1. Research Background

It is a common method to test base station antennas in a microwave darkroom. Due to the limitation of the darkroom size, the far-field test conditions are often not met for antennas with higher gain. The test results in this case are quite different from those in the far-field case. This report provides a method to calculate the far-field pattern from the pattern measured at a quasi-far-field distance.

2. Basic Principles of Correction Algorithm

The AUT shown in Figure 1 is a base station antenna. The size of the antenna along the y-axis is small, which easily meets the far-field condition, while the size in the x-direction is large, which does not meet the far-field condition. For the directional pattern of this type of antenna, this method can be used to correct it.

Figure 1 Antenna coordinate system

With oy as the axis, a minimum cylinder is constructed that can completely surround the antenna to be tested, and the radius of the cylinder is set to rmin. Outside the cylinder, the electric field generated by the antenna can be expressed as the weighted sum of vector wave functions, that is,

(1)

Assuming the field point is located on the xoz plane (i.e., y = 0), and ρ is large, equation (1) can be expressed as

(2)

Where: Nm=krmin+10

Since the field point (ρ, φ, 0) is already in the quasi-far zone of the antenna, and ρ is already large relative to the vertical dimension (y-axis direction) of the antenna, the integral in the above formula can be calculated using the one-dimensional stationary phase method, and taking into account , we have

(3)

For any linearly polarized electric field component, it can be expressed as

     (4)

If the electric field measured at ρ = ρo is Em, then

       (5)

Can be found

    (6)

Substituting Cn into formula (5), and letting ρ → ∞, we get the far field of the antenna:

(7)

Where C is a constant that is independent of angle and can be ignored. The far-field pattern of the antenna is

            (8)

Based on the above relationship, it is easy to get the difference between the antenna gain under far-field conditions and the gain under quasi-far-field conditions is

 3. Numerical Simulation Verification

In order to verify the correctness of the algorithm, numerical simulation verification is carried out. An array antenna with an operating frequency of 900MHz and an aperture of 2.6m is selected for numerical simulation analysis, and the quasi-far-field test distance is 29m (this test distance does not meet the far-field condition). The numerical simulation process and numerical simulation results are shown in Figure 2 and Figure 3 respectively.

Figure 2 Numerical simulation flow chart

Figure 3 Numerical simulation results

As shown in Figure 3, the measured results (Measured Pattern) are quite different from the theoretical results (Theoretic Pattern), while the corrected results (Corrected Pattern) are in good agreement with the theoretical results (Theoretic Pattern).

IV. Experimental Verification

In order to verify the correctness of the above algorithm, the given antenna is tested in the following two ways: quasi-far field test and spherical near field test. The correction algorithm is used to correct the quasi-far field test results, and the corrected far field pattern is compared with the spherical near field pattern. The results are shown in Figure 4.

 Figure 4 Experimental results and correction results

As shown in Figure 4, there is a large gap between the quasi-far field test result (Comba Finite Field) and the spherical near field test result (Comba SG128), and the corrected result (Corrected Far Field) is in good agreement with the spherical near field test result (Comba SG128).

V. Conclusion

Numerical simulation analysis and experimental tests have proved the feasibility and accuracy of the above algorithm.