ECE 451 Advanced Microwave Measurements. TL Characterization

Transcription

1 ECE 451 Advanced Microwave Measurements TL Characterization Jose E. Schutt-Aine Electrical & Computer Engineering University of Illinois ECE 451 Jose Schutt-Aine 1

2 Maxwell s Equations E B t Faraday s Law of Induction H J D t Ampère s Law D Gauss Law for electric field B 0 Gauss Law for magnetic field Constitutive Relations B H D E ECE 451 Jose Schutt-Aine 2

3 Wave Propagation z Wavelength : = propagation velocity frequency ECE 451 Jose Schutt-Aine 3

4 Why Transmission Lines? In Free Space At 10 KHz : = 30 km At 10 GHz : = 3 cm Transmission line behavior is prevalent when the structural dimensions of the circuits are comparable to the wavelength. ECE 451 Jose Schutt-Aine 4

5 Transmission Line Model Let d be the largest dimension of a circuit circuit z If d <<, a lumped model for the circuit can be used ECE 451 Jose Schutt-Aine 5

6 Transmission Line Model circuit z If d, or d > then use transmission line model ECE 451 Jose Schutt-Aine 6

7 Modeling Interconnections Low Frequency Mid-range Frequency L T High Frequency C T /2 C T /2 Z o Short L T /2 or L T /2 Transmission Line C T Lumped Reactive CKT ECE 451 Jose Schutt-Aine 7

8 Dispersion & Velocities 2 f LC Ideal channel velocity 1 LC 2 fh( f ) Dispersive channel velocity g( f ) Phase velocity / Group velocity d d 1 ECE 451 Jose Schutt-Aine 8

9 Parallel Plate Waveguide 2 2 E E 0 TE mn modes: E 0, H 0, H 0 z z x jkz m Ey Eosinxxe x a Wave will propagate if f f TM mn modes: H H cos xe y o x c 2 m k z a m 2a H 0, E 0, E 0 jkz z z x Same dispersion relation as TE mn modes 2 ECE 451 Jose Schutt-Aine 9

10 TEM Mode Special case m=0 TM 0 or TEM mode E 0, H 0, E 0, H 0 z z x y jkz Ex Eoe Hoe H y He o jkz jkz k Z o z ECE 451 Jose Schutt-Aine 10

11 Parallel Plate in TEM w a L = a w C = w a ECE 451 Jose Schutt-Aine 11

12 Solution :, L Coaxial Cables Laplace s Equation for potential ln b/ a 2 V o For a TEM mode of propagation ln b/ ln b/ a C 2 ln b/ a / LC Z / ln / o L C b a 2 ECE 451 Jose Schutt-Aine 12

13 Coaxial Cables Higher order modes: TE modes: j z H h, e z z k h z The first higher order mode is the TE 11 mode Approximate solution for k c is: From k c, find cutoff frequency f c f c k c 2c c ab2 ab r r 2 a b f c 2 ck c r vk c 2 ECE 451 Jose Schutt-Aine 13

14 Coaxial Line with Losses a b Infinite Conductivity Zo / ln b/ a 2 Finite Conductivity / 1/ a1/ b Zo ln b/ a1 1 j 2 4 f ln( b/ a) ECE 451 Jose Schutt-Aine 14

15 Types of Transmission Lines r Coaxial line Air Waveguide e r Coplanar line e r Microstrip e r Stripline e r Slot line ECE 451 Jose Schutt-Aine 15

16 Parallel plate Transmission Line w a L = a w C = w a ECE 451 Jose Schutt-Aine 16

17 Microstrip and Stripline Microstrip Stripline Wave propagation in stripline is closer to the TEM mode of propagation and the propagation of velocity is approximately c/ r. ECE 451 Jose Schutt-Aine 17

18 Microstrip Analysis Equations Z o w/h < h h ln ( r 1) w w Z o w/h > w ln(4) ln( e /16) r h 2 r r r 1 e w + ln ln r 2 2h ECE 451 Jose Schutt-Aine 18

19 Microstrip Analysis & Synthesis Equations Z e o r 1 r d/ W 60 8d W ln for W / d 1 W 4d e 120 for W / d 1 e W / d ln( W / d 1.444) W d A A 8e for W / d 2 2 A e 2 2 r B-1ln(2B1) ln( B1) 0.39 for W / d 2 2r r Zo r 1 r B 60 2 r 1 r Z 2 o r ECE 451 Jose Schutt-Aine 19

20 Microstrip Microstrip Characteristic Impedance Zo (ohms) h = 21 mils h = 14 mils h = 7 mils W/h dielectric constant : 4.3. ECE 451 Jose Schutt-Aine 20

21 Surface Waves TM Modes Assume the form: j z E ( x, y, z) e ( x, y) e z z (, ) 0 2 rk o ez x y x Inside dielectric k (, ) 0 2 o ez x y x Outside dielectric dielectric x Dispersion relations d o r o z k k c r o h k o Ground plane ECE 451 Jose Schutt-Aine 21

