The antenna calibrations according to the classic SSM of ANSI C63.5-2006 with three antennas are performed, as described in [4] and as briefly mentioned in Section I. The antennas used in the experiments are listed in Table 2. The biconical antenna B3 and the log-periodic antenna L1 are the ones tested. We note that the other study included the calibrations of antennas B2 and L2, which are different from those in this study. All the other instruments and components in both studies are the same. The test geometry is depicted in Fig. 2.

With the use of three antennas (B_n: biconical, L_n: log-periodic, 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:

where f_M is the frequency in MHz, and EDmaxdenotes the maximum electric field strength.

For the SSM with a known antenna, Eq. (4) can be used to measure the AF according to ANSI C63.5-2006 [1]:

Actually, this equation can be derived by adding Eqs. (1) and (2) side by side. Here, AF₁ is the AF of the antenna under calibration (AUC), whereas AF₂ stands for the AF of the known antenna. Therefore, only one site attenuation measurement, A₁, between two antennas is sufficient to determine the AF of the AUC.

In this study, for the biconical antenna calibration, R&S HK116 biconical antenna (antenna B3 in Table 2) was the one to be calibrated, whereas R&S HK116 biconical antenna (antenna B2 in Table 2) served as the known antenna. The latter has a calibration certificate from the reference institute (TUBITAK-UME). For log-periodic antenna calibration, R&S HL223 logperiodic antenna (antenna L1 in Table 2) was the one to be calibrated, whereas R&S HL223 log-periodic antenna (antenna L2 in Table 2) was the known antenna, which also has a calibration certificate from the reference institute. Some AF values from calibration certificates (AF_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.

Except for the antennas, the rest of the instruments used in this calibration process are the same as those in the three-antenna case (Section II-1).

In case the two antennas in Section II-2 are identical that they have approximately the same AFs (AF₁ = AF₂ = AF), Eq. (4) can be arranged as Eq. (5):

Here, A denotes the site attenuation between the transmit and receive antennas.

It is certain that no two antennas can be exactly the same. However, some structures, such as the antennas of dipole sets, show nearly identical characteristics. In such cases, 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.

The dipole sets calibrated in this study by applying SSM-IA are listed in Table 4. The set numbered 1 (Model HZ-12) is used in the 30 MHz–300 MHz frequency range, whereas the set numbered 2 (Model HZ-13) is used for the calibration in the frequency range of 300 MHz–1,000 MHz.

Before the experiments were started, the site was validated considering possible interference [4].

The calibrations of the biconical antenna HK 116 (B3 in Table 2) and the log-periodic antenna HL 223 (L1 in Table 2), both from R&S, were performed using both SSM-3A and SSM-KA.

The experimental results are given in Tables 5 and 6 as follows:

The results are also graphically shown in Figs. 4 and 5, respectively.

In Table 5 and Fig. 4, we observe similar behavior in terms of the results for SSM-3A and SSM-KA for biconical AUC across the entire frequency range. However, some differences stand out. The maximum absolute difference between the two cases is calculated as 1.96 dB.

In Table 6 and Fig. 5, the results of SSM-3A and SSM-KA are compared for the log-periodic antenna. We observe a parallel trend of the results with some offset. The maximum absolute difference between two cases reaches 1.55 dB.

The uncertainty calculations in the measurements are conducted according to two basic documents in this field [17, 18].

Assuming that the parameter uncertainties are uncorrelated, the absolute squared combined uncertainty in a result r calculated as r = f(x₁, x₂, …, x_N) is expressed as:

where u(x_i) denotes the absolute uncertainty of the parameter x_i. The expanded measurement uncertainty U(r) is calculated as in Eq. (7), where k is the coverage factor.

Data on uncertainty budgets are presented in Table 7. For the classical method SSM-3A, a detailed uncertainty analysis was conducted in [4]. In Table 7, we once again present the main components involved in the calculation of the combined measurement uncertainty for SSM-3A. In the table, u_Aj (j:1–3) represents the combined uncertainty in site attenuation measurement, u_site stands for the uncertainty contribution because of site imperfections, and u_σ is the repeatability in the overall AF calculation. We note that in [4], to indicate the site quality, we defined the uncertainty component u_site, 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].

For SSM-KA, by applying Eq. (6) to Eq. (4), the combined uncertainty u_AF–KA = u(AF₁) can be determined as in Eq. (8). Here, we note that in Eq. (4), the parameters f_M, A₁, and AF₂ have individual uncertainties, and, thus, partial derivatives of AF₁ 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_A1 and u_site remain the same as in SSM-3A because the same site is used with the same instrumentation. U_REF = k · u(AF₂) is the expanded measurement uncertainty of the known antenna, which is given in its calibration certificate. We note that u(A₁) in Eq. (8) includes both the measurement uncertainty of site attenuation measurement (u_A1) and site contribution in uncertainty calculation (u_site), yielding u(A1)2=uA12+usite2.

Regarding the measurement uncertainties of the two methods, SSM-KA is supposed to have the advantage of only one site attenuation measurement. However, because of the dependency on the uncertainty of the known antenna, which is stated as 1.50 dB (for k = 2) in its calibration certificate, the overall expanded measurement uncertainty U_AF–KA is found to be 1.89 dB, which is higher than U_AF–3A 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.

As a result, SSM-KA can be used for antenna calibration depending on the application in which the respective antenna will be used, the acceptable accuracy, and the tolerance. As an example, we refer to the standard CISPR 16-4-2, in which measurement instrumentation uncertainties (MIUs) are defined to determine compliances [19]. According to CISPR 16-4-2, the determination of compliance/non-compliance with a disturbance limit is as follows:

In Table 8, the frequency range conditions for radiated disturbance measurements (at an OATS, in a SAC, or in a FAR) match exactly those in our study. Here, the 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.

As we highlighted earlier in this section, for the biconical antenna, the calibration with SSM-KA presents a curve similar to that with SSM-3A, while for the log-periodic antenna, we observe a small offset between the results of the two methods. Moreover, the maximum differences between the results of the two methods for both the biconical and log-periodic antennas almost fall within the measurement uncertainty of the known antenna method. As for the calibration process, SSM-KA shortens the experiment time by around 66% compared to SSM-3A.

In summary, considering the usage area, the calibration of EMC antennas can be performed by applying the SSM-KA method even in non-ideal test sites, such as the narrow one used in our study. This will have key advantages, such as practicality, fast implementation, and cost effectiveness. However, the experimenter should be careful in using a known antenna with low uncertainty, as this is the dominant contributor to the overall calibration uncertainty.

As an application of SSM-IA, we measured the AFs of the R&S precision half-wave dipole sets listed in Table 4 (HZ-12, HZ-13) in our study. In the measurement process, the antenna height scan was limited to 1–3.5 m because of mechanical conditions/restrictions (vibration, mechanical stress, and bending). The comparison of the measured AFs, AF_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.

Again, similar to SSM-KA, the calibration time with SSM-IA is reduced to approximately one-third compared with that with SSM-3A.