Time-Domain Analysis of Transmission Line Circuits (Part 3)

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1 igna Integrity an High-pee Intercnnects Time-Dmain Anaysis f Transmissin Line Circuits (Part 3) Dr. Jsé Ernest Rayas ánchez 1 Outine Buncing iagrams fr TLs with iea ecitatin puses an resistive terminatins Eampe f a TL with resistive terminatins an iea puse ecitatin Transients in TLs with capacitive as Eampes f TLs with capacitive a (ver-riven an uner-riven cases) Cncusins n TLs with capacitive as 2 Dr. J. E. Rayas ánchez erayas@ites.m

TL with resistive terminatins an iea puse ecitatin Transients in TLs with capacitive as Eampes f TLs with

2 igna Integrity an High-pee Intercnnects Lattice Diagrams fr a DC Ecitatin Z, ε r R L t R Γ R V Z Z V Z R Z R ΓL R v p L L Z Z c ε e t v p 4t 3t 2t t Γ 2 Γ L 2 V Γ Γ L 2 V Γ Γ L V Γ L V V 3 v A Lattice Diagrams fr Puses PW v v v ON OFF t where v ON Au Au( t PW ) v v OFF Z, ε r R L We buit tw attice iagrams, ne fr v ON an ne fr v OFF The attice iagram fr v OFF is a negative an eaye versin f that ne fr v ON The resutant signas are btaine by aing bth attice iagrams 4 Dr. J. E. Rayas ánchez erayas@ites.m

v OFF Z, ε r R L We buit tw attice iagrams, ne fr v ON an ne fr v OFF The attice iagram fr v OFF is a negative an eaye versin f

3 igna Integrity an High-pee Intercnnects Lattice Diagrams fr Puses (cnt) v A PW t t v t Z, ε r R L 4t 3t Γ 2 Γ L 2 V Γ Γ L 2 V 3t PW 2t PW Γ Γ L 2 V Γ Γ L V 2t t Γ Γ L V Γ L V t PW PW Γ L V V V 5 Eampe f TL with a Puse Ecitatin v A v Z, ε r R L PW t 75Ω; R L 0Ω; A V; PW 2.5ns Z ; cm 6 Dr. J. E. Rayas ánchez erayas@ites.m

t PW PW Γ L V V V 5 Eampe f TL with a Puse Ecitatin v A v Z, ε r R L PW t 75Ω; R L 0Ω;

4 igna Integrity an High-pee Intercnnects Eampe imuate with Apac Rs Length $ meters L288.68nH $ nh/m C115.47pF $ pf/m $ Z50hms, epse3 Lssess_TL in L Vs 75 RL 30 $ DCLeve Amp Deay RiseT FaT PWith Peri PULE 0 3V ps 0.01ps 2.5ns 9ns weep "Lssess Transmissin Line" LOOP 300 TIME LIN 0 8ns W0 gri Y "" "" hw W0 YVtran() YVtran(in) YVtran(L) Enweep 7 Eampe imuate with Apac n 4.000n 6.000n 8.000n t/s Vtran() Vtran(in) Vtran(L) 8 Dr. J. E. Rayas ánchez erayas@ites.m

5ns 9ns weep "Lssess Transmissin Line" LOOP 300 TIME LIN 0 8ns W0 gri Y "" "" -0.5 3.

5 igna Integrity an High-pee Intercnnects Transients in TLs with Capacitive Las Z, ε r can be treate as a time-epenent impeance Initiay, is ischarge, hence Γ L 1 At the steay state, is fuy charge, hence Γ L 1 At any ther time, Γ L can nt be cacuate 9 Transients in TLs with Capacitive La ( Z ) R t Z v p V Z Z, ε r C τ L v( 0, t) v ( t) v(, t) v ( t) I L time v I 0 t t t V Z V V R Z 2 0 ) / t t < 2 V / 2 [1 ( t t V τ e ] t /τ t 2t 0 V [1 e ] ( t 2t ) / τ t 2t V [1 ) / e ] [1 ( t t V τ e ] 10 Dr. J. E. Rayas ánchez erayas@ites.m

Capacitive La ( Z ) R t Z v p V Z Z, ε r C τ L v( 0, t) v ( t) v(, t) v ( t) I L time v I 0 t t t V Z V V R Z 2 0 ) / t t < 2 V / 2 [1 (

6 igna Integrity an High-pee Intercnnects Transients in TLs with Capacitive La ( Z ) time v I 0 t t V v I t t < 2 t Z V v t t I 2V t /τ t 2t 0 V [1 e ] t 2t Z Z 2V t 2t v I 2V t t 11 TL with Capacitive La Eampe 1 Z, ε r V; 50Ω Z cm 0pF V V 2 1.5V v I ( 2t ) 0 2V [1 e / t τ 2V [1 e 2 / t τ ] 1.46V ] 2.21V 12 Dr. J. E. Rayas ánchez erayas@ites.m

with Capacitive La Eampe 1 Z, ε r V; 50Ω Z 17.321cm 0pF V V 2 1.

