Evolution of Single-Element Antenna

The evolution of the single-element antenna involves three steps: first-, second-, and third-generation antennas, as shown Fig. 3a–c. The first-generation antenna is of dual-arm antenna structure with a rectangular feeding patch separated by a coupling gap. The simulation results demonstrate that the first-generation antenna fails to cover the entire operating frequency band (i.e., 3.5–5.5 GHz). Specifically, the first-generation antenna suffers from a narrow impedance bandwidth, covering 3.8–5.0 GHz.

Evolutionary stages of the single-element antenna: (a) first generation, (b) second generation, (c) third generation.

In the second-generation antenna, the rectangular feeding patch is transformed into a T-shaped feeding patch to improve the impedance bandwidth. In addition, the length of the coupling gap is extended. However, the second-generation antenna still fails to cover the entire operating frequency band, covering 3.4–5.0 GHz.

In the third-generation antenna, the T-shaped feeding patch is reshaped into a hemispherical T-shaped feeding patch, and the ground plane is reconfigured into conjoined triangles (i.e., defected ground plane). The third-generation antenna covers the entire operating frequency band, covering 3.4–5.6 GHz.

Figure 4 compares the simulated impedance bandwidths (|S₁₁|≤ − 6 dB) of the first-, second-, and third-generation single-element antennas. The first- and second-generation antennas have a narrow impedance bandwidth, covering 3.8–5.0 GHz and 3.4–5.0 GHz, respectively. The third-generation antenna achieves a wider impedance bandwidth, covering 3.4–5.6 GHz. Figure 5 shows the simulated antenna gains of the first-, second-, and third-generation single-element antennas.

Simulated impedance bandwidths (|S₁₁|≤ − 6 dB) of the first-, second-, and third-generation single-element antennas.

Simulated antenna gains of the first-, second-, and third-generation single-element antennas.

Figure 6 shows the simulated xz- and yz-plane radiation patterns of the first-, second-, and third-generation single-element antennas. Although the radiation patterns of the three antennas closely resemble one another, only the third-generation antenna can cover the entire operating frequency band (3.5–5.5 GHz). As a result, the third-generation single-element antenna is selected for subsequent experiment.

Simulated xz- and yz-plane radiation patterns of the first-, second-, and third-generation single-element antennas at the center frequency of 4.5 GHz.

Figure 7 illustrates the equivalent circuit model of the third-generation single-element antenna to determine the impedance matching and bandwidth across the operating frequency band. The equivalent circuit model consists of a series RLC, three parallel RLC circuits, and a series LC component. The initial values of the equivalent circuit elements are calculated by⁴³, and the optimized component values are determined by using ADS software.

Equivalent circuit model of the third-generation single-element antenna.

Figure 8 compares the simulated impedance bandwidths (|S₁₁|≤ − 6 dB) of the third-generation single-element antenna by CST and by ADS. In the figure, the first, second, and third parallel RLC circuits resonate at 3.5, 4.4, and 5.25 GHz, respectively, corresponding to the surface current distribution in Figs. 9 and 10. Both CST and ADS models achieve wide impedance bandwidth across the operating frequency band of 3.5 to 5.5 GHz.

Comparison between the simulated impedance bandwidths (|S₁₁|≤ − 6 dB) of the third-generation single-element antenna by CST and by Advanced Design System (ADS).

Simulated surface current distribution of the twin-element MIMO antenna scheme with the first antenna element excited and the second antenna element terminated: (a) 3.5 GHz, (b) 4.5 GHz, (c) 5.5 GHz.

Simulated surface current distribution of the twin-element MIMO antenna scheme with the first antenna element terminated and the second antenna element excited: (a) 3.5 GHz, (b) 4.5 GHz, (c) 5.5 GHz.

Surface Current Distribution of Twin-Element MIMO Antenna Scheme

The surface current distribution of the twin-element MIMO antenna scheme is simulated by exciting one element and terminating the other element using a 50 Ω load. The twin-element MIMO antenna scheme comprises two elements of the third-generation antenna due to the wide impedance bandwidth and high gain characteristics (Figs. 4 and 5).

