ECE 497 JS Lecture -07 Planar Transmission Lines

Transcription

1 ECE 497 JS Lecture -07 Planar Transmission Lines Spring 2004 Jose E. Schutt-Aine Electrical & Computer Engineering University of Illinois 1

2 Microstrip ε Z o w/h < h h = ln ( εr 1) w w Z o w/h > π w ln(4) ln( eπ /16) εr 1 = 2 2 ε 2h π 2π ε r r εr 1 πe w ln ln πε r 2 2h 2

3 Three-Line Microstrip V1 I1 I2 I = L11 L12 L13 z t t t 3 I1 V1 V2 V = C11 C12 C13 z t t t 3 V2 I1 I2 I = L21 L22 L23 z t t t 3 I2 V1 V2 V = C21 C22 C23 z t t t 3 V I I I = L L L z t t t I V V V = C C C z t t t

4 Three-Line Alpha Mode Subtract (1c) from (1a) and (2c) from (2a), we get Vα I = ( L11 L13) z t Iα V = ( C11 C13) z t This defines the Alpha mode with: α α and Vα = V1 V Iα = I1 I3 3 The wave impedance of that mode is: Z α = L C L C and the velocity is u α = 1 ( L L )( C C )

5 Three-Line Modal Decomposition In order to determine the next mode, assume that V = V βv V β I = I β I I β Vβ I I I = z t t t ( L βl L ) ( L βl L ) ( L βl L ) I β V V V = z t t t ( C βc C ) ( C βc C ) ( C βc C ) By reciprocity L 32 = L 23, L 21 = L 12, L 13 = L 31 By symmetry, L 12 = L 23 Also by approximation, L 22 L 11, L 11 L 13 L 11 5

6 Three-Line Modal Decomposition Vβ I I3 I = ( L βl L ) ( 2L βl ) z t t t In order to balance the right-hand side into I β, we need to have ( β ) = β ( β ) β ( β ) 2L L I L L L I L L I L = β L or β =± 2 Therefore the other two modes are defined as The Beta mode with 6

7 The Beta mode with Three-Line Beta Mode Vβ = V 2V V I = I β 2I I The characteristic impedance of the Beta mode is: Z β = L 2L L C 2C C and propagation velocity of the Beta mode is 1 u = β ( L11 2L12 L13 )( C11 2C12 C13 ) 7

8 Three-Line Delta Mode The Delta mode is defined such that V = V δ 2V V I = I δ 2I I The characteristic impedance of the Delta mode is Z δ = L 2L L C 2C C The propagation velocity of the Delta mode is: 1 u = δ ( L11 2L12 L13 )( C11 2C12 C13 ) 8

9 Symmetric 3-Line Microstrip In summary: we have 3 modes for the 3-line system E = Alpha mode Beta mode* Delta mode* *neglecting coupling between nonadjacent lines 9

10 Coplanar Waveguide ε r = LnH ( / m) = C( pf/ m) = E = H =

11 Coplanar Waveguide ε r = 4.3 Z m ( Ω ) = Z c ( Ω ) = vp ( m/ ns) =

12 Coplanar Waveguide S' W S W S' h ε r Kk ( ) : Complete Elliptic Integral of the first kind S k = 30 π K'( k) S 2W Zocp = (ohm) ε ( ) r 1 Kk K'( k) = K( k') 2 k' = (1 k ) 2 1/2 v cp 2 = εr 1 1/2 c 12

13 Coplanar Strips W S W h ε r Z ocs = 120 π K'( k) (ohm) ε 1 Kk ( ) r 2 13

14 Qualitative Comparison Characteristic Microstrip Coplanar Wguide Coplanar strips e 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 ε r =10 and h=0.025 inch 14

15 3-Line Matching Network Extend matching network synthesis to multiconductor transmission line (MTL) systems, specifically coupled microstrip Characterize MTL systems by their normal mode parameters Mode configurations Propagation constants Characteristic impedance matrices 15

16 Longitudinal Immittance Matrix Functions (LIMFs) Given terminations, the immittance matrices are expressed as input longitudinal functions looking toward the load S Y m,c m,c in,out, Γ,, Z m,c in,out m,c in,out 16

17 Calibration Methods 1st order calibration: 6 distinct TRL calibrations were required to deembed the fan-in and fan-out sections 2nd order calibration: 1 multimode TRL calibration required to deembed all fan-ins and fan-outs Multiconductor transmission line matching network device under test 17

18 Bias Networks and Multiline/Multimode TRL Self-biasing for DC power done using air bridges Regulator circuit may be built on board with surface mount/chip components Calibration must include all modes and allow for the 6- port discontinuity S- parameter measurement Proposed calibration fixture for transistor amplifier device discontinuity with self-biasing network 18

19 3-line Transistor Amplifier The general amplifier structure with generic matching networks Note that a transistor seating hole may be present for convenience, but is not necessary Photograph of a three-line transistor amplifier autobiased w/o matching networks 19

20 Transistor Amplifier Matching Matching pf chip cap pf chip cap. Gains GHz m=5.14 / um= GHz m=6.54 / um= 0.32 S-parameter comparison between unmatched and matched three-line amplifier. Dotted line - unmatched; dashed line - matched. Design frequency: 3.1 GHz. 20

21 V Transmission Line w signal strip h dielectric α ground 2p 21

22 V-Line Characteristic Impedance 250 CHARACTERISTIC IMPEDANCE Zo (ohms) º 37.5º 45º 52.5º 60º Microstrip w/h Calculated values of the characteristic impedance for a single-line v-strip structure as a function of width-to-height ratio w/h. The relative dielectric constant is εr =

23 V-Line Effective Permittivity º 37.5º EFFECTIVE PERMITTIVITY º 52.5º Effective Relative Dielectric Constant º Microstrip w/h Calculated values of the effective relative dielectric constant for a single-line v-strip structure as a function of width-to-height ratio w/h. The relative dielectric constant is εr =

24 Three-Line V Transmission Line y signal strip w s 2p h ground surface dielectric x Region 1 Region 2 Region 3 Region 4 Region 5 Region 6 24

25 V-Line and Microstrip Microstrip C (pf/m) = L (nh/m) = V-line C (pf/m) = L (nh/m) = y w s signal strip 2p h ground surface dielectric x Region 1 Region 2 Region 3 Region 4 Region 5 Region 6 Comparison of the inductance and capacitance matrices between a three-line v-line and microstrip structures. The parameters are p/h = 0.8 mils, w/h = 0.6 and ε r =

26 V-Line: Coupling Coefficients 350 Mutual Inductance 40 Mutual Capacitance L m (nh/m) V-line microstrip C m (pf/m) V-line microstrip s/h s/h Plot of mutual inductance (top) and mutual capacitance (bottom) versus spacing-to-height ratio for v-line and microstrip configurations. The parameters are w/h = 0.24, εr =

27 V-Line vs Microstrip: Coupling Coefficients Coupling Coefficient V-line microstrip K v s/h Plot of the coupling coefficient versus spacing-to-height ratio for v-line and microstrip configurations. The parameters are w/h = 0.24, εr =

28 Advantages of V-Line ground reference signal strip w signal strip dielectric substrate h dielectric α ground ground reference 2p Propagation Function Advantages of V Line * Higher bandwidth microstrip V-60 V-30 * Lower crosstalk * Better transition Linear Attenuation Frequency (GHz) 28

29 V-Line vs Microstrip: Insertion Loss 0 Insertion Loss 20*log10* S Vline Microstrip Frequency (GHz) 29