### I. Introduction

*S-*parameters using the substitution loss, and with the measured results [13].

### II. Analysis of the Site Attenuation Measurement System

### 1. Total Power Losses

*x*-axis (horizontal polarization, HP) or the

*z*-axis (vertical polarization, VP) above a ground plane. The height of the TX antenna was

*h*

_{1}, and the height of the RX antenna was

*h*

_{2}. Additionally,

*d*was the distance between the TX and RX antennas.

*L*and a radius of

*a*. The balun was designed such that its complex

*S-*parameters could be easily measured. Two semi-rigid cables with a length of

*L*

*from the 3-dB hybrid coupler were connected to the antenna terminal, as shown in Figs. 1 and 2. A 50-Ω load was connected to the sum port (Σ) of the hybrid, and a matched measuring instrument was connected to the other port (Δ) using a coaxial cable with a length of*

_{B}*L*

_{2}. The inner conductors of the two semi-rigid cables were connected to the balanced dipole elements, while the outer conductors were in contact with each other electrically (i.e., short-circuited at the feeding point of the dipole elements). Since this structure was perfectly symmetrical, the two matched output voltages of the balun had the same amplitude and a phase difference of

*π*radians. The details of calculable dipole antenna analysis using the concept of power mismatch and dissipative loss are given in [4, 15, 18].

##### (1)

*M*

*and*

_{T}*M*

*are the power mismatch and dissipative losses in the TX part (SG–coaxial cable) and the RX part (coaxial cable–receiver), respectively, and*

_{R}*M*

*denotes the power mismatch and dissipative losses of the site with a ground plane between the two antennas that included the baluns. In comparison to*

_{SITE}*M*

*and*

_{T}*M*

*, the site power loss*

_{R}*M*

*was significantly large.*

_{SITE}### 2. Site Attenuation

*h*

_{1},

*h*

_{2}, and

*d*in the SA calculation are listed in Table 2 [1]. For the given values of

*d*,

*h*

_{1}, and

*h*

_{2}, the theoreticcal SA of the OATS was defined from

*M*

*as follows:*

_{SITE}*M*

*is the minimum value of the power loss.*

_{SITE}##### (3)

### 3. Power Losses on the Coaxial Cables

*M*

*and*

_{T}*M*

*must be evaluated. The power losses on the coaxial cables connected to the SG and receiver are expressed as follows:*

_{R}*γ*=

*α*+

*jβ*where

*α*and

*β*are the attenuation and phase constants of the dielectric between the inner and outer conductors of a coaxial cable. Additionally,

*β*is given by

*ω*√(

*ɛμ*), where

*ω*= 2π

*f*(

*f*is the frequency) is the angular frequency, and

*ɛ*and

*μ*are the permittivity and permeability of the dielectric inside the coaxial cable, respectively. The analysis results of each part of the SA measurement system are shown later.

### III. Calculated Site Attenuations

*S*-parameters by the National Physical Laboratory (NPL) [13].

*a*= 3.175 mm; 30 MHz ≤

*f*< 300 MHz and

*a*= 0.794 mm; 300 MHz ≤

*f*< 1 GHz) was chosen to be less than 0.007λ (thin-wire approximation), and a nominal value of 50 Ω was used for the characteristic impedance

*Z*

_{0}. A coaxial cable (RG-214/U; the velocity of propagation was 66% of the velocity in free space; dielectric constant,

*ɛ*

*= 2.3) with a length of 10 m was selected for the numerical calculation. This cable had an attenuation of 0.049 dB/m at 50 MHz, 0.069 dB/m at 100 MHz, 0.165 dB/m at 500 MHz, and 0.269 dB/m at 1,000 MHz [22].*

_{r}*S*-parameters [13]. In [13], MININEC was used for the dipole length and the antenna calculations, while the present study employed the piecewise sinusoidal basis functions with a Galerkin procedure. The difference between the calculated and MININEC SA was less than 0.09 dB, excepting 866 MHz. Additionally, the difference in the dipole length was less than 0.007λ for the seven frequencies. These differences were due to the differences in the basis functions.

*S*-parameters as well as with the experiments.

*S*-parameters expression given in [13]. The calculated SAs were better matched to the

*S-*parameter SA as the distance between the TX and RX antennas increased. However, in the low frequency range of 30–90 MHz at the 3-m distance, the differences between the calculated SA and the

*S*-parameter SA were greater but still less than ±0.73 dB. This difference was thought to be due to how the conversion errors of the impedance- and

*S*-parameters affected the height pattern of the RX antenna under the strong mutual coupling of the antennas and ground plane. However, more research is needed.

### IV. Constituent Losses for the Site Attenuation Measurement System

*M*

*,*

_{T}*M*

*, and*

_{R}*M*

*. In other words, the total power loss of the SA measurement system consisted of a combination of the TX part (SG–coaxial cable) and the RX part (coaxial cable–receiver) of the power mismatch and dissipative losses in the open-field site transmission path loss*

_{SITE}*M*

*as follows:*

_{SITE}*S*

*and*

_{T}*S*

*are the power losses (mismatch and dissipative losses) of thse TX and RX parts at a minimum site transmission path loss, respectively.*

_{R}*S*

*and*

_{T}*S*

*were calculated to be in the order of 0.490 to 2.690 decibels; hence,*

_{R}*S*

*+*

_{T}*S*

*<*

_{R}*S*

*. Therefore, the site power loss*

_{A}*M*

*was significantly large.*

_{SITE}*K*

*. Table 7 lists both these losses in the SA as well as the values of the percentage comparison of the SA components.*

_{ASA}*K*

*. This was due to the fact that the mutual coupling effects between the two antennas and the ground plane became large at the low frequencies for the 3-m distance. However, the variation of the input impedance of the TX and RX antennas was very small because the mutual coupling effects between the two antennas and the ground plane was reduced at frequencies above about 90 MHz. Therefore, the mismatch loss*

_{ASA}*K*

*) for the HP and 1.54% for the VP at the 3-m distance. As for the 10-m distance, it was within 1.13% and 0.81% of the half-space dissipative loss for the HP and the VP, respectively. Additionally, for the 30-m distance, the average value of the mismatch loss was within 0.63% and 0.58% of the halfspace dissipative loss for the HP and the VP, respectively.*

_{ASA}*K*

*was the dominant component in the SA, because the mismatch loss*

_{ASA}*K*

*for all three distances. In addition, the mismatch loss of the HP was larger than that of the VP because the HP had a stronger mutual coupling with the ground plane than the VP did.*

_{ASA}