### I. Introduction

The SSM sub-case with a known antenna: This is the case in which there is already an antenna with known AFs. Such an antenna has a valid calibration certificate from a relevant laboratory or manufacturer.

The SSM sub-case with identical antennas: This sub-case refers to the calibration process of an equivalent antenna set, for which the AFs will be determined. Clearly, it is practically impossible for any two antennas to be exactly the same. However, in practical applications, some structures as in the two antennas in a set of precision half-wave dipole are considered nearly identical, having nearly the same AFs.

### II. Test Method and Setup

### 1. The Classic SSM with Three Antennas (SSM-3A)

*B*

*: biconical,*

_{n}*L*

*: log-periodic,*

_{n}*n*= 1,2,3) and with three site attenuation measurements performed (

*A*

*,*

_{n}*n*= 1,2,3), the AFs of the antennas B3 and L1, together with those of the two other biconical and log-periodic antennas (

*AF*

*,*

_{n}*n*= 1,2,3), are obtained using the following three equations in accordance with the classical application of the SSM in ANSI C63.5-2006:

*f*

*is the frequency in MHz, and*

_{M}### 2. The SSM Sub-case with a Known Antenna (SSM-KA)

*AF*

_{1}is the AF of the antenna under calibration (AUC), whereas

*AF*

_{2}stands for the AF of the known antenna. Therefore, only one site attenuation measurement,

*A*

_{1}, between two antennas is sufficient to determine the AF of the AUC.

_{ref}) are presented in Table 3 for both log-periodic and biconical antennas (the known antennas). In the certificates, expanded measurement uncertainties were given as 1.50 dB for both antennas.

### 3. The SSM Sub-Case with Identical Antennas (SSM-IA)

*AF*

_{1}=

*AF*

_{2}=

*AF*), Eq. (4) can be arranged as Eq. (5):

*A*denotes the site attenuation between the transmit and receive antennas.

*AF*in Eq. (5) will be the geometric mean (in linear units) of the AFs of the antenna set members. This situation is also stated in ANSI C63.5-2006, in which Eq. (5) can be used to determine the AF of identical antennas by performing only a single site attenuation (

*A*) measurement between the transmit and receive antennas.

### III. Experimental Results

### 1. Comparative Results of SSM-3A and SSM-KA

*r*calculated as

*r*=

*f*(

*x*

_{1},

*x*

_{2}, …,

*x*

*) is expressed as:*

_{N}*u*(

*x*

*) denotes the absolute uncertainty of the parameter*

_{i}*x*

*. The expanded measurement uncertainty*

_{i}*U*(

*r*) is calculated as in Eq. (7), where

*k*is the coverage factor.

*u*

_{Aj}(

*j*:1–3) represents the combined uncertainty in site attenuation measurement,

*u*

*stands for the uncertainty contribution because of site imperfections, and*

_{site}*u*

*is the repeatability in the overall AF calculation. We note that in [4], to indicate the site quality, we defined the uncertainty component*

_{σ}*u*

*, determined as the highest standard deviation of the results from normalized site attenuation measurements across the entire frequency range. It is also worth emphasizing that the related parameter does not appear in the expression that gives the AF, but it is indirectly effective in determining the true value of the AF [4].*

_{site}*u*

_{AF}_{–}

*=*

_{KA}*u*(

*AF*

_{1}) can be determined as in Eq. (8). Here, we note that in Eq. (4), the parameters

*f*

*,*

_{M}*A*

_{1}, and

*AF*

_{2}have individual uncertainties, and, thus, partial derivatives of

*AF*

_{1}exist only with respect to these parameters. In Eq. (8), the value of

*u*

_{fM}, which is defined as the uncertainty in frequency, is at a negligible level alongside other uncertainty components and is therefore not included in Table 7. The values for

*u*

_{A}_{1}and

*u*

*remain the same as in SSM-3A because the same site is used with the same instrumentation.*

_{site}*U*

*=*

_{REF}*k*·

*u*(

*AF*

_{2}) is the expanded measurement uncertainty of the known antenna, which is given in its calibration certificate. We note that

*u*(

*A*

_{1}) in Eq. (8) includes both the measurement uncertainty of site attenuation measurement (

*u*

_{A}_{1}) and site contribution in uncertainty calculation (

*u*

*), yielding*

_{site}*k*= 2) in its calibration certificate, the overall expanded measurement uncertainty

*U*

_{AF}_{–}

*is found to be 1.89 dB, which is higher than*

_{KA}*U*

_{AF}_{–3}

*calculated as 1.20 dB. An examination of the comparative measurement uncertainty calculations in Table 7 clearly reveals that the uncertainty of the known antenna heavily predominates among all contributors. This indicates that with known antennas that have lower measurement uncertainty, the overall measurement uncertainty of the method can be significantly reduced.*

_{A}If

*U*_{lab}(expanded MIU for test laboratory) ≤*U*_{cispr}: Compliance is deemed to have been achieved if no measured disturbance level is over the limit.If

*U*_{lab}>*U*_{cispr}: Compliance is deemed to have been achieved if no measured disturbance level increased by (*U*_{lab}–*U*_{cispr}) is over the limit Some limit measurement uncertainty values specified in CISPR 16-4-2 (*U*_{cispr}) are given in Table 8.

*U*

_{cispr}values indicate the total uncertainty of the entire radiated disturbance measurement system. These values are used to demonstrate that the AF uncertainties within our study are acceptable. Considering the

*U*

_{cispr}values specified as 6.3 dB and 5.3 dB for these measurements, we can conclude that antennas calibrated with an uncertainty of 1.89 dB in our study can be easily used for these measurements in such a way that there is enough room for the uncertainties of other components of the measurement system.

### 2. Comparative Results of SSM-3A and SSM-IA

_{MEAS}, and the values specified in the manufacturer’s manual, AF

_{MANU}, is presented in Table 9 and Fig. 6. The AF

_{MANU}values in Table 9 are obtained by adding the correction values in the manufacturer’s manual regarding the height of the antenna (R&S) [20]. As can be seen from Table 9, the difference between the measured AF and the values provided by the manufacturer (ΔAF = AF

_{MEAS}– AF

_{MANU}) is maximum at 40 MHz with 2.02 dB and drops significantly above 50 MHz. As stated in Section II.3, the antenna set HZ-13 was used for the 300 MHz–1,000 MHz frequency range; with this antenna pair, we therefore have a maximum difference of 1.36 dB at 700 MHz. At this point, we make our comments similar to those in the SSM-KA case. That is, the values should be evaluated depending on the intended use of the antenna, and in practice, these values are easily acceptable in many applications related to EMC measurements.

### IV. Conclusion

Electromagnetic compatibility antenna calibrations are crucial, as these antennas are used for EMC tests of almost all electrical/electronic devices.

All around the world, there are test sites similar to that used in our study, but they are not ideal in terms of their dimensions. Nevertheless, they can still be used for antenna calibrations.

Calibration takes too long in accordance with the classic SSM-3A, so experimenters attempt to shorten the calibration process in order to save time and money.