*3.2. Study of the Role of the DBs*

This section presents the simulated results with/without DBs. As shown in Figure 3a, when there is no DB1, the simulated S11 and S22 can still cover the desired bands. However, the first resonant frequency of Ant. 1 moves to 3.6 GHz, while the other operation band causes little influence. Figure 3b illustrates the simulated isolation curves S12 and S23 with/without DB1 and DB2. The utilization of the DBs can effectively attenuate the mutual coupling at 3.5 GHz, while there is little impact on the mutual coupling at 4.9 GHz, as shown in Figure 4. The worst simulated isolation (14 dB) appeared at S12. Figure 3c portrays the simulated S23 with various values of *S1*. Relatively low isolation (8 dB) at 3.5 GHz was obtained when no DB was used. After the DB1 is constructed between Ant. 2 and Ant. 3, a distinctly improving trend occurred to S23, as depicted in Figure 3c, but it was still insufficient. By adjusting the length of *S1*, isolation performance can be improved. When the value of *S1* is 9 mm, the simulated S23 satisfies the requirement of 15 dB within the desired bands at 3.5 GHz. When the value of *S1* decreases to 7 mm, some deterioration happens to S23, as shown in Figure 3c. The final optimized value of *S1* is 9 mm.

#### *3.3. Current Distribution and Parametric Analysis*

The simulated current distribution of Ant. 1 and Ant. 2 at two operating frequencies when the DB1 is adopted or not are portrayed in Figure 4. When Ant. 1 is excited at 3.5 GHz, the strongest current density is allocated over the upper L-shaped slot of Ant. 1 and the inner edges of slots of the lateral section of DB1. The introduction of DB1 significantly decreases the current density coupled in Ant. 2 when Ant. 1 is excited at 3.5 GHz. When Ant. 2 is excited at 4.9 GHz, the maximum current spread around the middle rectangular slot of Ant. 2. There is no significant difference in the coupling current of distribution of Ant. 1 when DB1 is applied or not. The utilization of DB1 powerfully absorbs the mutual magnetic coupling existing between Ant. 1 and Ant. 2 at 3.5 GHz, hence enhancing the isolation. The slight improvement resulting from the DB1 is realized upon S12 at 4.9 GHz, which is also consistent with the simulated curves in Figure 3b.

**Figure 3.** Simulated (**a**) S11 and S22 and (**b**) S12/23 with/without DBs, (**c**) S23 with various values of *S1*.

**Figure 4.** Current distribution at two resonant modes when DB1 is utilized or not.

According to the current distribution, numerous parameters are selected to make a parametric analysis, as shown in Figure 5. Little resonant frequency offset of the latter band arises with the increase in *L1*, and almost no impact is caused on the first operating band. The final value of *L1* is 5.4 mm. As illustrated in Figure 5b, the variation in *L2* affects all three resonant points. With the increase in *L2*, the impedance matching condition at 3.5 GHz deteriorates, the middle resonant mode around 3.7 GHz shifts to the higher frequency, and the ultimately optimized length of *L2* is 0.8 mm. Without influencing the first resonant mode of Ant. 1, the addition of the value of *W1* contributes a lot to the movement of the other two resonant modes. As illustrated in Figure 5c, the second resonant mode moves to 4 GHz when the value of *W1* is 2.2 mm, and the final impedance band is not satisfied. The ultimately modified value of *W1* is 2.8 mm. Parameter *L3* mainly affects the decoupling performance. A significant difference in the isolation at 3.5 GHz occurs

with the varying of *L3*. When the value of *L3* equals 0.6 mm, the simulated S21 is separately larger than 15 dB and 14 dB at 3.5 GHz and 4.9 GHz, respectively.

**Figure 5.** Simulated S11 with various (**a**) *L1*, (**b**) *L2*, (**c**) *W1*, and (**d**) S21 with different *L3*.
