**2. Microwave power standard and traceability of power sensor calibration**

Although the chapter is focusing on the power sensor calibration, it has to talk about first the primary microwave power standard so that the traceability of power sensor calibration is clearly defined.

According to the definition, primary standard is derived directly in terms of base units of the International System of Units (SI). Now the prevalently accepted primary microwave power standard is the calorimeter or microcalorimeter, which is a substitution type of primary standard based on heat measurement (Brunetti & Vremera, 2003; Clague, 1995; Cui, X. & Crowley, T. P. (2011); Famton, 1990; JCGM 200:2008; Oldfield, 1989).

The primary microwave power standard determines the effective efficiency and calibration factor through DC power substitution to realize the traceability to SI units. Power is measured in terms of heat capacity and rate of temperature rise. When microwave power is applied to a terminating device or load through transmission line, the microwave energy is absorbed and converted to heat energy, causing the load temperature to change. Similarly, when DC power is applied to the same load, the DC energy is converted to heat, causing the load temperature to change. When the temperature change caused by the DC power is equivalent to that caused by the microwave power, the DC power can be used to precisely determine the corresponding microwave power. This is the principle of DC power substitution. The substitution technique obviates the need for detailed knowledge of heat losses and thermal capacities.

The terminating device may not react in the same way for microwave and DC power absorption, so the effective efficiency *ηe* is used to perform the correction. In equation (1), microwave power *PHF* absorbed by the terminating device is calculated by dividing the substituted DC power *PDC* by the effective efficiency *ηe*:

$$
\eta\_c = \frac{P\_{\rm DC}}{P\_{\rm HF}} \tag{1}
$$

Since the effective efficiency is independent of the mismatch correction, the calibration factor *K* is used to describe both the effective efficiency *ηe* and mismatch ડas follows:

$$K = \eta\_c \times (1 \text{--} \left| \Gamma \right|^2) \tag{2}$$

The calibration factor *K* is generally used at the time of calibration transfer from a reference standard to an unknown microwave power sensor. It is the focus in the following sections.

The measurement uncertainty is a non-negative parameter characterizing the dispersion of the effective efficiency *ηe* or the calibration factor *K* being attributed to the standards. The uncertainty is evaluated using "law of propagation of uncertainty" following "Guide to the expression of Uncertainty in Measurement" (GUM) (JCGM 100:2008). Evaluation of measurement and calibration uncertainty by Monte Carlo Method (MCM) is to use Monte Carlo simulation in the uncertainty evaluation of output quantities based on "uncertainty probability distribution propagation" (JCGM 101:2008). The following sections will cover both methods for the measurement uncertainty evaluations.

The value of a primary standard is disseminated to a secondary standard through calibration or comparison. Then the reference standard and working power sensors will be calibrated for use. The measurement results through such relations as unbroken chain of calibrations establish the metrological traceability, each contributing to the measurement uncertainty. The traceability is illustrated in Fig. 1. Here for reference purpose we deliberately provide not only the hierarchy, but also the uncertainties typically related. The real uncertainties depend on the frequency band and each laboratory conditions.

Fig. 1. Dissemination of primary standard to end user- Traceability Chart
