What is the GUM method for evaluating measurement uncertainty in RF testing?

What is the GUM method for evaluating measurement uncertainty in RF testing? The GUM (Guide to the Expression of Uncertainty in Measurement, JCGM 100:2008) is the internationally accepted framework for evaluating and expressing measurement uncertainty, and it is the required method for ISO 17025 accredited RF laboratories: (1) GUM procedure (8 steps): Step 1: define the measurand. Precisely state what is being measured (e.g., S21 of a filter at 2.4 GHz using a VNA with ECal calibration). Step 2: identify the measurement model. Express the measurand as a function of input quantities: Y = f(X1, X2, ..., Xn). Example for gain measurement: G = P_out - P_in - L_cable (where P_out, P_in are power measurements and L_cable is cable loss). Step 3: estimate the input quantities. Assign a value to each Xi from measurements (Type A) or other information (Type B). Step 4: evaluate the standard uncertainty of each input. Type A: u(xi) = s/√N. Type B: u(xi) from specifications, certificates, engineering judgment (divide by √3 for rectangular, by 2 for normal k=2). Step 5: evaluate correlations. If input quantities are correlated (e.g., the same cable affects both P_out and P_in): account for the covariance. In most RF measurements: the inputs are assumed uncorrelated (conservative but usually valid). Step 6: calculate the combined standard uncertainty. u_c(y) = √(Σ (∂f/∂xi)² × u(xi)²) (law of propagation of uncertainty). For simple models (Y = X1 + X2 or Y = X1 - X2): u_c = √(u(x1)² + u(x2)²). Step 7: determine the expanded uncertainty. U = k × u_c, where k is the coverage factor. k = 2: 95.45% confidence (standard practice). k = 3: 99.73% confidence (used for safety-critical measurements). Step 8: report the result. Y = y ± U (k=2, 95% confidence). Example: Gain = 15.3 ±0.4 dB (k=2, 95% confidence). (2) GUM application to RF: the GUM is applied identically to all RF measurements. The measurement model and input quantities change depending on the measurand: S-parameters: inputs include VNA residual errors, mismatch, connector repeatability, temperature. Power: inputs include sensor calibration factor, mismatch, linearity, zero set. Noise figure: inputs include ENR, mismatch, receiver NF correction, connector repeatability.