ECE 598 JS Lecture 08 Lossy Transmission Lines

Transcription

1 ECE 598 JS Lecture 8 Lssy Transmissin Lines Spring 22 Jse E. Schutt-Aine Electrical & Cmputer Engineering University f Illinis jesa@illinis.edu

2 Lss in Transmissin Lines RF SOURCE Signal amplitude decreases with distance frm the surce. 2

3 Skin Effect in Lines δ Lw Frequency High Frequency Very High Frequency 3

4 Skin Effect in Micrstrip ε r H. A. Wheeler, "Frmulas fr the skin effect," Prc. IRE, vl. 3, pp ,942 4

5 Skin Effect in Micrstrip Current density varies as J = J e e y/ δ jy/ δ Nte that the phase f the current density varies as a functin f y y/ δ jy/ δ Jw δ j I = J we e dy = + J σ E = J E = σ The vltage measured ver a sectin f cnductr f length D is: V = E D= JD σ 5

6 The skin effect impedance is where with V JD ( + j) ( ) Zskin = = = + j π f I σ Jwδ w ρ = Skin Effect in Micrstrip σ D D R = skin X = skin f w π μσ μρ is the bulk resistivity f the cnductr Zskin = Rskin + jxskin Skin effect has reactive (inductive) cmpnent 6

7 Lssy Transmissin Line I + R L V - C G Δz Telegraphers Equatin: Time Dmain V =RI+L z I t I = GV + C z V t 7

8 Lssy Transmissin Line I + R L V - C G Δz Telegraphers Equatin: Frequency Dmain V z = (R+jωL)I = ZI I z = (G+jωC)V = YV 8

9 Lssy Transmissin Line z R, L, G, C, frward wave backward wave 9

10 Lssy Transmissin Line V s z Z Z γ β Z 2 l V( z) = Ae e α z jβ z + α z + jβ z + Be αz jβz + α z + jβ z I( z) = Ae e Z Be e e Z = ( R + jω L) ( G+ jωc) ( )( ) γ = α + jβ = R + jωl G+ jωc

11 Effects f Lsses Signal attenuatin Dispersin ( )( ) γ = αω ( ) + jβ( ω) = R + jωl G+ jωc Rise time degradatin Vlts Far End Respnse Bard VLSI Submicrn Deep Submicrn Time (ns)

12 RC Transmissin Line R l Z in C R : series resistance per unit length C : shunt capacitance per unit length Z = in Rl Rl Cω cth ( + j) 2 R Rl Cω ( + j) 2 R Fr very high ω, arg(z ) 45 in 2

13 RC Transmissin Line R l Z in C If 2 ω << RCl 2 then Rl RT Z in = + = + 2 jclω 2 jc ω T R T = Rl : ttal resistance C T = Cl : ttal capacitance 3

14 RC Transmissin Line Line Pulse Characteristics: rise time: ps fall time: ps pulse width: 4ns Line Characteristics length : 3 mm near end terminatin: 5 Ω far end terminatin 65 Ω Near End Respnse.7 Far End Respnse Vlts Bard VLSI Submicrn Deep Submicrn Lgic threshld Vlts Bard VLSI Submicrn Deep Submicrn Lgic threshld Time (ns) Time (ns) 4

15 Lng Cable m Categry 5 Cable Simulatin Simulatin Measurement.55 Categry 5/ -meter Measurement 3 Categry 5/ -meter.5 2 S Magnitude S Phase (deg) S2 Magnitude Frequency (GHz) Simulatin Measurement Categry 5/ -meter Frequency (GHz) S2 Phase (deg) Frequency (GHz) Simulatin Measurement Categry 5/ -meter Frequency (GHz) 5

16 Shrt Cable m Categry 5 Cable Simulatin S Magnitude Measurement Categry 5/ -meter S Phase (deg) Simulatin Measurement Categry 5/ -meter Frequency (GHz) Frequency (GHz) Simulatin Measurement.95 Categry 5/ -meter Simulatin Measurement 2 5 Categry 5/ -meter S2 magnitude Frequency (GHz) S2 phase (deg) Frequency (GHz) 6

17 Categry 5 Cable Resistance and velcity 6 Categry 5/ -meter Categry 5/ -meter Resistance (Ohms/m) Velcity Rati Frequency (GHz) Frequency (GHz) 7

18 Cable Lss Mdel R( f) = R * f p v = v + v * f s r r rs Z = R( f) + jω L= R + j( R + ωl) skin skin Z v r v rs R s p f max (Ω) (m/ns) (m/ns-ghz) (Ω/m-GHz p ) (GHz) Categry Ga Categry SMA

19 A Z = = Lssy TL Simulatin T simulate lssy TL with resistive lads N clsed frm slutin Simplest methd is t use IFFT z j z z j z { α β + α + β } v(, t z) = IFFT Ae e + Be e αz jβz αz jβz i(, t z) = IFFT Ae e + Ae + e + Z ( R + jω L) ( G+ jωc) TV ( ω) ΓΓ s 2 l 2e γ 2γ l B = Γ2e A ( )( ) γ = α + jβ = R+ jωl G+ jωc Γ 2 Z Z T 2 = 2 Z + Z = Z Z + Z Γ = Z Z Z + Z 9

20 Time Dmain Simulatins near end far end V s Z s = 5 Ω cable pen 2

21 Pulse Prpagatin (CAT 5) 2 22GA/Cu/4-cnd Near End.5 vlts Time (ns) 22GA/Cu/4-cnd Far End vlts Time (ns) 2

22 Pulse Prpagatin (MP/CM) 2 MP/CM Shielded Near End.5 vlts Time (ns).5 MP/CM Shielded Far End vlts Time (ns) 22

23 Pulse Prpagatin (RG74) vlts RG74 Near End Time (ns) vlts RG Time (ns) 23