 0.0 | 1.6 | Normal at 2σ | 2 | 0.0 | 0.8 |

Zero Set | 0.0 | 3.2 | Rectangular | √3 | 0.0 | 1.8 |

Zero Drift | 0.0 | 0.9 | Normal at 2σ | 2 | 0.0 | 0.6 |

Calibration Factor Uncertainty | 2.5 | 2.5 | Normal at 2σ | 2 | 1.25 | 1.25 |

Mismatch Uncertainty | 4.0 | 4.0 | Rectangular | √3 | 2.3 | 2.3 |

Combined Uncertainty (RSS), Room Temperature | 3.2 | 3.8 | ||||

Expanded Uncertainty with K=2, Room Temperature | 6.3 | 7.6 | ||||

Temperature Compensation | 1.4 | 1.4 | Rectangular | √3 | 0.8 | 0.8 |

Combined Uncertainty (RSS, 0 to 50 °C) | 3.3 | 3.9 | ||||

Expanded Uncertainty with K=2 (RSS, 0 to 50 °C) | 6.5 | 7.7 |

Noise Calculations at 12 dBm (16 mW): | |

Noise | 1 μW/16 mW = 0.0 % |

Zero Set | 1 μW/16 mW = 0.0 % |

Zero Drift | 0.5 μW/16 mW = 0.0 % |

Noise Calculations at –35 dBm (316 nW): | |

Noise | 5 nW/316 nW = 1.6 % |

Zero Set | 10 nW/316 nW = 3.2 % |

Zero Drift | 3 nW/316 nW = 0.9 % |

Two measurement uncertainty calculations are shown for the MA242x8A sensor in Table: MA24208A and MA24218A Measurement Uncertainty Example. The power sensor is used to measure the power of a 3 GHz, +12.0 dBm and –35 dBm CW signal from a signal source with a 1.5:1 VSWR. The example is based on an aperture time of 20 ms and 64 measurement averages.

Uncertainty Term | Uncertainty Specification at +12 dBm (%) | Uncertainty Specification at –35 dBm (%) | Probability Distribution | Divisor | Adjusted Uncertainty at +12 dBm (%) | Adjusted Uncertainty at –35 dBm (%) |

Linearity and Calibration Factor | 2.33 | 3.16 | Normal at 2σ | 2 | 1.16 | 1.58 |

Noise | 0.02 | 0.11 | Normal at 2σ | 2 | 0.01 | 0.05 |

Zero Set | 0.01 | 0.11 | Rectangular | √3 | 0.00 | 0.06 |

Zero Drift | 0.01 | 0.11 | Normal at 2σ | 2 | 0.00 | 0.05 |

Mismatch | 4 | 4 | Rectangular | √3 | 2.31 | 2.31 |

Combined Uncertainty (RSS), 20 °C to 30 °C | 2.59 | 2.80 | ||||

Expanded Uncertainty with K=2, 20 °C to 30 °C | 5.18 | 5.60 |

Noise Calculations at 12 dBm (16 mW): | |

Noise | 2.41 µW/15.85 mW = 0.01% |

Zero Set | 1.07 µW/15.85 mW = 0.01% |

Zero Drift | 1 µW/15.85 mW = 0.01% |

Noise Calculations at –35 dBm (316.2 nW): | |

Noise | 0.346 nW/316.2 nW = 0.11% |

Zero Set | 0.332 nW/316.2 nW = 0.11% |

Zero Drift | 0.343 nW/316.2 nW = 0.11% |