22 Surface Waves TM Modes: Solutions Solutions are: e ( x, y) Asink xbcosk x z c c hx e ( x, y) Ce De z hx Inside dielectric Outside dielectric Ez ( x, y, z) 0 at x=0 dielectric x E ( x, y, z), for x z Ez ( x, y, z) continuous at boundary d o r o z H y ( x, y, z) continuous at boundary Ground plane Asin kdde c hd k tan k d h c c r r A cos kd c k c D e h hd k h 1 k c r o ECE 451 Jose Schutt-Aine 22

23 Surface Waves TM Modes: Solutions 2 kd hd 1kd 2 2 c r o hd kdtan kd hd c c r Solution is found at intersection of curves - - k c d First TM mode is TM o mode Cutoff frequencies for TM modes are given by: f c nc, n0,1,2,... 2d 1 r ECE 451 Jose Schutt-Aine 23

24 Surface Waves TE Modes Assume the form: j z H ( x, y, z) h ( x, y) e z z (, ) 0 2 rko hz x y x Inside dielectric k (, ) 0 2 o hz x y x Outside dielectric dielectric x Dispersion relations d o r o z k k c r o h k o Ground plane ECE 451 Jose Schutt-Aine 24

25 Surface Waves TE Modes: Solutions Solutions are: h ( x, y) Asink xbcosk x z c c hx h ( x, y) Ce De z hx Inside dielectric Outside dielectric dielectric x After matching the boundary conditions d o r o z Ground plane B sin kd c k c D e h hd k cot k d h c c Bcos k d De c hd k h 1 k c r o ECE 451 Jose Schutt-Aine 25

26 Surface Waves TE Modes: Solutions 2 kd hd 1kd 2 2 c r o hd kdcot kdhd c c Solution is found at intersection of curves Negative values of h must be excluded - - k c d Cutoff frequencies for TE modes are given by: f c (2n1) c, n1,2,3,... 4d r 1 Modes will occur in the following order: TM 0, TE 1, TM 1, TE 2, TM 2 ECE 451 Jose Schutt-Aine 26

27 Coplanar Waveguide S' W S W S' h r Kk ( ) : Complete Elliptic Integral of the first kind S k 30 K'( k) S 2W Zocp (ohm) ( ) r 1 Kk K'( k) K( k') 2 k' (1 k ) 2 1/2 v cp 2 r 1 1/2 c ECE 451 Jose Schutt-Aine 27

28 Coplanar Strips W S W h r Z ocs 120 K'( k) (ohm) 1 Kk ( ) r 2 ECE 451 Jose Schutt-Aine 28

29 Qualitative Comparison Characteristic Microstrip Coplanar Wguide Coplanar strips eff * ~6.5 ~5 ~5 Power handling High Medium Medium Radiation loss Low Medium Medium Unloaded Q High Medium Low or High Dispersion Small Medium Medium Mounting (shunt) Hard Easy Easy Mounting (series) Easy Easy Easy * Assuming r =10 and h=0.025 inch ECE 451 Jose Schutt-Aine 29

30 TEM PROPAGATION I L + V C - z z Z 1 Z o Z 2 V s ECE 451 Jose Schutt-Aine 30

31 Telegrapher s Equations L I + V C - z V z I L t I z C V t L: Inductance per unit length. C: Capacitance per unit length. ECE 451 Jose Schutt-Aine 31

32 Transmission Line Solutions z (Frequency Domain) Z o forward wave backward wave LC V( z) j z Ae j z Be Z o = L C I( z) 1 j z j z Ae Z Be o ECE 451 Jose Schutt-Aine 32

33 Coaxial Microstrip Transition Board with traces Center pin Flange-mount connector screw L-shaped support Remove effects of discontinuities before processing data! ECE 451 Jose Schutt-Aine 33 33

34 Coaxial Microstrip Transition With parasitics No parasitics ECE 451 Jose Schutt-Aine 34

35 Coaxial Microstrip Transition In SMA C L1 L 1 C L2 TL1 C R1 L 2 SMA C R2 Out Equivalent Circuit TDR Plot ECE 451 Jose Schutt-Aine 35

36 Low Frequency TL Approximation L R C/2 C/2 P = (R + jl)(1 + jcz /2) o Y = jcz o/2 S = 11 P 2YZo YP 2Z P2YZ YP o o S = 21 2Zo 2Z P2YZ YP o o A 2 Z (1 - S ) o 21 A 2S11S21Zo S11A Y = 4 S Z 2 S S Z S A A 21 o o 11 P A - 2 YS Z S (1 Y) 21 o 21 ECE 451 Jose Schutt-Aine 36

37 R e Low-Frequency Model for Microstrip - Lumped Model - Use extraction algorithm fiberglassubst r at e copper mi crost rip w =5 mi l l =20.2cm SMA connect or 1 Microstrip 30 Microstrip I n Frequency (GHz) Frequency (GHz) ECE 451 Jose Schutt-Aine 37

38 High Frequency Characterization Transmission-Line Scattering Parameters S 2 (1 ) X e d Zc Z Z Z c o o X X S Z 2 (1 X ) c 1 X R j L G jc ( R jl)( G jc) ECE 451 Jose Schutt-Aine 38

