Antenna design & prototyping overview From model design to prototype measurement Maxime SPIRLET 29/05/2019 ULi`ege, Department of Electrical Engineering and Computer Science, Montefiore Institute, Applied and Computational Electromagnetics (ACE) 1 / 17 Introduction What is an antenna? An antenna is an electromagnetic energy converter between conducted and radiated electromagnetic energy. Designing an antenna mainly consists in maximizing the energy conversion ratio. 2 / 17 Antenna Modeling and Simulation Introduction Focus on microstrip antennas (cheap, compact, versatile, ...). Antenna design complementary to EMC rules: How to make a PCB track (NOT) radiate? Design a patch antenna to use @ 2:45 GHz. 3 / 17 Antenna Modeling and Simulation Microstrip "patch"antenna h λ and L ≈ λ, Radiation from the fringing fields, Cavity model with E~ field alongz ^ and vanishing H~ t at edges, Solution of Maxwell equations and boundary conditions Hy (x) = 0 at x = ±L=2 (lowest resonant mode L ≥ W ): πx E (x) = −E sin (1) z 0 L πx H (x) = −H cos ; (2) y 0 L for −L=2 ≤ x ≤ L=2 and −W =2 ≤ y ≤ W =2, p H0 = −|E0=Z, Z = Z0= r . 4 / 17 Antenna Modeling and Simulation Resonant frequency π Identifying k to L (standing waves: A sin (kx ± !t) in 1-D), πc ! = ; (3) L The resonant frequency is c c f = 0:5 = 0:5 p0 ; (4) L L r The length of the patch should be λ L = 0:5p ; (5) r where r is the relative permittivity of the dielectric (typ. 4.5 @ 2:5 GHz for epoxy FR4). 5 / 17 Antenna Modeling and Simulation Magnetic currents Fringing fields extended over a length a around patch edges, Due to h λ, Fringing fields replaced by E~a, tangential to substrate surface, Eliminate ground plane using image theory: ~Jms = −2^n × E~a, Sides 1 and 3: I hE0 2hE0 E~ · dl~ = ∓E0 ± Eaa = 0 ) E~a =x ^ ) ~Jms = −y^ ; ABCD a a (6) Sides 2 and 4: hE (x) hE πx 2hE πx E~ = ±y^ z = ∓y^ 0 sin ) ~J = ±x^ 0 sin : a a a L ms a L (7) 6 / 17 Antenna Modeling and Simulation Radiation vectors Radiated electric field: e−|kr E~ = |k ^r × F~ ; (8) 4πr m Magnetic radiation vector: Z |kx x+|ky y F~m(θ; φ) = ~Jms (x; y)e dS; (9) A Z W =2 2hE0 −|kx L=2 |kx L=2 |ky y F~m;1;3 = −y^ e + e e a dy; a −W =2 (10) Z L=2 2hE0 −|ky W =2 |ky W =2 πx |kx x F~m;2;4 =x ^ e + e sin e a dx; a −L=2 L (11) 7 / 17 Antenna Modeling and Simulation Radiation vectors sin (πνy ) F~m;1;3 = −y^4E0hW cos (πνx ) ; (12) πνy ~ 4νx cos (πνx ) Fm;2;4 =x ^4E0hL 2 sin (πνy ) ; (13) π (1 − 4νx ) with the normalized wavenumbers k L L ν = x = sin θ cos φ, (14) x 2π λ k W W ν = y = sin θ sin φ. (15) y 2π λ 8 / 17 Antenna Modeling and Simulation Radiation pattern From sides 1 and 3: e−|kr E~ (θ; φ) = −|k 4E hW φ^ cos θ sin φ − θ^cos φ F (θ; φ) ; 4πr 0 (16) with sin (πνy ) F (θ; φ) = cos (πνx ) ; (17) πνy From side 2 and 4: e−|kr E~ (θ; φ) = |k 4E hL φ^ cos θ cos φ + θ^sin φ f (θ; φ) ; 4πr 0 (18) with 4νx cos (πνx ) f (θ; φ) = 2 sin (πνy ) : (19) π (1 − 4νx ) 9 / 17 Antenna Modeling and Simulation Radiation pattern Normalized gain for sides 1 and 3 (left): 2 ~ E (θ; φ) 2 g (θ; φ) = = cos2 θ sin2 φ + cos2 φ F~ (θ; φ) ; 2 ~ Emax (20) Normalized gain for sides 2 and 4 (right): 2 2 2 2 ~ g (θ; φ) = cos θ cos φ + sin φ f (θ; φ) : (21) 10 / 17 Antenna Modeling and Simulation Radiation pattern E-plane gain obtained by setting φ = 0 (left): jE j2 L g (θ; φ) = θ = jcos (πν )j2 ; ν = sin θ; (22) E 2 x x λ jEθjmax H-plane gain obtained by setting φ = 90 (right): 2 2 jEφj sin (πνy ) W gH (θ; φ) = = cos (θ) ; νy = sin θ: 2 πν λ jEφjmax y (23) 0 0 −10 −2 −20 −4 −30 −40 −90 −60 −30 0 30 60 90 −90 −60 −30 0 30 60 90 θ θ 11 / 17 Antenna Modeling and Simulation Numerical modeling of the patch antenna Modeling with the free FEM solver ONELAB (http://onelab.info), Fullwave 3D model, Antenna surrounded by air (vacuum), Copper replaced by a Perfect Electric Conductor (σ = 1), Free-space modeled with PML's or ABC's to avoid spurious reflections (i.e. numeric model of infinity), 12 / 17 Antenna Modeling and Simulation Numerical modeling of the patch antenna 3D Radiation pattern can be computed, Input impedance and other parameters can also be obtained. Mesh size is the critical parameter, Computation time vs accuracy. 13 / 17 Antenna Modeling and Simulation Numerical modeling of the patch antenna Frequency sweep to get reflections −2 coefficient wrt frequency, −3 Parameter sweep to −4 optimize antenna dimensions, R (dB) −5 Finite size ground −6 plane taken into account, −7 Housing can be taken 2:4 2:42 2:44 2:46 2:48 2:5 into account, Frequency (Hz) ·109 ... 14 / 17 R&S®ZVA Vector Network Analyzer High performance up to Antenna110 GHz Measurementwith up to four test ports 2D radiation pattern, 3D radiation pattern, Reflection coefficient, VSWR and matching circuit, Antenna efficiency. Test & Measurement & Test Important: measure the antenna as it will be Product Brochure | 11.00 used in practice. ZVA_bro_en_5213-5680-12_v1100.indd 1 30.07.2014 13:17:26 15 / 17 Antenna Measurement New ULi`ege's FAC External dimensions: 4 m × 4 m × 7:5 m, Test frequency range: 700 MHz - 18 GHz (validated), Test device/antenna: max. 10 kg - 30 cm × 30 cm × 30 cm. 16 / 17 Q/A Questions? Contact: V´eronique Beauvois ([email protected]), Maxime Spirlet ([email protected]). 17 / 17.