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:

• Sensor Linearity and Temperature Compensation: Sensor Linearity and Temperature Compensation describe 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 differing impedances between the power sensor and the device to which the power sensor is connected. Mismatch uncertainty can be calculated as follows:

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

dB Mismatch Uncertainty = 10log|1 + Γ1Γ2|

where

Γ1 and Γ2 are the reflection coefficients of the power sensor and the device under test

• Sensor Calibration Factor Uncertainty: Sensor Calibration Factor Uncertainty is defined as the accuracy of the sensor calibrated at a standard calibration condition. Anritsu follows the industry standard condition of calibration at a reference power of 0 dBm (1 mW) and an ambient temperature of 25 °C.

Uncertainty Example

Two measurement uncertainty calculations for Low Aperture Time mode are shown for the MA24106A in Table: Measurement Uncertainty Example. The MA24106A is used to measure the power of a 3 GHz, +12.0 dBm and –35 dBm CW signal from a signal source with 1.5:1 VSWR. The example is based on 128 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 | 1.8 | 1.8 |

Noise | 0.0 | 0.8 | Normal at 2σ | 2 | 0.0 | 0.4 |

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 | 1.4 | 1.4 | Normal at 2σ | 2 | 0.7 | 0.7 |

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 | 7.2 | ||||

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

Combined Uncertainty (RSS, 0 to 50 °C) | 3.1 | 3.7 | ||||

Expanded Uncertainty with K=2 (RSS, 0 to 50 °C) | 6.2 | 7.4 |

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

Noise | 400 nW/16 mW = 0.0 % |

Zero Set | 1700 nW/16 mW = 0.0 % |

Zero Drift | 500 nW/16 mW = 0.0 % |

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

Noise | 2.5 nW/316 nW = 0.8 % |

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

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