Symbol	Unit	Description	Location
a	mm	Cavity width (transverse dimension, along x)	Sec. 1, Eq. (1)
b	mm	Cavity height (along y, direction of no field variation for TE₁₀₁	Sec. 1
c	m s⁻¹	Speed of light in vacuum (≈ 3 × 10⁸)	Eq. (1)
d	mm	Cavity length (along z)	Sec. 1, Eq. (1)
f	GHz	Frequency (independent variable)	Throughout
f₀	GHz	Resonant frequency	Sec. 1–2, Eq. (1)
L	mm	Length of dielectric slab (equal to cavity height b)	Sec. 2, Eq. (4)
Q_L	–	Loaded quality factor of the resonant system	Sec. 1, Eq. (2)
S_ij	–	Scattering parameters (i, j = 1, 2)	Sec. 2, Eq. (5)
Z₀	Ω	Reference impedance of measurement system (typically 50 Ω)	Sec. 2, Eq. (5)
Z_c	Ω	Characteristic impedance of dielectric-filled transmission line	Sec. 2, Eq. (4)
γ	m⁻¹	Complex propagation constant: γ = jω√(μ₀ε₀)	Sec. 2, Eq. (4)
ε	–	Complex relative permittivity: ε = ε′ − jε″	Abstract, Sec. 1
ε′	–	Real part of relative permittivity (energy storage)	Throughout
ε″	–	Imaginary part of relative permittivity (loss)	Throughout
ε₀	F m⁻¹	Permittivity of free space (≈ 8.854 × 10⁻¹²)	Sec. 2, Eq. (4)
μ₀	H m⁻¹	Permeability of free space (4π × 10⁻⁷)	Sec. 2, Eq. (4)
φ	rad	Phase of S₂₁: φ = ∠S₂₁(f)	Sec. 1, Eq. (2)
tan δ	–	Loss tangent: ε″/ε′	Sec. 1, Eq. (3)
ω	rad s⁻¹	Angular frequency: ω = 2πf	Sec. 2, Eq. (4)

Table 1: List of symbols and variables used in the manuscript.

Table 2: Complex permittivity of the novel dielectric material at detected resonances (8.37–13.77 GHz).

Table 1

Table 2

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 1: Flowchart of the multi-resonance anchored permittivity extraction algorithm.

Figure 2: XRD comparison of composite (a) BaTiO₃V₂O₅ with (b) BaTiO₃ and (c) V₂O₅.

Figure 3: Two-dimensional AFM image (1.7 µm × 1.4 µm) of the BaTiO₃/V₂O₅ composite.

Figure 4: Experimentation and S matrix measurement : (a) composite filling (b) measurement on VNA- SHN914A (c): S viewing (d) 4 complex S_ij

Figure 5: Reflection S₁₁ and transmission S₂₁ in dB. Red dashed lines mark the 16 detected resonances.

Figure 6: Permittivity magnitude at 16 resonances.

Figure 7: Permittivity profile around 8.65 and 10.07 GHz resonances.

Figure 8: Full-band complex permittivity of FE − BTV over 8.00 GHz to 14.0 GHz.