7. Evaluation using the two numerical methods

### 7.1. Evaluation using mutual coupling measurement

of two antennas is around 3 m. The configuration of both antennas is also shown in Figure 6. In a similar way, coupling integral is calculated, and the comparison of the results is shown in Table 1. Considering that the cross-pol component becomes significant in off-axis radiation

Figure 6. (a) On-axis mutual coupling between C-band 2 m and 1.9 m reflector antennas and (b) off-axis mutual coupling

Figure 7. (a) Setup of horn antenna inside near-field anechoic chamber and (b) far-field radiation pattern from the

Coupling level 77.14 dB 80.81 dB

Table 1. Off-axis mutual coupling between the two reflector antennas.

FEKO Integral coupling

between the two reflector antennas.

measurement.

pattern, the comparison shows reasonable agreement within 3 dB difference.

66 Emerging Microwave Technologies in Industrial, Agricultural, Medical and Food Processing

The coupling level between two identical Ku-band standard gain horns is measured in order to evaluate the proposed formula. The standard gain horn operates at 12.7GHz, the center frequency of Ku-band, and the radius of the sphere, which encloses the horn antenna, is around 2.15λ. The radiation pattern of the Ku-band standard gain horn is measured inside the UCLA spherical near-field range as shown in Figure 7. The amplitude and phase of the radiated near-field are acquired by rotating the horn mounted on the positioner. The near-field information can be converted into far-field radiation pattern. The comparison between measured far-field and the simulated far-field pattern using FEKO is depicted in Figure 8. The max simulated and measured gain patterns are 15.28 dB and 15.47 dB, respectively.

As shown in Figure 8, the two horn antennas are mounted on an optical table and the mutual coupling S21 is measured using a vector network analyzer. To properly measure S21, we need to carefully setup the measurement as below:


The separation distance R varies from 4 to 31λ in the on-axis direction. The mutual coupling levels using different methods are compared as shown in Figure 8. The simulated results show

Figure 8. (a) Indoor measurement of mutual coupling and (b) measured mutual coupling level in order to evaluate the simulated coupling level.

measurement are addressed. Those methods can be also expanded to the antenna measurement

Proximity of range Fresnel region Radiating near-field Entire near-field

Required information Low High —

Flexibility of geometry Low High High

Friis formula with correction term Integral form of coupling formula Full-wave simulation

Electromagnetic Computation of the Short-range Wireless Linkbuget for Biomedical Communication

http://dx.doi.org/10.5772/intechopen.76141

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and near-field applications.

Author details

Address all correspondence to: ilkyukim@gmail.com

Table 2. Comparison of the proposed numerical methods.

Defense Agency for Technology and Quality, South Korea

Ilkyu Kim

References

April 2009;57(4):900-909

February 2014;56(1):271-291

Figure 9. (a) Evaluation using Friis formula, asymptotic Friis formula, integral form of coupling formula, and FEKO simulation and (b) close up in the radiating near-field region.

a good agreement with the measurements. It can be concluded that the validity of the simulation is successfully evaluated with the measurement.

#### 7.2. Error analysis of the two numerical methods

An error of the proposed numerical methods is evaluated with respect to the full-wave simulation. The mutual coupling between identical Ku-band horn antennas is computed using the two methods: (1) Friis formula with gain reduction factor and (2) Integral form of coupling formula. The graphs of the proposed methods and measurement are shown in Figure 9. It is worthy noting that the proposed two methods are all effective within Fresnel region while the integral coupling formula extends its effectiveness to the radiating near-field region. The mutual coupling of the asymptotic Friis formula and integral form of coupling formula deviates from the simulated one at the distance of less than R = 3λ and R = 2.3λ, respectively. Beyond the each nearest separation distance, it is observed that maximum error with respect to the simulated result is less than 0.5 dB, which corresponds to around 11% deviation in power level. It verifies that the two numerical methods can provide the reasonable agreement with respect to the full-wave simulation.

#### 8. Conclusion

The mutual coupling between one antennas placed in radiating near-field and far-field ranges of the other antenna is calculated using proposed formulas and evaluated through full-wave simulation and measurement. It is shown that those formulas enable to provide enhancement in the radiating near-field region in comparison to the standard Friis formula. The optimal formula can be selected depending on the availability of input information, the proximity of range, and the flexibility of antenna geometry. The important features of those two formulas are summarized in Table 2. The validity of simulated mutual coupling level is evaluated through the measurement. The setup of indoor measurement is discussed, and the key factors to affect the accuracy of the measurement are addressed. Those methods can be also expanded to the antenna measurement and near-field applications.


Table 2. Comparison of the proposed numerical methods.
