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 ˆ 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, √ H0 = −E0/Z, Z = Z0/ r .

4 / 17 Antenna Modeling and Simulation Resonant frequency

π Identifying k to L (standing waves: A sin (kx ± ωt) in 1-D), πc ω = , (3) L The resonant frequency is c c f = 0.5 = 0.5 √0 , (4) L L r The length of the patch should be λ L = 0.5√ , (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 = −2nˆ × E~a,

Sides 1 and 3: I hE0 2hE0 E~ · dl~ = ∓E0 ± Eaa = 0 ⇒ E~a =x ˆ ⇒ ~Jms = −yˆ , ABCD a a (6) Sides 2 and 4: hE (x) hE πx  2hE πx  E~ = ±yˆ z = ∓yˆ 0 sin ⇒ ~J = ±xˆ 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 ˆr × 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 = −yˆ 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 ˆ 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 = −yˆ4E0hW cos (πνx ) , (12) πνy ~ 4νx cos (πνx ) Fm,2,4 =x ˆ4E0hL 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 φˆ cos θ sin φ − θˆcos 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 φˆ cos θ cos φ + θˆsin 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): |E |2 L g (θ, φ) = θ = |cos (πν )|2 , ν = sin θ, (22) E 2 x x λ |Eθ|max H-plane gain obtained by setting φ = 90 (right): 2 2 |Eφ| sin (πνy ) W gH (θ, φ) = = cos (θ) , νy = sin θ. 2 πν λ |Eφ|max 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 = ∞), 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]).

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