To decrease the radiation losses of RF coils especially at higher frequencies an RF shield is used (1). Whereas external circuitry can be easily applied to decouple adjacent array elements, non-adjacent array elements cannot easily be decoupled. In this study we investigated the effect of an RF shield on the mutual coupling between adjacent and non-adjacent array elements in a simple cylindrical coil array model mimicking our previously developed eight channel transceiver head array (2).

Both the experimental and simulated setup consisted of two rectangular window coils (80x100mm²) surrounding a 200 mm long cylindrical dielectric phantom with given electromagnetic properties (s. Fig 1). The loops were placed on an FR4-holder with an inner diameter of 211 mm and an outer diameter of 215 mm. Their centers were separated by an angle of α and a wire diameter of 1.5 mm was used. The shield had a distance of 40 mm to the holder. The S-parameter measurements were done with a network analyzer (E5071C, Agilent Technologies). The reference plane for the two-port calibration was directly in series to the capacitors number 1 and 2. Cable traps were used, tuned to 124 MHz and 400 MHz. Simulations were done in CST Microwave Studio 2015. After the acquisition of the 2-port S-parameter matrix the open-port impedance matrix was extracted and the magnetic (k_m) and electric (k_e) coupling coefficients could be calculated:

$$ k_e=\frac{Re\{Z_{12}\} }{\sqrt{Re\{Z_{11}\}\cdot Re\{Z_{22}\}}}\quad \quad k_m = \frac{M}{\sqrt{L_{11}L_{22}}} $$

Without any external circuitry the resulting transmission coefficient S₁₂ is directly related to the coupling coefficients:

$$S_{12} = \frac{2(k_e+jk_mQ)}{4-(k_e+jk_mQ)^2}$$

The above formula is a result of the transformation formulas between Z-and S-matrices (3) for two power-matched series resonant circuits. It is worth noting here, that the transmission coefficient S₁₂ depends on the product of the Q-factor and k_m.

In Fig. 2 we plotted the measured and simulated coupling factors for a frequency of 124 MHz and 400 MHz over the entire range of the angle α. For the exemplary eight channel transceiver head array (2) nearest neighbor coupling is characterized by an angle α = 45°. In this case the shield modified the mutual inductance by less than 10% at both frequencies, while k_e was reduced by 25% at 124 MHz and 40% at 400 MHz. The curve for k_e at 400 MHz was obtained after inductively decoupling the two loops of our model, because measured and simulated values did only agree qualitatively but not quantitatively when the two loops were strongly coupled (k_m>0.05). To evaluate the effect of a shield on the transmission coefficient S₁₂ for non-adjacent array elements (90°, 135° and 180° separation in a 1x8 array) the above equation indicates that knowledge of the Q-factor is required. The measured Q-factor at 124 MHz was about 55 without and 85 with shield and for 400 MHz we measured 40 and 50 respectively. For such high Q-factors even small values of k_m are critical and have a substantial contribution to S₁₂. Therefore we increased the scaling of the ordinate in Fig. 2 in the range from 60° to 180° and replotted k_m in Fig. 3. The shield decreases magnetic coupling substantially by more than a factor of two for α > 60° at 124 MHz and to a varying degree for 60° < α < 140° at 400 MHz (for α > 140° the shield has no effect on k_m). How this translates into the transmission coefficient S₁₂ is illustrated in Fig. 4. At 124 MHz the shield lowers S₁₂ by about 2 dB (90°), 4.5 dB (135°) and 5 dB (180°). The dashed curves indicate the limiting cases for either k_e = 0 or k_m = 0. We see that it is k_m which is mostly responsible for the coupling at angles below 100° and k_e at α=180°. At 400 MHz the usage of a shield can also be beneficial regarding decoupling in the range between 80° and 160°: At 90° S₁₂ decreases by almost 3 dB and at 135° by more than 6 dB.Our investigations have shown that the usage of an RF shield can be a helpful tool to improve decoupling among non-adjacent array elements in a transmit/transceiver array. Future studies need to be done to see the impact of a shield and its specific geometry and distance from coil elements on element coupling versus radiation loss and hence on SNR and transmit efficiency and to find the best possible tradeoff.