Figure 9a–c show the surface current distribution of the twin-element MIMO antenna scheme at 3.5, 4.5, and 5.5 GHz, with the 1^st antenna element excited and the 2^nd antenna element terminated. At 3.5 GHz, the surface current flows along the left-shoulder of the feeding patch, the left-arm radiating patch, and the larger triangular ground plane. At 5.5 GHz, the surface current flows along the right-shoulder of the feeding patch, the right-arm radiating patch, and the smaller triangular ground plane. Specifically, the left-arm radiating patch resonates at the lower frequency of 3.5 GHz, while the right-arm radiating patch resonates at the higher frequency of 5.5 GHz. At 4.5 GHz, the surface current is concentrated around the head of the feeding patch. Given the perfect symmetry of the twin-element antenna scheme, the same behavior is observed when the 1^st antenna element is terminated while the 2^nd antenna element is excited, as shown in Fig. 10a–c. The mutual coupling (|S₁₂|) between the two antenna elements is less than − 40 dB with negligible current leakage.

Parametric Study of Twin-Element MIMO Antenna Scheme

This section examines the effects of antenna parameters on the impedance bandwidth (|S₁₁|, |S₂₂|≤ − 6 dB) and mutual coupling (|S₁₂|) of the proposed twin-element MIMO antenna scheme, as shown in Figs. 11, 12, 13, 14, 15, 16, 17 and 19, 20.

Figure 11a shows the simulated impedance bandwidth (|S₁₁|, |S₂₂|≤ − 6 dB) and mutual coupling (|S₁₂|) under variable L₁: 10.9, 12.9, and 14.9 mm. With L₁ = 10.9 mm, the resonance frequency is at 3.8 GHz, with the impedance matching of − 54 dB. With L₁ = 12.9 mm, the resonance frequency is at 4.5 GHz (− 60 dB). Given L₁ = 14.9 mm, the resonance frequency is at 4.25 GHz (− 15 dB). The optimal L₁ is thus 12.9 mm. The mutual coupling (|S₁₂|) is less than − 40 dB for the entire operating frequency band, independent of L₁.

Figure 11b shows the simulated |S₁₁|, |S₂₂| and |S₁₂| under variable L₂: 4.84, 6.84, and 8.84 mm. Given L₂ = 6.84 mm, the lowest impedance matching of − 60 dB is achieved at 4.5 GHz (i.e., the resonance frequency). The optimal L₂ is 6.84 mm. The mutual coupling (|S₁₂|) is less than − 40 dB for the entire operating frequency band, independent of L₂.

Simulated impedance bandwidth (|S₁₁|, |S₂₂|≤ − 6 dB) and mutual coupling (|S₁₂|) under variable lengths of left- (L₁) and right-arm radiating patches (L₂): (a) L₁, (b) L₂.

Figure 12a shows the simulated |S₁₁|, |S₂₂| and |S₁₂| under variable lengths of the left shoulder of the feeding patch (F₁): 1.87, 3.87, and 5.87 mm. Given F₁ = 3.87 mm, the lowest impedance matching of − 60 dB is achieved at 4.5 GHz. |S₁₂| is below − 40 dB for the entire operating frequency band, independent of F₁.

Figure 12b shows the simulated |S₁₁|, |S₂₂| and |S₁₂| under variable lengths of the right shoulder of the feeding patch (F₂): 0.32, 2.32, and 4.32 mm. With F₂ = 0.32 mm, the resonance frequency is at 4.3 GHz, with the impedance matching of − 28 dB. With F₂ = 2.32 mm, the resonance frequency is at 4.5 GHz (− 60 dB). With F₂ = 4.32 mm, the resonance frequency is at 3.6 GHz (− 15 dB). The optimal F₂ is 2.32 mm. |S₁₂| is less than − 40 dB for the entire operating frequency band, independent of F₂.

Simulated impedance bandwidth (|S₁₁|, |S₂₂|≤ − 6 dB) and mutual coupling (|S₁₂|) under variable lengths of the left (F₁) and right shoulders of the feeding patch (F₂): (a) F₁, (b) F₂.

Figure 13a, b show the simulated |S₁₁|, |S₂₂| and |S₁₂| of the left and right shoulders of the feeding patch under variable widths of coupling gap (g_A): 0.23, 0.73, and 1.23 mm. In Fig. 11a (for the left shoulder of the feeding patch), with g_A = 0.23 mm, the resonance frequency is at 4.5 GHz, with the impedance matching of − 60 dB. With g_A = 0.73 mm, the resonance frequency is at 4.75 GHz (− 32 dB) and at 5 GHz (− 35 dB) for g_A = 1.23 mm.

Simulated impedance bandwidth (|S₁₁|, |S₂₂|≤ − 6 dB) and mutual coupling (|S₁₂|) of the left and right shoulders of the feeding patch under variable width of coupling gap (g_A): (a) the left (long) shoulder, (b) the right (short) shoulder.

