### I. Introduction

*S*-parameters using the substitution loss and also with the measured results.

### II. Formulation of the Normalized Site Attenuation

### 1. Classical Site Attenuation

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

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

*h*

_{1}and RX antenna height of

*h*

_{2}. Further,

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

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

*L*

*from the 3-dB hybrid coupler are connected to the antenna terminal, as shown in Figs. 1 and 2. A 50-Ω load is connected to the sum port (∑) of the hybrid, and a matched measuring instrument is 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 are connected to the balanced dipole elements. Their outer conductors are in contact with each other electrically (i.e., short-circuited) at the feeding point of the dipole elements.

##### (1)

### 2. Normalized Site Attenuation

*AF*

_{1}and

*AF*

_{2}are the AFs for the TX and RX antennas, respectively. These include the mutual coupling effect between the ground plane and two antennas when TX and RX antennas are located for the measurement of the NSA. Note that the quantities in Eq. (3) are linear. All quantities in decibels appearing in the rest of the paper are given with (dB).

### 3. Normalized Site Attenuation by Free-Space Antenna Factors

*SA*

*, is normalized from the CSA by using the FSAFs.*

_{FS}*AF*

*, is necessary to obtain the true NSA, as shown in Eq. (5).*

_{TOT}*AF*

_{1}and

*AF*

_{2}) and the FSAFs (

*AF*

_{1}

*and*

_{FS}*AF*

_{2}

*) is expressed as follows:*

_{FS}*NSA*

*is expressed as Δ*

_{FS}*NSA*:

*AF*

*is the same value as −Δ*

_{TOT}*NSA*.

### 4. Antenna Factors

*AF*

_{1}and

*AF*

_{2}, are needed to calculate the NSA. Fig. 3 shows the TX and RX antennas for the evaluation of the AFs. Note that the power loss parameters of the TX antenna part in Fig. 3(a) are different from those in Fig. 2 because the AF is defined in the receiving mode. To unify the AF representation, the TX and RX parts are represented by the superscripts

*T*and

*R*, respectively. For the RX part, Fig. 3(b) is the same as Fig. 2—i.e.,

*AF*

_{1}(

*h*

_{1},

*h*

_{2},

*d*) and

*AF*

_{2}(

*h*

_{1},

*h*

_{2},

*d*), can be expressed as follows:

*R*

*and*

_{G}*R*

*are the input resistance of the SG and receiver, respectively. The major parameters for AF calculation are listed in Table 2.*

_{L}##### (14a)

##### (14b)

*AF*

_{1}and

*AF*

_{2}values are different from the FSAFs (

*AF*

_{1}

*and*

_{FS}*AF*

_{2}

*). The*

_{FS}*AF*

_{1}is also different from the

*AF*

_{2}because the height of the TX antenna is fixed, but the RX antenna’s height is scanned above the ground plane.

*AF*

*corresponds to the total AF correction factor and is known as the mutual impedance correction factor, as explained in Section II-3.*

_{TOT}### III. Numerical Results and Discussions

### 1. Normalized Site Attenuation

*λ*is used for the piecewise sinusoidal Galerkin’s methods of moment analysis, as presented in [19–21]. The dipole radius (

*α*= 3.175 mm; 30 MHz ≤ f < 300 MHz and

*α*= 0.794 mm; 300 MHz ≤ f ≤ 1 GHz ) was chosen to be less than 0.007

*λ*(thin-wire approximation). A nominal value of 50 Ω was used for the characteristic impedance

*Z*

_{0}. A coaxial cable (RG-214/U) with a length of 10 m was selected for the numerical calculation (the velocity of propagation is 66% of the velocity in free space, and the dielectric constant

*ɛ*

*is 2.3). Fig. 4 shows the frequency characteristics of the calculated theoretical NSA from Eq. (3) for the horizontal and vertical polarizations at given distances of 3 m, 10 m, and 30 m. The detailed values of the theoretical NSAs calculated in this paper are shown in Table 3. In these tables, the resonant dipole lengths for a CalDA with a 3-dB hybrid balun in the frequency range of 30 MHz to 1 GHz are shown for 24 individual frequencies. The height of the RX antenna when measuring the CSA at the given distances is also shown. These theoretical NSA values (Fig. 4, Table 3) were used as reference theoretical NSA values for the validation test of an OATS or a semi-anechoic chamber using the CalDAs.*

_{r}### 2. Antenna Factors

*AF*

_{1},

*AF*

_{2}, and CSA values calculated from Eqs. (13) and (1). For example, a CSA of 13.34 dB is obtained when

*h*

_{1}= 2 m and

*h*

_{2}= 1.72 m with

*d*= 3 m, H-polarization, and

*f*= 100 MHz. In this case, TX and RX AFs are

*AF*

_{1}(2 m) = 8.15 dB(1/m) and

*AF*

_{2}(1.72 m) = 7.87 dB(1/m), respectively. From these CSAs,

*AF*

_{1}, and

*AF*

_{2}, the theoretical NSA from Eq. (4) is calculated as −2.68 dB. The resulting NSA values for 24 individual frequencies are shown in Fig. 4 and Table 3. Tables 4 and 5 are also useful for checking the AFs (

*AF*

_{1}and

*AF*

_{2}) above the ground plane giving the NSA.

### 3. Normalized Site Attenuation by Free-Space Antenna Factors

*NSA*

*, is used for the NSA measurement using the CalDA, the measured NSAs are different from the true NSA. Hence, Δ*

_{FS}*AF*

*for the CalDA is necessary.*

_{TOT}*NSA*

*from the FSAFs of the TX and RX antennas and the mutual impedance correction factors Δ*

_{FS}*AF*

*for the CalDA. Δ*

_{TOT}*AF*

*is calculated from Eq. (16) and is known as the total AF difference, as explained in Section II-3. Hence, the FSAFs,*

_{TOT}*AF*

_{1}

*and*

_{FS}*AF*

_{2}

*, are used to measure the NSA. Further, the mutual impedance correction factor, Δ*

_{FS}*AF*

*, is provided to obtain the true NSA. For example, the*

_{TOT}*NSA*

*of −3.06 dB is obtained from the CSA of 13.34 dB using the free space,*

_{FS}*AF*

_{1}

*, of 8.20 dB(1/m) at*

_{FS}*d*= 3 m, H-polarization, and

*f*= 100 MHz. In this case, the mutual impedance correction factor, Δ

*AF*

*, is necessary, and from Table 6, since Δ*

_{TOT}*AF*

*= −0.38 dB, the desired*

_{TOT}*NSA*= −2.68 dB is obtained from Eq. (8). Tables 6 and 7 are useful for actual NSA measurement, using the FSAFs and the mutual impedance correction factors of the CalDA.