**4.5 Measurement system setup and type N connection result**

The realization and implementation of coaxial splitter based power sensor calibration by direct comparison transfer shown in Fig. 4 is illustrated in Fig. 6 for the type N connector system setup (up to 18 GHz).

The calibration results of calibration factor of a power sensor with the measurement uncertainties are illustrated in Fig. 7. The DUT sensor is calibrated by a power standard (CN mount) in the frequency range 50 MHz to 18 GHz using the direct comparison transfer method with Weinshel 1870A splitter. The effective efficiency of power standard was measured using a micro-calorimeter. The calibration factor is calculated using equation (33). The expanded uncertainties are less than 0.9% for the frequency range at coverage factor of *k* = 2.

Compared with the results obtained in section 3, it is shown that with insertion of the passive splitter with monitoring arm, measurement uncertainties are much improved. And such measurement transfer system adds little measurement uncertainty when transfer the value from standard to DUT.

Uncertainty budget table is listed in Table 4 for the calibration system at frequency of 8 GHz.

Fig. 6. Type N connection realization of splitter based power sensor calibration by direct comparison transfer

Fig. 7. measurement results by direct comparison method for power sensor 8481A vs CN


Table 4. Uncertainty budget at 8 GHz for Fig. 4 measurement setup. Uncertainties *ui* are at one standard deviation. Powers are measured in mW.

#### **4.6 Cartesian model**

190 Modern Metrology Concerns

The Monte Carlo numerical simulation is performed through program developed using MATLAB software. It allows estimating the measurement uncertainties based on the

The realization and implementation of coaxial splitter based power sensor calibration by direct comparison transfer shown in Fig. 4 is illustrated in Fig. 6 for the type N connector

The calibration results of calibration factor of a power sensor with the measurement uncertainties are illustrated in Fig. 7. The DUT sensor is calibrated by a power standard (CN mount) in the frequency range 50 MHz to 18 GHz using the direct comparison transfer method with Weinshel 1870A splitter. The effective efficiency of power standard was measured using a micro-calorimeter. The calibration factor is calculated using equation (33). The expanded uncertainties are less than 0.9% for the frequency range at coverage factor of

Compared with the results obtained in section 3, it is shown that with insertion of the passive splitter with monitoring arm, measurement uncertainties are much improved. And such measurement transfer system adds little measurement uncertainty when transfer the

Uncertainty budget table is listed in Table 4 for the calibration system at frequency of 8 GHz.

Fig. 6. Type N connection realization of splitter based power sensor calibration by direct

**4.5 Measurement system setup and type N connection result** 

mathematical models.

*k* = 2.

system setup (up to 18 GHz).

value from standard to DUT.

comparison transfer

Real and imaginary expression of the measurement models in the three cases are derived as follows:

$$\eta\_{\rm DIT} = \eta\_{\rm Sfd} \times \frac{P\_{\rm DIT}}{P\_{\rm Sfd}} \frac{P\_{3\rm Std}}{P\_{3\rm DIT}} \times \frac{1 \cdot A^2 \cdot B^2}{1 \cdot C^2 \cdot D^2} \times \frac{1 + 2DF \cdot 2CE + C^2 E^2 + D^2 E^2 + C^2 F^2 + D^2 F}{1 + 2BF \cdot 2AE + A^2 E^2 + B^2 E^2 + A^2 F^2 + B^2 F^2} \tag{34}$$

$$K\_{DLT} = K\_{Sld} \times \frac{P\_{DUT}}{P\_{Sld}} \frac{P\_{3Sld}}{P\_{3DUT}} \times \frac{1 + 2DF \text{-} 2CE + \text{C}^2 E^2 + D^2 E^2 + \text{C}^2 F^2 + D^2 F}{1 + 2BF \text{-} 2AE + A^2 E^2 + B^2 E^2 + A^2 F^2 + B^2 F^2} \tag{35}$$

$$K\_{\rm OUT} = \eta\_{\rm Sfd} \times \frac{P\_{\rm DUT}}{P\_{\rm Std}} \frac{P\_{\rm Sfd}}{P\_{\rm 3DUT}} \times (1 - A^2 \cdot B^2) \times \frac{1 + 2DF \cdot 2CE + C^2 E^2 + D^2 E^2 + C^2 F^2 + D^2 F}{1 + 2BF \cdot 2AE + A^2 E^2 + B^2 E^2 + A^2 F^2 + B^2 F^2} \tag{36}$$

where for all three cases, *Std A DUT EG jB C jD E jF* , , .