39 TL Extraction Formulas X=e e e - d j d d 2 Q Q 1 R Re{ Z c } 1 L Im{Z } c X d S11 S21 1 S S e Q G C { S11 S21} 1 2S Re{ } Z c 11 1 Im{ } Z c ECE 451 Jose Schutt-Aine 39

40 Low Loss Approximation If we assume and R G L C Z c L C R C + j LC = R 2 L 2Zc p R 2Z c v p j v ECE 451 Jose Schutt-Aine 40

41 TL Extraction Formulas ln d X R 2Z ln X c d d v p v p d ECE 451 Jose Schutt-Aine 41

42 Example: Category 5 Cable (long) Simulation Simulation Measurement 0.55 Category 5/ 100-meter Measurement 30 Category 5/ 100-meter S11 Magnitude S11 Phase (deg) S21 Magnitude Frequency (GHz) Simulation Measurement Category 5/ 100-meter Frequency (GHz) S21 Phase (deg) Frequency (GHz) Simulation Measurement Category 5/ 100-meter Frequency (GHz) ECE 451 Jose Schutt-Aine 42

43 Example: Category 5 Cable (short) Simulation S11 Magnitude Measurement Category 5/ 1-meter S11 Phase (deg) Simulation Measurement Category 5/ 1-meter Frequency (GHz) Frequency (GHz) Simulation Measurement Category 5/ 1-meter Simulation Measurement Category 5/ 1-meter S21 magnitude Frequency (GHz) S21 phase (deg) Frequency (GHz) ECE 451 Jose Schutt-Aine 43

44 Category 5 Cable Loss Characteristics 6 Category 5/ 100-meter 1 Category 5/ 100-meter Resistance (Ohms/m) Velocity Ratio Frequency (GHz) Frequency (GHz) ECE 451 Jose Schutt-Aine 44

45 Cable Loss Model R( f) R * f p v v v * f s r ro rs Z R( f) j L R j( R L) skin skin Z o v ro v rs R s p f max () (m/ns) (m/ns-ghz) (/m-ghz p ) (GHz) Category Ga Category SMA ECE 451 Jose Schutt-Aine 45

46 Time Domain Simulations near end far end V s Z s = 50 cable open ECE 451 Jose Schutt-Aine 46

47 Lossy Transmission Line V s z Z 1 Z o Z 2 l V( z) Ae e z j z Be e z j z 1 z jz I( z) Ae e Z z Be e j z o Z o R( ) G jl jc ( ) j R jl G jc ECE 451 Jose Schutt-Aine 47

48 Pulse Propagation (CAT 5) 2 22GA/Cu/4-cond Near End volts Time (ns) 22GA/Cu/4-cond Far End volts Time (ns) ECE 451 Jose Schutt-Aine 48

49 Pulse Propagation (MP/CM) 2 MP/CM Shielded Near End 1.5 volts Time (ns) 1.5 MP/CM Shielded Far End 1 volts Time (ns) ECE 451 Jose Schutt-Aine 49

50 Pulse Propagation (RG174) volts RG174 Near End Time (ns) volts RG Time (ns) ECE 451 Jose Schutt-Aine 50

51 Characterization of DIP Packages DIP Mounted on PCB with SMA connector center pin package pin PC board View of DIP Lead Frame microwave connector CROSS SECTION ECE 451 Jose Schutt-Aine 51

52 Package Characterization Procedure Devise Model for Package + Environment Obtain accurate model for topology Determine frequency range for model Calibrate ANA and Perform Measurements De-embed connector or use TRL S Parameters can be converted Optimize Model using Simulator ADS or SPICE Select accurate optimization scheme ECE 451 Jose Schutt-Aine 52

53 Example Topology & Model C C1-2 C C2-3 C C3-4 C C4-5 C C5-6 C C6-7 C C7-8 C C8-9 C C9-10 C C10-11 C C11-12 C Circuit model for 2-port measurement Between 2 pins C12-13 ECE 451 Jose Schutt-Aine 53

54 DIP Example S Parameters Model Measured Model S11 for L = 5.2 nh Measured 80 S11 for L = 5.2 nh Frequency (GHz) Frequency (GHz) Model S21 for L = 5.2 nh Measured 1 0 Model S21 for L = 5.2 nh Measured Frequency (GHz) Frequency (GHz) -180 Model and Measured scattering parameters for pins for the case were model inductance is assumed to be 5.2 nh. ECE 451 Jose Schutt-Aine 54

55 DIP Example Inductance Model Mesured S11 for Inductance X 2 Model Measured 0.6 S11 for Inductance X Frequency (GHz) Frequency (GHz) Model Measured Model Measured 1 S21 for Inductance X S21 for Inductance X Phase (degrees) Frequency (GHz) Frequency (GHz) -180 Model and Measured scattering parameters for pins for the case were model inductance is assumed to be 10.4 nh. ECE 451 Jose Schutt-Aine 55