7 igna Integrity an High-pee Intercnnects TL with Capacitive La Eampe 2 Z, ε r V; 50Ω Z cm pf 13 TLs with Capacitive La an Unmatche urce R t Z v p V Z Z, ε r C τ L v( 0, t) v ( t) v(, t) v ( t) time v I 0 t t t 2 t < t t 2t V V Z 0 R Z V V V ΓV 2 t < 3 ) / V 2 [1 ( t t V τ e ] /τ Γ 2V [1 t e ] ( t 2t ) / t t [2V 2ΓV ][1 e τ ] ΓV t t [2V Γ t / 2ΓV ][1 e τ ] V 2V [1 e 2V [1 e t > 3t?? I L ( t t ) / τ 2t / τ ] ] 14 Dr. J. E. Rayas ánchez erayas@ites.m

t t t 2 t < t t 2t V V Z 0 R Z V V V ΓV 2 t < 3 ) / V 2 [1 ( t t V τ e ] /τ Γ 2V [1 t e ] ( t 2t ) / t t [2V 2ΓV ][1 e

8 igna Integrity an High-pee Intercnnects TLs with Capacitive La an Unmatche urce time v I 0 t t V v I t t < 2 t Z V v I t t 2V t 2t 2 t t < 3 Z t 2t 2V Γ V t /τ Γ V 2V [1 t e ] v I 2V Z t t t t [2V Γ t / 2ΓV ][1 e τ ] V 2V [1 e t > 3t?? 2t / τ ] 15 TLs with Capacitive La an Unmatche urce v (2t ) I ΓV 1.2 Nrmaize Input Vtage Ampitue at 2t v I (2t ) / /Z 16 Dr. J. E. Rayas ánchez erayas@ites.m

> 3t?? 2t / τ ] 15 TLs with Capacitive La an Unmatche urce v (2t ) I ΓV 1.

9 igna Integrity an High-pee Intercnnects TL with Capacitive La Eampe 3 Z, ε r V VZ /( R Z) 2V R Z Γ R Z v ( 2t ) Γ V 0.667V I / [1 t τ 2V e 2V [1 e 2 / t τ ] 1.946V ] 2.946V t / τ [2V 2Γ V ][1 e ] Γ V 1.964V V; 25Ω Z cm 0pF 17 TL with Capacitive La Eampe 3b Z, ε r V; 25Ω Z cm 0pF 18 Dr. J. E. Rayas ánchez erayas@ites.m

946V t / τ [2V 2Γ V ][1 e ] Γ V 1.964V V; 25Ω Z 17.

10 igna Integrity an High-pee Intercnnects TL with Capacitive La Eampe 4 Z, ε r V; 25Ω Z cm pf 2V [2V [1 e ] 2 / τ V 2Γ V ][1 e 4V / τ ] 2 V Γ V.333V Γ V 19 TL with Capacitive La Eampe 5 Z, ε r V VZ /( R Z) 2.5V R Z Γ R Z v ( 2t ) Γ V 1.667V I 2V [1 e ] 2 / τ V 2 V Γ V.331V 5V V; 10Ω Z cm pf 20 Dr. J. E. Rayas ánchez erayas@ites.m

333V Γ V 19 TL with Capacitive La Eampe 5 Z, ε r V VZ /( R Z) 2.5V R Z Γ 0.

11 igna Integrity an High-pee Intercnnects TL with Capacitive La Eampe 5b Z, ε r V; 10Ω Z cm pf 21 TL with Capacitive La Eampe 6 Z, ε r V; 0.01Ω Z cm pf 22 Dr. J. E. Rayas ánchez erayas@ites.m

321cm pf 21 TL with Capacitive La Eampe 6 Z, ε r V; 0.

12 igna Integrity an High-pee Intercnnects TL with Capacitive La Eampe 6b Z, ε r V; 0.01Ω Z cm pf 23 TL with Capacitive La Eampe 6c Z, ε r V; 0.01Ω Z cm pf 24 Dr. J. E. Rayas ánchez erayas@ites.m

321cm pf 23 TL with Capacitive La Eampe 6c Z, ε r V; 0.

13 igna Integrity an High-pee Intercnnects TL with Capacitive La Eampe 6 Z, ε r V; 0.01Ω Z cm pf 25 TL with Capacitive La Eampe 6e Z, ε r V; 0.01Ω Z cm pf 26 Dr. J. E. Rayas ánchez erayas@ites.m

321cm pf 25 TL with Capacitive La Eampe 6e Z, ε r V; 0.

14 igna Integrity an High-pee Intercnnects TL with Capacitive La Eampe 7 Z, ε r V; 0.01Ω Z cm 0.3pF 27 TL with Capacitive La Eampe 8 Z, ε r V; 100Ω Z cm pf V VZ /( R Z) 1V R Z Γ R Z v ( 2t ) Γ V 0.333V I 2V [1 e ] 2 / τ V 2 V Γ V 2.333V 2V 28 Dr. J. E. Rayas ánchez erayas@ites.m

321cm pf V VZ /( R Z) 1V R Z Γ 0.333 R Z v ( 2t ) Γ V 0.

15 igna Integrity an High-pee Intercnnects TL with Capacitive La Eampe 9 Z, ε r V; 200Ω Z cm pf 29 Transients in TLs with Capacitive Las Z, ε r OME CONCLUION: Lattice iagrams can nt be irecty appie If Γ 0 anaytica sutins are easy, therwise the prbem becmes t cmpe fr t > 3t (simuatin require) If Γ > 0, the ine behaves as an uner-riven ine If Γ < 0, there wi be vershting vtages at the a (ver-riven ine) If Γ << 0, there wi be significant sciatins at the a 30 Dr. J. E. Rayas ánchez erayas@ites.m

sutins are easy, therwise the prbem becmes t cmpe fr t > 3t (simuatin require) If Γ > 0, the ine behaves as an uner-riven ine If Γ

Transient-Domain Analysis of Transmission Line Circuits (Part 1)

Transient-Domain Analysis of Transmission Line Circuits (Part 1) Transien-Dmain Anaysis f Transmissin ine Circuis (Par Dr. Jsé Ernes ayas Sánchez March, 9 Transien-Dmain Anaysis f Transmissin ine Circuis (Par Dr. Jsé Ernes ayas Sánchez Ouine Quarer-wave ransfrmer seay