NI USB-5680 Uncertainty Calculator

Introduction

When performing radio frequency (RF) measurements, it is important to accurately estimate the uncertainty of the measurement. In this document, we show how to calculate the total (or combined) uncertainty of NI USB-5680 RF power meter measurements.

Absolute uncertainty percentages are not included in the NI USB-5680 RF Power Meter Specifications since many of the factors are dependent on the sourcing instrument. Moreover, we need to follow a careful procedure to calculate the combined uncertainty from the individual uncertainties, which you can find in the specifications. On this web page, we include the step-by-step process to calculate the combined uncertainty, a numeric example, and an application that will do these calculations for you with the numeric inputs you specify. 

To learn more about the types of uncertainties, refer to the National Institute of Standards and Technology (NIST) reference, below.

Calculating Individual Uncertainties

The first step in calculating the combined uncertainty is to calculate the individual uncertainties (refer to the specifications document for these values). To give a numeric example, we will use a power level of 10 dBm and frequency of 2 GHz. Given these values, we can get the following uncertainty quantities from the specifications document:

Table 1

Linearity and mismatch contribute the most to the combined uncertainty at higher powers, while at lower powers, noise, zero set and zero drift are also very important. To convert noise power to a percentage, divide the specification by the actual input power: 10 dBm or 0.01 W, in this example.

At higher power levels, noise is not be a major contributor to power accuracy. For reference, the table below illustrates the effect of noise, zero set, and zero drift at two distinct power levels. These numbers account for a coverage factor K=2. More details about coverage factor are explained below.

Table 2

You can calculate mismatch uncertainty using a combination of both the source VSWR and the instrument VSWR. While mismatch uncertainty varies according to the DUT, let's assume that our DUT has a VSWR of 1.3. We also know from the specifications document that the NI USB-5680 has a VSWR of 1.2 at 2 GHz. Therefore:

Solving for Γ in the equation VSWR = (1-Γ)/(1+Γ)

Γ_Sensor = –0.0909

Γ_Source = –0.1304

Mismatch (%) = 100 x [(1 ± (|Γ_Sensor| x |Γ_Source|))² - 1] = 2.3856%

We will now convert all dB units to percentage units:

% = (10^(dB/10) – 1 ) x 100

The important concept here is to convert all uncertainties into statistical variances. To do this, we need to know what type of probability distribution function each uncertainty has. The following table summarize each uncertainty, the type of probability distribution the uncertainty follows, and the divisor that can be used to convert the uncertainty to one variance.

Table 3

Calculating Combined Standard Uncertainty

The combined standard uncertainty is defined by combining all the individual uncertainties in the following way:

Combined uncertainty (σ) = √(∑σ²)

Combined uncertainty is the square root of the sum of square of standard deviations. In our example, the combined uncertainty is σ=2.53%

Expanded Uncertainty

The final step is calculating the expanded uncertainty. This value is the product of the combined uncertainty and the coverage factor (k):

Expanded Uncertainty = kσ

The value of k defines the confidence of the measurement. With a normal (Gaussian) distribution, a value k = 2 defines a confidence value of 95%, meaning 95% of measurements fall within ±kσ of the average value. A value k = 3 defines 99%.

Figure 1

National Instruments uses k = 2 in the NI USB-5680 specifications.

Downloads

We have created a simple calculator that calculates each uncertainty value for you. You can download this uncertainty calculator below.

LabVIEW users who would like to see the code can download it below.

References

1. Guide to the Expression of Uncertainty in Measurement (GUM) International Organization for Standardization (1995), ISBN 92-67-10188-9.

2. NIST reference on uncertainty

3. NI USB-5680 RF Power Meter Specifications

Downloads

niusb5680calc_installer.zip

niusb-5680_uncert_calc.llb

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