Uncertainty of a Measurement

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.

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:

• Source Mismatch:

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

dB Mismatch Uncertainty = 20log|1 + Γ1Γ2|

• Load Mismatch (not considering inline power sensor insertion loss):

% Load Mismatch Uncertainty = 100[|1 + Γ2Γ3|2 – 1]

dB Load Mismatch Uncertainty = 20log|1 + Γ2Γ3|

• Load Mismatch (considering inline power sensor insertion loss):

% Load Mismatch Uncertainty = 100[|1 + t2Γ2Γ3|2 – 1]

dB Load Mismatch Uncertainty = 20log|1 + t2Γ2Γ3|

• Directivity Uncertainty:

% Uncertainty due to Finite Directivity = 100[(1 + Γ3 /D)2 – 1]

where:

D is the directivity of the inline power sensor expressed in linear units

Γ1 is the reflection coefficient of the inline power sensor

Γ2 is the reflection coefficient of the source

Γ3 is the reflection coefficient of the load

t is the inline power sensor’s transmission coefficient

t = 10(IL/20)

IL = Insertion Loss of the inline power sensor

Uncertainty Examples

Noise Measurement Uncertainty is shown in Table: Noise Measurement Uncertainty Calculations.

Noise Calculations at 50 dBm (100 W): | |

Noise | 1.9 mW/100 W = 0.0 % |

Zero Set | 3 mW/100 W = 0.0 % |

Zero Drift | 2.7 mW/100 W = 0.0 % |

Noise Calculations at +10 dBm (10 mW): | |

Noise | 170 μW/10 mW = 1.7 % |

Zero Set | 250 μW/10 mW = 2.5 % |

Zero Drift | 230 μW/10 mW = 2.3 % |

Two measurement uncertainty calculations for the MA24105A are shown in Table: Measurement Uncertainty Examples. The MA24105A is used to measure the power of a 1 GHz, +50.0 dBm and +10 dBm CW signal from a signal source with a 1.5:1 VSWR and a load having a 1.2:1 VSWR. The example is based on 128 measurement averages.

Uncertainty Term | Uncertainty at +50 dBm(%) | Uncertainty at +10 dBm(%) | Probability Distribution | Divisor | Adjusted Uncertainty at +50 dBm (%) | Adjusted Uncertainty at +10 dBm (%) |

Measurement Uncertainty | 3.8 | 3.8 | Normal at 2σ | 2 | 1.9 | 1.9 |

Noise | 0.0 | 1.7 | Normal at 2σ | 2 | 0.0 | 0.9 |

Zero Set | 0.0 | 2.5 | Rectangular | √3 | 0.0 | 1.4 |

Zero Drift | 0.0 | 2.3 | Normal at 2σ | 2 | 0.0 | 1.3 |

Directivity Induced Uncertainty | 0.6 | 0.6 | Rectangular | √3 | 0.3 | 0.3 |

Source Mismatch Uncertainty | 1.4 | 1.4 | Rectangular | √3 | 0.8 | 0.8 |

Load Mismatch Uncertainty | 3.7 | 3.7 | Rectangular | √3 | 2.1 | 2.1 |

Effect of Digital Modulation | 0 | 0 | Rectangular | √3 | 0 | 0 |

Combined Uncertainty (RSS) Room Temperature | 3.0 | 3.7 | ||||

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

Temperature Compensation | 1.9 | 1.9 | Rectangular | √3 | 1.1 | 1.1 |

Combined Uncertainty (RSS, 0 to 50 °C) | 3.2 | 3.8 | ||||

Expanded Uncertainty with K=2 (RSS, 0 to 50 °C) | 6.3 | 7.6 |

Table: Uncertainty Example - Pulse Signal (MA24105A) shows another example measuring a pulse signal of +50 dBm at a repetition rate of 80/S with a duty cycle of 8 %.

PEP Uncertainty Components | ||||

Power Sensor | Uncertainty at +50 dBm (%) | Probability Distribution | Divisor | Adjusted Uncertainty at +50 dBm (%) |

Base Unc (Average Power Uncertainty) | 6.3 | Normal | 2 | 3.2 |

Peak Circuit Contribution | 7.3 | Rectangular | √3 | 4.2 |

Burst Repetition Rate | 1.8 | Rectangular | √3 | 1.0 |

Burst Width | 0.0 | Rectangular | √3 | 0.0 |

Burst Duty Cycle | 0.1 | Rectangular | √3 | 0.1 |

PEP Measurement Uncertainty | ||||

Combined Uncertainty (%) (Base Unc + RSS) | 7.5 | |||

Expanded Uncertainty (%) with K=2 | 15.0 |