Table 1 Validation circuits.

Substrate

RO4003 (ε_r = 3.38, h = 0.76 mm)

AD300 (ε_r = 2.97, h = 0.76 mm)

RO4003 (ε_r = 3.5, h = 0.51 mm)

Design parameters

x = [l₁ l₂ l₃ d w w₁]^T

x = [g l_1r l_a l_b w₁ w_2r w_3r w_4r w_a w_b]^T

x = [L_s W_s l_3r w₁ w₂ w₃ w₄ w₅ w_v]^T

High-fidelity model^#

~ 115,000 mesh cells; simulation time 350 s

~ 85,000 mesh cells; simulation time 90 s

~ 120,000 mesh cells; simulation time 150 s

Low-fidelity model^#

~ 48,000 mesh cells; simulation time 125 s

~ 27,000 mesh cells; simulation time 33 s

~ 61,000 mesh cells; simulation time 68 s

Other parameters

d₁ = d +|w − w₁|, d = 1.0, w₀ = 1.7, and l₀ = 15

L = 2dL + L_s, L_s = 4w₁ + 4 g + s + l_a + l_b, W = 2dL + W_s, W_s = 4w₁ + 4 g + s + 2w_a, l₁ = l_bl_1r, w₂ = w_aw_2r, w₃ = w_3rw_a, w₄ = w_4rw_a

d_L = d_W = 10 mm, L = 2d_L + L_s, W = 2d_W + 2w₁ + (W_s − 2w_f), l₁ = W_s/2, l₂ = l₃2^1/2, l₃ = l_3r((L_s − w₃)/2 − w₄/2^1/2), l_v1 = l₃/3, l_v3 = L_s/2 − w₃/2 − l₃ + l_v1; w_f = 1.15 mm

Operating bands

0.89–1.11 GHz

1.45–1.55 GHz

2.36–2.44 GHz

5.16–5.24 GHz

Maximum power split error

0.4 dB at 1 GHz

0.5 dB at 1.5 GHz

0.5 dB at 2.4 GHz

0.5 dB at 5.2 GHz

Nominal design

x⁽⁰⁾ = [4.50 11.08 21.81 0.65 0.94 0.86]^T

x⁽⁰⁾ = [0.63 5.90 9.34 12.45 1.29 2.02 0.99 0.32 2.81 0.22]^T

x⁽⁰⁾ = [25.05 0.85 0.76 1.90 1.23 0.36 0.71 0.30 0.30]^T