Omar M. Ramahi University of Waterloo Waterloo, Ontario, Canada

Traditional Material!! Electromagnetic Wave ε, μ r r The only properties an electromagnetic wave sees: 1. Electric permittivity, ε 2. Magnetic Permeability, μ 3

Metamaterial and Bandgap Structures!! But what if ε < 0, μ < r r or ε > 0, μ < r r 0 0 or ε < 0, μ > 0 r < r or even if ε 0, or μ r r 0 4

Maxwell Equations β E = μ H β H β E β H Negative Index or Double = ε E = μ H = ε E Negative Media Positive media Or Right Handed Negative media Or Left Handed Dispersion Relationship: 2 2 2 ω εμ = β x + β y 2 2 2 ω εμ = β x + β y ; ; positive media negative media 5

Index of Refraction: Need Consistent Interpretation with ME n 2 =ε μ n = ±1 n = + 1; n = 1; positive media negative media 6

The case of μ, ε < 0 Positive Index Medium Negative Index Medium ε>0 μ>0 ε<0 μ<0 θ r θ t θ r θ i θ i θ t 7

Flat Lens! (without optical axis!) ε < 0 μ < 0 Perfect focusing of traveling waves Image Source Image still Incomplete! 8

Flat Lens! Evanescent wave Source ε < 0 μ < 0 Perfect focusing of traveling waves Image Traveling wave To complete the image need remaining spectrum, The evanescent part Note: If the source is far away from the NIR media, the evanescent spectrum will be lost forever. 9

Time-Domain Simulation Right Handed medium Left Handed medium Source Image Source: Zilkowski; Optics Express, April 2002 10

µ-ε diagram E H k K S K E S K H 11

Metamaterial!! But what ht if ε < 0, μ < r or < r 0 or ε < 0, μ > r r 0 ε r > 0, μ < r 0 or even if ε 0, or μ r r 0 13

IC subject to Internal and External Noise Via 4 (Subject to Noise ) Multi Layer Stack up Package IC Via 3 (Radiator) (Internal Source of Noise ) Die IC Package Subject to External Noise Multi Layer Stack up PCB Via 1 (Radiator) (Source of Noise ) Via 2 (Subject to Noise ) 15

EBGs Can Take Various Shapes Substrate Patch t conductor (a) Via g d T=a+g (b) a 17

Source: D. Seivenpiper, High Impedance Electromagnetic Surfaces, PhD Thesis, UCLA, 1999 18

Textured (High Impedance) Surfaces Ideal for EMI/EMC Applications Source: D. Seivenpiper, High Impedance Electromagnetic Surfaces, PhD Thesis, UCLA, 1999 19

Design of EBG structure using S- parameters simulation Filter/resonator t Ports 20

EBGs as an EM Wave Suppressor S_p parameters 0-5 -10-15 -20-25 -30-35 -40-45 -50-55 -60-65 -70-75 S11 S12 0 2 4 6 8 10 12 14 16 18 20 Frequency (GHz) 21

Surface Wave Mitigation using EBG Materials EBG Materials BUT will the above work for any antenna? 22

at g W Top view of HIS with square patches Surface wave propagation TM waves at low Freq. No propagation around f res TE waves at high Freq. f res = 2π 1 LC Resonance comes from lumped behavior of vias and patches period must be much smaller than wavelength: 23

a M Top view side view Γ w g/2 X PEC PEC Frequ uency [GHz z] 8 7 fh 6 5 4fL 3 2 1 0 Mode 3 Mode 1 Mode 2 Light Line BAND GAP Γ-X X-M M-Γ Phase constant β Analysis of a unit cell provides eigenmode solutions for Maxwell s equations 24

Characterization using Dispersion Equations (approximate Analysis) In B A In 1 + Z s Vn D C B A D C B A D C B A Vn 1 + + + L L V s Z L d B A γ Floquet s theorem : = + + 1 1 n n n n I V D C B A I V = 0 d d e A C B e A γ γ In order to have a l ti = + + n n d n n I V e I V γ 1 1 YZ solution 25 α n jβ n γ + = ) sin( 2 ) cos( ) cosh( d YZ j d d w β β γ + =

Transmission Line and Periodic Structure Theory y( (TLPS) Modeling YZw cosh( γ d) = cos( βd) + j sin( βd) 2 For the first cell: YZw cosh( α 1d)cos( β1d) + j sinh( α1d)sin( β1d) = cos( βd) + j sin( βd) 2 Case 1, α 1 = 0: (outside the gap, wave propagation) YZ cos( β 1 d) = cos( βd) + j 2 w sin( βd) Case 2, α 1 0 and β 1 = 0 or π: (inside the gap, amplitude decay) YZw cosh( α 1 d)cos( β1 d) = cos( β d) + j sin( β d) 2 26