In Fig. 13b (for the right shoulder of the feeding patch), with g_A = 0.23 mm, the resonance frequency is at 4.5 GHz, with the impedance matching of − 60 dB. With g_A = 0.73 mm, the resonance frequency is at 4.4 GHz (− 40 dB) and at 4.35 GHz (− 30 dB) for g_A = 1.23 mm. The optimal g_A is thus 0.23 mm, achieving the lowest impedance matching (− 60 dB) at the center frequency of 4.5 GHz for the left and right shoulders of the feeding patch.

Figure 14a shows the simulated |S₁₁|, |S₂₂| and |S₁₂| under variable width of the T-shaped shoulder (W_f): 0.49, 0.79, and 1.09 mm. With W_f = 0.49 mm, the resonance frequency is at 4.45 GHz, with the impedance matching of − 50 dB, and the resonance frequency is at 4.5 GHz (− 60 dB) for W_f = 0.79 mm. Given W_f = 1.09 mm, the resonance frequency is at 4.65 GHz (− 38 dB). The optimal W_f is 0.79 mm. The mutual coupling (|S₁₂|) is below − 40 dB for the entire operating frequency band, independent of W_f.

Figure 14b shows the simulated |S₁₁|, |S₂₂| and |S₁₂| under variable width of the expanded width of ground plane (W_g): 0.22, 0.42, and 0.62 mm. The resonance frequency is almost identical (at 4.5 GHz), independent of W_g. However, the lowest impedance matching of − 60 dB is achieved with W_g = 0.42. Therefore, the optimal W_g is 0.42.

Simulated impedance bandwidth (|S₁₁|, |S₂₂|≤ − 6 dB) and mutual coupling (|S₁₂|) under variable W_f and W_g: (a) width of the T-shaped shoulder (W_f), (b) expanded width of ground plane (W_g).

Figure 15a shows the simulated |S₁₁|, |S₂₂| and |S₁₂| under variable width between the feeding patch and ground plane (g_B): 1.01, 1.51, and 2.01 mm. With g_B = 1.01 mm, the resonance frequency is at 4.7 GHz, with the impedance matching of − 30 dB, and the resonance frequency is at 4.5 GHz (− 60 dB) for g_B = 1.51 mm. Given g_B = 2.01 mm, the resonance frequency is at 4.3 GHz (− 50 dB). The optimal g_B is 1.51 mm. The mutual coupling (|S₁₂|) is below − 40 dB for the entire operating frequency band, independent of g_B.

Simulated impedance bandwidth (|S₁₁|, |S₂₂|≤ − 6 dB) and mutual coupling (|S₁₂|) under variable g_B and T_g: (a) distance between the feeding patch and ground plane (g_B), (b) height of the base of small- and large- triangle ground plane (T_g).

Figure 15b shows the simulated |S₁₁|, |S₂₂| and |S₁₂| under variable height of the base of small- (right) and large-triangle (left) ground plane (T_g): 0.80,1.30, and 1.80 mm. Given T_g = 1.30 mm, the resonance frequency is at the center frequency of 4.5 GHz, achieving the lowest impedance matching of − 60 dB. The optimal T_g is 1.30 mm. The mutual coupling |S₁₂| is below − 40 dB for the entire operating frequency band, independent of T_g.

Figure 16a shows the simulated |S₁₁|, |S₂₂| and |S₁₂| under variable width of the left-arm radiating patch (W₁): 1.07, 1.57, and 2.07 mm. With W₁ = 1.07 mm, the resonance frequency is at 4.4 GHz, with the impedance matching of − 35 dB, and the resonance frequency is at 4.5 GHz (− 60 dB) for W₁ = 1.57 mm. Given W₁ = 2.07 mm, the resonance frequency is at 4.5 GHz (− 28 dB). The optimal W₁ is 1.57 mm. The mutual coupling (|S₁₂|) is below − 40 dB for the entire operating frequency band, independent of W₁.

Figure 16b shows the simulated |S₁₁|, |S₂₂| and |S₁₂| under variable width of the right-arm radiating patch (W₂): 1.27, 1.77, and 2.27 mm. With W₂ = 1.27 mm, the resonance frequency is at 4.35 GHz, with the impedance matching of − 25 dB, and the resonance frequency is at 4.5 GHz (− 60 dB) for W₂ = 1.77 mm. Given W₂ = 2.27 mm, the resonance frequency is at 4.8 GHz (− 30 dB). The optimal W₂ is 1.77 mm. The mutual coupling (|S₁₂|) is less than − 40 dB for the entire operating frequency band, independent of W₂.