EBGs for Switching Noise Suppression 27

EBGs for Switching Noise Suppression Driver Vss Vdd Vdd Vss Load Power supply Switching noise source 28

Switching and switching noise Driver Vss Vdd Vdd Vss Load Power supply Switching noise source 29

Switching noise: Propagation point of view Power planes radiate like patch antennas Noise-generating device Device subject to noise Signal passing through the power planes Signal layers Power bus layers 30

Model for Power Plane Analysis Metallic planes Load Cavity resonances ε r Model for noise source In nsertion Lo oss [db] Frequency [GHz] 31

10 cm 0-10 10 cm -20 S12(dB) -30 Port 2-40 Port 1-50 -60-70 experimental data with decaps from [5] simulation with decaps simulation without decaps 0 0.5 1 1.5 2 2.5 3 3.5 4 Frequency (GHz) Z cap = 1 jωc + R + jωl 32

Noise mitigation with decoupling capacitors around noise source Surface Current on Ground Plane (No Capacitors) Surface Current on Ground Plane (99 Capacitors) 33

RC dissipative edge termination Mitigates low frequency Does not address parallel-plate l l resonance Separation of Vdd plane Stops parallel-plate plate propagation to and from sensitive devices localized solution Embedded capacitance Does not remove parallel-plate resonance Worsens reliability of board d(fragile) 34

Switching noise suppression in the presence of EEBG structures Power Bus Buried via EBG Patch 35

Vdd Plane g d t a g w a 36

What is the result of using them? g v d h 1 h 2 w 0 2r d w d h 2 Magnitud de of S21(d db) -10-20 -30-40 -50-60 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 Frequency (GHz) 37

Experimental setup 38

Wide Band Noise Mitigation Magnitude of S21(dB B) 0-10 -20-30 -40-50 -60-70 -80 Without EEBG With EEBG 0 1 2 3 4 5 6 7 8 9 10 Frequency (GHz) 39

EMI suppression Power planes edge radiation 40

EMI reduction: Experiment setup Board under test (6.5 cm x 10 cm) fabricated on commercial FR4. Four Rows of 5mm EEBG Excitation Point Board under test Monopole Antenna Vector network analyzer SMA connector 41

EMI reduction: Experiment results EMI suppression is omni-directional Results at different test points are similar Without EEBG Board Under Test 5cm 5cm 3.25cm 5cm TP With EEBG Magnitud de of S21(dB) -20-30 -40-50 -60-70 -80-90 -100-110 0 1 2 3 4 5 6 7 8 9 10 Frequency (GHz) 42

Ultra Wide-Band EMI Reduction Four Rows of Four Rows of 5 mm HIS 10 mm HIS Excitation Point Magnitude of S21(dB) -20-30 -40-50 -60-70 -80-90 -100 Without EEBG With EEBG 0 1 2 3 4 5 6 7 8 9 10 Frequency (GHz) 43

The Challenge of Modeling C L 1 f res = 2 π L ( C 1 + C 2 ) Z LC = jlω 2 1 LCω 45

2D Model based on new unit cell Model based on TEM-transmission-line model combined with the LIS model V s R s R L w( ε r1 + ε r 2) ε 0 1 C3 6 = 2 cosh ( d / g) π μ0 L3 6 = h 2 46

2D Model based on new unit cell nitude of S21(dB) Mag 0-25 -50-75 -100-125 -150 HFSS TM simulation Circuit model using Agilent ADS TM 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Frequency (GHz) Accuracy limited to low frequencies 47

Modeling Complex EBG Structures! 0-10 Magnitu ude of S 21 (db) -20-30 -40-50 -60 S 21 Short Spiral -70 S 21 Long Spiral S 21 Patch -80 S 21 No Spiral 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Frequency (GHz) 48

Planar EBG Structures Patches of different shapes without vias! 49

L-bridge Lb 30mm Cg Lb: bridge inductance unit cell Cg: gap capacitance T. L. Wu, C. C. Yang, Y. H. Lin, et al. A novel power plane with super-wideband elimination of ground bounce noise on high speed circuits IEEE Microwave and Wireless Components Letters, Vol. 15 No.3, pp. 174-176, 2005 50

Unit Cell Top View 2mm 26mm 30mm Port 1 Port 2 90mm FR4 150mm 1.54mm 51

LPKF ProtoMat C100/HF circuit plotter Physical size of board: 3x5 unit cells ( 90x150mm) 52

0 (db) -20 Magnitud de of S21-40 -60-80 Ref Exp Ref Sim Meander-L Exp Meander-L Sim -100 0 1 2 3 4 5 6 7 8 9 10 11 12 Frequency (GHz) VNA measurement 53

Structure B: Structure A: Port 1 Port 2 Port 1 Port 2 Signal Port 1 trace Port 2 EBG Via FR4 1.54mm Side view 54

1200 1000 Input 1200 (test signal) 1000 Voltag ge (mv) 800 600 400 Voltage (mv) 800 600 400 200 0 Output (structure B) 200 0-200 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 time (ns) -200 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 time (ns) 1200 1000 (mv) Voltage 800 600 400 200 0-200 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 time (ns) 55

1200 1000 V1 w=2mm V2 3mm oltage (mv) V 800 600 400 200 0-200 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 time (ns) 56

V1 w=2mm V2 3mm 57

Different Varieties of Metamaterials Complementary Structures!

Split-Ring Resonator and Complementary Split Ring Reson. E H k b r in a a g r out (a) SRR Cu (b) CSRR

Excellent very small filter! Falcone et al., IEEE MWCL, June 2004

Design of PCBs using Split-Ring Resonators (Negative media)

Experiment with Rogers Board 2 (db) S 12 0-10 -20-30 -40-50 -60. -70 solid board -80 0 1 2 3 4 5 6 7 8 9 10 Frequency (GHz)

Split-Ring Resonator and Complementary Split Ring Reson. 14mm Port 2 14mm w=1.19mm Port 1 41mm h

Experiment with FR4 S 12 (d db) 0-10 -20-30 -40-50 -60-70 -80-90 Solid (measured) Solid (simulated) CSRRs (measured) CSRRs (simulated) 0 1 2 3 4 5 6 7 8 9 10 11 12 Frequency (GHz)

Next challenges:

EBG or?

Dispersion Diagram.. How important? ( 1 st, 2 nd, 3 rd, and 4 th ) propagating modes g (Mm/s) v g 8 7 6 5 4 3 2 1 0 Region: Γ > X 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 Frequency (GHz)

Suppression Bandwidth 20 db Suppression Band 20 0 f S 21 (db B) Magn nitude o -20-40 -60-80 -100-120 -140-160 Without EBG Pattern (Reference) With EBG Pattern 0 2 4 6 8 10 12 14 Frequency (GHz)

Suppression Bandwidth ( 1 st, 2 nd, 3 rd, and 4 th ) propagating modes Port 1 Port 2 v g (Mm/s s) 8 7 6 5 4 3 2 1 0 Region: Γ > X 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 Frequency (GHz)

Suppression Bandwidth vs. Bandgap 1.0 on Loss Radiati 0.9 EBG Patterned Parallel Planes Solid Parallel Planes 0.8 07 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Frequency (GHz)

Reduction of Coupling between Patch antennas

Reduction of Coupling between Patch antennas Patch Antenna Patch Antenna Substrate h

Reduction of Coupling between Patch antennas Patch Antenna Patch Antenna Substrate Surface Waves E

Complementary Split Ring Resonator SRR CSRR H E

Design of PCBs using Complementary Split-Ring Resonators Patch Antenna SCSRR structure Patch Antenna

Fr requency (GHz) 8 7 6 5 4 3 2 1 Bandgap mode1 mode 2 0 0 Γ XX

Fr requen ncy (GH Hz) 8 7 6 5 4 3 2 1 0 Bandgap zone Γ X Mode 1 Mode 2

SCSRR SCSRR structure

Surface Currents on Ground Plane Patch antennas y x

Performance of SCSRR -10-15 -20 without SCSRRs with SCSRRs S 12 (db) -25-30 -35-40 -45-50 4.0 4.5 5.0 5.5 6.0 Frequency (GHz)

Antennas Matching Practically not affected! 0-5 S (db) i i -10-15 -20-25 Air (S ) 11 Air (S 22 ) SCSRRs (S 11 ) SCSRRs (S 22 ) -30 4.0 4.5 5.0 5.5 6.0 Frequency (GHz)

Radiation Patterns 0 0 10 330 30 10 330 30 5 5 0-5 300 60 0-5 300 60-10 -10-15 -15-20 270 90-20 270 90-15 -15-10 -10-5 240 without SCSRRs 120-5 without SCSRRs 0 with SCSRRs 240 120 0 with SCSRRs 5 10 5 210 150 10 210 180 150 180 H-plane E-plane

EBGs Perhaps has the most important application in the field of EMI/EMC!!.