Simulated impedance bandwidth (|S₁₁|, |S₂₂|≤ − 6 dB) and mutual coupling (|S₁₂|) under variable width of the left- (W₁) and right-arm radiating patches (W₂): (a) W₁, (b) W₂.

Figure 17a shows the simulated |S₁₁|, |S₂₂| and |S₁₂| under variable length of the larger triangle of the ground plane (L_T1): 14.41, 16.41, and 18.41 mm. The resonance frequency is almost identical (at 4.5 GHz), independent of L_T1. However, the lowest impedance matching of − 60 dB is achieved with L_T1 = 18.41. Therefore, the optimal L_T1 is 18.41. The mutual coupling (|S₁₂|) is below − 40 dB for the entire operating frequency band, independent of L_T1.

Figure 17b shows the simulated |S₁₁|, |S₂₂| and |S₁₂| under variable length of the smaller triangle of the ground plane (L_T2): 6.79, 8.79, and 10.79 mm. With L_T2 = 6.79 mm, the resonance frequency is at 5.1 GHz, with the impedance matching of − 32 dB, and the resonance frequency is at 5.1 GHz (− 25 dB) for L_T2 = 8.79 mm. Given L_T2 = 10.79 mm, the resonance frequency is at 4.5 GHz (− 60 dB). The optimal L_T2 is 10.79 mm. The mutual coupling (|S₁₂|) is below − 40 dB for the entire operating frequency band, independent of L_T2.

Simulated impedance bandwidth (|S₁₁|, |S₂₂|≤ − 6 dB) and mutual coupling (|S₁₂|) under variable length of large- (left) (L_T1) and small-triangular (right) ground plane (L_T2): (a) L_T1, (b) L_T2.

Figure 18a–c depict the laptop model at variable angles (α) of 90°, 120°, and 150°, respectively. Figure 19a–d show the corresponding simulated |S₁₁|, |S₂₂|, |S₁₂|, and radiation pattern of the proposed twin-element MIMO antenna scheme integrated with the laptop model.

The angle (α) between the horizontal and vertical slats of the laptop model: (a) 90°, (b) 120°, (c) 150°.

In Fig. 19a, b, the simulated |S₁₁| and |S₂₂| are less than − 6 dB across the operating frequency band, independent of α. The results are consistent with⁴³, indicating that the angle (α) of the laptop model has no impact on the impedance bandwidth of the antenna. In Fig. 19c, given α = 90°, the lowest |S₁₂| is closest to the center frequency of 4.5 GHz. In Fig. 19d, the radiation patterns closely resemble one another, independent of α.

The simulated results of the proposed twin-element MIMO antenna scheme integrated with the laptop model at variable angles between the horizontal and vertical slats: (a) |S₁₁|, (b) |S₂₂|, (c) |S₁₂|, (d) radiation pattern.

Figure 20a shows the simulated |S₁₁|, |S₂₂| and |S₁₂| under variable edge-to-edge distance between the two antenna elements (d_A): 38.79, 98.79, and 158.79 mm. The resonance frequency is almost identical (at 4.5 GHz), independent of d_A. The mutual coupling (|S₁₂|) is higher than − 40 dB between 3.1 and 5.5 GHz for d_A = 38.79 mm. In contrast, the mutual coupling (|S₁₂|) is below − 40 dB for the entire operating frequency band for d_A = 98.79 mm and 158.79 mm. Due to its smaller distance, d_A = 98.79 mm is the optimal choice.

Figure 20b shows the simulated |S₁₁|, |S₂₂| and |S₁₂| under variable vertical distance between the reflector and the base of the antenna element (d_S): 8, 13, and 18 mm. The resonance frequency is almost identical (at 4.5 GHz), independent of d_S. However, the lowest impedance matching of − 60 dB is achieved with d_S = 13 mm. Therefore, the optimal d_S is 13 mm. The mutual coupling (|S₁₂|) exceeds − 40 dB between 3.1 and 3.5 GHz for d_S = 8 mm. With d_S = 13 mm and 18 mm, the mutual coupling (|S₁₂|) remains below − 40 dB across the entire frequency band. Given its smaller distance, d_S of 13 mm is selected.

Simulated impedance bandwidth (|S₁₁|, |S₂₂|≤ − 6 dB) and mutual coupling (|S₁₂|) of the proposed twin-element MIMO antenna scheme integrated with the laptop model under variable edge-to-edge distance between the two antenna elements (d_A) and vertical distance between the reflector and the base of the antenna element (d_S): (a) d_A, (b) d_S.